X-Git-Url: http://git.tremily.us/?p=sawsim.git;a=blobdiff_plain;f=src%2Fsawsim.nw;h=2e0f0c45bdb40472d9e626db6403f81b28303521;hp=f84cc587a5a19550fb8639b6968d8fbb23aa4354;hb=19ff30c04333ead9466575688eb3f00f0b95c03a;hpb=35480effa70eca4428ce4e57607f5d044f5ff7f8 diff --git a/src/sawsim.nw b/src/sawsim.nw index f84cc58..2e0f0c4 100644 --- a/src/sawsim.nw +++ b/src/sawsim.nw @@ -1,5 +1,25 @@ +% sawsim - simulating single molecule mechanical unfolding. +% Copyright (C) 2008-2010 William Trevor King +% +% This program is free software: you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation, either version 3 of the License, or +% (at your option) any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with this program. If not, see . +% +% The author may be contacted at on the Internet, or +% write to Trevor King, Drexel University, Physics Dept., 3141 Chestnut St., +% Philadelphia PA 19104, USA. + %%%%%%%%%%%%%%%%%%%%%%%%% Start LaTeX boilerplate %%%%%%%%%%%%%%%%%%%%%%%%%%% -% we have our own preamble, +% we have our own preamble, % use `noweave -delay` to not print noweb's automatic one % -*- mode: Noweb; noweb-code-mode: c-mode -*- \documentclass[letterpaper, 11pt]{article} @@ -11,10 +31,15 @@ \usepackage[breaklinks,colorlinks]{hyperref} % for internal links, \phantomsection % breaklinks breaks long links % colorlinks colors link text instead of boxing it -\usepackage{amsmath} % for \text{}, \xrightarrow[sub]{super} +\usepackage{amsmath} % for \text{}, \xrightarrow[sub]{super} \usepackage{amsthm} % for theorem and proof environments \newtheorem{theorem}{Theorem} +\usepackage{subfig} % Support side-by-side figures +\usepackage{pgf} % Fancy graphics +\usepackage{tikz} % A nice, inline PGF frontend +\usetikzlibrary{automata} % Graph-theory library + \usepackage{doc} % BibTeX \usepackage[super,sort&compress]{natbib} % fancy citation extensions % super selects citations in superscript mode @@ -72,6 +97,9 @@ \today \\ \end{centering} \bigskip + +\tableofcontents + %%%%%%%%%%%%%%%%%%%%%%%%%%%% End LaTeX boilerplate %%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Introduction} @@ -99,7 +127,29 @@ to share the burden and increase the transparency of data analysis. \subsection{Related work} -TODO References +Sawim has been published\citep{king10}! It is, as far as I know, the +only open-source Monte Carlo force spectroscopy simulator, but similar +closed source simulators have been around since the seminal paper by +\citet{rief97a}. In chronological order, major contributions have +come from + +\begin{packed_item} + \item \citet{rief97a} \citeyear{rief97a}: + \item \citet{rief97b} \citeyear{rief97b}: + \item \citet{kellermayer97} \citeyear{kellermayer97}: + \item \citet{rief98} \citeyear{rief98}: + first paper to focus mainly on the simulation + \item \citet{oberhauser98} \citeyear{oberhauser98}: + \item \citet{carrion-vazquez99a} \citeyear{carrion-vazquez99a}: + \item \citet{best02} \citeyear{best02}: + pointed out large fit valley + \item \citet{zinober02} \citeyear{zinober02}: + introduced the scaffold effect + \item \citet{jollymore09} \citeyear{jollymore09}: + \item \citet{king10} \citeyear{king10}: + introduced sawsim +\end{packed_item} + \subsection{About this document} @@ -133,15 +183,42 @@ be controlled from the command line. Also added interpolating lookup tables to accelerate slow unfolding rate model evaluation, and command line control of tension groups. +Version 0.5 added the stiffness environmental parameter and it's +associated unfolding models. + +Version 0.6 generalized from two state unfolding to arbitrary +$N$-state rate reactions. This allows simulations of +unfolding-refolding, metastable intermediates, etc., but required +reorganizing the command line interface. + +Version 0.7 added tension model inverses, which seems to reduce +computation time by about a factor of 2. I was expecting more, but +I'll take what I can get. + +Version 0.8 fixed a minor bug in unfolding probability for +multi-domain groups. The probability of at least one domain unfolding +had been calculated as $P_N=NP_1$, rather than $P_N=1-(1-P_1)^N$. +However, for small $P$ the two are equivalent. + +Version 0.9 added the [[-P]] option to sawsim, setting the target +probability for the per-state transition $P_N$, not the per-domain +transisiton $P_1$. + +Version 0.10 added the [[-F]] option to sawsim, setting a limit on the +force change $dF$ in a single timestep for continuous pulling +simulations. It also added the piston tension model (Section +\ref{sec.piston_tension}), and adjusted the stiffness calculations to +handle domains with undefined stiffness. + <>= -#define VERSION "0.4" -@ +#define VERSION "0.10" +@ \subsection{License} <>= - sawsim - program for simulating single molecule mechanical unfolding. - Copyright (C) 2008, William Trevor King + sawsim - simulating single molecule mechanical unfolding. + Copyright (C) 2008-2010, William Trevor King This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as @@ -150,31 +227,78 @@ line control of tension groups. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License - along with this program; if not, write to the Free Software - Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA - 02111-1307, USA. + along with this program. If not, see . The author may be contacted at on the Internet, or write to Trevor King, Drexel University, Physics Dept., 3141 Chestnut St., Philadelphia PA 19104, USA. -@ +@ <>= /* <> */ -@ +@ \section{Main} +\label{sec.main} + +The unfolding system is stored as a chain of \emph{domains} (Figure +\ref{fig.domain_chain}). Domains can be folded, globular protein +domains, unfolded protein linkers, AFM cantilevers, or other +stretchable system components. The system is modeled as graph of +possible domain states with transitions between them (Figure +\ref{fig.domain_states}). -The unfolding system is stored as a chain of \emph{domains}. Domains -can be folded, globular protein domains, unfolded protein linkers, AFM -cantilevers, or other stretchable system components. +\begin{figure} +\begin{center} +\subfloat[][]{\label{fig.domain_chain} +\begin{tikzpicture}[->,node distance=2cm,font=\footnotesize] + \tikzstyle{every state}=[fill,draw=red!50,very thick,fill=red!20] + \node[state] (A) {domain 1}; + \node[state] (B) [below of=A] {domain 2}; + \node[state] (C) [below of=B] {.~.~.}; + \node[state] (D) [below of=C] {domain $N$}; + \node (S) [below of=D] {Surface}; + \node (E) [above of=A] {}; + + \path[-] (A) edge (B) + (B) edge node [right] {Tension} (C) + (C) edge (D) + (D) edge (S); + \path[->,green] (A) edge node [right,black] {Extension} (E); +\end{tikzpicture} +} +\qquad +\subfloat[][]{\label{fig.domain_states} +\begin{tikzpicture}[->,node distance=2.5cm,shorten <=1pt,shorten >=1pt,font=\footnotesize] + \tikzstyle{every state}=[fill,draw=blue!50,very thick,fill=blue!20] + \node[state] (A) {cantilever}; + \node[state] (C) [below of=A] {transition}; + \node[state] (B) [left of=C] {folded}; + \node[state] (D) [right of=C] {unfolded}; + + \path (B) edge [bend left] node [above] {$k_1$} (C) + (C) edge [bend left] node [below] {$k_1'$} (B) + edge [bend left] node [above] {$k_2$} (D) + (D) edge [bend left] node [below] {$k_2'$} (C); +\end{tikzpicture} +} +\caption{\subref{fig.domain_chain} Extending a chain of domains. One end + of the chain is fixed, while the other is extended at a constant + speed. The domains are coupled with rigid linkers, so the domains + themselves must stretch to accomodate the extension. + \subref{fig.domain_states} Each domain exists in a discrete state. At + each timestep, it may transition into another state following a + user-defined state matrix such as this one, showing a metastable + transition state and an explicit ``cantilever'' domain.} +\end{center} +\end{figure} Each domain contributes to the total tension, which depends on the chain extension. The particular model for the tension as a function @@ -186,69 +310,82 @@ following models have been implemented: \item Hookean spring (Appendix \ref{sec.hooke}), \item Worm-like chain (WLC, Appendix \ref{sec.wlc}), and \item Freely-jointed chain (FJC, Appendix \ref{sec.fjc}). + \item Piston (Appendix \ref{sec.piston_tension}), \end{packed_item} The tension model and parameters used for a particular domain depend -on whether the domain is folded or unfolded. The transition rate from -the folded state to the unfolded state is also handled generally with -function pointers, with implementations for +on the domain's current state. The transition rates between states +are also handled generally with function pointers, with +implementations for \begin{packed_item} \item Null (Appendix \ref{sec.null_k}), \item Bell's model (Appendix \ref{sec.bell}), + \item Spring constant corrected Bell model (Appendix \ref{sec.kbell}), \item Kramers' integral model (Appendix \ref{sec.kramers_integ}), and \item Kramers' saddle point model (Appendix \ref{sec.kramers}). \end{packed_item} The unfolding of the chain domains is modeled in two stages. First the tension of the chain is calculated. Then the tension (assumed to -be constant over the length of the chain), is applied to each folded -domain, and used to calculate the probability of that subdomain -unfolding in the next timestep $dt$. Then the time is stepped -forward, and the process is repeated. - +be constant over the length of the chain, see Section +\ref{sec.timescales}), is applied to each domain, and used to +calculate the probability of that domain changing state in the next +timestep $dt$. Then the time is stepped forward, and the process is +repeated. The simulation is complete when a pre-set time limit +[[t_max]] is reached or a pre-selected state [[stop_state]] is empty. <
>= int main(int argc, char **argv) { <> <> - list_t *domain_list=NULL; /* variables initialized in get_options() */ + + /* variables initialized in get_options() */ + list_t *state_list=NULL, *transition_list=NULL; environment_t env={0}; - double P, dt_max, v, xstep; - int num_folded=0, unfolding; - double x=0, dt, F; /* variables used in the simulation loop */ - get_options(argc, argv, &P, &dt_max, &v, &xstep, &env, NUM_TENSION_MODELS, - tension_models, NUM_K_MODELS, k_models, &domain_list, &num_folded); + double P, dF, t_max, dt_max, v, x_step; + state_t *stop_state=NULL; + + /* variables used in the simulation loop */ + double t=0, x=0, dt, F; /* time, distance, timestep, force */ + int transition=1; /* boolean marking a transition for tension and timestep optimization */ + + get_options(argc, argv, &P, &dF, &t_max, &dt_max, &v, &x_step, + &stop_state, &env, NUM_TENSION_MODELS, tension_models, + NUM_K_MODELS, k_models, &state_list, &transition_list); setup(); - if (flags & FLAG_OUTPUT_FULL_CURVE) printf("#Position (m)\tForce (N)\n"); - if (flags & FLAG_OUTPUT_UNFOLDING_FORCES) printf("#Unfolding Force (N)\n"); - while (num_folded > 0) { - F = find_tension(NUM_TENSION_MODELS, tension_handlers, domain_list, &env, x, unfolding); - if (xstep == 0) - dt = determine_dt(NUM_TENSION_MODELS, tension_handlers, domain_list, &env, x, P, dt_max, v); + + if (flags & FLAG_OUTPUT_FULL_CURVE) printf("#Distance (m)\tForce (N)\tStiffness (N/m)\n"); + if (flags & FLAG_OUTPUT_TRANSITION_FORCES) printf("#Force (N)\tInitial state\tFinal state\n"); + while ((t_max > 0 && t <= t_max) || (stop_state != NULL && stop_state->num_domains > 0)) { + F = find_tension(state_list, &env, x, transition, 0); + if (x_step == 0) + dt = determine_dt(state_list, transition_list, &env, F, x, dF, P, dt_max, v, transition); else - dt = determine_dt(NUM_TENSION_MODELS, tension_handlers, domain_list, &env, x, P, dt_max, 0); - unfolding=random_unfoldings(domain_list, F, dt, &env, &num_folded); - if (flags & FLAG_OUTPUT_FULL_CURVE) printf("%g\t%g\n", x, F); - if (xstep == 0) { + dt = determine_dt(state_list, transition_list, &env, F, x, dF, P, dt_max, 0, transition); + transition=random_transitions(transition_list, F, dt, &env); + if (flags & FLAG_OUTPUT_FULL_CURVE) printf("%g\t%g\t%g\n", x, F, env.stiffness); + t += dt; + if (x_step == 0) { x += v*dt; } else { if (dt == dt_max) { /* step completed */ - x += xstep; - dt_max = xstep / v; + x += x_step; + dt_max = x_step / v; } else { /* still working on this step */ dt_max -= dt; } } } - destroy_domain_list(domain_list); + destroy_state_list(state_list); + destroy_transition_list(transition_list); free_accels(); return 0; } @ The meat of the simulation is bundled into the three functions -[[find_tension]], [[determine_dt]], and [[random_unfoldings]]. +[[find_tension]], [[determine_dt]], and [[random_transitions]]. [[find_tension]] is discussed in Section \ref{sec.find_tension}, [[determine_dt]] in Section \ref{sec.adaptive_dt}, and -[[random_unfoldings]] in Section \ref{sec.unfolding_rate}. +[[random_transitions]] in Section \ref{sec.transition_rate}. The stretched distance is extended in one of two modes depending on [[xstep]]. If [[xstep == 0]], then the pulling is continuous, at @@ -265,23 +402,27 @@ styles implemented, the effects of the discretization can be easily calculated, bridging the gap between theory and experiment. Environmental parameters important in determining reaction rates and -tensions (e.g. temperature, pH) are stored in a single structure to +tensions (e.g.\ temperature, pH) are stored in a single structure to facilitate extension to more complicated models in the future. -<>= +<>= typedef struct environment_struct { double T; + double stiffness; } environment_t; -@ +@ <>= #ifndef GLOBAL_H #define GLOBAL_H + +#define DOUBLE_PRECISION 1e-12 + <> <> <> <> #endif /* GLOBAL_H */ -@ +@ Where the [[GLOBAL_H]] defines are protecting [[global.h]] from being included multiple times. @@ -291,56 +432,48 @@ included multiple times. <> <> <> -<> -<> -@ +<> +<> +@ \subsection{Tension} \label{sec.find_tension} Because the stretched system may be made up of several parts (folded domains, unfolded domains, spring-like cantilever, \ldots), we will -assign the domains to models and groups. The models are used to -determine a domain's tension (Hookean spring, WLC, \ldots). Groups -will represent collections of domains which the model should treat as -a single entity. A domain may belong to different groups or models -depending on its state. For example, a domain might be modeled as a -freely-jointed chain when it is folded and as a worm-like chain when -it is unfolded. The domains are assumed to be commutative, so -ordering is ignored. The interactions between the groups are assumed -to be linear, but the interactions between domains of the same group -need not be. This allows for non-linear group models such as th -worm-like or freely-jointed chains. Each model has a tension handler -function, which gives the tension $F$ needed to stretch a given group -of domains a distance $x$. - -To understand the purpose of groups, consider a chain of proteins -where two folded proteins $A$ and $B$ are modeled as WLCs with -persistence length $p_f$ and two unfolded proteins $C$ and $D$ are -modeled as WLCs with persistence length $p_u$. The proteins are -attached to a cantilever $E$ qof spring constant $κ$. The string -would get split into three lists: -\begin{center} - \begin{tabular}{llll} - Model & Group & List & Tension \\ - WLC & 0 & $[A,B]$ & $F_\text{WLC}(x, p_f, L_A+L_B)$ \\ - WLC & 1 & $[C,D]$ & $F_\text{WLC}(x, p_u, L_C+L_D)$ \\ - Hooke & 0 & $[E]$ & $F_\text{Hooke}(x, κ)$ \\ - \end{tabular} -\end{center} -Note that group numbers only matter \emph{within} model classes, since -grouping domains with seperate models doesn't make sense. +assign the domains to states with tension models and groups. The +models are used to determine the tension of all the domain in a given +state following some model (Hookean spring, WLC, \ldots). The domains +are assumed to be commutative, so ordering is ignored. The +interactions between the groups are assumed to be linear, but the +interactions between domains of the same group need not be. Each +model has a tension handler function, which gives the tension $F$ +needed to stretch a given group of domains a distance $x$. + +Groups represent collections of states which the model should treat as +a single entity. To understand the purpose of groups, consider a +system with two unfolded domain states (e.g.\ for two different +proteins) that were both modeled as WLCs. If both unfolded states had +the same persistence length, it would be wise to assign them to the +same group. This would reduce both the computational cost of +balancing the tension and the error associated with the inter-group +interaction linearity. Note that group numbers only matter +\emph{within} model classes, since grouping domains with seperate +models doesn't make sense. Within designated groups, the tension +parameters for each domain are still checked for compatibility, so if +you accidentally assign incompatible domains to the same group you +should get an appropriate error message. <>= -#define NUM_TENSION_MODELS 5 +#define NUM_TENSION_MODELS 6 -@ +@ <>= extern one_dim_fn_t *tension_handlers[]; @ -<>= +<>= one_dim_fn_t *tension_handlers[] = { NULL, &const_tension_handler, @@ -349,77 +482,81 @@ one_dim_fn_t *tension_handlers[] = { &fjc_handler, }; -@ +@ <>= <> -@ +@ <>= typedef struct tension_handler_data_struct { - /* int num_domains; */ - /* domain_t *domains; */ - list_t *group; + list_t *group_tension_params; /* one item for each domain in the group */ environment_t *env; void *persist; } tension_handler_data_t; -@ +@ After sorting the chain into separate groups $G_i$, with tension handlers $F_i(G_i; x_i)$, we need to balance the extension $x_i$ of each group to get a consistent tension $F_i(x_i) = F_j(x_j) \;\; -\forall i,j$. Note that there may be several groups within each model -class. [[find_tension]] is basically a wrapper to feed proper input -into the [[tension_balance]] function. [[unfolding]] should be set to -0 if there were no unfoldings since the previous call to -[[find_tension]]. +\forall i,j$. Note that there may be several states within each +group. [[find_tension]] is basically a wrapper to feed proper input +into the [[tension_balance]] function. [[transition]] should be set +to 0 if there were no transitions since the previous call to +[[find_tension]] to support some optimizations that assume a small +increase in tension between steps (only true if no transition has +occured). While we're messing with the tension handlers and if +[[const_env==0]], we also grab a measure of the current linker +stiffness for the environmental variable, which is needed by some of +the unfolding rate models (e.g.\ the linker-stiffness corrected Bell +model, Appendix \ref{sec.kbell}). <>= -double find_tension(int num_tension_handlers, one_dim_fn_t **tension_handlers, list_t *domain_list, environment_t *env, double x, int unfolding) -{ +double find_tension(list_t *state_list, environment_t *env, double x, + int transition, int const_env) +{ // TODO: !cont_env -> step_call, only alter env or statics if step_call==1 static int num_active_groups=0; static one_dim_fn_t **per_group_handlers = NULL; - static void **per_group_params = NULL; + static one_dim_fn_t **per_group_inverse_handlers = NULL; + static void **per_group_data = NULL; /* array of pointers to tension_handler_data_t */ static double last_x; tension_handler_data_t *tdata; - double F; + double F, *pStiffness; int i; #ifdef DEBUG - fprintf(stderr, "finding tension at distance %g%s\n", x, unfolding ? " after an unfolding" : ""); - list_print(stderr, domain_list, "domain list"); + fprintf(stderr, "%s:\tfinding tension at distance %g%s\n", __FUNCTION__, x, transition ? " after a transition" : ""); #endif - if (unfolding != 0 || num_active_groups == 0) { /* setup statics */ - /* free old statics */ - if (per_group_handlers != NULL) - free(per_group_handlers); - if (per_group_params != NULL) { - for (i=0; i < num_active_groups; i++) { - assert(per_group_params[i] != NULL); - free(per_group_params[i]); - } - free(per_group_params); - } - - /* get new statics */ - get_active_groups(domain_list, num_tension_handlers, tension_handlers, &num_active_groups, &per_group_handlers, &per_group_params); + if (transition != 0 || num_active_groups == 0) { /* setup statics */ + /* get new statics, freeing the old ones if they aren't NULL */ + get_active_groups(state_list, &num_active_groups, &per_group_handlers, &per_group_inverse_handlers, &per_group_data); /* fill in the group handlers and params */ +#ifdef DEBUG + fprintf(stderr, "%s:\t%d groups, tension handler array %p, inverse tension handler array %p, handler data array %p, (lead data element %p)\n", __FUNCTION__, num_active_groups, per_group_handlers, per_group_inverse_handlers, per_group_data, per_group_data[0]); +#endif for (i=0; igroup, " parameters"); + fprintf(stderr, "%s:\tactive group %d of %d (data %p, param list %p)", __FUNCTION__, i, num_active_groups, tdata, tdata->group_tension_params); + list_print(stderr, tdata->group_tension_params, " parameters"); #endif tdata->env = env; /* tdata->persist continues unchanged */ } last_x = -1.0; - } /* else roll with the current statics */ + } /* else continue with the current statics */ + + if (const_env == 1) + pStiffness = NULL; + else + pStiffness = &env->stiffness; + + F = tension_balance(num_active_groups, per_group_handlers, per_group_inverse_handlers, (void **)per_group_data, last_x, x, pStiffness); - F = tension_balance(num_active_groups, per_group_handlers, (void **)per_group_params, last_x, x); last_x = x; + return F; } @ For the moment, we will restrict our group boundaries to a single @@ -433,102 +570,188 @@ complicated, but without much loss of practicality we can restrict ourselves to strictly monotonically increasing, non-negative tension functions $F_i(x)$, with $F_i(0)=0$, which makes the situation much simpler. For example, it guarantees the existence of a unique, real -solution for finite forces. See Appendix \ref{app.tension_balance} +solution for finite forces. See Appendix \ref{sec.tension_balance} for the tension balancing implementation. Each group must define a parameter structure if the tension model is parametrized, a function to create the parameter structure, a function to destroy the parameter structure, and - a tension function of type [[one_dim_fn_t]] that receives a [[tension_handler_data_t *]] as it's data argument. + a tension function of type [[one_dim_fn_t]] that receives a [[tension_handler_data_t *]] as its data argument. The tension-specific parameter structures are contained in the domain -group field. See the Section \ref{app.model_selection} for a -discussion on the command line framework. See the worm-like chain +group field. For optimization, a group may also define an inverse +tension function as an optimization. See the Section +\ref{sec.model_selection} for a discussion on the command line +framework and inverse function discussion. See the worm-like chain implementation for an example (Section \ref{sec.wlc}). The major limitation of our approach is that all of our tension models are Markovian (memory-less), which is not really a problem for the chains (see \citet{evans99} for WLC thermalization rate calculations). -\subsection{Unfolding rate} -\label{sec.unfolding_rate} +\subsection{Transition rate} +\label{sec.transition_rate} -Each folded domain is modeled as unimolecular, first order reaction +Each state transition is modeled as unimolecular, first order reaction $$ - \text{Folded} \xrightarrow{k} % in tex: X atop Y - \text{Unfolded} + \text{State 1} \xrightarrow{k} \text{State 2} $$ With the rate constant $k$ defined by $$ - \frac{d[\text{Folded}]}{dt} = -k [\text{Folded}]. + \frac{d[\text{State 2}]}{dt} = -\frac{d[\text{State 1}]}{dt} = k [\text{State 1}]. +$$ +So the probability of a given domain transitioning in a short time +$dt$ is given by $$ -So the probability of a given protein unfolding in a short time $dt$ -is given by + P_1 = k \cdot dt. $$ - P = k \cdot dt. + +For a group of $N$ identical domains, and therefore identical +unfolding probabilities $P_1$, the probability of $n$ domains +unfolding in a given timestep is given by the binomial distribution +$$ + P(n) = \frac{N!}{n!(N-n)!}P_1^n(1-P_1)^{(N-n)}. +$$ +The probability that \emph{none} of these domains unfold is then +$$ + P(0) = (1-P_1)^N, +$$ +so the probability that \emph{at least one} domain unfolds is +$$ + P_N = 1-(1-P_1)^N. +$$ +Note that for small $P$, +$$ + p(n>0) = 1-(1-NP_1+\mathcal{O}(P_1^2)) = NP_1 - \mathcal{O}(P^2) + \approx NP_1. $$ +This conversion from $P_1$ to $P_N$ is handled by the [[pN]] macro +<>= +/* find multi-domain transition rate from the single domain rate */ +#define PN(P,N) (1.0-pow(1.0-(P), (N))) -<>= -int domain_unfolds(double F, double dt, environment_t *env, domain_t *domain) -{ /* returns 1 or 0, F in N, dt in s, pointer to env. data, pointer to a folded domain */ +@ + +We can also define a macro to find the approprate $dt$ to achieve a +target $P_N$ with a given $k$ and $N$. +\begin{align} + P_N &= 1-(1-P_1)^N \\ + 1-P_1 &= (1-P_N)^{1/N} \\ + P_1 &= 1-(1-P_N)^{1/N} +\end{align} +<>= +#define P1(PN,N) (1.0-pow(1.0-(PN), 1.0/(N))) +@ + +We take some time to discuss the meaning of $p(n>1)$ +(i.e. multi-unfolding timesteps) in Section \ref{sec.timescales}. + +<>= +int domain_transitions(double F, double dt, environment_t *env, transition_t *transition) +{ /* returns 1 or 0, F in N, dt in s, pointer to env. data, pointer to transition structure */ double k; - k = accel_k(domain->k, F, env, domain->k_params); - //(*domain->k)(F, env, domain->k_params); + k = accel_k(transition->k, F, env, transition->k_params); + //(*transition->k)(F, env, domain->k_params); //printf("k = %g,\tdt = %g,\tk dt = %g\n", k, dt, k*dt); - return happens(k*dt); /* dice roll for prob. k*dt event */ -} -@ [[happens]] is a random decision making function defined in Appendix \ref{app.utils}. - -Only one domain can unfold in each timestep, because the timescale of -a domain unfolding $dt_u$ is assumed to be less than the simulation -timestep $dt$, so a domain will completely unfold in a single -timestep. We adapt our timesteps to keep the probability of a single -domain unfolding low, so the probability of two domains unfolding in -the same timestep is negligible. This approach breaks down as the -adaptive timestep scheme approaches $dt \sim dt_u$, but $dt_u \sim -1\U{$\mu$s}$ for Ig27-like proteins \citep{klimov00}, so this -shouldn't be a problem. To reassure yourself, you can ask the -simulator to print the smallest timestep that was used with TODO. -<>= -int random_unfoldings(list_t *domain_list, double tension, - double dt, environment_t *env, - int *num_folded_domains) -{ /* returns 1 if there was an unfolding and 0 otherwise */ - while (domain_list != NULL) { - if (D(domain_list)->state == DS_FOLDED - && domain_unfolds(tension, dt, env, D(domain_list))) { - if (flags & FLAG_OUTPUT_UNFOLDING_FORCES) - fprintf(stdout, "%g\n", tension); - D(domain_list)->state = DS_UNFOLDED; - (*num_folded_domains)--; - return 1; /* our one domain has unfolded, stop looking for others */ + return happens(PN(k*dt, N_INIT(transition))); +} +@ [[happens]] is a random decision making function defined in Appendix \ref{sec.utils}. + +<>= +int random_transitions(list_t *transition_list, double tension, + double dt, environment_t *env) +{ /* returns 1 if there was a transition and 0 otherwise */ + while (transition_list != NULL) { + if (T(transition_list)->initial_state->num_domains > 0 + && domain_transitions(tension, dt, env, T(transition_list))) { + if (flags & FLAG_OUTPUT_TRANSITION_FORCES) + fprintf(stdout, "%g\t%s\t%s\n", tension, T(transition_list)->initial_state->name, T(transition_list)->final_state->name); + T(transition_list)->initial_state->num_domains--; + T(transition_list)->final_state->num_domains++; + return 1; /* our one domain has transitioned, stop looking for others */ } - domain_list = domain_list->next; + transition_list = transition_list->next; } return 0; } -@ +@ + +\subsection{Timescales} +\label{sec.timescales} + +The simulation assumes that chain equilibration is instantaneous +relative to the simulation timestep $dt$, so that tension is uniform +along the chain. The quality of this assumption depends on your +particular chain. For example, a damped spring thermalizes on a +timescale of order $\tau = 1/\gamma$ where the damping ratio $\gamma +\equiv \omega_0(-\zeta \pm \sqrt{\zeta^2-1})$, the natural angular +frequency $\omega_0 \equiv \sqrt{k/m}$, $\zeta \equiv b/2\sqrt{km}$, +and $b$ sets the drag $F_b = -bv$. For our cantilevers $\tau$ is +on the order of milliseconds, which is longer than a timestep. +However, the approximation is still reasonable, because there is +rarely unfolding during the cantilever return. You could, of course, +take cantilever, WLC, etc.\ response times into effect, but that +would significantly complicate a simulation that seems to work +well enough without bothering :p. For WLC and FJC relaxation times, +see the Appendix of \citet{evans99} and \citet{kroy07}. + +Besides assuming our timestep is much greater than equilibration +times, we also force it to be short enough so that only one domain may +unfold in a given timestep. For an unfolding timescale of $dt_u = +1/k$, we adapt our timesteps to keep $dt \ll dt_u$, so the probability +of two domains unfolding in the same timestep is small (see +[[determine_dt]] in Section \ref{sec.adaptive_dt} and [[P]] in +[[main()]] in Section \ref{sec.main} set by [[-P]] in +[[get_options()]] in Section \ref{sec.get_options}). This approach +breaks down as the adaptive timestep scheme approaches the transition +timestep $dt_t$, but $dt_t \sim 1\U{$\mu$s}$ for Ig27-like proteins +\citep{klimov00}, so this shouldn't be a problem. To reassure +yourself, you can ask the simulator to print the smallest timestep +that was used with TODO. + +Even if the likelyhood of two domains unfolding in the same timestep +is small, if you run long enough simulations it will eventually occur. +In this case, we assume that $dt_t \ll dt$, so even if two domains +would unfold if we stuck to our unfolding rate $k$ for an entire +timestep $dt$, in ``reality'' only one of those domains unfolds. +Because we do not know when in the timestep the unfolding took place, +we move on to the next timestep without checking for further +unfoldings. This ``unchecked timestep portion'' should not contribute +significant errors to the calculation, because if $dt$ was small +enough that unfolding was unlikely at the pre-unfolding force, it +should be even more unlikely at the post-unfolding force, especially +over only a fraction of the timestep. The only dangerous cases for +the current implementation are those where unfolding intermediates are +much less stable than their precursor states, in which case an +unfolding event during the remaining timestep may actually be likely. +A simple workaround for such cases is to pick the value for [[P]] to +be small enough that the $dt \ll dt_u$ assumption survives even under +a transition populating the unstable intermediate. \subsection{Adaptive timesteps} \label{sec.adaptive_dt} -We'd like to pick $dt$ so the probability of unfolding in the next -timestep is small. If we don't adapt our timestep, we risk breaking -our approximation that $F(x' \in [x, x+v \cdot dt]) = F(x)$ or that -only one domain unfolds in a given timestep. Because $F(x)$ is -monotonically increasing, excessively large timesteps will lead to -erroneously large unfolding forces. The simulation would have been -accurate for sufficiently small fixed timesteps, but adaptive -timesteps will allow us to move through low tension regions in fewer -steps, leading to a more efficient simulation. +We'd like to pick $dt$ so the probability of changing state +(e.g.\ unfolding) in the next timestep is small. If we don't adapt our +timestep, we also risk breaking our approximation that $F(x' \in [x, + x+v \cdot dt]) = F(x)$ or that only one domain changes state in a +given timestep. The simulation would have been accurate for +sufficiently small fixed timesteps, but adaptive timesteps will allow +us to move through low tension regions in fewer steps, leading to a +more efficient simulation. + +Consider the two state folded $\rightarrow$ unfolded transition. +Because $F(x)$ is monotonically increasing between unfoldings, +excessively large timesteps will lead to erroneously small unfolding +rates (an thus, higher average unfolding force). The actual adaptive timestep implementation is not particularly interesting, since we are only required to reduce $dt$ to somewhere below a set threshold, so I've removed it to Appendix -\ref{app.adaptive_dt}. +\ref{sec.adaptive_dt_implementation}. \section{Models} - + TODO: model intro. The models provide the physics of the simulation, but the simulation @@ -536,12 +759,13 @@ allows interchangeable models, and we are currently focusing on the simulation itself, so we remove the actual model implementation to the appendices. -The tension models are defined in Appendix \ref{sec.tension_models} +The tension models are defined in Appendix \ref{sec.tension_models}, and unfolding models are defined in Appendix \ref{sec.k_models}. <>= #define k_B 1.3806503e-23 /* J/K */ -@ + +@ \section{Command line interface} @@ -550,12 +774,11 @@ and unfolding models are defined in Appendix \ref{sec.k_models}. <> <> <> -<> <> -@ +@ \subsection{Model selection} -\label{app.model_selection} +\label{sec.model_selection} The main difficulty with the command line interface in \prog\ is developing an intuitive method for accessing the possibly large number @@ -564,18 +787,50 @@ of available models, containing their important parameters. <>= <> -@ +@ <>= typedef void *create_data_func_t(char **param_strings); typedef void destroy_data_func_t(void *param_struct); -@ +@ <>= <> <> -@ +@ +In order to choose models, we need a method of assembling a reaction +graph such as that in Figure \ref{fig.domain_states} and population +the graph with a set of domains. First we declare the domain states +following +\begin{center} +[[-s ,[,] -S [-N ,, -K ]] \\ +\end{center} +e.g. +\begin{center} + [[-k folded,unfolded,bell -K 3.3e-4,0.25e-9]] +\end{center} +This creates a reaction going from the [[folded]] state to the +[[unfolded]] state, with the rate constant given by the Bell model +(Appendix \ref{sec.bell}). The unfolding parameters are then set to +[[3.3e-4,0.25e-9]], which in the case of the Bell model are the +unforced rate and transition state distance respectively. \subsubsection{Tension} @@ -584,7 +839,8 @@ a structure that contains all the neccessary information about the model. <>= typedef struct tension_model_getopt_struct { - one_dim_fn_t *handler; /* fn implementing the model on a group */ + one_dim_fn_t *handler; /* fn implementing the model on a group */ + one_dim_fn_t *inverse_handler; /* fn implementing inverse on group */ char *name; /* name string identifying the model */ char *description; /* a brief description of the model */ int num_params; /* number of extra params for the model */ @@ -593,7 +849,10 @@ typedef struct tension_model_getopt_struct { create_data_func_t *creator; /* param-string -> model-data-struct fn */ destroy_data_func_t *destructor; /* fn to free the model data structure */ } tension_model_getopt_t; -@ +@ Set [[inverse_handler]] to [[NULL]] if you wish to invert using +bisection. Obviously, this will be slower than computing an +analytical inverse and more prone to rounding errors, but it may be +easier if a closed-form inverse does not exist. <>= tension_model_getopt_t tension_models[NUM_TENSION_MODELS] = { @@ -601,14 +860,15 @@ tension_model_getopt_t tension_models[NUM_TENSION_MODELS] = { <>, <>, <>, - <> + <>, + <> }; -@ +@ \subsubsection{Unfolding rate} <>= -#define NUM_K_MODELS 5 +#define NUM_K_MODELS 6 typedef struct k_model_getopt_struct { char *name; @@ -620,75 +880,81 @@ typedef struct k_model_getopt_struct { create_data_func_t *creator; destroy_data_func_t *destructor; } k_model_getopt_t; -@ +@ <>= k_model_getopt_t k_models[NUM_K_MODELS] = { <>, <>, <>, + <>, <>, <> }; -@ +@ \subsection{help} <>= -void help(char *prog_name, double P, double dt_max, double v, double xstep, - environment_t *env, +void help(char *prog_name, double P, double dF, + double t_max, double dt_max, double v, double x_step, + state_t *stop_state, environment_t *env, int n_tension_models, tension_model_getopt_t *tension_models, - int folded_tension_model, int unfolded_tension_model, int n_k_models, k_model_getopt_t *k_models, - int k_model) + int k_model, list_t *state_list) { + state_t *state=NULL; int i, j; + + if (state_list != NULL) + state = S(tail(state_list)); + printf("usage: %s [options]\n", prog_name); printf("Version %s\n\n", VERSION); printf("Monte Carlo simulation of a multi-globular domain protein unfolding\n\n"); + printf("Simulation options:\n"); - printf("-P P\tTarget probability for dt (currently %g)\n", P); - printf("-t dt\tMaximum allowed timestep dt (currently %g)\n", dt_max); + printf(""); + printf("-q state\tStop simulation when this state empties (- for no limit, currently %s)\n", stop_state ? stop_state->name : "-" ); + printf("-t tmax\tMaximum simulated time (-1 for no limit, currently %g s)\n", t_max); + printf("-d dt\tMaximum allowed timestep dt (currently %g s)\n", dt_max); + printf("-P P\tMaximum transition probability for dt (currently %g)\n", P); + printf("-F dF\tMaximum change in force over dt. Only relevant if dx > 0. (currently %g N)\n", dF); printf("-v v\tPulling velocity v (currently %g nm/s)\n", v); - printf("-x dx\tPulling step size (currently %g m)\n", xstep); - printf("\tWhen dx = 0, the pulling is continuous\n"); - printf("\tWhen dx > 0, the pulling occurs in discrete steps\n"); + printf("-x dx\tPulling step size (currently %g m)\n", x_step); + printf("\tWhen dx = 0, the pulling is continuous.\n"); + printf("\tWhen dx > 0, the pulling occurs in discrete steps.\n"); + printf("Environmental options:\n"); printf("-T T\tTemperature T (currently %g K)\n", env->T); printf("-C T\tYou can also set the temperature T in Celsius\n"); - printf("Model options:\n"); - printf("The domains exist in either the folded or unfolded state\n"); - printf("The following options change the default behavior in each state.\n"); - printf("-m model[,group]\tFolded tension model (currently %s)\n", - tension_models[folded_tension_model].name); - printf("-a args\tFolded tension model argument string (currently %s)\n", - tension_models[folded_tension_model].params); - printf("-M model[,group]\tUnfolded tension model (currently %s)\n", - tension_models[unfolded_tension_model].name); - printf("-A args\tUnfolded tension model argument string (currently %s)\n", - tension_models[unfolded_tension_model].params); - printf("The following options change the unfolding rate.\n"); - printf("-k model\tTransition rate model (currently %s)\n", - k_models[k_model].name); - printf("-K args\tTransition rate model argument string (currently %s)\n", - k_models[k_model].params); - printf("Domain creation options:\n"); - printf("Once you've set up the appropriate default models, you need to add the domains\n"); - printf("-F n\tAdd n folded domains with the current models\n"); - printf("-U n\tAdd n unfolded domains with the current models\n"); - printf("Output mode options:\n"); - printf("There are two output modes. In standard mode, only the unfolding\n"); + + printf("State creation options:\n"); + printf("-s name,model[[,group],params]\tCreate a new state.\n"); + printf("Once you've set up the state, you may populate it with domains\n"); + printf("-N n\tAdd n domains in the current state (%s)\n", state ? state->name : "-"); + + printf("Transition creation options:\n"); + printf("-k initial_state,final_state,model[,params]\tCreate a new transition\n"); + + printf("To double check your reaction graph, you can produce graphviz dot output\n"); + printf("describing the current states and transitions.\n"); + printf("-D\tPrint dot description of states and transitions and exit.\n"); + + printf("Simulation output mode options:\n"); + printf("There are two output modes. In standard mode, only the transition\n"); printf("events are printed. For example:\n"); - printf(" #Unfolding Force (N)\n"); - printf(" 123.456e-12\n"); + printf(" #Force (N)\tInitial state\tFinal state\n"); + printf(" 123.456e-12\tfolded\tunfolded\n"); printf(" ...\n"); printf("In verbose mode, the entire Force-vs-distance curve is output:\n"); - printf(" #Position (m)\tForce (N)\n"); - printf(" 0.001\t0.0023\n"); + printf(" #Distance (m)\tForce (N)\tStiffness (N/m)\n"); + printf(" 0.001\t0.0023\t0.002\n"); printf(" ...\n"); - printf("-V\tChange output to verbose mode\n"); - printf("-h\tPrint this help and exit\n"); + printf("-V\tChange output to verbose mode.\n"); + printf("-h\tPrint this help and exit.\n"); printf("\n"); + printf("Tension models:\n"); for (i=0; i>= -void get_options(int argc, char **argv, - double *pP, double *pDt_max, double *pV, double *pXstep, - environment_t *env, +<> +void get_options(int argc, char **argv, double *pP, double *pDF, + double *pT_max, double *pDt_max, double *pV, + double *pX_step, state_t **pStop_state, environment_t *env, int n_tension_models, tension_model_getopt_t *tension_models, int n_k_models, k_model_getopt_t *k_models, - list_t **pDomain_list, int *pNum_folded) + list_t **pState_list, list_t **pTransition_list) { char *prog_name = NULL; - char c, options[] = "P:t:v:x:T:C:m:a:M:A:k:K:F:U:Vh"; - int ftension_model=0, utension_model=0, k_model=0; - char *ftension_params=NULL, *utension_params=NULL; - int i, n, ftension_group=0, utension_group=0; + char c, options[] = "q:t:d:P:F:v:x:T:C:s:N:k:DVh"; + int tension_model=0, k_model=0, initial_state=-1, final_state=-1; + char *state_name=NULL; + int i, n, tension_group=0; + list_t *temp_list=NULL; int num_strings; char **strings; + void *model_params; /* for INIT_MODEL() */ + int num_param_args; /* for INIT_MODEL() */ + char **param_args; /* for INIT_MODEL() */ extern char *optarg; extern int optind, optopt, opterr; - assert (argc > 0); + assert(argc > 0); #ifdef DEBUG for (i=0; iT = 300.0; /* K */ + *pStop_state = NULL; + *pT_max = -1; /* s, -1 removes this limit */ + *pDt_max = 0.001; /* s */ + *pP = 1e-3; /* % pop per s */ + *pDF = 1e-12; /* N */ + *pV = 1e-6; /* m/s */ + *pX_step = 0.0; /* m */ + env->T = 300.0; /* K */ + *pState_list = NULL; + *pTransition_list = NULL; while ((c=getopt(argc, argv, options)) != -1) { switch(c) { - case 'P': *pP = atof(optarg); break; - case 't': *pDt_max = atof(optarg); break; - case 'v': *pV = atof(optarg); break; - case 'x': *pXstep = atof(optarg); break; - case 'T': env->T = atof(optarg); break; - case 'C': env->T = atof(optarg)+273.15; break; - case 'm': - parse_list_string(optarg, SEP, '{', '}', &num_strings, &strings); - assert(num_strings == 1 || num_strings == 2); - if (num_strings == 1) - ftension_group = 0; - else - ftension_group = atoi(strings[1]); - ftension_model = index_tension_model(n_tension_models, tension_models, strings[0]); - ftension_params = tension_models[ftension_model].params; - free_parsed_list(num_strings, strings); - break; - case 'a': - ftension_params = optarg; + case 'q': + if (STRMATCH(optarg, "-")) { + *pStop_state = NULL; + } else { + temp_list = head(*pState_list); + while (temp_list != NULL) { + if (STRMATCH(S(temp_list)->name, optarg)) { + *pStop_state = S(temp_list); + break; + } + temp_list = temp_list->next; + } + } break; - case 'M': + case 't': *pT_max = safe_strtod(optarg, "-t"); break; + case 'd': *pDt_max = safe_strtod(optarg, "-d"); break; + case 'P': *pP = safe_strtod(optarg, "-P"); break; + case 'F': *pDF = safe_strtod(optarg, "-F"); break; + case 'v': *pV = safe_strtod(optarg, "-v"); break; + case 'x': *pX_step = safe_strtod(optarg, "-x"); break; + case 'T': env->T = safe_strtod(optarg, "-T"); break; + case 'C': env->T = safe_strtod(optarg, "-C")+273.15; break; + case 's': parse_list_string(optarg, SEP, '{', '}', &num_strings, &strings); - assert(num_strings == 1 || num_strings == 2); - if (num_strings == 1) - utension_group = 0; + assert(num_strings >= 2 && num_strings <= 4); + + state_name = strings[0]; + if (state_index(*pState_list, state_name) != -1) { + fprintf(stderr, "Invalid option '%s', repeated state name '%s'\n", optarg, state_name); + exit(1); + } + tension_model = index_tension_model(n_tension_models, tension_models, strings[1]); + if (num_strings == 4) + tension_group = safe_strtoi(strings[2], optarg); else - utension_group = atoi(strings[1]); - utension_model = index_tension_model(n_tension_models, tension_models, strings[0]); - utension_params = tension_models[utension_model].params; + tension_group = 0; + if (num_strings >= 3) + tension_models[tension_model].params = strings[num_strings-1]; +#ifdef DEBUG + fprintf(stderr, "%s:\t%s -> state %s, model %s, params %s, group %d\n", __FUNCTION__, optarg, state_name, tension_models[tension_model].name, tension_models[tension_model].params, tension_group); +#endif + INIT_MODEL(state_name, &tension_models[tension_model], tension_models[tension_model].params, model_params); + push(pState_list, create_state(state_name, + tension_models[tension_model].handler, + tension_models[tension_model].inverse_handler, + tension_group, + model_params, + tension_models[tension_model].destructor, + 0), 1); + *pState_list = tail(*pState_list); + state_name = NULL; free_parsed_list(num_strings, strings); break; - case 'A': - utension_params = optarg; + case 'N': + n = safe_strtoi(optarg, "-N"); +#ifdef DEBUG + fprintf(stderr, "%s:\tadding %d domains to %s\n", __FUNCTION__, n, S(*pState_list)->name); +#endif + S(*pState_list)->num_domains += n; break; case 'k': - k_model = index_k_model(n_k_models, k_models, optarg); - break; - case 'K': - k_models[k_model].params = optarg; - break; - case 'F': - n = atoi(optarg); - assert(n > 0); - for (i=0; i= 3 && num_strings <= 4); + initial_state = state_index(*pState_list, strings[0]); + final_state = state_index(*pState_list, strings[1]); + k_model = index_k_model(n_k_models, k_models, strings[2]); +#ifdef DEBUG + fprintf(stderr, "%s:\t%s -> %s reaction from state %s (%d) -> state %s (%d)\n", __FUNCTION__, optarg, strings[2], strings[0], initial_state, strings[1], final_state); +#endif + assert(initial_state != final_state); + if (num_strings == 4) + k_models[k_model].params = strings[3]; + INIT_MODEL(state_name, &k_models[k_model], k_models[k_model].params, model_params); + push(pTransition_list, create_transition(list_element(*pState_list, initial_state), + list_element(*pState_list, final_state), + k_models[k_model].k, + model_params, + k_models[k_model].destructor), 1); + free_parsed_list(num_strings, strings); break; - case 'U': - n = atoi(optarg); - assert(n > 0); - for (i=0; i 0.0); assert(*pP < 1.0); assert(*pDt_max > 0.0); assert(*pV > 0.0); assert(env->T > 0.0); + + crosslink_groups(*pState_list, *pTransition_list); + return; } -@ +@ <>= int index_tension_model(int n_models, tension_model_getopt_t *models, char *name) @@ -855,7 +1153,7 @@ int index_tension_model(int n_models, tension_model_getopt_t *models, char *name } return i; } -@ +@ <>= int index_k_model(int n_models, k_model_getopt_t *models, char *name) @@ -870,7 +1168,7 @@ int index_k_model(int n_models, k_model_getopt_t *models, char *name) } return i; } -@ +@ <>= /* requires int num_param_args and char **param_args in the current scope @@ -880,56 +1178,73 @@ int index_k_model(int n_models, k_model_getopt_t *models, char *name) */ #define INIT_MODEL(role, model, param_string, param_pointer) \ do { \ - parse_list_string(param_string, SEP, '{', '}', \ + parse_list_string((param_string), SEP, '{', '}', \ &num_param_args, ¶m_args); \ - if (num_param_args != model->num_params) { \ + if (num_param_args != (model)->num_params) { \ fprintf(stderr, \ "%s model %s expected %d params,\n", \ - role, model->name, model->num_params); \ + (role), (model)->name, (model)->num_params); \ fprintf(stderr, \ "not the %d params in '%s'\n", \ - num_param_args, param_string); \ - assert(num_param_args == model->num_params); \ + num_param_args, (param_string)); \ + assert(num_param_args == (model)->num_params); \ } \ - if (model->creator) \ - param_pointer = (*model->creator)(param_args); \ + if ((model)->creator) \ + param_pointer = (*(model)->creator)(param_args); \ else \ param_pointer = NULL; \ free_parsed_list(num_param_args, param_args); \ } while (0); -@ - -<>= -void *generate_domain(enum domain_state_t state, - tension_model_getopt_t *folded_model, - int folded_group, - char *folded_param_string, - tension_model_getopt_t *unfolded_model, - int unfolded_group, - char *unfolded_param_string, - k_model_getopt_t *k_model) -{ - void *folded_params, *unfolded_params, *k_params; - int num_param_args; /* for INIT_MODEL() */ - char **param_args; /* for INIT_MODEL() */ +@ -#ifdef DEBUG - fprintf(stderr, "generating %s ", state==DS_FOLDED ? "folded" : "unfolded"); - fprintf(stderr, "domain (k: \"%s\", \"%s\", f: \"%s\" (%p) group %d \"%s\", u: \"%s\" (%p) group %d \"%s\")\n", - k_model->name, k_model->params, - folded_model->name, folded_model->handler, folded_group, folded_param_string, - unfolded_model->name, unfolded_model->handler, unfolded_group, unfolded_param_string); -#endif - INIT_MODEL("folded", folded_model, folded_param_string, folded_params); - INIT_MODEL("unfolded", unfolded_model, unfolded_param_string, unfolded_params); - INIT_MODEL("k", k_model, k_model->params, k_params); - return create_domain(state, - k_model->k, k_params, k_model->destructor, - folded_model->handler, folded_group, folded_params, folded_model->destructor, - unfolded_model->handler, unfolded_group, unfolded_params, unfolded_model->destructor - ); +First we define some safe string parsing functions. Currently these +abort on any irregularity, but in the future they could print error +messages, etc. [[static]] because the functions are currently +defined in each [[*.c]] file that uses them, but perhaps they should +be moved to [[utils.h/c]] or some such instead\ldots + +<>= +static int safe_strtoi(const char *s, const char *description) { + char *endp = NULL; + long int ret; + assert(s != NULL); + ret = strtol(s, &endp, 10); + if (endp[0] != '\0') { //strlen(endp) > 0) { + fprintf(stderr, "Error: unparsable '%s' while parsing '%s' for %s\n", + endp, s, description); + assert(1==0); //strlen(endp) == 0); + } if (endp == s) { + fprintf(stderr, "Error: unparsable empty string '%s' for %s\n", + s, description); + assert(endp != s); + } else if (errno == ERANGE) { + fprintf(stderr, "Error: '%s' out of range for %s\n", s, description); + assert(errno != ERANGE); + } + return (int) ret; +} + +static double safe_strtod(const char *s, const char *description) { + char *endp = NULL; + double ret; + assert(s != NULL); + ret = strtod(s, &endp); + if (endp[0] != '\0') { //strlen(endp) > 0) { + fprintf(stderr, "Error: unparsable '%s' while parsing '%s' for %s\n", + endp, s, description); + assert(1==0); //strlen(endp) == 0); + } if (endp == s) { + fprintf(stderr, "Error: unparsable empty string '%s' for %s\n", + s, description); + assert(endp != s); + } else if (errno == ERANGE) { + fprintf(stderr, "Error: '%s' out of range for %s\n", s, description); + assert(errno != ERANGE); + } + return ret; } -@ + +@ \phantomsection \appendix @@ -941,23 +1256,25 @@ void *generate_domain(enum domain_state_t state, The general layout of our simulation code is: <<*>>= +//#define DEBUG <> <> <> <> <> <
> -@ +@ We include [[math.h]], so don't forget to link to the libm with `-lm'. <>= #include /* assert() */ -#include /* malloc(), free(), rand() */ +#include /* malloc(), free(), rand(), strto*() */ #include /* fprintf(), stdout */ #include /* strlen, strtok() */ #include /* exp(), M_PI, sqrt() */ #include /* pid_t (returned by getpid()) */ #include /* getpid() (for seeding rand()), getopt() */ +#include /* errno, ERANGE (for safe_strto*()) */ #include "global.h" #include "list.h" #include "tension_balance.h" @@ -965,7 +1282,8 @@ We include [[math.h]], so don't forget to link to the libm with `-lm'. #include "tension_model.h" #include "parse.h" #include "accel_k.h" -@ + +@ <>= <> @@ -974,38 +1292,43 @@ We include [[math.h]], so don't forget to link to the libm with `-lm'. <> <> <> -<> -@ +<> +<> +@ <>= <> <> -@ +@ <>= -<> -<> +<> +<> +<> +<> +<> +<> <> <> <> -@ +@ <>= <> <> -@ +@ <>= void setup(void) { srand(getpid()*time(NULL)); /* seed rand() */ } -@ +@ <>= /* in octal b/c of prefixed '0' */ -#define FLAG_OUTPUT_FULL_CURVE 01 -#define FLAG_OUTPUT_UNFOLDING_FORCES 02 +#define FLAG_OUTPUT_FULL_CURVE 01 +#define FLAG_OUTPUT_TRANSITION_FORCES 02 @ <>= @@ -1013,12 +1336,12 @@ static unsigned long int flags = 0; @ \subsection{Utilities} -\label{app.utils} +\label{sec.utils} <>= #define MAX(a,b) ((a)>(b) ? (a) : (b)) #define MIN(a,b) ((a)<(b) ? (a) : (b)) -@ +@ Note that [[STRMATCH]] chokes if one of the strings is [[NULL]]. <>= @@ -1029,7 +1352,7 @@ static char *temp_string_B; strlen(temp_string_A) != strlen(temp_string_B) ? 0 : \ !strncmp(temp_string_A,temp_string_B,strlen(temp_string_B)+1) ) /* +1 to also compare the '\0' */ -@ +@ We also define a macro for our [[check]] unit testing <>= @@ -1044,7 +1367,8 @@ We also define a macro for our [[check]] unit testing -(received-expected)/expected, max_err, #received, \ expected, received); \ } while(0) -@ + +@ <>= int happens(double probability) @@ -1056,41 +1380,41 @@ int happens(double probability) \subsection{Adaptive timesteps} -\label{app.adaptive_dt} - -$F(x)$ increases with $x$, possibly exploding, as in the worm-like chain model, -so basing the timestep on the the unfolding probability at the current tension -is dangerous, and we need to search for a $dt$ for which -$P(F(x+v*dt)) < P_\text{target}$. -There are two cases to consider. -In the most common, no domains have unfolded since the last step, -and we expect the next step to be slightly shorter than the previous one. -In the less common, domains did unfold in the last step, -and we expect the next step to be considerably longer than the previous one. +\label{sec.adaptive_dt_implementation} + +$F(x)$ increases with $x$, possibly exploding (e.g.\ in the worm-like +chain model), so basing the timestep on the unfolding probability at +the current tension is dangerous, and we need to search for a $dt$ for +which $P_N(F(x+v*dt))>= -double search_dt(int num_tension_handlers, one_dim_fn_t **tension_handlers, - list_t *domain_list, +double search_dt(transition_t *transition, + list_t *state_list, environment_t *env, double x, - double target_prob, double max_dt, double v) -{ /* Returns the timestep dt in seconds for the current folded domain. - * Takes a list of tension handlers, the list of domains, - * a pointer env to the environmental data, a starting separation x in m, - * a target_prob between 0 and 1, + double max_prob, double max_dt, double v) +{ /* Returns a valid timestep dt in seconds for the given transition. + * Takes a list of all states, a pointer env to the environmental data, + * a starting separation x in m, a max_prob between 0 and 1, * max_dt in s, stretching velocity v in m/s. */ - double F, k, dtCur, dtU, dtUCur, dtL, dt; + double F, k, P, dtCur, dtU, dtUCur, dtL, dt; /* get upper bound using the current position */ - F = find_tension(num_tension_handlers, tension_handlers, domain_list, env, x, 0); /* BUG. repeated calculation */ + F = find_tension(state_list, env, x, 0, 1); /* BUG. repeated calculation */ //printf("Start with x = %g (F = %g)\n", x, F); - k = accel_k(D(domain_list)->k, F, env, D(domain_list)->k_params); + k = accel_k(transition->k, F, env, transition->k_params); //printf("x %g\tF %g\tk %g\n", x, F, k); - dtU = target_prob / k; /* P = k dt, dtU is an upper bound on dt */ + dtU = P1(max_prob, N_INIT(transition)) / k; /* upper bound on dt */ if (dtU > max_dt) { - //printf("overshot max_dt\n"); + //printf("overshot max_dt\n"); dtU = max_dt; } - if (v == 0) /* discrete stepping, so force is temporatily constant */ + if (v == 0) /* discrete stepping, so force is temporarily constant */ return dtU; /* set a lower bound on dt too */ @@ -1099,361 +1423,525 @@ double search_dt(int num_tension_handlers, one_dim_fn_t **tension_handlers, /* The dt determined above may produce illegitimate forces or ks. * Reduce the upper bound until we have valid ks. */ dt = dtU; - F = find_tension(num_tension_handlers, tension_handlers, domain_list, env, x+v*dt, 0); + F = find_tension(state_list, env, x+v*dt, 0, 1); while (F == HUGE_VAL) { /* reduce step until we hit a valid force */ dtU /= 2.0; dt = dtU; - F = find_tension(num_tension_handlers, tension_handlers, domain_list, env, x+v*dt, 0); + F = find_tension(state_list, env, x+v*dt, 0, 1); } //printf("Try for dt = %g (F = %g)\n", dt, F); - k = accel_k(D(domain_list)->k, F, env, D(domain_list)->k_params); + k = accel_k(transition->k, F, env, transition->k_params); /* returned k may be -1.0 */ - //printf("x %g\tF %g\tdt %g\tv dt %g\tk %g\n", x, F, dt, v*dt, k); + //printf("x %g\tF %g\tdt %g\tv dt %g\tk %g\n", x, F, dt, v*dt, k); while (k == -1.0) { /* reduce step until we hit a valid k */ dtU /= 2.0; dt = dtU; /* hopefully, we can use the max dt, see if it works */ - F = find_tension(num_tension_handlers, tension_handlers, domain_list, env, x+v*dt, 0); + F = find_tension(state_list, env, x+v*dt, 0, 1); //printf("Try for dt = %g (F = %g)\n", dt, F); - k = accel_k(D(domain_list)->k, F, env, D(domain_list)->k_params); - //printf("x %g\tF %g\tdt %g\tv dt %g\tk %g\n", x, F, dt, v*dt, k); + k = accel_k(transition->k, F, env, transition->k_params); + //printf("x %g\tF %g\tdt %g\tv dt %g\tk %g\n", x, F, dt, v*dt, k); } assert(dtU > 1e-14); /* timestep to valid k too small */ - dtUCur = target_prob / k; /* safe timestep back from x+dtU */ + /* safe timestep back from x+dtU */ + dtUCur = P1(max_prob, N_INIT(transition)) / k; if (dtUCur >= dt) return dt; /* dtU is safe. */ /* dtU wasn't safe, lets see what would be. */ while (dtU > 1.1*dtL) { /* until the range is reasonably small */ dt = (dtU + dtL) / 2.0; - F = find_tension(num_tension_handlers, tension_handlers, domain_list, env, x+v*dt, 0); + F = find_tension(state_list, env, x+v*dt, 0, 1); //printf("Try for dt = %g (F = %g) (dt bounds %g, %g)\n", dt, F, dtL, dtU); - k = accel_k(D(domain_list)->k, F, env, D(domain_list)->k_params); - dtCur = target_prob / k; + k = accel_k(transition->k, F, env, transition->k_params); + dtCur = P1(max_prob, N_INIT(transition)) / k; //printf("x %g\tF %g\tdt %g\tv dt %g\tk %g\tdtCur = %g\n", x, F, dt, v*dt, k, dtCur); if (dtCur > dt) /* safe timestep back from x+dt covers dt */ dtL = dt; else if (dtCur < dt) { /* unsafe timestep back from x+dt, but... */ - dtU = dt; /* ... stepping out only dtCur would be safe */ + dtU = dt; /* ... stepping out only dtCur would be safe */ dtUCur = dtCur; } else break; /* dtCur = dt */ } return MAX(dtUCur, dtL); } -@ -To determine $dt$ for an array of potentially different folded domains, -we need to find the maximum $dt$ that satisfies $k dt < P$ for all domains. +@ + +Determine $dt$ for an array of potentially different folded domains. +We apply [[search_dt()]] to each populated domain to find the maximum +$dt$ the domain can handle. The final $dt$ is less than the +individual domain $dt$s (to satisfy [[search_dt()]], see above). If +$v>0$ (continuous pulling), $dt$ is also reduced to satisfy +$|F(x+v*dt)-F(x)|>= <> -double determine_dt(int num_tension_handlers, one_dim_fn_t **tension_handlers, list_t *domain_list, - environment_t *env, double x, - double target_prob, double dt_max, double v) +double determine_dt(list_t *state_list, list_t *transition_list, + environment_t *env, double F, double x, double max_dF, + double max_prob, double dt_max, double v, int transition) { /* Returns the timestep dt in seconds. - * Takes the list of folded domains, target_prob between 0 and 1, - * F in N, and T in K. */ - double dt=dt_max, new_dt; - assert(target_prob > 0.0); assert(target_prob < 1.0); + * Takes the state and transition lists, a pointer to the environment, + * the force F(x) in N, an extension x in m, max_dF in N, + * max_prob between 0 and 1, dt_max in s, v in m/s, and transition in {0,1}*/ + double dt=dt_max, new_dt, F_new; + assert(max_dF > 0.0); + assert(max_prob > 0.0); assert(max_prob < 1.0); assert(dt_max > 0.0); - - while (domain_list != NULL) { - if (D(domain_list)->state == DS_FOLDED) { - new_dt = search_dt(num_tension_handlers, tension_handlers, domain_list, env, x, target_prob, dt, v); + assert(state_list != NULL); + assert(transition_list != NULL); + transition_list = head(transition_list); + + if (v > 0) { + /* Ensure |dF| < max_dF */ + F_new = find_tension(state_list, env, x+v*dt, transition, 1); + while (fabs(F_new - F) > max_dF) { + dt /= 2.0; + F_new = find_tension(state_list, env, x+v*dt, transition, 1); + } + } + + /* Ensure all individual domains pass search_dt() */ + while (transition_list != NULL) { + if (T(transition_list)->initial_state->num_domains > 0) { + new_dt = search_dt(T(transition_list),state_list,env,x,max_prob,dt,v); dt = MIN(dt, new_dt); } - domain_list = domain_list->next; + transition_list = transition_list->next; } return dt; } -@ -\subsection{Domain data} - -Currently domains exist in two states, folded and unfolded, and the -only allowed transitions are folded $\rightarrow$ unfolded. Of -course, it wouldn't be too complicated to extent this to a multi-state -system, with an array containing the domains group for each possible -state, and a matrix of transition-rate-calculating functions. -However, at this point such generality seems unnecessary at this -point. -<>= -enum domain_state_t {DS_FOLDED, - DS_UNFOLDED -}; +@ -typedef struct domain_struct { - enum domain_state_t state; - one_dim_fn_t *folded_handler; - int folded_group; - one_dim_fn_t *unfolded_handler; - int unfolded_group; - k_func_t *k; /* function returning unfolding rate */ - void *folded_params; /* pointer to folded parameters */ - void *unfolded_params; /* pointer to unfolded parameters */ - void *k_params; /* pointer to k parameters */ - destroy_data_func_t *destroy_folded; - destroy_data_func_t *destroy_unfolded; - destroy_data_func_t *destroy_k; -} domain_t; - -/* get the domain data for the current list node */ -#define D(list) ((domain_t *)(list)->d) -/* get the tension params for the current list node */ -#define D_TP(list) (((domain_t *)(list)->d)->state == DS_FOLDED \ - ? ((domain_t *)(list)->d)->folded_params \ - : ((domain_t *)(list)->d)->unfolded_params) -@ -[[k]] is a pointer to the function determining the unfolding rate for a given tension. -[[folded_params]] is a pointer to the parameters used by the function pointed to by [[k]]. -[[unfolded_params]] is a pointer to the parameters used by the group-appropriate handler function when determining the tension. -The [[destroy_*]] pointers point to functions for freeing the memory [[*_params]]. -We store them with the domain data so that [[destroy_domain]] doesn't have to know which type of domain it's cleaning up after. - -[[create_]] and [[destroy_domain]] are simple wrappers around [[malloc]] and [[free]]. -<>= -domain_t *create_domain(enum domain_state_t state, - k_func_t *k, - void *k_params, - destroy_data_func_t *destroy_k, - one_dim_fn_t *folded_handler, - int folded_group, - void *folded_params, - destroy_data_func_t *destroy_folded, - one_dim_fn_t *unfolded_handler, - int unfolded_group, - void *unfolded_params, - destroy_data_func_t *destroy_unfolded) -{ - domain_t *ret = (domain_t *)malloc(sizeof(domain_t)); +\subsection{State data} +\label{sec.state_data} + +The domains exist in one of an array of possible states. Each state +has a tension model which determines it's force/extension curve +(possibly [[null]] for rigid states, see Appendix +\ref{sec.null_tension}). + +Groups are, for example, for two domain states with WLC tensions; one +with $p=0.4\U{nm}$, $L=10\U{nm}$ and the other with $p=0.4\U{nm}$, +$L=28\U{nm}$. Since the persistence lengths are the same, you would +like to add the contour lengths of all the domains in \emph{both} +states, and plug that total contour length into a single WLC +evaluation (see Section \ref{sec.find_tension}). +<>= +typedef struct state_struct { + char *name; /* name string */ + one_dim_fn_t *tension_handler; /* tension handler */ + one_dim_fn_t *inverse_tension_handler; /* inverse tension handler */ + int tension_group; /* for grouping similar tension states */ + void *tension_params; /* pointer to tension parameters */ + destroy_data_func_t *destroy_tension; + int num_domains; /* number of domains currently in state */ + /* cached lookups generated from the above data */ + int num_out_trans; /* length of out_trans array */ + struct transition_struct **out_trans; /* transitions leaving this state */ + int num_grouped_states; /* length of grouped states array */ + struct state_struct **grouped_states; /* states grouped with this one (doesn't include self) */ +} state_t; + +/* get the state data for the current list node */ +#define S(list) ((state_t *)(list)->d) + +@ [[tension_params]] is a pointer to the parameters used by the +handler function when determining the tension. [[destroy_tension]] +points to a function for freeing [[tension_params]]. We it in the +state structure so that [[destroy_state]] and will have an easier job +cleaning up. + +[[create_]] and [[destroy_state]] are simple wrappers around +[[malloc]] and [[free]]. +<>= +state_t *create_state(char *name, + one_dim_fn_t *tension_handler, + one_dim_fn_t *inverse_tension_handler, + int tension_group, + void *tension_params, + destroy_data_func_t *destroy_tension, + int num_domains) +{ + state_t *ret = (state_t *)malloc(sizeof(state_t)); assert(ret != NULL); - if (state == DS_FOLDED) { - assert(k != NULL); /* the pointer points somewhere valid */ - assert(*k != NULL); /* and there is something useful there */ - } else - assert(state == DS_UNFOLDED); - ret->state = state; - ret->folded_handler = folded_handler; - ret->folded_group = folded_group; - ret->unfolded_handler = unfolded_handler; - ret->unfolded_group = unfolded_group; - ret->k = k; - ret->folded_params = folded_params; - ret->unfolded_params = unfolded_params; - ret->k_params = k_params; - ret->destroy_folded = destroy_folded; - ret->destroy_unfolded = destroy_unfolded; - ret->destroy_k = destroy_k; + /* make a copy of the name, so we aren't dependent on the original */ + ret->name = (char *)malloc(sizeof(char)*(strlen(name)+1)); + assert(ret->name != NULL); + strcpy(ret->name, name); /* we know ret->name is long enough */ + + ret->tension_handler = tension_handler; + ret->inverse_tension_handler = inverse_tension_handler; + ret->tension_group = tension_group; + ret->tension_params = tension_params; + ret->destroy_tension = destroy_tension; + ret->num_domains = num_domains; + + ret->num_out_trans = 0; + ret->out_trans = NULL; + ret->num_grouped_states = 0; + ret->grouped_states = NULL; + #ifdef DEBUG - fprintf(stderr, "generated domain %p. state %d\n", ret, ret->state); + fprintf(stderr, "generated state %s (%p) with tension handler %p, inverse handler %p, params %p, group %d.\n", ret->name, ret, ret->tension_handler, ret->inverse_tension_handler, ret->tension_params, ret->tension_group); #endif return ret; } -void destroy_domain(domain_t *domain) +void destroy_state(state_t *state) { - if (domain) { - //printf("domain %p & %p\n", *domain, domain); - if (domain->destroy_folded) - (*domain->destroy_folded)(domain->folded_params); - if (domain->destroy_unfolded) - (*domain->destroy_unfolded)(domain->unfolded_params); - if (domain->destroy_k) - (*domain->destroy_k)(domain->k_params); - free(domain); + if (state) { +#ifdef DEBUG + fprintf(stderr, "freeing state %s (%p)\n", state->name, state); +#endif + if (state->name) + free(state->name); + if (state->destroy_tension) + (*state->destroy_tension)(state->tension_params); + if (state->out_trans) + free(state->out_trans); + if (state->grouped_states) + free(state->grouped_states); + free(state); } } + @ -<>= -void destroy_domain_list(list_t *domain_list) +We'll be storing the states in a list (see Appendix \ref{sec.lists}), +so we also define a convenience function for cleaning up. +<>= +void destroy_state_list(list_t *state_list) { - domain_list = head(domain_list); - while (domain_list != NULL) - destroy_domain((domain_t *) pop(&domain_list)); + state_list = head(state_list); + while (state_list != NULL) + destroy_state((state_t *) pop(&state_list)); } -@ -\subsection{Domain model and group handling} - -<>= -<> -<> -<> -<> -<> -<> -<> -@ - -<>= -one_dim_fn_t *get_tension_handler(domain_t *domain) -{ - if (domain->state == DS_FOLDED) - return domain->folded_handler; - else { - if (domain->state != DS_UNFOLDED) - fprintf(stderr, "oops, domain %p state %d\n", domain, domain->state); - assert(domain->state == DS_UNFOLDED); - return domain->unfolded_handler; - } -} -@ +@ -<>= -int get_group(domain_t *domain) +We can also define a convenient way to get a state index from it's name. +<>= +int state_index(list_t *state_list, char *name) { - if (domain->state == DS_FOLDED) - return domain->folded_group; - else { - if (domain->state != DS_UNFOLDED) - fprintf(stderr, "oops, domain %p state %d\n", domain, domain->state); - assert(domain->state == DS_UNFOLDED); - return domain->unfolded_group; + int i=0; + state_list = head(state_list); + while (state_list != NULL) { + if (STRMATCH(S(state_list)->name, name)) return i; + state_list = state_list->next; + i++; } + return -1; } -@ - -We already know all possible tension classes, since they are all -hardcoded into \prog. However, there may be any number of possible -groups. We define a function [[find_possible_groups]] to search for -possible (not neccessarily active) groups. It can search for -subgroups of a single [[handler]], or by setting [[handler]] to -[[NULL]], subgroups of \emph{any} handler. It returns a list of group -integers. -<>= -list_t *find_possible_groups(list_t *list, one_dim_fn_t *handler) { - list_t *ret = NULL; - list = head(list); - while (list != NULL) { - if (handler == NULL || get_tension_handler(D(list)) == handler) { - push(&ret, &D(list)->folded_group, 1); - push(&ret, &D(list)->unfolded_group, 1); - } - list = list->next; - } - if (ret == NULL) - return ret; /* no groups with this handler, no processing needed */ +@ - /* sort the ret list, and remove duplicates */ - sort(&ret, &int_comparison); - unique(&ret, &int_comparison); +\subsection{Transition data} +\label{sec.transition_data} + +Once you've created states (Sections \ref{sec.main}, +\ref{sec.model_selection}, and \ref{sec.state_data}), you need to +create transitions between them. +<>= +typedef struct transition_struct { + state_t *initial_state; + state_t *final_state; + k_func_t *k; /* transition rate model */ + void *k_params; /* pointer to k parameters */ + destroy_data_func_t *destroy_k; +} transition_t; + +/* get the transition data for the current list node */ +#define T(list) ((transition_t *)(list)->d) + +/* get the number of initial state population for a transition state */ +#define N_INIT(transition) ((transition)->initial_state->num_domains) + +<> +<> +@ [[k]] is a pointer to the function determining the transition rate +for a given tension. [[k_params]] and [[destroy_k]] have similar +roles with regards to [[k]] as [[tension_params]] and +[[destroy_tension]] have with regards to [[tension_handler]] (see +Section \ref{sec.state_data}). + +[[create_]] and [[destroy_transition]] are simple wrappers around +[[malloc]] and [[free]]. +<>= +transition_t *create_transition(state_t *initial_state, state_t *final_state, + k_func_t *k, + void *k_params, + destroy_data_func_t *destroy_k) +{ + transition_t *ret = (transition_t *)malloc(sizeof(transition_t)); + assert(ret != NULL); + assert(initial_state != NULL); + assert(final_state != NULL); + ret->initial_state = initial_state; + ret->final_state = final_state; + ret->k = k; + ret->k_params = k_params; + ret->destroy_k = destroy_k; #ifdef DEBUG - fprintf(stderr, "handler %p possible groups:", handler); - list = head(ret); - while (list != NULL) { - fprintf(stderr, " %d", *((int *)list->d)); - list = list->next; - } - fprintf(stderr, "\n"); + fprintf(stderr, "generated transition %p from %s to %s, params %p\n", ret, ret->initial_state->name, ret->final_state->name, ret->k_params); #endif return ret; } -@ -Search a [[list]] of domains, and determine whether a particular model -class and group number combination is active. -<>= -int is_group_active(list_t *list, one_dim_fn_t *handler, int group) +void destroy_transition(transition_t *transition) { - list = head(list); - while (list != NULL) { - if (get_tension_handler(D(list)) == handler && get_group(D(list)) == group) - return 1; - list = list->next; + if (transition) { +#ifdef DEBUG + fprintf(stderr, "freeing transition %p (%s to %s)\n", transition, transition->initial_state->name, transition->final_state->name); +#endif + if (transition->destroy_k) + (*transition->destroy_k)(transition->k_params); + free(transition); } - return 0; } -@ -Search a [[list]] of domains, and return all domains matching a -particular model class and group number. -<>= -list_t *get_group_list(list_t *list, one_dim_fn_t *handler, int group) +@ + +We'll be storing the transitions in a list (see Appendix +\ref{sec.lists}), so we also define a convenience function for +cleaning up. +<>= +void destroy_transition_list(list_t *transition_list) { - list_t *ret = NULL; - list = head(list); - while (list != NULL) { - if (get_tension_handler(D(list)) == handler && get_group(D(list)) == group) { - push(&ret, D_TP(list), 1); /* add a pointer to the appropriate tension parameters to our new list. */ -#ifdef DEBUG - fprintf(stderr, "push domain %p %s tension parameters %p onto active group %p %d list %p\n", D(list), D(list)->state == DS_FOLDED ? "folded" : "unfolded", D_TP(list), handler, group, ret); -#endif - } - list = list->next; + transition_list = head(transition_list); + while (transition_list != NULL) + destroy_transition((transition_t *) pop(&transition_list)); +} + +@ + +\subsection{Graphviz output} +\label{sec.graphviz_output} + +<>= +void print_state_graph(FILE *file, list_t *state_list, list_t *transition_list) +{ + state_list = head(state_list); + transition_list = head(transition_list); + fprintf(file, "digraph states {\n node [shape=record,color=black,fillcolor=white,style=filled];\n\n"); + while (1) { + fprintf(file, " n%d [label=\"%s\"]\n", state_index(state_list, S(state_list)->name), S(state_list)->name); + if (state_list->next == NULL) break; + state_list = state_list->next; } - return ret; + fprintf(file, "\n"); + while (transition_list != NULL) { + fprintf(file, " n%d -> n%d;\n", state_index(state_list, T(transition_list)->initial_state->name), state_index(state_list, T(transition_list)->final_state->name)); + transition_list = transition_list->next; + } + fprintf(file, "}\n"); } -@ -Because all the node data in lists returned by [[get_group_list]] is -also in the main domain list, you shouldn't destroy the node data -popped off when destroying the group lists. It will all get cleaned -up when the main domain list is destroyed. +@ + +\subsection{Domain model and group handling} + +<>= +<> +<> +@ -Put all this together to scan through a list of domains and construct -an array of all the active groups. +Scan through a list of states and construct an array of all the +active groups. <>= -void get_active_groups(list_t *list, - int num_tension_handlers, one_dim_fn_t **tension_handlers, - int *pNum_active_groups, one_dim_fn_t ***pPer_group_handlers, void ***pActive_groups) +void get_active_groups(list_t *state_list, + int *pNum_active_groups, + one_dim_fn_t ***pPer_group_handlers, + one_dim_fn_t ***pPer_group_inverse_handlers, + void ***pPer_group_data /* pointer to array of pointers to tension_handler_data_t */) { void **active_groups=NULL; - one_dim_fn_t *handler, **per_group_handlers=NULL; - int i, num_active_groups, *group; - list_t *possible_group_numbers, *active_group_list, *active_groups_list=NULL, *per_group_handlers_list=NULL; + one_dim_fn_t *handler, *old_handler, *inverse_handler, *old_inverse_handler; + one_dim_fn_t **per_group_handlers=NULL, **per_group_inverse_handlers=NULL; + void **per_group_data=NULL; /* array of pointers to tension_handler_data_t */ + int i, j, num_domains, group, old_group, num_active_groups=0; + list_t *active_states_list=NULL; + tension_handler_data_t *tdata=NULL; + state_t *state; /* get all the active groups in a list */ - for (i=0; id); - list_print(stderr, active_group_list, "active group"); + fprintf(stderr, "%s:\t", __FUNCTION__); + list_print(stderr, state_list, "states"); #endif - } - } + while (state_list != NULL) { + state = S(state_list); + handler = state->tension_handler; + inverse_handler = state->inverse_tension_handler; + group = state->tension_group; + num_domains = state->num_domains; + if (list_index(active_states_list, state) == -1) { + /* we haven't added this state (or it's associated group) yet */ + if (num_domains > 0 && handler != NULL) { /* add the state */ + num_active_groups++; + push(&active_states_list, state, 1); +#ifdef DEBUG + fprintf(stderr, "%s:\tactive %s state (%p) with %d domain(s)\n", __FUNCTION__, state->name, state, state->num_domains); +#endif + for (i=0; i < state->num_grouped_states; i++) { + if (state->grouped_states[i]->num_domains > 0) { + /* add this related (and active) state now */ + assert(state->grouped_states[i]->tension_handler == handler); + assert(state->grouped_states[i]->tension_group == group); + push(&active_states_list, state->grouped_states[i], 1); +#ifdef DEBUG + fprintf(stderr, "%s:\tactive grouped %s state (%p) with %d domain(s)\n", __FUNCTION__, state->grouped_states[i]->name, state->grouped_states[i], state->grouped_states[i]->num_domains); +#endif + } + } + } /* else empty state or NULL handler */ + } /* else state already added */ + state_list = state_list->next; } +#ifdef DEBUG + fprintf(stderr, "%s:\t", __FUNCTION__); + list_print(stderr, active_states_list, "active states"); +#endif - /* allocate the array we'll be returning */ - num_active_groups = list_length(active_groups_list); - active_groups = (void **) malloc(sizeof(void *)*num_active_groups); - assert(active_groups != NULL); + assert(num_active_groups <= list_length(active_states_list)); + assert(num_active_groups > 0); + + /* allocate the arrays we'll be returning */ per_group_handlers = (one_dim_fn_t **)malloc(sizeof(one_dim_fn_t *)*num_active_groups); assert(per_group_handlers != NULL); + per_group_inverse_handlers = (one_dim_fn_t **)malloc(sizeof(one_dim_fn_t *)*num_active_groups); + assert(per_group_inverse_handlers != NULL); + per_group_data = (void **)malloc(sizeof(void *)*num_active_groups); + assert(per_group_data != NULL); +#ifdef DEBUG + fprintf(stderr, "%s:\tallocating per group data %p:", __FUNCTION__, per_group_data); +#endif + for (i=0; igroup = active_group_list; - ((tension_handler_data_t *)active_groups[i])->env = NULL; - ((tension_handler_data_t *)active_groups[i])->persist = NULL; + /* populate the arrays we'll be returning */ + active_states_list = head(active_states_list); + old_handler = NULL; + old_inverse_handler = NULL; + j = -1; /* j is the current active _group_ index */ + while (active_states_list != NULL) { + state = (state_t *) pop(&active_states_list); + handler = state->tension_handler; + inverse_handler = state->inverse_tension_handler; + group = state->tension_group; + num_domains = state->num_domains; + if (handler != old_handler || inverse_handler != old_inverse_handler || group != old_group) { + j++; /* move to the next group */ + tdata = (tension_handler_data_t *) per_group_data[j]; + per_group_handlers[j] = handler; + per_group_inverse_handlers[j] = inverse_handler; + tdata->group_tension_params = NULL; + tdata->env = NULL; + tdata->persist = NULL; /* we might want to grab any appropriate data from the old persist here... */ + } +#ifdef DEBUG + fprintf(stderr, "%s:\tadding active state %s to group %d (%p:%p:%d) with %d domain(s)\n", __FUNCTION__, state->name, j, handler, inverse_handler, group, num_domains); +#endif + for (i=0; igroup_tension_params, state->tension_params, 1); + } +#ifdef DEBUG + fprintf(stderr, "%s:\tpushed %d copies of %p onto data %p's param list %p\n", __FUNCTION__, num_domains, state->tension_params, tdata, tdata->group_tension_params); +#endif + old_handler = handler; + old_inverse_handler = inverse_handler; + old_group = group; } - assert(active_groups_list == NULL); - assert(per_group_handlers_list == NULL); + /* free old groups */ + if (*pPer_group_handlers != NULL) + free(*pPer_group_handlers); + if (*pPer_group_inverse_handlers != NULL) + free(*pPer_group_inverse_handlers); + if (*pPer_group_data != NULL) { + for (i=0; i<*pNum_active_groups; i++) + free((*pPer_group_data)[i]); + free(*pPer_group_data); + } + + /* set new groups */ +#ifdef DEBUG + fprintf(stderr, "%s:\t%d groups, tension handler array %p, inverse tension handler array %p, handler data array %p (lead data element %p)\n", __FUNCTION__, num_active_groups, per_group_handlers, per_group_inverse_handlers, per_group_data, per_group_data[0]); +#endif *pNum_active_groups = num_active_groups; *pPer_group_handlers = per_group_handlers; - *pActive_groups = active_groups; + *pPer_group_inverse_handlers = per_group_inverse_handlers; + *pPer_group_data = per_group_data; +} +@ + +<>= +void crosslink_groups(list_t *state_groups, list_t *transition_list) +{ + list_t *list, *out_trans=NULL, *associates=NULL; + one_dim_fn_t *handler; + int i, n, group; + + state_groups = head(state_groups); + while (state_groups != NULL) { + /* find transitions leaving this state */ +#ifdef DEBUG + fprintf(stderr, "finding transitions leaving %s\n", S(state_groups)->name); +#endif + list = head(transition_list); + while (list != NULL) { + if (T(list)->initial_state == S(state_groups) && list_index(associates, T(list)->initial_state) != -1) { + push(&out_trans, T(list), 1); + } + list = list->next; + } + n = list_length(out_trans); + S(state_groups)->num_out_trans = n; + S(state_groups)->out_trans = (transition_t **)malloc(sizeof(transition_t *)*n); + assert(S(state_groups)->out_trans != NULL); + for (i=0; iout_trans[i] = (transition_t *)pop(&out_trans); + } + + /* find states grouped with this state */ +#ifdef DEBUG + fprintf(stderr, "finding states grouped with %s\n", S(state_groups)->name); +#endif + handler = S(state_groups)->tension_handler; + group = S(state_groups)->tension_group; + list = head(state_groups); + while (list != NULL) { + if (S(list)->tension_handler == handler && S(list)->tension_group == group && list != state_groups) { + push(&associates, S(list), 1); + } + list = list->next; + } + n = list_length(associates); + S(state_groups)->num_grouped_states = n; + S(state_groups)->grouped_states = (state_t **)malloc(sizeof(state_t *)*n); + assert(S(state_groups)->grouped_states != NULL); + for (i=0; igrouped_states[i] = (state_t *)pop(&associates); + } + state_groups = state_groups->next; + } } -@ +@ \section{String parsing} -For handling command line arguments, we need parse delimited strings (e.g. [["param1,param2,param3..."]]). +For handling command line arguments, we need parse delimited strings (e.g.\ [["param1,param2,param3..."]]). The model handling in getopt is set up to handle a fixed number of arguments for each model, so models (like [[kramers_integ]]) that have complicated parameters (location of spline knots) need to take care of parsing those parameters themselves. @@ -1466,23 +1954,23 @@ We implement this parsing in [[parse.c]], define the interface in [[parse.h]], a <> <> #endif /* PARSE */ -@ +@ <>= NW_SAWSIM_MODS += parse CHECK_BINS += check_parse -check_parse_MODS = -@ +check_parse_MODS = +@ <>= #define SEP ',' /* argument separator character */ -@ +@ <>= extern void parse_list_string(char *string, char sep, char deeper, char shallower, int *num, char ***string_array); extern void free_parsed_list(int num, char **string_array); -@ +@ [[parse_list_string]] allocates memory, don't forget to free it afterward with [[free_parsed_list]]. It does not alter the original. @@ -1572,7 +2060,7 @@ void free_parsed_list(int num, char **string_array) <> #include "parse.h" <> -@ +@ <>= #include /* assert() */ @@ -1580,43 +2068,44 @@ void free_parsed_list(int num, char **string_array) #include /* fprintf(), stdout *//*!!*/ #include /* strlen() */ #include "parse.h" -@ +@ \subsection{Parsing unit tests} Here we check to make sure the various functions work as expected, using \citetalias{sw:check}. <>= +<> <> <> <> <> <
> -@ +@ <>= -#include /* EXIT_SUCCESS and EXIT_FAILURE, atof() */ -#include /* printf() */ -#include /* assert() */ -#include /* strlen() */ +#include /* EXIT_SUCCESS and EXIT_FAILURE */ +#include /* printf() */ +#include /* assert() */ +#include /* strlen() */ <> #include "parse.h" -@ +@ <>= <> <> -@ +@ <>= Suite *test_suite (void) { - Suite *s = suite_create ("k model"); + Suite *s = suite_create ("parse"); <> - <> + <> return s; } -@ +@ <>= @@ -1672,16 +2161,28 @@ START_TEST(test_parse_list_double_simple) fail_unless(STRMATCH(param_args[1],"def"), NULL); } END_TEST +START_TEST(test_parse_list_compound) +{ + int num_param_args; + char **param_args; + parse_list_string("abc,{def,ghi}", SEP, '{', '}', + &num_param_args, ¶m_args); + fail_unless(num_param_args == 2, NULL); + fail_unless(STRMATCH(param_args[0],"abc"), NULL); + fail_unless(STRMATCH(param_args[1],"def,ghi"), NULL); +} +END_TEST @ <>= TCase *tc_parse_list_string = tcase_create("parse list string"); @ -<>= +<>= //tcase_add_test(tc_parse_list_string, test_next_delim_index); tcase_add_test(tc_parse_list_string, test_parse_list_null); tcase_add_test(tc_parse_list_string, test_parse_list_single_simple); tcase_add_test(tc_parse_list_string, test_parse_list_single_compound); tcase_add_test(tc_parse_list_string, test_parse_list_double_simple); +tcase_add_test(tc_parse_list_string, test_parse_list_compound); suite_add_tcase(s, tc_parse_list_string); @ @@ -1699,39 +2200,36 @@ Here we check to make sure the various functions work as expected, using \citeta <> <> <
> -@ +@ <>= #include -@ +@ <>= -@ +@ <>= -<> <> <> -<> +<> <> <> -@ +@ <>= Suite *test_suite (void) { Suite *s = suite_create ("sawsim"); - <> <> <> - <> + <> <> - <> - <> - <> - <> - <> + <> + <> + <> + <> /* tcase_add_checked_fixture(tc_strip_address, @@ -1740,7 +2238,7 @@ Suite *test_suite (void) */ return s; } -@ +@ <
>= int main(void) @@ -1753,60 +2251,15 @@ int main(void) srunner_free(sr); return (number_failed == 0) ? EXIT_SUCCESS : EXIT_FAILURE; } -@ - -\subsection{F tests} -<>= -<> -@ -<>= -<> -@ -<>= -<> -@ - -<>= -extern double wlc(double x, double T, double p, double L); -START_TEST(test_wlc_at_zero) -{ - double T=1.0, L=1.0, p=0.1, x=0.0, lim=1e-30; - fail_unless(abs(wlc(x, T, p, L)) < lim, \ - "abs(wlc(x=%g,T=%g,p=%g,L=%g)) = %g >= %g", - x, T, p, L, abs(wlc(x, T, p, L)), lim); -} -END_TEST - -START_TEST(test_wlc_at_half) -{ - double T=1.0, L=1.0, p=0.1*k_B, x=0.5; - /* prefactor = k_B T / p = k_B 1.0 / (k_B*0.1) = 10.0 J/nm = 10.0e21 pN - * nonlinear term = 0.25 (1/(1-x/L)^2-1) = 0.25(1/.25 - 1) - * = 0.25 * 3 = 3/4 - * linear term = x/L = 0.5 - * nonlinear + linear = 0.75 + 0.5 = 1.25 - * wlc = 10e21*1.25 = 12.5e21 - */ - fail_unless(wlc(x, T, p, L)-12.5e21 < 1e16, - "wlc(%g, %g, %g, %g) = %g != %g", - x, T, p, L, wlc(x, T, p, L), 12.5e21); -} -END_TEST -@ -<>= -TCase *tc_wlc = tcase_create("WLC"); -@ +@ -<>= -tcase_add_test(tc_wlc, test_wlc_at_zero); -tcase_add_test(tc_wlc, test_wlc_at_half); -suite_add_tcase(s, tc_wlc); -@ \subsection{Model tests} Check the searching with [[linear_k]]. Check overwhelming force treatment with the heavyside-esque step [[?]]. + +Hmm, I'm not really sure what I was doing here... <>= double linear_k(double F, environment_t *env, void *params) { @@ -1816,29 +2269,31 @@ double linear_k(double F, environment_t *env, void *params) START_TEST(test_determine_dt_linear_k) { - environment_t env; - double dt_max=3.0, Fnot=3.0; + state_t folded={0}; + transition_t unfold={0}; + environment_t env = {0}; double F[]={0,1,2,3,4,5,6}; - domain_t dom; /* use both parts at once for folded/unfolded */ + double dt_max=3.0, Fnot=3.0, x=1.0, max_p=0.1, max_dF=0.1, v=1.0; + list_t *state_list=NULL, *transition_list=NULL; int i; env.T = 300.0; -/* - dom->next = dom->prev = NULL; - dom->k_func_t = linear_k; - dom->folded_params = &Fnot; - dom->unfolded_params = !!!!!!!!! - dom->destroy_folded = dom->destroy_unfolded = NULL; + folded.tension_handler = &hooke_handler; + folded.num_domains = 1; + unfold.initial_state = &folded; + unfold.k = linear_k; + unfold.k_params = &Fnot; + push(&state_list, &folded, 1); + push(&transition_list, &unfold, 1); for( i=0; i < sizeof(F)/sizeof(double); i++) { - fail_unless(determine_dt(folded, unfolded, targ_p, dt_max, v, x, T)==1, NULL); + //fail_unless(determine_dt(state_list, transition_list, &env, x, max_p, max_dF, dt_max, v)==1, NULL); } -*/ } END_TEST @ <>= TCase *tc_determine_dt = tcase_create("Determine dt"); @ -<>= +<>= tcase_add_test(tc_determine_dt, test_determine_dt_linear_k); suite_add_tcase(s, tc_determine_dt); @ @@ -1847,26 +2302,26 @@ suite_add_tcase(s, tc_determine_dt); @ <>= @ -<>= +<>= @ -<>= +<>= @ -<>= +<>= @ -<>= +<>= @ <>= @ <>= @ -<>= +<>= @ \section{Balancing group extensions} -\label{app.tension_balance} +\label{sec.tension_balance} For a given total extension $x$ (of the piezo), the various domain models (WLC, FJC, Hookean springs, \ldots) and groups extend different @@ -1883,25 +2338,28 @@ the implementation in [[tension_balance.c]], and the unit testing in <> <> #endif /* TENSION_BALANCE_H */ -@ +@ <>= <> <> <> +<> +<> +<> <> -@ +@ <>= NW_SAWSIM_MODS += tension_balance CHECK_BINS += check_tension_balance -check_tension_balance_MODS = -@ +check_tension_balance_MODS = +@ The entire force balancing problem reduces to a solving two nested one-dimensional root-finding problems. First we define the one dimensional tension $F(x_0)$ (where $i=0$ is the index of the first -non-empty group). $x(x_0)$ is also strictly monotonically increasing, +populated group). $x(x_0)$ is also strictly monotonically increasing, so we can solve for $x_0$ such that $\sum_i x_i = x$. [[last_x]] stores the last successful value of $x$, since we expect to be taking small steps ($x \approx$ [[last_x]]). Setting [[last_x = -1]] @@ -1909,18 +2367,22 @@ indicates that the groups have changed. <>= double tension_balance(int num_tension_groups, one_dim_fn_t **tension_handlers, - void **params, + one_dim_fn_t **inverse_tension_handlers, + void **params, /* array of pointers to tension_handler_data_t */ double last_x, - double x); -@ + double x, + double *stiffness); +@ <>= double tension_balance(int num_tension_groups, one_dim_fn_t **tension_handlers, - void **params, + one_dim_fn_t **inverse_tension_handlers, + void **params, /* array of pointers to tension_handler_data_t */ double last_x, - double x) + double x, + double *stiffness) { - static x_of_xo_data_t x_xo_data = {0,NULL,NULL,NULL}; + static x_of_xo_data_t x_xo_data = {0,NULL,NULL,NULL,NULL}; double F, xo_guess, xo, lb, ub; double min_relx=1e-6, min_rely=1e-6; int max_steps=200, i; @@ -1930,24 +2392,36 @@ double tension_balance(int num_tension_groups, assert(params != NULL); assert(num_tension_groups > 0); + if (last_x == -1 || x_xo_data.xi == NULL) { /* new group setup, reset x_xo_data */ + /* x_xo_data tension_handler and handler_data arrays freed by find_tension() */ + if (x_xo_data.xi != NULL) + free(x_xo_data.xi); + /* construct new x_xo_data */ + x_xo_data.n_groups = num_tension_groups; + x_xo_data.tension_handler = tension_handlers; + x_xo_data.inverse_tension_handler = inverse_tension_handlers; + x_xo_data.handler_data = params; +#ifdef DEBUG + fprintf(stderr, "%s:\t%d groups, tension handler array %p, handler data array %p (lead data element %p), x_of_xo_data %p\n", __FUNCTION__, x_xo_data.n_groups, x_xo_data.tension_handler, x_xo_data.handler_data, x_xo_data.handler_data[0], &x_xo_data); +#endif + x_xo_data.xi = (double *) malloc(sizeof(double)*num_tension_groups); + assert(x_xo_data.xi != NULL); + for (i=0; i>= <> -@ +@ <>= typedef struct x_of_xo_data_struct { int n_groups; - one_dim_fn_t **tension_handler; /* array of fn pointers */ - void **handler_data; /* array of void* pointers */ - double *xi; + one_dim_fn_t **tension_handler; /* array of fn pointers */ + one_dim_fn_t **inverse_tension_handler; /* inverse fn pointers */ + void **handler_data; /* array of pointers to tension_handler_data_t */ + double *xi; /* array of group extensions */ } x_of_xo_data_t; -@ +@ <>= double x_of_xo(double xo, void *pdata) { x_of_xo_data_t *data = (x_of_xo_data_t *)pdata; - double F, x=0, xi, xi_guess, lb, ub; + double F, x=0, xi, xi_guess, lb, ub, slope; int i; double min_relx=1e-6, min_rely=1e-6; int max_steps=200; assert(data->n_groups > 0); data->xi[0] = xo; +#ifdef DEBUG + fprintf(stderr, "%s:\tget initial tension at %g with %d groups, handler %p, data %p (x_xo_data %p)\n", __FUNCTION__, xo, data->n_groups, data->tension_handler[0], data->handler_data[0], data); + fflush(stderr); +#endif F = (*data->tension_handler[0])(xo, data->handler_data[0]); #ifdef DEBUG - fprintf(stderr, "%s: finding x(x0=%g). F0(x0) = %g\n", __FUNCTION__, xo, F); + fprintf(stderr, "%s:\tfinding x(x0=%g). F0(x0) = %g\n", __FUNCTION__, xo, F); + fflush(stderr); #endif x += xo; if (data->xi) data->xi[0] = xo; for (i=1; i < data->n_groups; i++) { - if (data->xi[i] == -1) xi_guess = length_scale; /* HACK */ - else xi_guess = data->xi[i]; + if (data->inverse_tension_handler[i] != NULL) { + xi = (*data->inverse_tension_handler[i])(F, data->handler_data[i]); + } else { /* invert numerically */ + if (data->xi[i] == -1) xi_guess = length_scale; /* HACK */ + else xi_guess = data->xi[i]; #ifdef DEBUG - fprintf(stderr, "%s: searching for proper x[%d] for F[%d](x[%d]) = %g N\n", __FUNCTION__, i, i, i, F); + fprintf(stderr, "%s:\tsearching for proper x[%d] for F[%d](x[%d]) = %g N (handler %p, data %p)\n", __FUNCTION__, i, i, i, F, data->tension_handler[i], data->handler_data[i]); #endif - oneD_bracket(data->tension_handler[i], data->handler_data[i], F, xi_guess, &lb, &ub); - xi = oneD_solve(data->tension_handler[i], data->handler_data[i], F, lb, ub, min_relx, min_rely, max_steps, NULL); + oneD_bracket(data->tension_handler[i], data->handler_data[i], F, xi_guess, &lb, &ub); + xi = oneD_solve(data->tension_handler[i], data->handler_data[i], F, lb, ub, min_relx, min_rely, max_steps, NULL); + } + x += xi; + data->xi[i] = xi; #ifdef DEBUG - fprintf(stderr, "%s: found F[%d](x[%d]=%g) = %g N\n", __FUNCTION__, i, i, xi, F); + fprintf(stderr, "%s:\tfound F[%d](x[%d]=%g) = %g N\n", __FUNCTION__, i, i, xi, F); #endif - data->xi[i] = xi; - x += xi; - if (data->xi) data->xi[i] = xi; } #ifdef DEBUG - fprintf(stderr, "%s: found x(x0=%g) = %g\n", __FUNCTION__, xo, x); + fprintf(stderr, "%s:\tfound x(x0=%g) = %g\n", __FUNCTION__, xo, x); #endif return x; } -@ +@ + +Determine the stiffness of a single tension group by taking a small +step [[dx]] back from the position [[x]] for which we want the +stiffness. The touchy part is determining a good [[dx]] and ensuring +the whole interval is on [[x>=0]]. +<>= +double group_stiffness(one_dim_fn_t *tension_handler, void *handler_data, double x, double relx) +{ + double dx, xl, F, Fl, stiffness; + assert(x >= 0); + assert(relx > 0 && relx < 1); + if (x == 0 || relx == 0) { + dx = 1e-12; /* HACK, how to get length scale? */ + xl = x-dx; + if (xl < 0) { + xl = 0; + x = xl+dx; + } + } else { + dx = x*relx; + xl = x-dx; + } + F = (*tension_handler)(x, handler_data); + Fl = (*tension_handler)(xl, handler_data); + stiffness = (F-Fl)/dx; + assert(stiffness >= 0); + return stiffness; +} +@ + +Attempt to calculate the chain stiffness by adding group stiffnesses +as springs in series. In the case where a group has undefined +stiffness (e.g. piston tension, Section \ref{sec.piston_tension}), +this algorithm breaks down. In that case, [[tension_balance()]] +(\ref{sec.tension_balance}) should use [[full_chain_stiffness()]] +which uses the full chain's $F(x)$ rather than that of the individual +domains'. We attempt the series approach first because, lacking the +numerical inversion inside [[tension_balance()]], it is both faster +and more accurate than the full-chain derivative. +<>= +double chain_stiffness(x_of_xo_data_t *x_xo_data, double relx) +{ + double stiffness, gstiff; + int i; + /* add group stiffnesses in series */ + for (i=0; i < x_xo_data->n_groups; i++) { +#ifdef DEBUG + fprintf(stderr, "%s:\tgetting stiffness of active state %d of %d for x[%d]=%g, relx=%g\n", __FUNCTION__, i, x_xo_data->n_groups, i, x_xo_data->xi[i], relx); + fflush(stderr); +#endif + gstiff = group_stiffness(x_xo_data->tension_handler[i], x_xo_data->handler_data[i], x_xo_data->xi[i], relx); + if (gstiff == 0.0); + return 0.0; + stiffness += 1.0/gstiff; + } + stiffness = 1.0 / stiffness; + return stiffness; +} + +@ + +Determine the chain stiffness using only [[tension_balance()]]. This +works around difficulties with tension models that have undefined +stiffness (see discussion for [[chain_stiffness()]] above). +<>= +double full_chain_stiffness(int num_tension_groups, + one_dim_fn_t **tension_handlers, + one_dim_fn_t **inverse_tension_handlers, + void **params, /* array of pointers to tension_handler_data_t */ + double last_x, + double x, + double relx, + double F /* already evaluated F(x) */) +{ + double dx, xl, Fl, stiffness; + + assert(x >= 0); + assert(relx > 0 && relx < 1); + + /* Other option for dx that we ignore because of our poor tension_balance() + * resolution (i.e. bad slopes if you zoom in too close): + * if (last_x != -1.0 && last_x != x) // last_x limited + * dx fabs(x-last_x); + * else + * dx = HUGE_VAL; + * if (1==1) { // constant max-value limited + * dx_p = 1e-12; + * dx = MIN(dx, dx_p); + * } + * if (x != 0 && relx != 0) { // relx limited + * dx_p = x*relx; + * dx = MIN(dx, dx_p); + * } + * TODO, determine which of (min_relx, min_rely, max_steps) is actually + * limiting tension_balance. + */ + dx = 1e-12; /* HACK, how to get length scale? */ + + xl = x-dx; + if (xl >= 0) { + Fl = tension_balance(num_tension_groups, tension_handlers, + inverse_tension_handlers, params, + last_x, xl, NULL); + } else { + xl = x; + Fl = F; + x += dx; + F = tension_balance(num_tension_groups, tension_handlers, + inverse_tension_handlers, params, + last_x, x, NULL); + } + stiffness = (F-Fl)/dx; + assert(stiffness >= 0); + return stiffness; +} + +@ Solve $f(x) = y$ to a certain precision in $x$ or $y$ in a limited number of steps for monotonically increasing $f(x)$. Simple @@ -2052,17 +2665,17 @@ relative limits must be satisfied for the search to stop. <>= /* equivalent to gsl_func_t */ typedef double one_dim_fn_t(double x, void *params); -@ +@ <>= double oneD_solve(one_dim_fn_t *f, void *params, double y, double lb, double ub, - double min_relx, double min_rely, int max_steps, + double min_relx, double min_rely, int max_steps, double *pYx); -@ +@ <>= /* TODO, replace with GSL one d root finder http://www.gnu.org/software/gsl/manual/html_node/One-dimensional-Root_002dFinding.html */ double oneD_solve(one_dim_fn_t *f, void *params, double y, double lb, double ub, - double min_relx, double min_rely, int max_steps, + double min_relx, double min_rely, int max_steps, double *pYx) { double yx, ylb, yub, x; @@ -2070,10 +2683,10 @@ double oneD_solve(one_dim_fn_t *f, void *params, double y, double lb, double ub, assert(ub >= lb); ylb = (*f)(lb, params); yub = (*f)(ub, params); - + /* check some simple cases */ if (ylb == yub) { - if (ylb != y) return HUGE_VAL; /* error! f(x)=y not bounded */ + if (ylb != y) return HUGE_VAL; /* error! f(x)=y not bracketed */ else return lb; /* any x on the range [lb, ub] would work */ } if (ylb == y) { x=lb; yx=ylb; goto end; } @@ -2100,19 +2713,22 @@ double oneD_solve(one_dim_fn_t *f, void *params, double y, double lb, double ub, #endif return x; } -@ +@ The one dimensional solver needs a bracketed solution, which sometimes we don't have. Generate bracketing $x$ values through bisection or exponential growth. <>= void oneD_bracket(one_dim_fn_t *f, void *params, double y, double xguess, double *lb, double *ub); -@ +@ <>= void oneD_bracket(one_dim_fn_t *f, void *params, double y, double xguess, double *lb, double *ub) { double yx, step, x=xguess; int i=0; +#ifdef DEBUG + fprintf(stderr, "%s:\tbracketing %g (params %p)\n", __FUNCTION__, y, params); +#endif yx = (*f)(x, params); #ifdef DEBUG fprintf(stderr, "%s:\tbracketing %g, start at f(%g) = %g guessing x = %g (params %p)\n", __FUNCTION__, y, x, yx, xguess, params); @@ -2141,7 +2757,7 @@ void oneD_bracket(one_dim_fn_t *f, void *params, double y, double xguess, double } //fprintf(stdout, "ub %g, %g lb\n", *ub, *lb); } -@ +@ \subsection{Balancing implementation} @@ -2155,7 +2771,7 @@ double length_scale = 1e-10; /* HACK */ <> <> -@ +@ <>= #include /* assert() */ @@ -2163,16 +2779,17 @@ double length_scale = 1e-10; /* HACK */ #include /* HUGE_VAL, macro constant, so don't need to link to math */ #include /* fprintf(), stdout */ #include "global.h" -@ +@ \subsection{Balancing unit tests} Here we check to make sure the various functions work as expected, using \citetalias{sw:check}. <>= +<> <> <> <
> -@ +@ <>= #include /* EXIT_SUCCESS and EXIT_FAILURE */ @@ -2180,12 +2797,12 @@ Here we check to make sure the various functions work as expected, using \citeta <> #include "global.h" #include "tension_balance.h" -@ +@ <>= <> <> -@ +@ <>= Suite *test_suite (void) @@ -2196,7 +2813,7 @@ Suite *test_suite (void) <> return s; } -@ +@ <>= <> @@ -2211,22 +2828,24 @@ START_TEST(test_single_function) { double k=5, x=3, last_x=2.0, F; one_dim_fn_t *handlers[] = {&hooke}; + one_dim_fn_t *inverse_handlers[] = {NULL}; void *data[] = {&k}; - F = tension_balance(1, handlers, data, last_x, x); + F = tension_balance(1, handlers, inverse_handlers, data, last_x, x, NULL); fail_unless(F = k*x, NULL); } END_TEST -@ +@ We can also test balancing two springs with different spring constants. -The analytic solution for a general number of springs is given in Appendix \ref{app.math_hooke}. +The analytic solution for a general number of springs is given in Appendix \ref{sec.math_hooke}. <>= START_TEST(test_double_hooke) { double k1=5, k2=4, x=3, last_x=-1.0, F, Fe, x1e, x2e; one_dim_fn_t *handlers[] = {&hooke, &hooke}; + one_dim_fn_t *inverse_handlers[] = {NULL, NULL}; void *data[] = {&k1, &k2}; - F = tension_balance(2, handlers, data, last_x, x); + F = tension_balance(2, handlers, inverse_handlers, data, last_x, x, NULL); x1e = x*k2/(k1+k2); Fe = k1*x1e; x2e = x1e*k1/k2; @@ -2236,20 +2855,21 @@ START_TEST(test_double_hooke) CHECK_ERR(1e-6, Fe, F); } END_TEST -@ +@ TODO: test [[tension_balance()]] with another balance after the [[x_of_xo_data]] initializing balance we ran above. <>= TCase *tc_tbfunc = tcase_create("tension balance function"); -@ +@ <>= tcase_add_test(tc_tbfunc, test_single_function); tcase_add_test(tc_tbfunc, test_double_hooke); suite_add_tcase(s, tc_tbfunc); -@ +@ \section{Lists} +\label{sec.lists} The globular domains (and cantilever params, etc.) are saved in bi-directional lists. Since the list handling is so general, and separable from the bulk of the simulation, we break it out into a separate module. @@ -2262,7 +2882,7 @@ The interface is defined in [[list.h]], the implementation in [[list.c]], and th <> <> #endif /* LIST_H */ -@ +@ <>= <> @@ -2273,9 +2893,11 @@ The interface is defined in [[list.h]], the implementation in [[list.c]], and th <> <> <> +<> +<> <> <> -@ +@ <>= <> @@ -2287,15 +2909,17 @@ The interface is defined in [[list.h]], the implementation in [[list.c]], and th <> <> <> +<> +<> <> <> -@ +@ <>= NW_SAWSIM_MODS += list CHECK_BINS += check_list -check_list_MODS = -@ +check_list_MODS = +@ <>= typedef struct list_struct { @@ -2305,13 +2929,13 @@ typedef struct list_struct { } list_t; <> -@ +@ [[head]] and [[tail]] return pointers to the head and tail nodes of the list: <>= list_t *head(list_t *list); list_t *tail(list_t *list); -@ +@ <>= list_t *head(list_t *list) { @@ -2332,11 +2956,11 @@ list_t *tail(list_t *list) } return list; } -@ +@ <>= int list_length(list_t *list); -@ +@ <>= int list_length(list_t *list) { @@ -2351,7 +2975,7 @@ int list_length(list_t *list) } return i; } -@ +@ [[push]] inserts a node relative to the current position in the list without changing the current position. @@ -2361,10 +2985,10 @@ If below is zero, we insert above the current node (push(a>B>c,d,0) -> a>d>B>c), otherwise we insert below the current node (push(a>B>c,d,1) -> a>B>d>c). <>= void push(list_t **pList, void *data, int below); -@ +@ <>= void push(list_t **pList, void *data, int below) -{ +{ list_t *list, *new_node; assert(pList != NULL); list = *pList; @@ -2385,14 +3009,14 @@ void push(list_t **pList, void *data, int below) new_node->prev = list; } } -@ +@ [[pop]] removes the current domain node, moving the current position to the node after it, unless that node is [[NULL]], in which case move the current position to the node before it. <>= void *pop(list_t **pList); -@ +@ <>= void *pop(list_t **pList) { @@ -2414,14 +3038,14 @@ void *pop(list_t **pList) destroy_node(popped); return data; } -@ +@ [[list_destroy]] just pops all the nodes off a list, possibly excuting a clean-up function on their each node's data. If the cleanup function is [[NULL]], no cleanup function is called. The nodes are not popped in any particular order. <>= void list_destroy(list_t **pList, destroy_data_func_t *destroy); -@ +@ <>= void list_destroy(list_t **pList, destroy_data_func_t *destroy) { @@ -2437,12 +3061,12 @@ void list_destroy(list_t **pList, destroy_data_func_t *destroy) destroy(data); } } -@ +@ [[list_to_array]] converts a list to an array of pointers, preserving order. <>= void list_to_array(list_t *list, int *length, void ***array); -@ +@ <>= void list_to_array(list_t *list, int *pLength, void ***pArray) { @@ -2464,12 +3088,12 @@ void list_to_array(list_t *list, int *pLength, void ***pArray) *pLength = length; *pArray = array; } -@ +@ [[move]] moves the current element along the list in either direction. <>= void move(list_t **pList, int downstream); -@ +@ <>= void move(list_t **pList, int downstream) { @@ -2490,20 +3114,20 @@ void move(list_t **pList, int downstream) list = flipper; if (downstream == 0) { push(&list, data, 0); /* b>A>c>d */ - list = list->prev; /* B>a>c>d */ + list = list->prev; /* B>a>c>d */ } else { push(&list, data, 1); /* a>C>b>d */ list = list->next; /* a>c>B>d */ } *pList = list; } -@ +@ [[sort]] sorts a list from smallest to largest according to a user specified comparison. <>= typedef int (comparison_fn_t)(void *A, void *B); -@ +@ For example <>= int int_comparison(void *A, void *B) @@ -2515,10 +3139,11 @@ int int_comparison(void *A, void *B) else if (a == b) return 0; else return -1; } -@ + +@ <>= void sort(list_t **pList, comparison_fn_t *comp); -@ +@ Here we use the bubble sort algorithm. <>= void sort(list_t **pList, comparison_fn_t *comp) @@ -2541,7 +3166,49 @@ void sort(list_t **pList, comparison_fn_t *comp) } *pList = list; } -@ + +@ + +[[list_index]] finds the location of [[data]] in [[list]]. Returns +[[-1]] if [[data]] is not in [[list]]. +<>= +int list_index(list_t *list, void *data); +@ + +<>= +int list_index(list_t *list, void *data) +{ + int i=0; + list = head(list); + while (list != NULL) { + if (list->d == data) return i; + list = list->next; + i++; + } + return -1; +} + +@ + +[[list_element]] returns the data bound to the $i^\text{th}$ node of the list. +<>= +void *list_element(list_t *list, int i); +@ +<>= +void *list_element(list_t *list, int i) +{ + int j=0; + list = head(list); + while (list != NULL) { + if (i == j) return list->d; + list = list->next; + j++; + } + assert(0==1); +} + +@ + [[unique]] removes duplicates from a sorted list according to a user specified comparison. Don't do this unless you have other pointers @@ -2549,7 +3216,7 @@ any dynamically allocated data in your list, because [[unique]] just drops any non-unique data without freeing it. <>= void unique(list_t **pList, comparison_fn_t *comp); -@ +@ <>= void unique(list_t **pList, comparison_fn_t *comp) { @@ -2566,12 +3233,12 @@ void unique(list_t **pList, comparison_fn_t *comp) } *pList = list; } -@ +@ [[list_print]] prints a list to a [[FILE *]] stream. <>= void list_print(FILE *file, list_t *list, char *list_name); -@ +@ <>= void list_print(FILE *file, list_t *list, char *list_name) { @@ -2583,7 +3250,7 @@ void list_print(FILE *file, list_t *list, char *list_name) } fprintf(file, "\n"); } -@ +@ [[create_]] and [[destroy_node]] are simple wrappers around [[malloc]] and [[free]]. <>= @@ -2612,23 +3279,24 @@ The user must free the data pointed to by the node on their own. <> #include "list.h" <> -@ +@ <>= #include /* assert() */ #include /* malloc(), free(), rand() */ #include /* fprintf(), stdout, FILE */ #include "global.h" /* destroy_data_func_t */ -@ +@ \subsection{List unit tests} Here we check to make sure the various functions work as expected, using \citetalias{sw:check}. <>= +<> <> <> <
> -@ +@ <>= #include /* EXIT_SUCCESS and EXIT_FAILURE */ @@ -2636,13 +3304,13 @@ Here we check to make sure the various functions work as expected, using \citeta <> #include "global.h" #include "list.h" -@ +@ <>= <> <> <> -@ +@ <>= Suite *test_suite (void) @@ -2655,7 +3323,7 @@ Suite *test_suite (void) <> return s; } -@ +@ <>= START_TEST(test_push) @@ -2674,23 +3342,23 @@ START_TEST(test_push) } } END_TEST -@ +@ <>= TCase *tc_push = tcase_create("push"); -@ +@ <>= tcase_add_test(tc_push, test_push); suite_add_tcase(s, tc_push); -@ +@ <>= -@ +@ <>= -@ +@ <>= -@ +@ \section{Function string evaluation} @@ -2704,7 +3372,7 @@ This is one of the more complicated software ideas in \prog, so we'll go into mo Most of this is also POSIX-specific (as far as I know), so you'll have to do some legwork to port it to non-POSIX systems. We persevere despite the difficulties, because without command-line access to new functions, the saddle-point Kramers' approximation is of very limited utiltiy. -If you feel the benefits do \emph{not} outweigh the costs, or you are on a non-POSIX system (e.g. MS Windows without Cygwin), you should probably hardcode your functions in \lang. +If you feel the benefits do \emph{not} outweigh the costs, or you are on a non-POSIX system (e.g.\ MS Windows without Cygwin), you should probably hardcode your functions in \lang. Then you can either statically or dynamically link to those hardcoded functions. While much less flexible, this approach would be a fairly simple-to-implement fallback. @@ -2719,13 +3387,13 @@ The interface is defined in [[string_eval.h]], the implementation in [[string_ev <> <> #endif /* STRING_EVAL_H */ -@ +@ <>= NW_SAWSIM_MODS += string_eval CHECK_BINS += check_string_eval -check_string_eval_MODS = -@ +check_string_eval_MODS = +@ For an introduction to POSIX process control, see\\ \url{http://www.ibm.com/developerworks/aix/library/au-speakingunix8/} (very simple, but a good intro.), \\ @@ -2748,11 +3416,11 @@ to make it easy to change the evaluating subprocess to, say, Ruby, or the users //#define SUBPROCESS_ARGS {SUBPROCESS, "-ic", "import sys;sys.ps1='';sys.ps2=''", (char *)NULL} static char *SUBPROCESS_ARGS[] = {SUBPROCESS, "-ic", "import sys;sys.ps1='';sys.ps2=''", (char *)NULL}; //static char *SUBPROCESS_ARGS[] = {SUBPROCESS, "-ic", "pass", (char *)NULL}; -@ +@ The [[i]] option lets Python know that it should run in interactive mode. In it's standard mode, python reads all of the supplied instructions, and then acts on them in a single pass. In interactive mode, python acts on every instruction as soon as it is recieved. -The [[c]] option signals a command line instruction for Python to execute on startup, which in our case simply turns off the default prompting ([[ps1]] and [[ps2]]), since that is mostly for human users, and our program doesn't need it. +The [[c]] option signals a command line instruction for Python to execute on startup, which in our case simply turns off the default prompting ([[ps1]] and [[ps2]]), since that is mostly for human users, and our program doesn't need it. %The [[c]] option signals a command line instruction for Python to execute on startup, which in our case simply [[pass]]es so that the silly Python header information is not printed. We leave the prompts in, because we scan for them to determine when the output has completed. Since the call to [[execvp]] replaces the calling program, we need to split out original program in half useing [[fork]]. @@ -2772,14 +3440,14 @@ We store the pipe file descriptors in an array of 4 [[int]]s, and use the follow #define STDIN 0 /* initial index of stdin pair */ #define STDOUT 2 /* initial index of stdout pair */ -@ +@ So [[pfd[STDIN+PIPE_READ]]] is the file descriptor you would read from for the [[stdin]] pipe, and similarly for the other combinations. As a finishing touch, we can promote the POSIX file descriptors ([[read]]/[[write]] interface) into the more familiar [[stdio.h]] \emph{streams} ([[fprintf]]/[[fgetc]] interface) using [[fdopen]], which creates a stream from an open file descriptor. <>= extern void string_eval_setup(FILE **pIn, FILE **pOut); -@ +@ <>= void string_eval_setup(FILE **pIn, FILE **pOut) { @@ -2788,7 +3456,7 @@ void string_eval_setup(FILE **pIn, FILE **pOut) int rc; assert(pipe(pfd+STDIN) != -1); /* stdin pair (in, out) */ assert(pipe(pfd+STDOUT) != -1); /* stdout pair (in, out) */ - + pid = fork(); /* split process into two copies */ if (pid == -1) { /* fork error */ @@ -2841,7 +3509,7 @@ void string_eval(FILE *in, FILE *out, char *input, int buflen, char *output) The [[alarm]] calls set and clear a timeout on the returned output. If the timeout expires, the process would get a [[SIGALRM]], but it doesn't have a [[SIGALRM]] handler, so it gets a [[SIGKILL]] and dies. This protects against invalid input for which a line of output is not printed to [[stdout]]. -Other invalid inputs (e.g. those generating multiple lines on [[stdout]] or a single line on [[stdout]] and more in [[stderr]]) are silently ignored. +Other invalid inputs (e.g.\ those generating multiple lines on [[stdout]] or a single line on [[stdout]] and more in [[stderr]]) are silently ignored. If you are getting strange results, check your python code seperately. TODO, better error handling. Cleanup is fairly straightforward, we just close the connecting streams from the parent side. @@ -2850,7 +3518,7 @@ The parent waits to confirm the child closing, recieves the child's exit status, As an added touch, we redirect Python's [[stderr]] before closing the pipes, otherwise it prints a blank line when it exits. <>= extern void string_eval_teardown(FILE **pIn, FILE **pOut); -@ +@ <>= void string_eval_teardown(FILE **pIn, FILE **pOut) @@ -2884,7 +3552,7 @@ void string_eval_teardown(FILE **pIn, FILE **pOut) } */ } -@ +@ The [[while]] loop around [[wait]] protects [[wait]] from interrupting signals. \subsection{String evaluation implementation} @@ -2895,7 +3563,7 @@ The [[while]] loop around [[wait]] protects [[wait]] from interrupting signals. #include "string_eval.h" <> <> -@ +@ <>= #include /* assert() */ @@ -2905,43 +3573,44 @@ The [[while]] loop around [[wait]] protects [[wait]] from interrupting signals. #include /* pid_t */ #include /* pipe(), fork(), execvp(), alarm() */ #include /* wait() */ -@ +@ <>= <> <> -@ +@ <>= <> <> <> -@ +@ \subsection{String evaluation unit tests} Here we check to make sure the various functions work as expected, using \citetalias{sw:check}. <>= +<> <> <> <> <
> -@ +@ <>= -#include /* EXIT_SUCCESS and EXIT_FAILURE, atof() */ -#include /* printf() */ -#include /* assert() */ -#include /* strlen() */ -#include /* SIGKILL */ +#include /* EXIT_SUCCESS and EXIT_FAILURE */ +#include /* printf() */ +#include /* assert() */ +#include /* strlen() */ +#include /* SIGKILL */ <> #include "string_eval.h" -@ +@ <>= <> <> -@ +@ <>= Suite *test_suite (void) @@ -2949,10 +3618,10 @@ Suite *test_suite (void) Suite *s = suite_create ("string eval"); <> - <> + <> return s; } -@ +@ <>= START_TEST(test_setup_teardown) @@ -2967,8 +3636,8 @@ START_TEST(test_invalid_command) FILE *in, *out; char input[80], output[80]={}; string_eval_setup(&in, &out); - sprintf(input, "print ABCDefg\n"); - string_eval(in, out, input, 80, output); + sprintf(input, "print undefined_name__traceback_should_be_printed_to_stderr\n"); + string_eval(in, out, input, 80, output); string_eval_teardown(&in, &out); } END_TEST @@ -2978,7 +3647,7 @@ START_TEST(test_simple_eval) char input[80], output[80]={}; string_eval_setup(&in, &out); sprintf(input, "print 3+4*5\n"); - string_eval(in, out, input, 80, output); + string_eval(in, out, input, 80, output); fail_unless(STRMATCH(output,"23\n"), NULL); string_eval_teardown(&in, &out); } @@ -2989,10 +3658,10 @@ START_TEST(test_multiple_evals) char input[80], output[80]={}; string_eval_setup(&in, &out); sprintf(input, "print 3+4*5\n"); - string_eval(in, out, input, 80, output); + string_eval(in, out, input, 80, output); fail_unless(STRMATCH(output,"23\n"), NULL); sprintf(input, "print (3**2 + 4**2)**0.5\n"); - string_eval(in, out, input, 80, output); + string_eval(in, out, input, 80, output); fail_unless(STRMATCH(output,"5.0\n"), NULL); string_eval_teardown(&in, &out); } @@ -3005,7 +3674,7 @@ START_TEST(test_eval_with_state) sprintf(input, "print 3+4*5\n"); fprintf(in, "A = 3\n"); sprintf(input, "print A*3\n"); - string_eval(in, out, input, 80, output); + string_eval(in, out, input, 80, output); fail_unless(STRMATCH(output,"9\n"), NULL); string_eval_teardown(&in, &out); } @@ -3014,7 +3683,7 @@ END_TEST <>= TCase *tc_string_eval = tcase_create("string_eval"); @ -<>= +<>= tcase_add_test(tc_string_eval, test_setup_teardown); tcase_add_test_raise_signal(tc_string_eval, test_invalid_command, SIGKILL); tcase_add_test(tc_string_eval, test_simple_eval); @@ -3027,8 +3696,8 @@ suite_add_tcase(s, tc_string_eval); \section{Accelerating function evaluation} My first version-0.3 code was running very slowly. -With the options suggested in the help -([[-v1e-6 -Mhooke -A.05 -U1 -kbell -K3.3e-4,.25e-9 -mnull -Mwlc -A0.39e-9,28e-9 -F8]]), +With the options suggested in the help +([[-v1e-6 -Mhooke -A.05 -U1 -kbell -K3.3e-4,.25e-9 -mnull -Mwlc -A0.39e-9,28e-9 -F8]]), the program spent almost all of it's time in the functions [[oneD_solve]], [[wlc]], and [[wlc_handler]], making 0.66 million calls to [[oneD_solve]] and [[9.6]] million calls each to the WLC functions. That's only 15 calls per solution, so the search algorithm seems reasonable. @@ -3037,18 +3706,20 @@ The number of evaluation calls could be drastically reduced, however, by impleme <>= #ifndef ACCEL_K_H #define ACCEL_K_H +<> double accel_k(k_func_t *k, double F, environment_t *env, void *params); void free_accels(); #endif /* ACCEL_K_H */ -@ +@ <>= NW_SAWSIM_MODS += accel_k -#CHECK_BINS += check_accel_k -check_accel_k_MODS = -@ +CHECK_BINS += check_accel_k +check_accel_k_MODS = interp k_model parse string_eval tavl +@ <>= +<> #include /* assert() */ #include /* realloc(), free(), NULL */ #include "global.h" /* environment_t */ @@ -3090,7 +3761,7 @@ static int add_accel_k(k_func_t *k, environment_t *env, void *params) { int i=num_accels; accels = (accel_k_t *)realloc(accels, sizeof(accel_k_t) * ++num_accels); - assert(accels != NULL); + assert(accels != NULL); accels[i].itable = interp_table_allocate(&k_wrap, &k_tol); accels[i].k = k; accels[i].env = env; @@ -3117,12 +3788,83 @@ double accel_k(k_func_t *k, double F, environment_t *env, void *params) * WARNING: we're assuming param and env are the same. */ return interp_table_eval(accels[i].itable, accels+i, F); } - } + } /* set up a new acceleration environment */ i = add_accel_k(k, env, params); return interp_table_eval(accels[i].itable, accels+i, F); } -@ +@ + +\subsection{Unit tests} + +Here we check to make sure the various functions work as expected, using \citetalias{sw:check}. +<>= +<> +<> +<> +<> +<> +<
> +@ + +<>= +#include /* EXIT_SUCCESS, EXIT_FAILURE */ +#include /* sprintf() */ +#include /* assert() */ +#include /* exp() */ +#include /* errno, ERANGE */ +<> +#include "global.h" +#include "k_model.h" +#include "accel_k.h" + +@ + +<>= +<> +<> +@ + +<>= +Suite *test_suite (void) +{ + Suite *s = suite_create ("accelerated k model"); + <> + + <> + return s; +} +@ + +<>= +TCase *tc_accel_k = tcase_create("accelerated k model"); +@ + +<>= +tcase_add_test(tc_accel_k, test_accel_k_accuracy); +suite_add_tcase(s, tc_accel_k); +@ + +<>= +START_TEST(test_accel_k_accuracy) +{ + double k, k_accel, F, Fm=0.0, FM=300e-12, dF=0.5e-12; + k_func_t *k_func = bell_k; + char *param_strings[] = {"3.3e-4", "0.25e-9"}; + void *params = string_create_bell_param_t(param_strings); + environment_t env = {}; + env.T = 300.0; + + for(F=Fm; F <= FM; F+=dF) { + k = k_func(F, &env, params); + k_accel = accel_k(k_func, F, &env, params); + CHECK_ERR(1e-8, k, k_accel); + } + destroy_bell_param_t(params); +} +END_TEST + +@ \section{Tension models} \label{sec.tension_models} @@ -3142,16 +3884,17 @@ The interface is defined in [[tension_model.h]], the implementation in [[tension <> <> <> +<> <> <> #endif /* TENSION_MODEL_H */ -@ +@ <>= NW_SAWSIM_MODS += tension_model -#CHECK_BINS += check_tension_model -check_tension_model_MODS = -@ +CHECK_BINS += check_tension_model +check_tension_model_MODS = list tension_balance +@ <>= TENSION_MODEL_MODS = tension_model parse list tension_balance TENSION_MODEL_SRC = $(BUILD_DIR)/tension_model_utils.c $(BUILD_DIR)/global.h \ @@ -3160,7 +3903,7 @@ TENSION_MODEL_SRC = $(BUILD_DIR)/tension_model_utils.c $(BUILD_DIR)/global.h \ $(BUILD_DIR)/tension_model_utils.c : $(SRC_DIR)/sawsim.nw | $(BUILD_DIR) notangle -Rtension-model-utils.c $< > $@ $(BIN_DIR)/tension_model_utils : $(TENSION_MODEL_SRC) | $(BIN_DIR) - gcc -g -o $@ $< $(TENSION_MODEL_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) + $(CC) $(CFLAGS) $(LDFLAGS) -g -o $@ $< $(TENSION_MODEL_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) clean_tension_model_utils : rm -f $(BUILD_DIR)/tension_model_utils.c $(BIN_DIR)/tension_model_utils @ The pipe symbol [[|]] marks the prerequisits following it (in this @@ -3178,37 +3921,40 @@ details For unstretchable domains. <>= -{NULL, "null", "an unstretchable domain", 0, NULL, NULL, NULL, NULL} -@ +{NULL, NULL, "null", "an unstretchable domain", 0, NULL, NULL, NULL, NULL} +@ \subsection{Constant} \label{sec.const_tension} +An infinitely stretchable domain providing a constant tension. +Obviously this cannot be inverted, so you can't put this domain in +series with any other domains. We include it mostly for testing +purposes. + <>= <> <> -@ +@ <>= <> <> <> -@ - -An infinitely stretchable domain providing a constant tension. +@ <>= extern double const_tension_handler(double x, void *pdata); -@ +@ <>= double const_tension_handler(double x, void *pdata) { tension_handler_data_t *data = (tension_handler_data_t *)pdata; - list_t *list = data->group; + list_t *list = data->group_tension_params; double F; - assert (x >= 0.0); + assert(x >= 0.0); list = head(list); assert(list != NULL); /* empty active group?! */ F = ((const_tension_param_t *)list->d)->F; @@ -3222,19 +3968,19 @@ double const_tension_handler(double x, void *pdata) return F; } -@ +@ <>= typedef struct const_tension_param_struct { double F; /* tension (force) in N */ } const_tension_param_t; -@ +@ <>= extern void *string_create_const_tension_param_t(char **param_strings); extern void destroy_const_tension_param_t(void *p); -@ +@ <>= const_tension_param_t *create_const_tension_param_t(double F) @@ -3248,7 +3994,8 @@ const_tension_param_t *create_const_tension_param_t(double F) void *string_create_const_tension_param_t(char **param_strings) { - return create_const_tension_param_t(atof(param_strings[0])); + return create_const_tension_param_t( + safe_strtod(param_strings[0],__FUNCTION__)); } void destroy_const_tension_param_t(void *p) @@ -3263,52 +4010,55 @@ void destroy_const_tension_param_t(void *p) extern int num_const_tension_params; extern char *const_tension_param_descriptions[]; extern char const_tension_param_string[]; -@ +@ <>= int num_const_tension_params = 1; char *const_tension_param_descriptions[] = {"tension F, N"}; char const_tension_param_string[] = "0"; -@ +@ <>= -{&const_tension_handler, "const", "an infinitely stretchable domain with constant tension", 1, const_tension_param_descriptions, const_tension_param_string, &string_create_const_tension_param_t, &destroy_const_tension_param_t} -@ +{&const_tension_handler, NULL, "const", "an infinitely stretchable domain with constant tension", num_const_tension_params, const_tension_param_descriptions, const_tension_param_string, &string_create_const_tension_param_t, &destroy_const_tension_param_t} +@ \subsection{Hooke} \label{sec.hooke} <>= -<> +<> +<> +<> <> -@ +@ <>= <> <> <> -@ +@ The tension of a single spring is given by $F=kx$ for some spring constant $k$. The behavior of a series of springs $k_i$ in series is given by $$ F = \p({\sum_i \frac{1}{k_i}})^{-1} x $$ -For a simple proof, see Appendix \ref{app.math_hooke}. +For a simple proof, see Appendix \ref{sec.math_hooke}. <>= extern double hooke_handler(double x, void *pdata); -@ +extern double inverse_hooke_handler(double F, void *pdata); +@ -<>= -double hooke_handler(double x, void *pdata) -{ - tension_handler_data_t *data = (tension_handler_data_t *)pdata; - list_t *list = data->group; +First we define a function that computes the effective spring constant +(stored in a single [[hooke_param_t]]) for the entire group. +<>= +static void hooke_param_grouper(tension_handler_data_t *data, + hooke_param_t *param) { + list_t *list = data->group_tension_params; double k=0.0; - assert (x >= 0.0); list = head(list); assert(list != NULL); /* empty active group?! */ while (list != NULL) { @@ -3322,23 +4072,55 @@ double hooke_handler(double x, void *pdata) } k = 1.0 / k; #ifdef DEBUG - fprintf(stderr, "%s: effective Hooke spring %g N/m at %g m -> F = %g N\n", - __FUNCTION__, k, x, k*x); + fprintf(stderr, "%s: effective Hooke spring %g N/m at %g m -> F = %g N (from data %p)\n", + __FUNCTION__, k, x, k*x, data); #endif - return k*x; + param->k = k; } -@ +@ + +Everyone knows Hooke's law: $F=kx$. +<>= +double hooke_handler(double x, void *pdata) +{ + hooke_param_t param = {0}; + + assert(x >= 0.0); + hooke_param_grouper((tension_handler_data_t *)pdata, ¶m); + return param.k*x; +} + +@ + +Inverting Hooke's law gives $x=F/k$. +<>= +double inverse_hooke_handler(double F, void *pdata) +{ + hooke_param_t param = {0}; + + assert(F >= 0.0); + hooke_param_grouper((tension_handler_data_t *)pdata, ¶m); + return F/param.k; +} + +@ + +Not much to keep track of for a single effective spring, just the +spring constant $k$. <>= typedef struct hooke_param_struct { double k; /* spring constant in N/m */ } hooke_param_t; -@ +@ + +We wrap up our Hooke implementation with some book-keeping functions. <>= extern void *string_create_hooke_param_t(char **param_strings); extern void destroy_hooke_param_t(void *p); -@ + +@ <>= hooke_param_t *create_hooke_param_t(double k) @@ -3351,7 +4133,7 @@ hooke_param_t *create_hooke_param_t(double k) void *string_create_hooke_param_t(char **param_strings) { - return create_hooke_param_t(atof(param_strings[0])); + return create_hooke_param_t(safe_strtod(param_strings[0], __FUNCTION__)); } void destroy_hooke_param_t(void *p) @@ -3365,34 +4147,43 @@ void destroy_hooke_param_t(void *p) extern int num_hooke_params; extern char *hooke_param_descriptions[]; extern char hooke_param_string[]; -@ +@ <>= int num_hooke_params = 1; char *hooke_param_descriptions[] = {"spring constant k, N/m"}; char hooke_param_string[]="0.05"; -@ +@ <>= -{hooke_handler, "hooke", "a Hookean spring (F=kx)", num_hooke_params, hooke_param_descriptions, (char *)hooke_param_string, &string_create_hooke_param_t, &destroy_hooke_param_t} -@ +{hooke_handler, inverse_hooke_handler, "hooke", "a Hookean spring (F=kx)", num_hooke_params, hooke_param_descriptions, (char *)hooke_param_string, &string_create_hooke_param_t, &destroy_hooke_param_t} +@ \subsection{Worm-like chain} \label{sec.wlc} We can model several unfolded domains with a single worm-like chain. <>= -<> +<> <> +<> <> -@ +@ <>= + <> +<> <> <> -@ +@ + +<>= +<> +<> +<> +@ The combination of all unfolded domains is modeled as a worm like chain, with the force $F_{\text{WLC}}$ approximately given by @@ -3406,8 +4197,8 @@ $T$ is the absolute temperature, $p$ is the persistence length, and $L$ is the total contour length of all unfolded domains\citep{bustamante94,marko95,hatfield99}. <>= -double wlc(double x, double T, double p, double L) -{/* N m K m m */ +static double wlc(double x, double T, double p, double L) +{/* N m K m m */ double xL=0.0; /* uses global k_B */ assert(x >= 0); assert(T > 0); assert(p > 0); assert(L > 0); @@ -3417,19 +4208,84 @@ double wlc(double x, double T, double p, double L) // k_B*T/p * ( 0.25*(1.0/((1-xL)*(1-xL))-1) + xL )); return k_B*T/p * ( 0.25*(1.0/((1-xL)*(1-xL))-1) + xL ); } -@ -This model assumes that each unfolded domain has the same persistence length. -<>= -extern double wlc_handler(double x, void *pdata); -@ +@ -<>= -double wlc_handler(double x, void *pdata) -{ - tension_handler_data_t *data = (tension_handler_data_t *)pdata; - list_t *list = data->group; - double p, L=0.0; +Inverting the approximate WLC is fairly straightforward, if a bit tedious. +Letting $x_L \equiv x/L$ and $F_T \equiv Fp/k_B T$ we have +\begin{align} + F_T &\approx \frac{1}{4} \p({\frac{1}{(1-x_L)^2} - 1}) + x_L \\ + F_T (1-x_L)^2 &\approx \frac{1}{4} - \frac{1}{4} (1-x_L)^2 + x_L(1-x_L)^2 \\ + 0 &\approx \frac{1}{4} - \p({F_T + \frac{1}{4}}) (1-x_L)^2 + x_L(1-x_L)^2 \\ + &\approx \frac{1}{4} - \p({F_T + \frac{1}{4}}) \p({1-2x_L+x_L^2}) + + x_L - 2x_L^2 + x_L^3 \\ + &\approx \p[{\frac{1}{4} - \p({F_T + \frac{1}{4}})}] + + x_L \p[{2F_T + \frac{1}{2} + 1}] + + x_L^2 \p[{-\p({F_T + \frac{1}{4}}) - 2}] + + x_L^3 \\ + &\approx -F_T + + x_L \p({2F_T + \frac{3}{2}}) + - x_L^2 \p({F_T + \frac{9}{4}}) + + x_L^3 \\ + &\approx ax_L^3 + bx_L^2 + cx_L + d +\end{align} +where $a \equiv 1$, $b \equiv -F_T - 9/4$, $c \equiv 2F_T + 3/2$, and +$d \equiv -F_T$. +% From \citet{wikipedia_cubic_function} the discriminant +%\begin{align} +% \Delta &= -4b^3d + b^2c^2 - 4ac^3 + 18abcd - 27a^2d^2 \\ +% &= -4F_T\p({F_T + \frac{9}{4}})^3 +% + \p({F_T + \frac{9}{4}})^2 \cdot \p({2F_T + \frac{3}{2}})^2 +% - 4 \p({2F_T + \frac{3}{2}})^3 +% + 18F_T \p({F_T + \frac{9}{4}}) \cdot \p({2F_T + \frac{3}{2}}) +% - 27F_T^2 \\ +% &= -4F_T \p({F_T^3 + \frac{27}{4}F_T^2 +\frac{243}{16}F_T +\frac{729}{64}}) +%% a^3 + 3a^2b + 3ab^2 + b^3 +% + \p({F_T^2 + \frac{9}{2}F_T + \frac{81}{16}}) +% \cdot \p({4F_T^2 + 6F_T + \frac{9}{4}}) \\ +% &\qquad - 4 \p({8F_T^3 + 18F_T^2 + \frac{27}{2}F_T + \frac{27}{8}}) +%% a^3 + 3a^2b + 3ab^2 + b^3 +% + 18F_T \p({2F_T^2 + 6F_T + \frac{27}{8}}) +% - 27F_T^2 \\ +% &= -4F_T^4 - 27F_T^3 - \frac{243}{4}F_T^2 - \frac{729}{16}F_T +% + 4F_T^4 + 24F_T^3 +\frac{99}{2}F_T^2 +\frac{81}{2}F_T +\frac{729}{64}\\ +% &\qquad - 32F_T^3 - 72F_T^2 - 54F_T - \frac{27}{2} +% + 36F_T^3 + 108F_T^2 + \frac{243}{4}F_T +% - 27F_T^2 \\ +% &= F_T^4 \p({-4 + 4}) + F_T^3 \p({-27 + 24 - 32 + 36}) +% + F_T^2 \p({-\frac{243}{4} + \frac{99}{2} - 72 + 108 -27}) \\ +% &\qquad + F_T \p({-\frac{729}{16} + \frac{81}{2} - 54 + \frac{243}{4}}) +% \p({\frac{729}{64} - \frac{27}{2}}) \\ +% &= F_T^3 - \frac{9}{4}F_T^2 + \frac{27}{16}F_T - \frac{135}{64} +%\end{align} +We can plug these coefficients into the GSL cubic solver to invert the +WLC\citep{galassi05}. The applicable root is always the one which +comes before the singularity, which will be the smallest real root. +<>= +static double inverse_wlc(double F, double T, double p, double L) +{/* m N K m m */ + double FT = F*p/(k_B*T); /* uses global k_B */ + double xL0, xL1, xL2; + int num_roots; + assert(F >= 0); + assert(T > 0); assert(p > 0); assert(L > 0); + if (F == HUGE_VAL) + return L; + num_roots = gsl_poly_solve_cubic(-(FT+2.25),2*FT+1.5,-FT, &xL0, &xL1, &xL2); + assert(num_roots > 0); assert(xL0 >= -DOUBLE_PRECISION); assert(xL0 < 1); + if (xL0 < 0) xL0 = 0.0; + return xL0*L; +} + +@ + +First we define a function that computes the effective WLC parameters +(stored in a single [[wlc_param_t]]) for the entire group. +<>= +static void wlc_param_grouper(tension_handler_data_t *data, + wlc_param_t *param) { + list_t *list = data->group_tension_params; + double p=0.0, L=0.0; list = head(list); assert(list != NULL); /* empty active group?! */ @@ -3448,21 +4304,58 @@ double wlc_handler(double x, void *pdata) fprintf(stderr, "%s: WLC(x=%g m, T=%g K, p=%g m, L=%g m) = %g N\n", __FUNCTION__, x, data->env->T, p, L, wlc(x, data->env->T, p, L)); #endif - return wlc(x, data->env->T, p, L); + param->p = p; + param->L = L; +} + +@ + +<>= +extern double wlc_handler(double x, void *pdata); +@ + +This model requires that each unfolded domain in the group have the +same persistence length. +<>= +double wlc_handler(double x, void *pdata) +{ + tension_handler_data_t *data = (tension_handler_data_t *)pdata; + wlc_param_t param = {0}; + + assert(x >= 0.0); + wlc_param_grouper(data, ¶m); + return wlc(x, data->env->T, param.p, param.L); } -@ + +@ + +<>= +extern double inverse_wlc_handler(double F, void *pdata); +@ + +<>= +double inverse_wlc_handler(double F, void *pdata) +{ + tension_handler_data_t *data = (tension_handler_data_t *)pdata; + wlc_param_t param = {0}; + + wlc_param_grouper(data, ¶m); + return inverse_wlc(F, data->env->T, param.p, param.L); +} + +@ <>= typedef struct wlc_param_struct { double p; /* WLC persistence length (m) */ double L; /* WLC contour length (m) */ } wlc_param_t; -@ +@ <>= extern void *string_create_wlc_param_t(char **param_strings); extern void destroy_wlc_param_t(void *p /* wlc_param_t * */); -@ +@ <>= wlc_param_t *create_wlc_param_t(double p, double L) @@ -3476,7 +4369,8 @@ wlc_param_t *create_wlc_param_t(double p, double L) void *string_create_wlc_param_t(char **param_strings) { - return create_wlc_param_t(atof(param_strings[0]), atof(param_strings[1])); + return create_wlc_param_t(safe_strtod(param_strings[0], __FUNCTION__), + safe_strtod(param_strings[1], __FUNCTION__)); } void destroy_wlc_param_t(void *p /* wlc_param_t * */) @@ -3484,6 +4378,7 @@ void destroy_wlc_param_t(void *p /* wlc_param_t * */) if (p) free(p); } + @ We define [[wlc_param_string]] as a global array because hard-coding the values into the tension model getopt structure gives a read-only version. @@ -3502,16 +4397,16 @@ string[1] = 'x'; extern int num_wlc_params; extern char *wlc_param_descriptions[]; extern char wlc_param_string[]; -@ +@ <>= int num_wlc_params = 2; char *wlc_param_descriptions[] = {"persistence length p, m", "contour length L, m"}; char wlc_param_string[]="0.39e-9,28.4e-9"; -@ +@ <>= -{wlc_handler, "wlc", "a worm-like chain (F=kbT/p{.25[(1-x/L)^-2 -1] + x/L})", num_wlc_params, wlc_param_descriptions, (char *)wlc_param_string, &string_create_wlc_param_t, &destroy_wlc_param_t} -@ +{&wlc_handler, &inverse_wlc_handler, "wlc", "a worm-like chain (F=kbT/p{.25[(1-x/L)^-2 -1] + x/L})", num_wlc_params, wlc_param_descriptions, (char *)wlc_param_string, &string_create_wlc_param_t, &destroy_wlc_param_t} +@ Titin parameters from Carrion-Vazquez 1999, PNAS USA 96, 3696. \subsection{Freely-jointed chain} @@ -3521,14 +4416,14 @@ Titin parameters from Carrion-Vazquez 1999, PNAS USA 96, 3696. <> <> <> -@ +@ <>= <> <> <> -@ +@ The freely jointed chain model approximates the protein as a series of rigid links of length $l$ with freely rotating joints. The tension of a chain of $N$ such links is given by @@ -3537,14 +4432,13 @@ $$ $$ where $L=Nl$ is the total length of the chain, and $\mathcal{L}(\alpha) \equiv \coth{\alpha} - \frac{1}{\alpha}$ is the Langevin function\citep{hatfield99}. <>= -double langevin(double x, void *params) +static double langevin(double x, void *params) { if (x==0) return 0; return 1.0/tanh(x) - 1/x; } -<> -<> -double inv_langevin(double x) + +static double inv_langevin(double x) { double lb=0.0, ub=1.0, ret; oneD_bracket(&langevin, NULL, x, 1.0, &lb, &ub); @@ -3552,23 +4446,24 @@ double inv_langevin(double x) return ret; } -double fjc(double x, double T, double l, int N) +static double fjc(double x, double T, double l, int N) { double L = l*(double)N; if (x == 0) return 0; //printf("x %g\tL%g\tx/L %g\n", x, L, x/L); return k_B*T/l * inv_langevin(x/L); } -@ + +@ <>= extern double fjc_handler(double x, void *pdata); -@ +@ <>= double fjc_handler(double x, void *pdata) { tension_handler_data_t *data = (tension_handler_data_t *)pdata; - list_t *list = data->group; + list_t *list = data->group_tension_params; double l; int N=0; @@ -3591,19 +4486,19 @@ double fjc_handler(double x, void *pdata) #endif return fjc(x, data->env->T, l, N); } -@ +@ <>= typedef struct fjc_param_struct { double l; /* FJC link length (m) */ int N; /* FJC number of links */ } fjc_param_t; -@ +@ <>= extern void *string_create_fjc_param_t(char **param_strings); extern void destroy_fjc_param_t(void *p); -@ +@ <>= fjc_param_t *create_fjc_param_t(double l, double N) @@ -3617,7 +4512,8 @@ fjc_param_t *create_fjc_param_t(double l, double N) void *string_create_fjc_param_t(char **param_strings) { - return create_fjc_param_t(atof(param_strings[0]), atof(param_strings[1])); + return create_fjc_param_t(safe_strtod(param_strings[0], __FUNCTION__), + safe_strtod(param_strings[1], __FUNCTION__)); } void destroy_fjc_param_t(void *p) @@ -3625,23 +4521,195 @@ void destroy_fjc_param_t(void *p) if (p) free(p); } -@ +@ <>= extern int num_fjc_params; extern char *fjc_param_descriptions[]; extern char fjc_param_string[]; -@ +@ <>= int num_fjc_params = 2; char *fjc_param_descriptions[] = {"link length l, m", "link count N, unitless integer"}; char fjc_param_string[]="0.5e-9,200"; -@ +@ <>= -{fjc_handler, "fjc", "a freely-jointed chain [F=kbT/l L^-1(x/L)]", num_fjc_params, fjc_param_descriptions, (char *)fjc_param_string, &string_create_fjc_param_t, &destroy_fjc_param_t} -@ +{fjc_handler, NULL, "fjc", "a freely-jointed chain [F=kbT/l L^-1(x/L)]", num_fjc_params, fjc_param_descriptions, (char *)fjc_param_string, &string_create_fjc_param_t, &destroy_fjc_param_t} +@ + +\subsection{Piston} +\label{sec.piston_tension} + +An infinitely stretchable domain with no tension for extensions less +than a particular threshold $L$, and infinite tension for $x>L$. The +tension at $x=L$ is undefined, but may be any positive value. The +model is called the ``piston'' model because it resembles a +frictionless piston sliding in a rigid cylinder of length $L$. +$$ + F = \begin{cases} + 0 & \text{if $xL$}. + \end{cases} +$$ + +Note that because of it's infinte stiffness at $x=L$, fully extended +domains with this tension model will be identical to completely rigid +domains. However, there is a distinction between this model and rigid +domains for $x>= +<> +<> +<> +<> +@ + +<>= +<> +<> +<> +<> + +@ + +First we define a function that computes the effective piston parameters +(stored in a single [[piston_tension_param_t]]) for the entire group. +<>= +static void piston_tension_param_grouper(tension_handler_data_t *data, + piston_tension_param_t *param) { + list_t *list = data->group_tension_params; + double L=0; + + list = head(list); + assert(list != NULL); /* empty active group?! */ + while (list != NULL) { + L += ((piston_tension_param_t *)list->d)->L; + list = list->next; + } + param->L = L; +} + +<>= +extern double piston_tension_handler(double x, void *pdata); +@ +<>= +double piston_tension_handler(double x, void *pdata) +{ + tension_handler_data_t *data = (tension_handler_data_t *)pdata; + piston_tension_param_t param = {0}; + double F; + + piston_tension_param_grouper(data, ¶m); + if (x <= param.L) F = 0; + else F = HUGE_VAL; +#ifdef DEBUG + fprintf(stderr, "%s: x %g, L %g, tension %g N\n", __FUNCTION__, x, param.L, F); +#endif + return F; +} + +@ + +We abuse [[x_of_xo()]] and [[oneD_solve()]] with this inverse +definition (see Section \ref{sec.tension_balance}), because the +$x(F=0)<=L$, but our function returns $x(F=0)=0$. This is fine when +the total extension \emph{is} zero, but cheats a bit when there is +some total extension. For any non-zero extension, the initial active +group produces some tension (we hope. True for all our other tension +models). This tension fully extends the piston group (of which there +should be only one, since all piston states can get lumped into the +same tension group.). If the total extension is $\le$ the target +extension, the full extension is accurate, so the inverse was valid +after all. If not, [[oneD_solve()]] will halve the extension of the +first group, reducing the overall tension. For total extension less +than the piston extension, this bisection continues for [[max_steps]], +leaving $x_0$ reduced by a factor of $2^\text{max\_steps}$, a very +small number. Because of this, the returned tension $F_0(x_0)$ is +very small, even though the total extension found by [[x_of_xo()]] +is still $>$ the piston length. + +While this works, it is clearly not the most elegant or robust +solution. TODO: think of (and implement) a better procedure. + +<>= +extern double inverse_piston_tension_handler(double x, void *pdata); +@ +<>= +double inverse_piston_tension_handler(double F, void *pdata) +{ + tension_handler_data_t *data = (tension_handler_data_t *)pdata; + piston_tension_param_t param = {0}; + + assert(F >= 0.0); + piston_tension_param_grouper(data, ¶m); + if (F == 0.0) return 0; + return param.L; +} + +@ + +<>= +typedef struct piston_tension_param_struct { + double L; /* length of piston in m */ +} piston_tension_param_t; + +@ + +<>= +extern void *string_create_piston_tension_param_t(char **param_strings); +extern void destroy_piston_tension_param_t(void *p); + +@ + +<>= +piston_tension_param_t *create_piston_tension_param_t(double L) +{ + piston_tension_param_t *ret + = (piston_tension_param_t *) malloc(sizeof(piston_tension_param_t)); + assert(ret != NULL); + ret->L = L; + return ret; +} + +void *string_create_piston_tension_param_t(char **param_strings) +{ + return create_piston_tension_param_t( + safe_strtod(param_strings[0],__FUNCTION__)); +} + +void destroy_piston_tension_param_t(void *p) +{ + if (p) + free(p); +} + +@ + +<>= +extern int num_piston_tension_params; +extern char *piston_tension_param_descriptions[]; +extern char piston_tension_param_string[]; + +@ + +<>= +int num_piston_tension_params = 1; +char *piston_tension_param_descriptions[] = {"length L, m"}; +char piston_tension_param_string[] = "0"; + +@ + +<>= +{&piston_tension_handler, &inverse_piston_tension_handler, "piston", "a domain that slides without tension for xL.", num_piston_tension_params, piston_tension_param_descriptions, piston_tension_param_string, &string_create_piston_tension_param_t, &destroy_piston_tension_param_t} +@ \subsection{Tension model implementation} @@ -3653,24 +4721,26 @@ char fjc_param_string[]="0.5e-9,200"; <> <> <> -@ +@ <>= #include /* assert() */ -#include /* NULL */ +#include /* NULL, strto*() */ #include /* HUGE_VAL, sqrt(), exp() */ #include /* fprintf(), stdout */ +#include /* errno, ERANGE */ #include "global.h" #include "list.h" #include "tension_balance.h" /* oneD_*() */ -@ +@ <>= <> <> <> <> -@ +<> +@ <>= <> @@ -3678,15 +4748,17 @@ char fjc_param_string[]="0.5e-9,200"; <> <> <> -@ +<> +@ <>= +<> <> <> <> <> -@ - +<> +@ \subsection{Utilities} @@ -3705,7 +4777,7 @@ range of $x$. <> <> <> -@ +@ <>= int main(int argc, char **argv) @@ -3727,8 +4799,8 @@ int main(int argc, char **argv) printf("#initializing model %s with parameters %s\n", model->name, model->params); } INIT_MODEL("utility", model, model->params, params); - tdata.group = NULL; - push(&tdata.group, params, 1); + tdata.group_tension_params = NULL; + push(&tdata.group_tension_params, params, 1); tdata.env = &env; tdata.persist = NULL; if (model->handler == NULL) { @@ -3738,133 +4810,375 @@ int main(int argc, char **argv) { int i,N=200; double x=0, F=0; - printf("#F (N)\tk (%% pop. per s)\n"); + printf("#Distance (m)\tForce (N)\n"); for (i=0; i<=N; i++) { x = Xmax*i/(double)N; F = (*model->handler)(x, &tdata); if (F < 0 || F > Fmax) break; printf("%g\t%g\n", x, F); } + if (flags & VFLAG && i <= N) { + /* explain exit condition */ + if (F < 0) + printf("Impossible force %g\n", F); + else if (F > Fmax) + printf("Reached large force limit %g > %g\n", F, Fmax); + } } - params = pop(&tdata.group); + params = pop(&tdata.group_tension_params); if (model->destructor) (*model->destructor)(params); return 0; } -@ +@ + +<>= +#include +#include +#include /* strlen() */ +#include /* assert() */ +#include /* errno, ERANGE */ +#include "global.h" +#include "parse.h" +#include "list.h" +#include "tension_model.h" +@ + +<>= +<> +#define VFLAG 1 /* verbose */ +<> +<> +<> + +@ + +<>= +<> +<> +<> +<> +@ + +<>= +void help(char *prog_name, + environment_t *env, + int n_tension_models, tension_model_getopt_t *tension_models, + int tension_model, double Fmax, double Xmax) +{ + int i, j; + printf("usage: %s [options]\n", prog_name); + printf("Version %s\n\n", VERSION); + printf("A utility for understanding the available tension models\n\n"); + printf("Environmental options:\n"); + printf("-T T\tTemperature T (currently %g K)\n", env->T); + printf("-C T\tYou can also set the temperature T in Celsius\n"); + printf("Model options:\n"); + printf("-m model\tFolded tension model (currently %s)\n", + tension_models[tension_model].name); + printf("-a args\tFolded tension model argument string (currently %s)\n", + tension_models[tension_model].params); + printf("F(x) is calculated for a range of x and printed\n"); + printf("For example:\n"); + printf(" #Distance (m)\tForce (N)\n"); + printf(" 123.456\t7.89\n"); + printf(" ...\n"); + printf("-F\tSet the maximum F value for the standard mode F(x) output (currently %g)\n", Fmax); + printf("-X\tSet the maximum x value for the standard mode F(x) output (currently %g)\n", Xmax); + printf("-V\tChange output to verbose mode\n"); + printf("-h\tPrint this help and exit\n"); + printf("\n"); + printf("Tension models:\n"); + for (i=0; i>= +void get_options(int argc, char **argv, environment_t *env, + int n_tension_models, tension_model_getopt_t *tension_models, + tension_model_getopt_t **model, double *Fmax, double *Xmax, + unsigned int *flags) +{ + char *prog_name = NULL; + char c, options[] = "T:C:m:a:F:X:Vh"; + int tension_model=0, num_strings; + extern char *optarg; + extern int optind, optopt, opterr; + + assert(argc > 0); + + /* setup defaults */ + + prog_name = argv[0]; + env->T = 300.0; /* K */ + *Fmax = 1e5; /* N */ + *Xmax = 1e-6; /* m */ + *flags = 0; + *model = tension_models; + + while ((c=getopt(argc, argv, options)) != -1) { + switch(c) { + case 'T': env->T = safe_strtod(optarg, "-T"); break; + case 'C': env->T = safe_strtod(optarg, "-C")+273.15; break; + case 'm': + tension_model = index_tension_model(n_tension_models, tension_models, optarg); + *model = tension_models+tension_model; + break; + case 'a': + tension_models[tension_model].params = optarg; + break; + case 'F': *Fmax = safe_strtod(optarg, "-F"); break; + case 'X': *Xmax = safe_strtod(optarg, "-X"); break; + case 'V': *flags |= VFLAG; break; + case '?': + fprintf(stderr, "unrecognized option '%c'\n", optopt); + /* fall through to default case */ + default: + help(prog_name, env, n_tension_models, tension_models, tension_model, *Fmax, *Xmax); + exit(1); + } + } + return; +} +@ + +\subsection{Tension model unit tests} + +Here we check to make sure the various functions work as expected, using \citetalias{sw:check}. +<>= +<> +<> +<> +<> +<> +<
> +@ + +<>= +#include /* EXIT_SUCCESS, EXIT_FAILURE */ +#include /* sprintf() */ +#include /* assert() */ +#include /* exp() */ +#include /* errno, ERANGE */ +<> +#include "global.h" +#include "list.h" +#include "tension_balance.h" /* oneD_*() */ +#include "tension_model.h" +@ + +<>= +<> +<> +<> +<> +<> +<> +<> +@ + +<>= +Suite *test_suite (void) +{ + Suite *s = suite_create ("tension model"); + <> + <> + <> + <> + <> + + <> + <> + <> + <> + <> + return s; +} +@ + +\subsubsection{Constant} + +<>= +TCase *tc_const_tension = tcase_create("Constant tension"); +@ + +<>= +tcase_add_test(tc_const_tension, test_const_tension_create_destroy); +suite_add_tcase(s, tc_const_tension); +@ + +<>= +START_TEST(test_const_tension_create_destroy) +{ + char *tension[] = {"1","2.2", "3"}; + char *params[] = {tension[0]}; + void *p = NULL; + int i; + for( i=0; i < sizeof(tension)/sizeof(char *); i++) { + params[0] = tension[i]; + p = string_create_const_tension_param_t(params); + destroy_const_tension_param_t(p); + } +} +END_TEST + +@ TODO: In order to test the constant tension handler itself, we'd +have to construct a group. + + +\subsubsection{Hooke} + +<>= +TCase *tc_hooke = tcase_create("Hooke"); +@ + +<>= +tcase_add_test(tc_hooke, test_hooke_create_destroy); +suite_add_tcase(s, tc_hooke); + +@ + +<>= +START_TEST(test_hooke_create_destroy) +{ + char *k[] = {"1","2.2", "3"}; + char *params[] = {k[0]}; + void *p = NULL; + int i; + for( i=0; i < sizeof(k)/sizeof(char *); i++) { + params[0] = k[i]; + p = string_create_hooke_param_t(params); + destroy_hooke_param_t(p); + } +} +END_TEST + +@ TODO: In order to test the Hooke tension handler itself, we'd +have to construct a group. + + +\subsubsection{Worm-like chain} + +<>= +TCase *tc_wlc = tcase_create("WLC"); +@ + +<>= +tcase_add_test(tc_wlc, test_wlc_at_zero); +tcase_add_test(tc_wlc, test_wlc_at_half); +suite_add_tcase(s, tc_wlc); + +@ + +<>= +<> +START_TEST(test_wlc_at_zero) +{ + double T=1.0, L=1.0, p=0.1, x=0.0, lim=1e-30; + fail_unless(abs(wlc(x, T, p, L)) < lim, \ + "abs(wlc(x=%g,T=%g,p=%g,L=%g)) = %g >= %g", + x, T, p, L, abs(wlc(x, T, p, L)), lim); +} +END_TEST + +START_TEST(test_wlc_at_half) +{ + double T=1.0, L=1.0, p=0.1*k_B, x=0.5; + /* prefactor = k_B T / p = k_B 1.0 / (k_B*0.1) = 10.0 J/nm = 10.0e21 pN + * nonlinear term = 0.25 (1/(1-x/L)^2-1) = 0.25(1/.25 - 1) + * = 0.25 * 3 = 3/4 + * linear term = x/L = 0.5 + * nonlinear + linear = 0.75 + 0.5 = 1.25 + * wlc = 10e21*1.25 = 12.5e21 + */ + fail_unless(wlc(x, T, p, L)-12.5e21 < 1e16, + "wlc(%g, %g, %g, %g) = %g != %g", + x, T, p, L, wlc(x, T, p, L), 12.5e21); +} +END_TEST -<>= -#include -#include -#include /* strlen() */ -#include /* assert() */ -#include "global.h" -#include "parse.h" -#include "list.h" -#include "tension_model.h" -@ +@ -<>= -<> -#define VFLAG 1 /* verbose */ -<> -<> -<> -@ +\subsubsection{Freely-jointed chain} -<>= -<> -<> -<> -@ +<>= +TCase *tc_fjc = tcase_create("FJC"); +@ -<>= -void help(char *prog_name, - environment_t *env, - int n_tension_models, tension_model_getopt_t *tension_models, - int tension_model, double Fmax, double Xmax) +<>= +tcase_add_test(tc_fjc, test_fjc_at_zero); +tcase_add_test(tc_fjc, test_fjc_at_half); +suite_add_tcase(s, tc_fjc); + +@ + +<>= +<> +START_TEST(test_fjc_at_zero) { - int i, j; - printf("usage: %s [options]\n", prog_name); - printf("Version %s\n\n", VERSION); - printf("A utility for understanding the available tension models\n\n"); - printf("Environmental options:\n"); - printf("-T T\tTemperature T (currently %g K)\n", env->T); - printf("-C T\tYou can also set the temperature T in Celsius\n"); - printf("Model options:\n"); - printf("-m model\tFolded tension model (currently %s)\n", - tension_models[tension_model].name); - printf("-a args\tFolded tension model argument string (currently %s)\n", - tension_models[tension_model].params); - printf("F(x) is calculated for a range of x and printed\n"); - printf("For example:\n"); - printf(" #Distance (x)\tForce (N)\n"); - printf(" 123.456\t7.89\n"); - printf(" ...\n"); - printf("-F\tSet the maximum F value for the standard mode F(x) output (currently %g)\n", Fmax); - printf("-X\tSet the maximum x value for the standart mode F(x) output (currently %g)\n", Xmax); - printf("-V\tChange output to verbose mode\n"); - printf("-h\tPrint this help and exit\n"); - printf("\n"); - printf("Tension models:\n"); - for (i=0; i= %g", + x, T, l, N, abs(fjc(x, T, l, N)), lim); } -@ +END_TEST -<>= -void get_options(int argc, char **argv, environment_t *env, - int n_tension_models, tension_model_getopt_t *tension_models, - tension_model_getopt_t **model, double *Fmax, double *Xmax, - unsigned int *flags) +START_TEST(test_fjc_at_half) { - char *prog_name = NULL; - char c, options[] = "T:C:m:a:F:X:Vh"; - int tension_model=0, num_strings; - extern char *optarg; - extern int optind, optopt, opterr; + int N = 10; + double T=1.0/k_B, l=1.0, x=5.0; + /* prefactor = k_B T / l = k_B (1.0/k_B) / 1.0 = 1.0 J/nm = 1.0e21 pN + * nonlinear term = 0.25 (1/(1-x/L)^2-1) = 0.25(1/.25 - 1) + * = 0.25 * 3 = 3/4 + * linear term = x/L = 0.5 + * nonlinear + linear = 0.75 + 0.5 = 1.25 + * fjc = 10e21*1.25 = 12.5e21 + */ + fail_unless(fjc(x, T, l, N)-12.5e21 < 1e16, + "fjc(%g, %g, %g, %d) = %g != %g", + x, T, l, N, fjc(x, T, l, N), 12.5e21); +} +END_TEST - assert (argc > 0); +@ - /* setup defaults */ - prog_name = argv[0]; - env->T = 300.0; /* K */ - *Fmax = 1e5; - *Xmax = 1e-6; - *flags = 0; - *model = tension_models; +\subsubsection{Piston} - while ((c=getopt(argc, argv, options)) != -1) { - switch(c) { - case 'T': env->T = atof(optarg); break; - case 'C': env->T = atof(optarg)+273.15; break; - case 'm': - tension_model = index_tension_model(n_tension_models, tension_models, optarg); - *model = tension_models+tension_model; - break; - case 'a': - tension_models[tension_model].params = optarg; - break; - case 'F': *Fmax = atof(optarg); break; - case 'X': *Xmax = atof(optarg); break; - case 'V': *flags |= VFLAG; break; - case '?': - fprintf(stderr, "unrecognized option '%c'\n", optopt); - /* fall through to default case */ - default: - help(prog_name, env, n_tension_models, tension_models, tension_model, *Fmax, *Xmax); - exit(1); - } +<>= +TCase *tc_piston = tcase_create("Piston"); +@ + +<>= +tcase_add_test(tc_piston, test_piston_create_destroy); +suite_add_tcase(s, tc_piston); + +@ + +<>= +START_TEST(test_piston_create_destroy) +{ + char *L[] = {"1","2.2", "3"}; + char *params[] = {L[0]}; + void *p = NULL; + int i; + for( i=0; i < sizeof(L)/sizeof(char *); i++) { + params[0] = L[i]; + p = string_create_piston_tension_param_t(params); + destroy_piston_tension_param_t(p); } - return; } -@ +END_TEST + +@ TODO: In order to test the piston tension handler itself, we'd +have to construct a group. \section{Unfolding rate models} @@ -3874,13 +5188,13 @@ We have two main choices for determining $k$: Bell's model, which assumes the folded domains exist in a single `folded' state and make instantaneous, stochastic transitions over a free energy barrier; and Kramers' model, which treats the unfolding as a thermalized diffusion process. -We deal with these options like we dealt with the different tension models: by bundling all model-specific +We deal with these options like we dealt with the different tension models: by bundling all model-specific parameters into structures, with model specific functions for determining $k$. <>= typedef double k_func_t(double F, environment_t *env, void *params); -@ +@ Because these models are independent of the rest of the simulation, we'll split their definitions out into their own set of files. The interface is defined in [[k_model.h]], the implementation in [[k_model.c]], the unit testing in [[check_k_model.c]], and some other tidbits in [[k_model_utils.c]]. @@ -3899,16 +5213,17 @@ which I don't like as much. <> <> <> +<> <> <> #endif /* K_MODEL_H */ -@ +@ <>= NW_SAWSIM_MODS += k_model CHECK_BINS += check_k_model check_k_model_MODS = parse string_eval -@ +@ [[check_k_model]] also depends on the parse module. <>= @@ -3918,10 +5233,10 @@ K_MODEL_SRC = $(BUILD_DIR)/k_model_utils.c $(BUILD_DIR)/global.h \ $(BUILD_DIR)/k_model_utils.c : $(SRC_DIR)/sawsim.nw | $(BUILD) notangle -Rk-model-utils.c $< > $@ $(BIN_DIR)/k_model_utils : $(K_MODEL_SRC) | $(BIN_DIR) - gcc -g -o $@ $< $(K_MODEL_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) + $(CC) $(CFLAGS) $(LDFLAGS) -g -o $@ $< $(K_MODEL_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) clean_k_model_utils : rm -f $(BUILD_DIR)/k_model_utils.c $(BIN_DIR)/k_model_utils -@ +@ \subsection{Null} \label{sec.null_k} @@ -3929,15 +5244,15 @@ clean_k_model_utils : For domains that are never folded. <>= -@ +@ <>= -@ +@ <>= -@ +@ <>= {"null", "a permanently unfolded domain", NULL, 0, NULL, NULL, NULL, NULL} -@ +@ \subsection{Constant rate model} \label{sec.k_const} @@ -3951,24 +5266,24 @@ where $k_0$ is the constant unfolding rate. <>= <> <> -@ +@ <>= <> <> <> -@ +@ <>= typedef struct const_k_param_struct { double knot; /* transition rate k_0 (frac population per s) */ } const_k_param_t; -@ +@ <>= double const_k(double F, environment_t *env, void *const_k_params); -@ +@ <>= double const_k(double F, environment_t *env, void *const_k_params) { /* Returns the rate constant k in frac pop per s. */ @@ -3977,12 +5292,12 @@ double const_k(double F, environment_t *env, void *const_k_params) assert(p->knot > 0); return p->knot; } -@ +@ <>= void *string_create_const_k_param_t(char **param_strings); void destroy_const_k_param_t(void *p); -@ +@ <>= const_k_param_t *create_const_k_param_t(double knot) @@ -3995,7 +5310,7 @@ const_k_param_t *create_const_k_param_t(double knot) void *string_create_const_k_param_t(char **param_strings) { - return create_const_k_param_t(atof(param_strings[0])); + return create_const_k_param_t(safe_strtod(param_strings[0], __FUNCTION__)); } void destroy_const_k_param_t(void *p /* const_k_param_t * */) @@ -4019,12 +5334,12 @@ char const_k_param_string[]="1"; <>= {"const", "constant rate transitions", &const_k, num_const_k_params, const_k_param_descriptions, (char *)const_k_param_string, &string_create_const_k_param_t, &destroy_const_k_param_t} -@ +@ \subsection{Bell's model} \label{sec.bell} -Quantitatively, Bell's model gives $k$ as +Quantitatively, Bell's model gives $k$ as $$ k = k_0 \cdot e^{F dx / k_B T} \;, $$ @@ -4036,25 +5351,25 @@ $k_B T$ is the thermal energy\citep{schlierf06}. <>= <> <> -@ +@ <>= <> <> <> -@ +@ <>= typedef struct bell_param_struct { double knot; /* transition rate k_0 (frac population per s) */ double dx; /* `distance to transition state' (nm) */ } bell_param_t; -@ +@ <>= double bell_k(double F, environment_t *env, void *bell_params); -@ +@ <>= double bell_k(double F, environment_t *env, void *bell_params) { /* Returns the rate constant k in frac pop per s. @@ -4063,7 +5378,7 @@ double bell_k(double F, environment_t *env, void *bell_params) bell_param_t *p = (bell_param_t *) bell_params; assert(F >= 0); assert(env->T > 0); assert(p != NULL); - assert(p->knot > 0); assert(p->dx >= 0); + assert(p->knot > 0); //assert(p->dx >= 0); /* p < 0 for refolding reactions, etc. */ /* printf("F %g\tT %g\tknot %g\tdx %g\tFdx/kbT %g\tk %g\n", F, env->T, p->knot, p->dx, F*p->dx/(k_B*env->T), @@ -4072,12 +5387,12 @@ double bell_k(double F, environment_t *env, void *bell_params) */ return p->knot * exp(F*p->dx / (k_B*env->T) ); } -@ +@ <>= void *string_create_bell_param_t(char **param_strings); void destroy_bell_param_t(void *p); -@ +@ <>= bell_param_t *create_bell_param_t(double knot, double dx) @@ -4091,7 +5406,8 @@ bell_param_t *create_bell_param_t(double knot, double dx) void *string_create_bell_param_t(char **param_strings) { - return create_bell_param_t(atof(param_strings[0]), atof(param_strings[1])); + return create_bell_param_t(safe_strtod(param_strings[0], __FUNCTION__), + safe_strtod(param_strings[1], __FUNCTION__)); } void destroy_bell_param_t(void *p /* bell_param_t * */) @@ -4115,10 +5431,112 @@ char bell_param_string[]="3.3e-4,0.25e-9"; <>= {"bell", "thermalized, two-state transitions", &bell_k, num_bell_params, bell_param_descriptions, (char *)bell_param_string, &string_create_bell_param_t, &destroy_bell_param_t} -@ -Initialized with Titin I27 parameters\citep{carrion-vazquez99b}. +@ +Initialized with Titin I27 parameters\citep{carrion-vazquez99a}. +% Titin I27 parameters from Carrion-Vazquez 1999, PNAS USA 96, 3696 + + +\subsection{Linker stiffness corrected Bell model} +\label{sec.kbell} + +Walton et. al showed that the Bell model constant force approximation +doesn't hold for biotin-streptavadin binding, and I extended their +results to I27 for the 2009 Biophysical Society Annual +Meeting\cite{walton08,king09}. More details to follow when I get done +with the conference\ldots + +We adjust Bell's model to +$$ + k = k_0 \cdot e^{\frac{F dx - \frac{1}{2} \kappa dx^2}{k_B T}} \;, +$$ +where $k_0$ is the unforced unfolding rate, +$F$ is the applied unfolding force, +$\kappa$ is the effective spring constant, +$dx$ is the distance to the transition state, and +$k_B T$ is the thermal energy\citep{schlierf06}. + +<>= +<> +<> +@ + +<>= +<> +<> +<> + +@ + +<>= +typedef struct kbell_param_struct { + double knot; /* transition rate k_0 (frac population per s) */ + double dx; /* `distance to transition state' (nm) */ +} kbell_param_t; +@ + +<>= +double kbell_k(double F, environment_t *env, void *kbell_params); +@ +<>= +double kbell_k(double F, environment_t *env, void *kbell_params) +{ /* Returns the rate constant k in frac pop per s. + * Takes F in N, T in K, knot in frac pop per s, and dx in m. + * uses global k_B in J/K */ + kbell_param_t *p = (kbell_param_t *) kbell_params; + assert(F >= 0); assert(env->T > 0); assert(env->stiffness >= 0); + assert(p != NULL); + assert(p->knot > 0); assert(p->dx >= 0); + return p->knot * exp((F*p->dx - 0.5*env->stiffness*(p->dx)*(p->dx))/(k_B*env->T) ); +} +@ + +<>= +void *string_create_kbell_param_t(char **param_strings); +void destroy_kbell_param_t(void *p); +@ + +<>= +kbell_param_t *create_kbell_param_t(double knot, double dx) +{ + kbell_param_t *ret = (kbell_param_t *) malloc(sizeof(kbell_param_t)); + assert(ret != NULL); + ret->knot = knot; + ret->dx = dx; + return ret; +} + +void *string_create_kbell_param_t(char **param_strings) +{ + return create_kbell_param_t(safe_strtod(param_strings[0], __FUNCTION__), + safe_strtod(param_strings[1], __FUNCTION__)); +} + +void destroy_kbell_param_t(void *p /* kbell_param_t * */) +{ + if (p) + free(p); +} +@ + +<>= +extern int num_kbell_params; +extern char *kbell_param_descriptions[]; +extern char kbell_param_string[]; +@ + +<>= +int num_kbell_params = 2; +char *kbell_param_descriptions[] = {"unforced unfolding rate knot, % pop per s", "distance to transition state, m"}; +char kbell_param_string[]="3.3e-4,0.25e-9"; +@ + +<>= +{"kbell", "thermalized, two-state transitions, corrected for effective linker stiffness", &kbell_k, num_kbell_params, kbell_param_descriptions, (char *)kbell_param_string, &string_create_kbell_param_t, &destroy_kbell_param_t} +@ +Initialized with Titin I27 parameters\citep{carrion-vazquez99a}. % Titin I27 parameters from Carrion-Vazquez 1999, PNAS USA 96, 3696 + \subsection{Kramer's model} \label{sec.kramers} @@ -4152,14 +5570,14 @@ $E_b(F) = E(F, x_{ts}(F)) - E(F, x_c(F))$ is the barrier energy <>= <> <> -@ +@ <>= <> <> <> -@ +@ <>= //typedef double kramers_x_func_t(double F, double T, double *E_params, int n); @@ -4180,12 +5598,12 @@ typedef struct kramers_param_struct { //double *E_params; /* parametrize the energy landscape */ //int n_E_params; /* length of E_params array */ } kramers_param_t; -@ +@ <>= extern double kramers_E(double F, environment_t *env, void *kramers_params, double x); /* for k_model_utils */ extern double kramers_k(double F, environment_t *env, void *kramers_params); -@ +@ <>= double kramers_x_fn(FILE *in, FILE *out, char *fn, double F, double T) { @@ -4195,7 +5613,7 @@ double kramers_x_fn(FILE *in, FILE *out, char *fn, double F, double T) fprintf(in, "F = %g; T = %g\n", F, T); sprintf(input, "print repr(%s)\n", fn); /* repr() to keep full precision */ string_eval(in, out, input, 80, output); - return atof(output); + return safe_strtod(output, __FUNCTION__); } double kramers_E_fn(FILE *in, FILE *out, char *fn, double F, double T, double x) @@ -4206,7 +5624,7 @@ double kramers_E_fn(FILE *in, FILE *out, char *fn, double F, double T, double x) fprintf(in, "F = %g;T = %g;x = %g\n", F, T, x); sprintf(input, "print repr(%s)\n", fn); /* repr() to keep full precision */ string_eval(in, out, input, 80, output); - return atof(output); + return safe_strtod(output, __FUNCTION__); } double kramers_E(double F, environment_t *env, void *kramers_params, double x) @@ -4241,12 +5659,12 @@ double kramers_k(double F, environment_t *env, void *kramers_params) //fprintf(stderr,"D = %g, lc = %g, lts = %g, Eb = %g, kbT = %g, k = %g\n", p->D, lc, lts, Eb, kbT, p->D/(lc*lts) * exp(-Eb/kbT)); return p->D/(lc*lts) * exp(-Eb/kbT); } -@ +@ <>= void *string_create_kramers_param_t(char **param_strings); void destroy_kramers_param_t(void *p); -@ +@ <>= kramers_param_t *create_kramers_param_t(double D, @@ -4283,7 +5701,7 @@ kramers_param_t *create_kramers_param_t(double D, /* takes an array of 4 functions: {"(1,2),(2,0),..."} */ void *string_create_kramers_param_t(char **param_strings) { - return create_kramers_param_t(atof(param_strings[0]), + return create_kramers_param_t(safe_strtod(param_strings[0], __FUNCTION__), param_strings[2], param_strings[3], param_strings[4], @@ -4306,7 +5724,7 @@ void destroy_kramers_param_t(void *p /* kramers_param_t * */) For our defaults, we'll follow \citet{schlierf06} and study ddFLN4. Schlierf and Rief used a cubic-spline interpolation routine and the double integral form of Kramers' theory, so we get to pick an actual function to approximate the energy landscape. We follow \citet{shillcock98} and use -$$ +$$ E(F,E_b,x,x_s) \equiv \frac{27}{4} E_b \p({\frac{x}{x_s}})^2 \p({2-3\frac{x}{x_s}}) -F x @@ -4340,13 +5758,13 @@ char kramers_param_string[]="0.2e-12,{Eb = 20*300*kB;xs = 1.5e-9},{(F*xs > 3*Eb) Which we initialized with parameters for ddFLN4\citep{schlierf06}. There is a bit of funny buisness in the $x_c$ definition to handle high force cases. When $F x_s > 3 E_b$, the root will be complex (negative energy barrier), and the saddle point analysis breaks down. -Returning an $x_c$ position of $-1\U{m}$ lets the simulation know that the rate is poorly defined for that force, and the timestepping algorithm in Section \ref{app.adaptive_dt} reduces it's timestep appropriately. +Returning an $x_c$ position of $-1\U{m}$ lets the simulation know that the rate is poorly defined for that force, and the timestepping algorithm in Section \ref{sec.adaptive_dt} reduces it's timestep appropriately. The [[(cond) and (val_1) or (val_2)]] construction is Python hackery to simulate [[C]]'s ternary operator [[(cond) ? (val_1) : (val_2)]]. It works so long as [[val_1]] is not [[false]]. <>= {"kramers", "thermalized, diffusion-limited transitions (function parameters are parsed by Python. For distances, the environment variables force 'F' and temperature 'T' are defined, as well as the Boltzmann constant 'kB'. For energies, the position 'x' is also defined. Functions must evaluate to a float representing their output and produce no output on stdout.", &kramers_k, num_kramers_params, kramers_param_descriptions, (char *)kramers_param_string, &string_create_kramers_param_t, &destroy_kramers_param_t} -@ +@ \subsection{Kramer's model (natural cubic splines)} \label{sec.kramers_integ} @@ -4376,14 +5794,14 @@ We'll let the \citetalias{galassi05} natural cubic spline implementation do the <> <> <> -@ +@ <>= <> <> <> -@ +@ <>= typedef double func_t(double x, void *params); @@ -4398,7 +5816,7 @@ typedef struct kramers_integ_param_struct { double F; /* for passing into GSL evaluations */ environment_t *env; } kramers_integ_param_t; -@ +@ <>= typedef struct spline_param_struct { @@ -4408,7 +5826,7 @@ typedef struct spline_param_struct { gsl_spline *spline; /* GSL spline parameters */ gsl_interp_accel *acc; /* GSL spline acceleration data */ } spline_param_t; -@ +@ We break the evaluation of $k$ into the two integrals, and use the \citetalias{galassi05} to do the heavy lifting. $$ @@ -4439,7 +5857,7 @@ double kramers_integ_k_integralA(double x, void *params) //fprintf(stderr, "integralA = %g\n", result); return result; } -@ +@ $$ \text{Integral}_B(x_\text{min}, x_\text{max}) \equiv @@ -4476,7 +5894,7 @@ double kramers_integ_k_integralB(double F, environment_t *env, void *params) //fprintf(stderr, "integralB = %g\n", result); return result; } -@ +@ With the integrals taken care of, evaluating $k$ is simply $$ @@ -4484,19 +5902,19 @@ $$ $$ <>= double kramers_integ_k(double F, environment_t *env, void *kramers_params); -@ +@ <>= double kramers_integ_k(double F, environment_t *env, void *kramers_params) { /* Returns the rate constant k in frac pop per s. Takes F in N. */ kramers_integ_param_t *p = (kramers_integ_param_t *) kramers_params; return p->D/kramers_integ_k_integralB(F, env, kramers_params); } -@ +@ <>= void *string_create_kramers_integ_param_t(char **param_strings); void destroy_kramers_integ_param_t(void *p); -@ +@ <>= kramers_integ_param_t *create_kramers_integ_param_t(double D, @@ -4520,11 +5938,11 @@ void *string_create_kramers_integ_param_t(char **param_strings) //printf("create kramers integ. D: %s, knots: %s, x in [%s, %s]\n", // param_strings[0],param_strings[1],param_strings[2],param_strings[3]); void *E_params = string_create_spline_param_t(param_strings+1); - return create_kramers_integ_param_t(atof(param_strings[0]), - atof(param_strings[2]), - atof(param_strings[3]), - &spline_eval, E_params, - destroy_spline_param_t); + return create_kramers_integ_param_t( + safe_strtod(param_strings[0], __FUNCTION__), + safe_strtod(param_strings[2], __FUNCTION__), + safe_strtod(param_strings[3], __FUNCTION__), + &spline_eval, E_params, destroy_spline_param_t); } void destroy_kramers_integ_param_t(void *params) @@ -4542,7 +5960,7 @@ Finally we have the GSL spline wrappers: <>= <> <> -@ +@ <>= double spline_eval(double x, void *spline_params) @@ -4550,7 +5968,7 @@ double spline_eval(double x, void *spline_params) spline_param_t *p = (spline_param_t *)(spline_params); return gsl_spline_eval(p->spline, x, p->acc); } -@ +@ <>= spline_param_t *create_spline_param_t(int n_knots, double *x, double *y) @@ -4605,7 +6023,7 @@ void destroy_spline_param_t(void *params) free(p); } } -@ +@ <>= extern int num_kramers_integ_params; @@ -4630,8 +6048,8 @@ char kramers_integ_param_string[]="0.2e-12,{(2e-9,0),(2.1e-9,-3.7e-20),(2.2e-9,- <>= {"kramers_integ", "thermalized, diffusion-limited transitions", &kramers_integ_k, num_kramers_integ_params, kramers_integ_param_descriptions, (char *)kramers_integ_param_string, &string_create_kramers_integ_param_t, &destroy_kramers_integ_param_t} -@ -Initialized with Titin I27 parameters\citep{carrion-vazquez99b}. +@ +Initialized with Titin I27 parameters\citep{carrion-vazquez99a}. % Titin I27 parameters from Carrion-Vazquez 1999, PNAS USA 96, 3696 \subsection{Unfolding model implementation} @@ -4643,70 +6061,78 @@ Initialized with Titin I27 parameters\citep{carrion-vazquez99b}. <> <> <> -@ +@ <>= -#include /* assert() */ -#include /* NULL, malloc() */ -#include /* HUGE_VAL, sqrt(), exp() */ -#include /* fprintf(), stdout */ -#include /* strlen(), strcpy() */ +#include /* assert() */ +#include /* NULL, malloc(), strto*() */ +#include /* HUGE_VAL, sqrt(), exp() */ +#include /* fprintf(), stdout */ +#include /* strlen(), strcpy() */ +#include /* errno, ERANGE */ #include #include #include "global.h" #include "parse.h" -@ +@ <>= <> <> +<> <> <> <> -@ +@ <>= <> <> <> +<> <> <> -@ +@ <>= +<> <> <> <> +<> <> <> -@ +@ \subsection{Unfolding model unit tests} Here we check to make sure the various functions work as expected, using \citetalias{sw:check}. <>= +<> <> <> <> <> <
> -@ +@ <>= -#include /* EXIT_SUCCESS and EXIT_FAILURE, atof() */ -#include /* sprintf() */ -#include /* assert() */ -#include /* exp() */ +#include /* EXIT_SUCCESS, EXIT_FAILURE */ +#include /* sprintf() */ +#include /* assert() */ +#include /* exp() */ +#include /* errno, ERANGE */ <> #include "global.h" #include "k_model.h" -@ +@ <>= +<> <> <> <> -@ +@ <>= Suite *test_suite (void) @@ -4719,19 +6145,19 @@ Suite *test_suite (void) <> return s; } -@ +@ \subsubsection{Constant} <>= TCase *tc_const_k = tcase_create("Constant k"); -@ +@ <>= tcase_add_test(tc_const_k, test_const_k_create_destroy); tcase_add_test(tc_const_k, test_const_k_over_range); suite_add_tcase(s, tc_const_k); -@ +@ <>= @@ -4743,7 +6169,7 @@ START_TEST(test_const_k_create_destroy) int i; for( i=0; i < sizeof(knot)/sizeof(char *); i++) { params[0] = knot[i]; - p = string_create_const_k_param_t(params); + p = string_create_const_k_param_t(params); destroy_const_k_param_t(p); } } @@ -4761,9 +6187,9 @@ START_TEST(test_const_k_over_range) env.T = T; for( i=0; i < sizeof(knot)/sizeof(char *); i++) { params[0] = knot[i]; - p = string_create_const_k_param_t(params); + p = string_create_const_k_param_t(params); for ( F=Fm; F>= TCase *tc_bell = tcase_create("Bell's k"); -@ +@ <>= tcase_add_test(tc_bell, test_bell_k_create_destroy); tcase_add_test(tc_bell, test_bell_k_at_zero); tcase_add_test(tc_bell, test_bell_k_at_one); suite_add_tcase(s, tc_bell); -@ +@ <>= START_TEST(test_bell_k_create_destroy) @@ -4796,7 +6222,7 @@ START_TEST(test_bell_k_create_destroy) int i; for( i=0; i < sizeof(knot)/sizeof(char *); i++) { params[0] = knot[i]; - p = string_create_bell_param_t(params); + p = string_create_bell_param_t(params); destroy_bell_param_t(p); } } @@ -4815,8 +6241,8 @@ START_TEST(test_bell_k_at_zero) env.T = T; for( i=0; i < sizeof(knot)/sizeof(char *); i++) { params[0] = knot[i]; - p = string_create_bell_param_t(params); - fail_unless(bell_k(F, &env, p)==atof(knot[i]), + p = string_create_bell_param_t(params); + fail_unless(bell_k(F, &env, p)==safe_strtod(knot[i], __FUNCTION__), "bell_k(%g, %g, &{%s,%s}) = %g != %s", F, T, knot[i], dx, bell_k(F, &env, p), knot[i]); destroy_bell_param_t(p); @@ -4830,7 +6256,7 @@ START_TEST(test_bell_k_at_one) char *knot[] = {"1","2","3","4","5","6"}; char *dx="1"; char *params[] = {knot[0], dx}; - double F= k_B*T/atof(dx); + double F= k_B*T/safe_strtod(dx, __FUNCTION__); void *p = NULL; environment_t env; char param_string[80]; @@ -4838,25 +6264,25 @@ START_TEST(test_bell_k_at_one) env.T = T; for( i=0; i < sizeof(knot)/sizeof(char *); i++) { params[0] = knot[i]; - p = string_create_bell_param_t(params); - CHECK_ERR(1e-6, atof(knot[i])*exp(1.0), bell_k(F, &env, p)); - //fail_unless(bell_k(F, &env, p)==atof(knot[i])*exp(1.0), + p = string_create_bell_param_t(params); + CHECK_ERR(1e-6, safe_strtod(knot[i], __FUNCTION__)*exp(1.0), bell_k(F, &env, p)); + //fail_unless(bell_k(F, &env, p)==safe_strtod(knot[i], __FUNCTION__)*exp(1.0), // "bell_k(%g, %g, &{%s,%s}) = %g != %g", - // F, T, knot[i], dx, bell_k(F, &env, p), atof(knot[i])*exp(1.0)); + // F, T, knot[i], dx, bell_k(F, &env, p), safe_strtod(knot[i], __FUNCTION__)*exp(1.0)); destroy_bell_param_t(p); } } END_TEST -@ +@ <>= -@ +@ -<>= -@ +<>= +@ -<>= -@ +<>= +@ <>= <> @@ -4873,7 +6299,7 @@ START_TEST(test_something) fail_unless(F = k*x, NULL); } END_TEST -@ +@ \subsection{Utilities} @@ -4890,7 +6316,7 @@ or special mode, where the operation depends on the specific model selected. <> <> <> -@ +@ <>= int main(int argc, char **argv) @@ -4961,7 +6387,7 @@ int main(int argc, char **argv) (*model->destructor)(params); return 0; } -@ +@ <>= double multi_model_E(k_func_t *k, void *model_params, environment_t *env, double x) @@ -4970,23 +6396,24 @@ double multi_model_E(k_func_t *k, void *model_params, environment_t *env, double double E; if (k == kramers_integ_k) E = (*p->E)(x, p->E_params); - else + else E = kramers_E(0, env, model_params, x); return E; } -@ +@ <>= #include #include -#include /* strlen() */ -#include /* assert() */ +#include /* strlen() */ +#include /* assert() */ +#include /* errno, ERANGE */ #include "global.h" #include "parse.h" #include "string_eval.h" #include "k_model.h" -@ +@ <>= <> @@ -4998,13 +6425,14 @@ enum mode_t {M_K_OF_F, M_SPECIAL}; <> <> -@ +@ <>= +<> <> <> <> -@ +@ <>= void help(char *prog_name, @@ -5026,12 +6454,12 @@ void help(char *prog_name, k_models[k_model].params); printf("There are two output modes. In standard mode, k(F) is printed\n"); printf("For example:\n"); - printf(" #Force (N)\tk (% pop. per s)\n"); + printf(" #Force (N)\tk (%% pop. per s)\n"); printf(" 123.456\t7.89\n"); printf(" ...\n"); printf("In special mode, the output depends on the model.\n"); printf("For models defining an energy function E(x), that function is printed\n"); - printf(" #Position (m)\tE (J)\n"); + printf(" #Distance (m)\tE (J)\n"); printf(" 0.0012\t0.0034\n"); printf(" ...\n"); printf("-m\tChange output to standard mode\n"); @@ -5050,7 +6478,7 @@ void help(char *prog_name, printf("\t\tdefaults: %s\n", k_models[i].params); } } -@ +@ <>= void get_options(int argc, char **argv, environment_t *env, @@ -5065,23 +6493,23 @@ void get_options(int argc, char **argv, environment_t *env, extern char *optarg; extern int optind, optopt, opterr; - assert (argc > 0); + assert(argc > 0); /* setup defaults */ prog_name = argv[0]; - env->T = 300.0; /* K */ + env->T = 300.0; /* K */ *mode = M_K_OF_F; *flags = 0; *model = k_models; - *Fmax = 1e-9; + *Fmax = 1e-9; /* N */ *special_xmax = 1e-8; *special_xmin = 0.0; while ((c=getopt(argc, argv, options)) != -1) { switch(c) { - case 'T': env->T = atof(optarg); break; - case 'C': env->T = atof(optarg)+273.15; break; + case 'T': env->T = safe_strtod(optarg, "-T"); break; + case 'C': env->T = safe_strtod(optarg, "-C")+273.15; break; case 'k': k_model = index_k_model(n_k_models, k_models, optarg); *model = k_models+k_model; @@ -5089,12 +6517,12 @@ void get_options(int argc, char **argv, environment_t *env, case 'K': k_models[k_model].params = optarg; break; - case 'm': *mode = M_K_OF_F; break; - case 'M': *mode = M_SPECIAL; break; - case 'F': *Fmax = atof(optarg); break; - case 'x': *special_xmin = atof(optarg); break; - case 'X': *special_xmax = atof(optarg); break; - case 'V': *flags |= VFLAG; break; + case 'm': *mode = M_K_OF_F; break; + case 'M': *mode = M_SPECIAL; break; + case 'F': *Fmax = safe_strtod(optarg, "-F"); break; + case 'x': *special_xmin = safe_strtod(optarg, "-x"); break; + case 'X': *special_xmax = safe_strtod(optarg, "-X"); break; + case 'V': *flags |= VFLAG; break; case '?': fprintf(stderr, "unrecognized option '%c'\n", optopt); /* fall through to default case */ @@ -5105,7 +6533,7 @@ void get_options(int argc, char **argv, environment_t *env, } return; } -@ +@ \section{\LaTeX\ documentation} @@ -5117,7 +6545,7 @@ $(BUILD_DIR)/sawsim.tex : $(SRC_DIR)/sawsim.nw | $(BUILD_DIR) noweave -latex -index -delay $< > $@ $(BUILD_DIR)/sawsim.bib : $(SRC_DIR)/sawsim.bib | $(BUILD_DIR) cp -f $< $@ -@ +@ and compiled using <>= $(DOC_DIR)/sawsim.pdf : $(BUILD_DIR)/sawsim.tex $(BUILD_DIR)/sawsim.bib \ @@ -5125,6 +6553,8 @@ $(DOC_DIR)/sawsim.pdf : $(BUILD_DIR)/sawsim.tex $(BUILD_DIR)/sawsim.bib \ $(SHELL) -e -c "cd $(BUILD_DIR) && pdflatex sawsim" $(SHELL) -e -c "cd $(BUILD_DIR) && bibtex sawsim" $(SHELL) -e -c "cd $(BUILD_DIR) && pdflatex sawsim" + $(SHELL) -e -c "cd $(BUILD_DIR) && bibtex sawsim" + $(SHELL) -e -c "cd $(BUILD_DIR) && pdflatex sawsim" $(SHELL) -e -c "cd $(BUILD_DIR) && pdflatex sawsim" mv $(BUILD_DIR)/sawsim.pdf $@ @ @@ -5134,14 +6564,14 @@ the remaining two [[pdflatex]] passes insert the citations and finalize the vari [[bibtex]] and [[pdflatex]] produce quite a few intermediate files, so provide a means to clean them up. <>= -semi-clean_latex : +semi-clean_latex : rm -f $(BUILD_DIR)/sawsim.aux $(BUILD_DIR)/sawsim.bbl \ $(BUILD_DIR)/sawsim.blg $(BUILD_DIR)/sawsim.log \ - $(BUILD_DIR)/sawsim.out $(BUILD_DIR)/sawsim.tex \ - $(BUILD_DIR)/sawsim.bib + $(BUILD_DIR)/sawsim.out $(BUILD_DIR)/sawsim.toc \ + $(BUILD_DIR)/sawsim.tex $(BUILD_DIR)/sawsim.bib clean_latex : semi-clean_latex rm -f $(DOC_DIR)/sawsim.pdf -@ +@ \section{Makefile} @@ -5161,17 +6591,23 @@ Extract the makefile with The sed is needed because notangle replaces tabs with eight spaces, but [[make]] needs tabs. <>= +# Customize compilation +CC = gcc +CFLAGS = +LDFLAGS = + # Decide what directories to put things in SRC_DIR = src BUILD_DIR = build BIN_DIR = bin DOC_DIR = doc -# Note: Cannot use, for example, `./build', because make eats the `./' -# and then $(BUILD_DIR) doesn't match in $$(subst $(BUILD_DIR), ...) +# Note: Cannot use, for example, `./build', because make eats the `./' +# and then $(BUILD_DIR) doesn't match in $$(subst $(BUILD_DIR), ...) # Modules (X.c, X.h) defined in the noweb file -NW_SAWSIM_MODS = -CHECK_BINS = +NW_SAWSIM_MODS = +# Check binaries (check_*) defined in the noweb file +CHECK_BINS = # Modules defined outside the noweb file FREE_SAWSIM_MODS = interp tavl @@ -5196,7 +6632,11 @@ BINS = sawsim tension_model_utils k_model_utils sawsim_profile DOCS = sawsim.pdf # Define the major targets -all : ./Makefile $(BINS:%=$(BIN_DIR)/%) $(DOCS:%=$(DOC_DIR)/%) ; +all : ./Makefile all_bin all_doc + +.PHONY: all_bin all_doc +all_bin : $(BINS:%=$(BIN_DIR)/%) +all_doc : $(DOCS:%=$(DOC_DIR)/%) view : $(DOC_DIR)/sawsim.pdf xpdf $< & @@ -5214,23 +6654,23 @@ clean : $(CHECK_BINS:%=clean_%) $(SAWSIM_MODS:%=clean_%) \ $(BUILD_DIR)/interp.c $(BUILD_DIR)/interp.h \ $(BUILD_DIR)/tavl.c $(BUILD_DIR)/tavl.h \ $(BUILD_DIR)/global.h ./gmon.out - $(SHELL) -e -c "rmdir $(BUILD_DIR) $(BIN_DIR) $(DOC_DIR)" + $(SHELL) -e -c "rm -rf $(BUILD_DIR) $(DOC_DIR)" # Various builds of sawsim $(BIN_DIR)/sawsim : $(SAWSIM_SRC) | $(BIN_DIR) - gcc -g -o $@ $< $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) + $(CC) $(CFLAGS) $(LDFLAGS) -g -o $@ $< $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) $(BIN_DIR)/sawsim_static : $(SAWSIM_SRC) | $(BIN_DIR) - gcc -g -static -o $@ $< $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) + $(CC) $(CFLAGS) $(LDFLAGS) -g -static -o $@ $< $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) $(BIN_DIR)/sawsim_profile : $(SAWSIM_SRC) | $(BIN_DIR) - gcc -g -pg -o $@ $< $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) + $(CC) $(CFLAGS) $(LDFLAGS) -g -pg -o $@ $< $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) $(LIBS:%=-l%) # Create the directories $(BUILD_DIR) $(BIN_DIR) $(DOC_DIR) : mkdir $@ # Copy over the source external to sawsim -# Note: Cannot use, for example, `./build', because make eats the `./' -# and then $(BUILD_DIR) doesn't match in $$(subst $(BUILD_DIR), ...) +# Note: Cannot use, for example, `./build', because make eats the `./' +# and then $(BUILD_DIR) doesn't match in $$(subst $(BUILD_DIR), ...) .SECONDEXPANSION: $(FREE_SAWSIM_MODS:%=$(BUILD_DIR)/%.h) : $$(subst $(BUILD_DIR),$(SRC_DIR),$$@)\ | $(BUILD_DIR) @@ -5263,7 +6703,7 @@ $(BUILD_DIR)/check_sawsim.c : $(SRC_DIR)/sawsim.nw $(BIN_DIR)/check_sawsim : $(BUILD_DIR)/check_sawsim.c $(BUILD_DIR)/global.h \ $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) \ $(SAWSIM_MODS:%=$(BUILD_DIR)/%.h) | $(BIN_DIR) - gcc -g -o $@ $< $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) $(CHECK_LIBS:%=-l%) + $(CC) $(CFLAGS) $(LDFLAGS) -g -o $@ $< $(SAWSIM_MODS:%=$(BUILD_DIR)/%.c) $(CHECK_LIBS:%=-l%) clean_check_sawsim : rm -f $(BIN_DIR)/check_sawsim $(BUILD_DIR)/check_sawsim.c # ... and the modules @@ -5274,10 +6714,10 @@ $(CHECK_BINS:%=$(BIN_DIR)/%) : $$(subst $(BIN_DIR),$(BUILD_DIR),$$@).c \ $$(patsubst %,$(BUILD_DIR)/%.c,$$($$(subst $(BIN_DIR)/,,$$@_MODS)))\ $$(patsubst %,$(BUILD_DIR)/%.h,$$($$(subst $(BIN_DIR)/,,$$@_MODS)))\ $$(BUILD_DIR)/global.h | $(BIN_DIR) - gcc -g -o $@ $< $(@:$(BIN_DIR)/check_%=$(BUILD_DIR)/%.c) \ + $(CC) $(CFLAGS) $(LDFLAGS) -g -o $@ $< $(@:$(BIN_DIR)/check_%=$(BUILD_DIR)/%.c) \ $(patsubst %,$(BUILD_DIR)/%.c,$($(subst $(BIN_DIR)/,,$@_MODS)))\ $(CHECK_LIBS:%=-l%) -# todo: clean up the required modules to +# TODO: clean up the required modules too $(CHECK_BINS:%=clean_%) : rm -f $(@:clean_%=$(BIN_DIR)/%) $(@:clean_%=$(BUILD_DIR)/%.c) @@ -5292,7 +6732,7 @@ $(SAWSIM_MODS:%=clean_%) : Makefile : $(SRC_DIR)/sawsim.nw notangle -Rmakefile $< | sed 's/ /\t/' > $@ -@ +@ This is fairly self-explanatory. We compile a dynamically linked version ([[sawsim]]) and a statically linked version ([[sawsim_static]]). The static version is about 9 times as big, but @@ -5302,7 +6742,7 @@ better format for distributing to a cluster for parallel evaluation. \section{Math} \subsection{Hookean springs in series} -\label{app.math_hooke} +\label{sec.math_hooke} \begin{theorem} The effective spring constant for $n$ springs $k_i$ in series is given by @@ -5317,7 +6757,7 @@ $$ x_i &= \frac{k_j}{k_i} x_j &&\forall i,j \le n \\ x &= \sum_i x_i = x_1 \sum_i \frac{k_1}{k_i} \\ F &= k_1 x_1 = k_\text{eff} x \\ - k_\text{eff} &= k_1 \frac{x_1}{x} = \frac{k_1}{\sum_i \frac{k_1}{k_i}} + k_\text{eff} &= k_1 \frac{x_1}{x} = \frac{k_1}{\sum_i \frac{k_1}{k_i}} = \p({\sum_{i \le n}\frac{1}{k_i}})^{-1}. \end{align} \end{proof} @@ -5327,4 +6767,3 @@ $$ \bibliography{sawsim} \end{document} -