\hspace{.25in}%
\subfloat[][]{\label{fig:piezo-schematic}
\asyinclude{figures/schematic/piezo}}
- \caption{\subref{fig:afm-schematic} Operating principle for an
- Atomic Force Microscope\index{AFM}. A sharp tip integrated at
- the end of a cantilever interacts with the sample. Cantilever
- bending is measured by a laser reflected off the cantilever and
- incident on a position sensitive photodetector.
- \subref{fig:piezo-schematic} Schematic of a tubular
+ \caption{\protect\subref{fig:afm-schematic} Operating principle
+ for an Atomic Force Microscope\index{AFM}. A sharp tip
+ integrated at the end of a cantilever interacts with the sample.
+ Cantilever bending is measured by a laser reflected off the
+ cantilever and incident on a position sensitive photodetector.
+ \protect\subref{fig:piezo-schematic} Schematic of a tubular
piezoelectric actuator. In our AFM, the substrate is mounted on
the top end of the tube, and the bottom end is fixed to the
microscope body. This allows the piezo to control the relative
\subfloat[][]{\asyinclude{figures/expt-sawtooth/expt-sawtooth}%
\label{fig:expt-sawtooth}}
% Possibly use carrion-vazquez00 figure 2 to show scale of afm tip
- \caption{\subref{fig:unfolding-schematic} Schematic of the
+ \caption{\protect\subref{fig:unfolding-schematic} Schematic of the
experimental setup for mechanical unfolding of proteins using an
AFM (not to scale). An experiment starts with the tip in contact
with the substrate surface, which is then moved away from the tip
at a constant speed. $x_t$ is the distance traveled by the
substrate, $x_c$ is the cantilever deflection, $x_u$ is the
extension of the unfolded polymer, and $x_f=x_{f1}+x_{f2}$ is the
- extension of the folded polymer. \subref{fig:expt-sawtooth} An
- experimental force curve from stretching a ubiquitin polymer with
- the rising parts of the peaks fitted to the WLC\index{WLC} model
+ extension of the folded polymer.
+ \protect\subref{fig:expt-sawtooth} An experimental force curve
+ from stretching a ubiquitin polymer with the rising parts of the
+ peaks fitted to the WLC\index{WLC} model
(\cref{sec:sawsim:tension:wlc})\citep{chyan04}. The pulling speed
used was $1\U{$\mu$m/s}$. The irregular features at the beginning
of the curve are due to nonspecific interactions between the tip
% \hspace{.25in}%
\subfloat[][]{\includegraphics[width=2in]{figures/schematic/dill97-fig4}%
\label{fig:folding:landscape}}
- \caption{\subref{fig:folding:pathway} A ``double T'' example of the
- pathway model of protein folding, in which the protein proceeds
- from the native state $N$ to the unfolded state $U$ via a series
- of metastable transition states $I_1$ and $I_2$ with two ``dead
- end'' states $I_1^X$ and $I_2^X$. Adapted from \citet{bedard08}.
- \subref{fig:folding:landscape} The landscape model of protein
- folding, in which the protein diffuses through a multi-dimensional
- free energy landscape. Separate folding attempts may take many
- distinct routes through this landscape on the way to the folded
- state. Reproduced from \citet{dill97}.
- \label{fig:folding}}
+ \caption{\protect\subref{fig:folding:pathway} A ``double T'' example
+ of the pathway model of protein folding, in which the protein
+ proceeds from the native state $N$ to the unfolded state $U$ via a
+ series of metastable transition states $I_1$ and $I_2$ with two
+ ``dead end'' states $I_1^X$ and $I_2^X$. Adapted from
+ \citet{bedard08}.
+ \protect\subref{fig:folding:landscape} The landscape model of
+ protein folding, in which the protein diffuses through a
+ multi-dimensional free energy landscape. Separate folding
+ attempts may take many distinct routes through this landscape on
+ the way to the folded state. Reproduced from
+ \citet{dill97}.\label{fig:folding}}
\end{center}
\end{figure}
$k_{u0}=3.3\E{-4}\U{s$^{-1}$}$, $\Delta x=0.35\U{nm}$. \\
\bottomrule
\end{tabular}}
- \caption{\subref{tab:sawsim:domains} Model for
+ \caption{\protect\subref{tab:sawsim:domains} Model for
I27\textsubscript{8} domain states and
- \subref{tab:sawsim:transitions} transitions between them
+ \protect\subref{tab:sawsim:transitions} transitions between them
(compare with \cref{fig:sawsim:domains}). The models and
parameters are those given by \citet{carrion-vazquez99b}.
\citet{carrion-vazquez99b} don't list their cantilever spring
\subfloat[][]{\asyinclude{figures/sim-hist/sim-hist}%
\label{fig:sawsim:sim-hist}%
}
- \caption{\subref{fig:sawsim:sim-sawtooth} Three simulated force
+ \caption{\protect\subref{fig:sawsim:sim-sawtooth} Three simulated force
curves from pulling a polymer of eight identical protein
molecules. The simulation was carried out using the parameters:
pulling speed $v=1\U{$\mu$m/s}$, cantilever spring constant
In experiments, detachments have been observed to occur at a
variety of forces. For clarity, the green and blue curves are
offset by $200$ and $400\U{pN}$ respectively.
- \subref{fig:sawsim:sim-hist} The distribution of the unfolding
+ \protect\subref{fig:sawsim:sim-hist} The distribution of the unfolding
forces from $400$ simulated force curves ($3200$ data points)
- such as those shown in \subref{fig:sawsim:sim-sawtooth}. The
+ such as those shown in \protect\subref{fig:sawsim:sim-sawtooth}. The
frequency is normalized by the total number of points, \ie, the
height of each bin is equal to the number of data points in that
bin divided by the total number of data
\subfloat[][]{\asyinclude{figures/v-dep/v-dep-sd}%
\label{fig:sawsim:width-v-dep}%
}
- \caption{\subref{fig:sawsim:v-dep} The dependence of the unfolding
- forces on the pulling speed for three different model protein
- molecules characterized by the parameters $k_{u0}$ and $\Delta
- x_u$. The polymer length is eight molecules, and each symbol is
- the average of $3200$ data points.
- \subref{fig:sawsim:width-v-dep} The dependence of standard
+ \caption{\protect\subref{fig:sawsim:v-dep} The dependence of the
+ unfolding forces on the pulling speed for three different model
+ protein molecules characterized by the parameters $k_{u0}$ and
+ $\Delta x_u$. The polymer length is eight molecules, and each
+ symbol is the average of $3200$ data points.
+ \protect\subref{fig:sawsim:width-v-dep} The dependence of standard
deviation of the unfolding force distribution on the pulling speed
- for the simulation data shown in \subref{fig:sawsim:v-dep}, using
- the same symbols. The insets show the force distribution
- histograms for the three proteins at the pulling speed of
- $1\U{$\mu$m/s}$. The left, middle and right histograms are for
- the proteins represented by the top, middle, and bottom lines in
- \subref{fig:sawsim:v-dep},
+ for the simulation data shown in
+ \protect\subref{fig:sawsim:v-dep}, using the same symbols. The
+ insets show the force distribution histograms for the three
+ proteins at the pulling speed of $1\U{$\mu$m/s}$. The left,
+ middle and right histograms are for the proteins represented by
+ the top, middle, and bottom lines in
+ \protect\subref{fig:sawsim:v-dep},
respectively.\label{fig:sawsim:all-v-dep}}
\end{center}
\end{figure}
edge [bend left] node [above] {$k_2$} (D)
(D) edge [bend left] node [below] {$k_2'$} (C);
\end{tikzpicture}}
- \caption{\subref{fig:sawsim: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
+ \caption{\protect\subref{fig:sawsim: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. Compare with
\cref{fig:unfolding-schematic}.
- \subref{fig:sawsim:domain-states} Each domain exists in a
- discrete state. At each timestep, it may transition into
+ \protect\subref{fig:sawsim: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.\label{fig:sawsim:domains}}
\hspace{.25in}%
\subfloat[][]{\asyinclude{figures/schematic/wlc-extension}%
\label{fig:wlc-extension}}
- \caption{\subref{fig:wlc-model} The wormlike chain models a
- polymer as an elastic rod with persistence length $p$ and
- contour length $L$. \subref{fig:wlc-extension} Force
- vs.~extension for a WLC using Bustamante's interpolation
- formula.\label{fig:wlc}}
+ \caption{\protect\subref{fig:wlc-model} The wormlike chain models
+ a polymer as an elastic rod with persistence length $p$ and
+ contour length $L$.
+ \protect\subref{fig:wlc-extension} Force vs.~extension for a WLC
+ using Bustamante's interpolation formula.\label{fig:wlc}}
\end{center}
\end{figure}
\hspace{.25in}%
\subfloat[][]{\asyinclude{figures/schematic/fjc-extension}%
\label{fig:fjc-extension}}
- \caption{\subref{fig:fjc-model} The freely-jointed chain models
- the polymer as a series of $N$ rigid links, each of length $l$,
- which are free to rotate about their joints. Each polymer state
- is a random walk, and the density of states for a given
- end-to-end distance is determined by the number of random walks
- that have such an end-to-end distance.
- \subref{fig:fjc-extension} Force vs.~extension for a
+ \caption{\protect\subref{fig:fjc-model} The freely-jointed chain
+ models the polymer as a series of $N$ rigid links, each of
+ length $l$, which are free to rotate about their joints. Each
+ polymer state is a random walk, and the density of states for a
+ given end-to-end distance is determined by the number of random
+ walks that have such an end-to-end distance.
+ \protect\subref{fig:fjc-extension} Force vs.~extension for a
hundred-segment FJC. The WLC extension curve (with $p=l$) is
shown as a dashed line for comparison.\label{fig:fjc}}
\end{center}
% \hspace{.25in}%
\subfloat[][]{\asyinclude{figures/schematic/kramers-integrand}%
\label{fig:kramers:integrand}}
- \caption{\subref{fig:landscape} Energy landscape schematic for
- Kramers integration (compare with \cref{fig:bell-landscape}).
- \subref{fig:kramers:integrand} A map of the magnitude of
+ \caption{\protect\subref{fig:landscape} Energy landscape schematic
+ for Kramers integration (compare with
+ \cref{fig:bell-landscape}).
+ \protect\subref{fig:kramers:integrand} A map of the magnitude of
Kramers' integrand, with black lines tracing the integration
region. The bulk of the contribution to the integral comes from
the bump in the upper left, with $x$ near the boundary and $x'$
projects / thesis.git / commitdiff