From 96f0b86f1dd480e0972b73db6122728a9a4e9f7e Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Mon, 20 May 2013 09:30:32 -0400 Subject: [PATCH] sawsim/discussion.tex: Normalize to k_u and U for eq:kramers-saddle Also add U_b(F), l_b, \rho_b, and l_{ts} to the nomenclature. Thanks Mom! --- src/sawsim/discussion.tex | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) diff --git a/src/sawsim/discussion.tex b/src/sawsim/discussion.tex index 713f1fc..053bce9 100644 --- a/src/sawsim/discussion.tex +++ b/src/sawsim/discussion.tex @@ -799,9 +799,10 @@ constant loading does indeed follow the Gumbel distribution. For the saddle-point approximation for Kramers' model for unfolding (\citet{evans97} Eqn.~3, \citet{hanggi90} Eqn. 4.56c, \citet{vanKampen07} Eqn. XIII.2.2). \begin{equation} - \kappa = \frac{D}{l_b l_{ts}} \cdot \exp\p({\frac{-E_b(F)}{k_B T}}) \;, + k_u = \frac{D}{l_b l_{ts}} \cdot \exp\p({\frac{-U_b(F)}{k_B T}}) \;, + \label{eq:kramers-saddle} \end{equation} -where $E_b(F)$ is the barrier height under an external force $F$, +where $U_b(F)$ is the barrier height under an external force $F$, $D$ is the diffusion constant of the protein conformation along the reaction coordinate, $l_b$ is the characteristic length of the bound state $l_b \equiv 1/\rho_b$, $\rho_b$ is the density of states in the bound state, and @@ -809,6 +810,15 @@ $l_{ts}$ is the characteristic length of the transition state \begin{equation} l_{ts} = TODO \end{equation} +% +\nomenclature{$U_b(F)$}{The barrier energy as a function of force + (\cref{eq:kramers-saddle}).} +\nomenclature{$l_b$}{The charicteristic length of the bound state $l_b + \equiv 1/\rho_b$ (\cref{eq:kramers-saddle}).} +\nomenclature{$\rho_b$}{The density of states in the bound state + (\cref{eq:kramers-saddle}).} +\nomenclature{$l_{ts}$}{The charicteristic length of the transition + state (\cref{eq:kramers-saddle}).} \citet{evans97} solved this unfolding rate for both inverse power law potentials and cusp potentials. -- 2.26.2