From ac8372fb657e6caba5ce032b06ab55d89fbddac6 Mon Sep 17 00:00:00 2001 From: Don Armstrong Date: Mon, 20 Mar 2017 19:57:05 -0700 Subject: [PATCH] add the rest of raphael's changes --- kinetic_formalism_competition.Rnw | 55 +++++++++++++++++-------------- 1 file changed, 30 insertions(+), 25 deletions(-) diff --git a/kinetic_formalism_competition.Rnw b/kinetic_formalism_competition.Rnw index c008d79..e2a375c 100644 --- a/kinetic_formalism_competition.Rnw +++ b/kinetic_formalism_competition.Rnw @@ -63,7 +63,7 @@ <>= opts_chunk$set(dev="CairoPDF",out.width="\\columnwidth",out.height="0.7\\textheight",out.extra="keepaspectratio") opts_chunk$set(cache=TRUE, autodep=TRUE) -options(scipen = -2, digits = 1) +options(scipen = -1, digits = 2) library("lattice") library("grid") library("Hmisc") @@ -151,19 +151,22 @@ kf <- (as.numeric(kf.prime)*10^-3)/(63e-20*6.022e23) @ Each of the 5 lipid types has different kinetic parameters; where -available, these were taken from literature. +available, these were taken from literature (\cref{tab:kinetic_parameters_lipid_types}). \begin{table} \centering \begin{tabular}{c c c c c c c c} \toprule - Type & $k_\mathrm{f}$ $\left(\frac{\mathrm{m}}{\mathrm{s}}\right)$ & $k'_\mathrm{f}$ $\left(\frac{1}{\mathrm{M} \mathrm{s}}\right)$ & $k_\mathrm{b}$ $\left(\mathrm{s}^{-1}\right)$ & Area $\left({Å}^2\right)$ & Charge & $\mathrm{CF}1$ & Curvature \\ - \midrule - PC & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[1]))}$ & $3.7 \times 10^6$ & $2 \times 10^{-5}$ & 63 & 0 & 2 & 0.8 \\ - PS & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[2]))}$ & $3.7 \times 10^6$ & $1.25\times 10^{-5}$ & 54 & -1 & 0 & 1 \\ - CHOL & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[3]))}$ & $5.1 \times 10^7$ & $2.8 \times 10^{-4}$ & 38 & 0 & -1 & 1.21 \\ - SM & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[4]))}$ & $3.7 \times 10^6$ & $3.1 \times 10^{-3}$ & 61 & 0 & 3 & 0.8 \\ - PE & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[5]))}$ & $2.3 \times 10^6$ & $1 \times 10^{-5}$ & 55 & 0 & 0 & 1.33 \\ + Type & $k_\mathrm{f}$ $\left(\frac{\mathrm{m}}{\mathrm{s}}\right)$ + & $k'_\mathrm{f}$ $\left(\frac{1}{\mathrm{M} \mathrm{s}}\right)$ + & $k_\mathrm{b}$ $\left(\mathrm{s}^{-1}\right)$ + & Area $\left({Å}^2\right)$ & Charge & $\mathrm{CF}1$ & Curvature \\ + \midrule + PC & $\Sexpr{kf[1]}$ & $3.7 \times 10^6$ & $2 \times 10^{-5}$ & 63 & 0 & 2 & 0.8 \\ + PS & $\Sexpr{kf[2]}$ & $3.7 \times 10^6$ & $1.25\times 10^{-5}$ & 54 & -1 & 0 & 1 \\ + CHOL & $\Sexpr{kf[3]}$ & $5.1 \times 10^7$ & $2.8 \times 10^{-4}$ & 38 & 0 & -1 & 1.21 \\ + SM & $\Sexpr{kf[4]}$ & $3.7 \times 10^6$ & $3.1 \times 10^{-3}$ & 61 & 0 & 3 & 0.8 \\ + PE & $\Sexpr{kf[5]}$ & $2.3 \times 10^6$ & $1 \times 10^{-5}$ & 55 & 0 & 0 & 1.33 \\ \bottomrule \end{tabular} \caption{Kinetic parameters and molecular properties of lipid types} @@ -189,7 +192,7 @@ however, \citet{Estronca2007:dhe_kinetics} measured the transfer of $\frac{1}{\mathrm{M} \mathrm{s}}$. We assume that this value is close to that of \ac{CHOL}, and use it for $k_{\mathrm{f}_\mathrm{\ac{CHOL}}}$. In the case of \ac{PE}, \citet{Abreu2004:kinetics_ld_lo} measured the association of -\ac{NBDDMPE} with \ac{POPC} \acp{LUV} found a value for $k_\mathrm{f}$ of $2.3 \times 10^{6}$~% +\ac{NBDDMPE} with \ac{POPC} \acp{LUV} and found a value for $k_\mathrm{f}$ of $2.3 \times 10^{6}$~% $\frac{1}{\mathrm{M} \mathrm{s}}$. These three authors used a slightly different kinetic formalism ($\frac{d\left[A_v\right]}{dt} = k'_\mathrm{f}[A_m][L_v] - k_\mathrm{b}[A_v]$), so we correct their values of $k_\mathrm{f}$ by @@ -1068,11 +1071,11 @@ popViewport(2) The less a monomer's intrinsic curvature matches the average curvature of the vesicle in which it is in, the greater its rate of efflux. If -the difference is 0, $cu_\mathrm{f}$ needs to be one. To map negative and +the curvatures match exactly, $cu_\mathrm{f}$ needs to be one. To map negative and positive curvature to the same range, we also need take the logarithm. -Positive and negative curvature lipids cancel each other out, -resulting in an average curvature of 0; the average of the log also -has this property. Increasing mismatches in curvature increase the +Positive ($cu > 1$) and negative ($0 < cu < 1$) curvature lipids cancel each other out, +resulting in an average curvature of 1; the average of the log also +has this property (average curvature of 0). Increasing mismatches in curvature increase the rate of efflux, but asymptotically. An equation which satisfies these criteria has the form $cu_\mathrm{f} = a^{1-\left(b\left( \left< \log cu_\mathrm{vesicle} \right> -\log @@ -1095,7 +1098,7 @@ $\Sexpr{format(digits=3,to.kcal(7^(1-1/(20*(-0.013-log(1.3))^2+1))))}\frac{\math for monomers with curvature 1.3 to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with curvature near 1. The full range of values possible for $cu_\mathrm{b}$ are shown in -\cref{fig:cub_graph} +\cref{fig:cub_graph}. % \RZ{What about the opposite curvatures that actually do fit to each % other?} @@ -1180,10 +1183,11 @@ will also show an increase in their dissociation constant. The most common $\left$ is around $17.75$, which leads to a range of $\Delta \Delta G^\ddagger$ from $\Sexpr{format(digits=3,to.kcal(3.2^abs(12-17.75)))} -\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with length 12 to +\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with length 12 +to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$ +for monomers with length near 18 to $\Sexpr{format(digits=3,to.kcal(3.2^abs(24-17.75)))}\frac{\mathrm{kcal}}{\mathrm{mol}}$ -for monomers with length 24 to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$ -for monomers with length near 18. The full range of possible values of +for monomers with length 24. The full range of possible values of $l_\mathrm{b}$ are shown in \cref{fig:lb_graph} % (for methods? From McLean84LIB: The activation free energies and free @@ -1384,15 +1388,15 @@ small number of components which are devoid of \ac{CHOL}. Once the components of the environment have been selected, their concentrations are determined. In experiments where the environmental concentration is the same across all lipid components, the -concentration is set to $10^{-10}\mathrm{M}$. In other cases, the +concentration is set to $10^{-10}$~M. In other cases, the environmental concentration is set to a random number from a gamma distribution with shape parameter 2 and an average of -$10^{-10}\mathrm{M}$. The base concentration ($10^{-10}\mathrm{M}$) +$10^{-10}$~M. The base concentration ($10^{-10}$~M) can also be altered at the initialization of the experiment to specific values for specific lipid types or components. The environment is a volume which is the maximum number of vesicles -from a single simulation (4096) times the maximum size of the vesicle +from a single simulation (4096) times the size of the vesicle (usually 10000) divided by Avagadro's number divided by the total environmental lipid concentration, or usually \Sexpr{4096*10000/6.022E23/141E-10}~L. @@ -1403,9 +1407,10 @@ Initial vesicles are seeded by selecting lipid molecules from the environment until the vesicle reaches a specific starting size. The vesicle starting size has gamma distribution with shape parameter 2 and a mean of the per-simulation specified starting size, with a -minimum of 5 lipid molecules. Lipid molecules are then selected to be -added to the lipid membrane according to four different methods. In -the constant method, molecules are added in direct proportion to their +minimum of 5 lipid molecules, or can be specified to have a precise +number of molecules. Lipid molecules are then selected to be added to +the lipid membrane according to four different methods. In the +constant method, molecules are added in direct proportion to their concentration in the environment. The uniform method adds molecules in proportion to their concentration in the environment scaled by a uniform random value, whereas the random method adds molecules in @@ -1453,7 +1458,7 @@ Determining the number of molecules to add to the lipid membrane vesicle $S_\mathrm{vesicle}$ (see \cref{sec:ves_prop}), the time interval $dt$ during which lipids are added, the base $k_{\mathrm{f}i}$, and the concentration of the monomer in the environment -$\left[C_{i\mathrm{vesicle}}\right]$ (see \cref{eq:state}). +$\left[C_{i\mathrm{monomer}}\right]$ (see \cref{eq:state}). $k_{\mathrm{f}i\mathrm{adj}}$ is calculated (see \cref{eq:kf_adj}) based on the vesicle properties and their hypothesized effect on the rate (in as many cases as possible, experimentally based) -- 2.39.2