add the rest of raphael's changes

diff --git a/kinetic_formalism_competition.Rnw b/kinetic_formalism_competition.Rnw
index c008d79bf1e1fe70456f9f5ad7444cab7be63c39..e2a375c65b64ebde0bae514aa9d912f9c965f49d 100644 (file)
--- a/kinetic_formalism_competition.Rnw
+++ b/kinetic_formalism_competition.Rnw
@@ -63,7 +63,7 @@
 <<load.libraries,echo=FALSE,results="hide",warning=FALSE,message=FALSE,error=FALSE,cache=FALSE>>=
 opts_chunk$set(dev="CairoPDF",out.width="\\columnwidth",out.height="0.7\\textheight",out.extra="keepaspectratio")
 opts_chunk$set(cache=TRUE, autodep=TRUE)
 <<load.libraries,echo=FALSE,results="hide",warning=FALSE,message=FALSE,error=FALSE,cache=FALSE>>=
 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")
 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
 @ 
 
 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
 
 \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}
     \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
 $\frac{1}{\mathrm{M} \mathrm{s}}$. 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
 $\frac{1}{\mathrm{M} \mathrm{s}}$. 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 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 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
 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
 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?}
 
 % \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 $\left<l_\mathrm{vesicle}\right>$ 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)))}
 The most common $\left<l_\mathrm{vesicle}\right>$ 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

 $\Sexpr{format(digits=3,to.kcal(3.2^abs(24-17.75)))}\frac{\mathrm{kcal}}{\mathrm{mol}}$
 $\Sexpr{format(digits=3,to.kcal(3.2^abs(24-17.75)))}\frac{\mathrm{kcal}}{\mathrm{mol}}$

-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
 $l_\mathrm{b}$ 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
 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
 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
 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.
 (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
 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
 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
 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)
 $k_{\mathrm{f}i\mathrm{adj}}$ 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)