add missing DPPE acronym

[ool/lipid_simulation_formalism.git] / kinetic_formalism_competition.Rnw

diff --git a/kinetic_formalism_competition.Rnw b/kinetic_formalism_competition.Rnw
index 2a47cf45e9154e5c6ea02824029f3d195a925c38..2ceb8116b3df87f6f9adfed6c26dccc4e0671654 100644 (file)
--- a/kinetic_formalism_competition.Rnw
+++ b/kinetic_formalism_competition.Rnw
@@ -22,11 +22,12 @@
 \usepackage{array}
 \usepackage{dcolumn}
 \usepackage{booktabs}
 \usepackage{array}
 \usepackage{dcolumn}
 \usepackage{booktabs}

-\usepackage[noblocks]{authblk}

 \usepackage[backend=biber,natbib=true,hyperref=true,citestyle=numeric-comp,style=nature,autocite=inline]{biblatex}
 \addbibresource{references.bib}
 \usepackage[hyperfigures,bookmarks,colorlinks,citecolor=black,filecolor=black,linkcolor=black,urlcolor=black]{hyperref}
 \usepackage[backend=biber,natbib=true,hyperref=true,citestyle=numeric-comp,style=nature,autocite=inline]{biblatex}
 \addbibresource{references.bib}
 \usepackage[hyperfigures,bookmarks,colorlinks,citecolor=black,filecolor=black,linkcolor=black,urlcolor=black]{hyperref}

+\usepackage[noblocks,auth-sc]{authblk}

 \usepackage[capitalise]{cleveref}
 \usepackage[capitalise]{cleveref}

+\usepackage[markifdraft,raisemark=0.01\paperheight,draft]{gitinfo2}

 %\usepackage[sectionbib,sort&compress,numbers]{natbib}
 % \usepackage[nomargin,inline,draft]{fixme}
 %\usepackage[x11names,svgnames]{xcolor}
 %\usepackage[sectionbib,sort&compress,numbers]{natbib}
 % \usepackage[nomargin,inline,draft]{fixme}
 %\usepackage[x11names,svgnames]{xcolor}


@@ -51,11 +52,15 @@
 \clubpenalty = 10000
 \widowpenalty = 10000
 \pagestyle{fancy}
 \clubpenalty = 10000
 \widowpenalty = 10000
 \pagestyle{fancy}

-\author{}
-\title{Supplemental Material}
-\date{}
-% rubber: module bibtex
-% rubber: module natbib
+\title{Kinetic formalism for R-GARD Simulations}
+\author[1,2]{Don Armstrong}
+%\ead{don@donarmstrong.com}
+\author[2]{Raphael Zidovetzki}
+%\ead{raphael.zidovetzki@ucr.edu}
+\affil[1]{Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL, USA}
+\affil[2]{Cell Biology and Neuroscience, University of California at Riverside, Riverside, CA, USA}
+\affil[ ]{don@donarmstrong.com, raphael.zidovetzki@ucr.edu}
+%\date{}

 \onehalfspacing
 \begin{document}
 \maketitle
 \onehalfspacing
 \begin{document}
 \maketitle


@@ -63,7 +68,7 @@
 <<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")


@@ -151,24 +156,27 @@ 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.
-
-% \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 \\
-%     \bottomrule
-%   \end{tabular}
-%   \caption{Kinetic parameters and molecular properties of lipid types}
-%   \label{tab:kinetic_parameters_lipid_types}
-% \end{table}
+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 $\left(\mathrm{Å}^2\right)$ & 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}
+  \label{tab:kinetic_parameters_lipid_types}
+\end{table}

 
 %%% \DLA{I think we may just reduce these three sections; area, $k_\mathrm{f}$
 %%%   and $k_\mathrm{b}$ to \cref{tab:kinetic_parameters_lipid_types} with
 
 %%% \DLA{I think we may just reduce these three sections; area, $k_\mathrm{f}$
 %%%   and $k_\mathrm{b}$ to \cref{tab:kinetic_parameters_lipid_types} with


@@ -189,7 +197,7 @@ 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


@@ -210,7 +218,7 @@ exchange of the fluorescent label \ac{C6NBD} attached to different
 lipid species. Although the values of $k_\mathrm{b}$ are different for the labeled
 and unlabeled lipids, we assume that the ratios of the kinetics
 constants for the lipid types are the same. Furthermore we assume that
 lipid species. Although the values of $k_\mathrm{b}$ are different for the labeled
 and unlabeled lipids, we assume that the ratios of the kinetics
 constants for the lipid types are the same. Furthermore we assume that

-PG behaves similarly to \ac{PS}. Thus, we can determine the $k_\mathrm{b}$ of \ac{PE} and
+\ac{PG} behaves similarly to \ac{PS}. Thus, we can determine the $k_\mathrm{b}$ of \ac{PE} and

 \ac{PS} from the already known $k_\mathrm{b}$ of \ac{PC}. For \ac{C6NBD} labeled \ac{PC},
 \citet{Nichols1982:ret_amphiphile_transfer} obtained a $k_\mathrm{b}$ of
 $0.89$~$\mathrm{min}^{-1}$, \ac{PE} of $0.45$~$\mathrm{min}^{-1}$ and PG of
 \ac{PS} from the already known $k_\mathrm{b}$ of \ac{PC}. For \ac{C6NBD} labeled \ac{PC},
 \citet{Nichols1982:ret_amphiphile_transfer} obtained a $k_\mathrm{b}$ of
 $0.89$~$\mathrm{min}^{-1}$, \ac{PE} of $0.45$~$\mathrm{min}^{-1}$ and PG of


@@ -251,16 +259,16 @@ minutes, leading to a $k_{\mathrm{b}_\mathrm{CHOL}} = \frac{\log 2}{41\times
 
 Different lipids have different headgroup surface areas, which contributes to
 $\left[S_\mathrm{vesicle}\right]$. \citet{Smaby1997:pc_area_with_chol}
 
 Different lipids have different headgroup surface areas, which contributes to
 $\left[S_\mathrm{vesicle}\right]$. \citet{Smaby1997:pc_area_with_chol}

-measured the surface area of POPC with a Langmuir film balance, and
+measured the surface area of \ac{POPC} with a Langmuir film balance, and

 found it to be 63~Å$^2$ at $30$~$\frac{\mathrm{mN}}{\mathrm{m}}$.
 Molecular dynamic simulations found an area of 54 Å$^2$ for
 found it to be 63~Å$^2$ at $30$~$\frac{\mathrm{mN}}{\mathrm{m}}$.
 Molecular dynamic simulations found an area of 54 Å$^2$ for

-DPPS\citep{Cascales1996:mds_dpps_area,Pandit2002:mds_dpps}, which is
+\ac{DPPS}\citep{Cascales1996:mds_dpps_area,Pandit2002:mds_dpps}, which is

 in agreement with the experimental value of 56~Å$^2$ found using a
 Langmuir balance by \citet{Demel1987:ps_area}.
 \citet{Shaikh2002:pe_phase_sm_area} measured the area of \ac{SM} using a
 Langmuir film balance, and found it to be 61~Å$^2$. Using $^2$H NMR,
 \citet{Thurmond1991:area_of_pc_pe_2hnmr} found the area of
 in agreement with the experimental value of 56~Å$^2$ found using a
 Langmuir balance by \citet{Demel1987:ps_area}.
 \citet{Shaikh2002:pe_phase_sm_area} measured the area of \ac{SM} using a
 Langmuir film balance, and found it to be 61~Å$^2$. Using $^2$H NMR,
 \citet{Thurmond1991:area_of_pc_pe_2hnmr} found the area of

-DPPE-d$_{62}$ to be 55.4 Å$^2$. \citet{Robinson1995:mds_chol_area}
+\ac{DPPE}-d$_{62}$ to be 55.4 Å$^2$. \citet{Robinson1995:mds_chol_area}

 found an area for \ac{CHOL} of 38~Å$^2$ using molecular dynamic
 simulations.
 
 found an area for \ac{CHOL} of 38~Å$^2$ using molecular dynamic
 simulations.
 


@@ -1068,11 +1076,11 @@ 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


@@ -1091,11 +1099,11 @@ The most common $\left<\log cu_\mathrm{vesicle}\right>$ is around
 $-0.013$, which leads to a range of $\Delta \Delta G^\ddagger$ from
 $\Sexpr{format(digits=3,to.kcal(7^(1-1/(20*(-0.013-log(0.8))^2+1))))}
 \frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with curvature 0.8 to
 $-0.013$, which leads to a range of $\Delta \Delta G^\ddagger$ from
 $\Sexpr{format(digits=3,to.kcal(7^(1-1/(20*(-0.013-log(0.8))^2+1))))}
 \frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with curvature 0.8 to

+to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with curvature
+near 1

 $\Sexpr{format(digits=3,to.kcal(7^(1-1/(20*(-0.013-log(1.3))^2+1))))}\frac{\mathrm{kcal}}{\mathrm{mol}}$
 $\Sexpr{format(digits=3,to.kcal(7^(1-1/(20*(-0.013-log(1.3))^2+1))))}\frac{\mathrm{kcal}}{\mathrm{mol}}$

-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}
+for monomers with curvature 1.3. The full range of values possible for
+$cu_\mathrm{b}$ are shown in \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?}


@@ -1180,11 +1188,12 @@ 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
-$l_\mathrm{b}$ are shown in \cref{fig:lb_graph}
+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
 % energies of transfer from self-micelles to water increase by 2.2 and
 
 % (for methods? From McLean84LIB: The activation free energies and free
 % energies of transfer from self-micelles to water increase by 2.2 and


@@ -1384,15 +1393,15 @@ 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 +1412,10 @@ 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 +1463,7 @@ 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)


@@ -1564,6 +1574,11 @@ to produce later output.
 % silhouette~\citep{Rousseeuw1987:silhouettes} is chosen as the ideal
 % clustering~\citep{Shenhav2005:pgard}.
 
 % silhouette~\citep{Rousseeuw1987:silhouettes} is chosen as the ideal
 % clustering~\citep{Shenhav2005:pgard}.
 

+\section*{Formalism}
+
+The most current revision of this formalism is available at
+\url{https://git.donarmstrong.com/ool/lipid_simulation_formalism.git}.
+This document is  \gitMarkPref • \gitMark.

 
 %\bibliographystyle{unsrtnat}
 %\bibliography{references.bib}
 
 %\bibliographystyle{unsrtnat}
 %\bibliography{references.bib}