add kinetic formalisms

git-svn-id: svn+ssh://hemlock.ucr.edu/srv/svn/misc/trunk/origins_of_life@492 25fa0111-c432-4dab-af88-9f31a2f6ac42

diff --git a/Makefile b/Makefile
new file mode 100644 (file)
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--- /dev/null
+++ b/Makefile
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+#!/bin/make
+
+all: kinetic_formalism.pdf
+
+R=R
+
+%.pdf: %.svg
+       inkscape -A $@ $<
+       pdfcrop $@
+       mv $(dir $@)*-crop.pdf $@
+
+%.png: %.svg
+       inkscape -e $@ -d 300 $<
+
+%.pdf: %.png
+       bmeps -lpdf -olevel=1.4 $< $@
+
+%.tex: %.Rnw
+       $(R) CMD Sweave $<
+
+%.pdf: %.tex $(wildcard *.bib) $(wildcard *.tex)
+       rubber -fd $<
+
+clean: 
+       rubber -d --clean *.tex
+       rm -f *.tmp
+
+.PHONY: clean all
+
+.DELETE_ON_ERROR: %.tex
\ No newline at end of file

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
new file mode 100644 (file)
index 0000000..d7d8bfe
--- /dev/null
+++ b/kinetic_formalism.Rnw
@@ -0,0 +1,266 @@
+\documentclass[english,12pt]{article}
+\usepackage{fancyhdr}
+%\usepackage[pdftex]{graphicx}
+\usepackage{graphicx}
+\usepackage[bf]{caption2}
+\usepackage{rotating}
+\usepackage{multirow}
+\usepackage{textcomp}
+\usepackage{mathrsfs}
+\usepackage{amssymb}
+\usepackage{setspace}
+\usepackage{txfonts}
+\usepackage[light,all]{draftcopy}
+\usepackage{fancyref}
+\usepackage[hyperfigures,backref,bookmarks,colorlinks]{hyperref}
+\usepackage[sectionbib,sort&compress,square,numbers]{natbib}
+\usepackage[margin,inline,draft]{fixme}
+\usepackage[x11names,svgnames]{xcolor}
+\usepackage{texshade}
+\newenvironment{narrow}[2]{%
+  \begin{list}{}{%
+      \setlength{\topsep}{0pt}%
+      \setlength{\leftmargin}{#1}%
+      \setlength{\rightmargin}{#2}%
+      \setlength{\listparindent}{\parindent}%
+      \setlength{\itemindent}{\parindent}%
+      \setlength{\parsep}{\parskip}}%
+  \item[]}{\end{list}}
+\newenvironment{paperquote}{%
+  \begin{quote}%
+     \it
+  }%
+  {\end{quote}}
+\renewcommand{\textfraction}{0.15}
+\renewcommand{\topfraction}{0.85}
+\renewcommand{\bottomfraction}{0.65}
+\renewcommand{\floatpagefraction}{0.60}
+%\renewcommand{\baselinestretch}{1.8}
+\newenvironment{enumerate*}%
+  {\begin{enumerate}%
+    \setlength{\itemsep}{0pt}%
+    \setlength{\parskip}{0pt}}%
+  {\end{enumerate}}
+\newenvironment{itemize*}%
+  {\begin{itemize}%
+    \setlength{\itemsep}{0pt}%
+    \setlength{\parskip}{0pt}}%
+  {\end{itemize}}
+\oddsidemargin 0.0in 
+\textwidth 6.5in
+\raggedbottom
+\clubpenalty = 10000
+\widowpenalty = 10000
+\pagestyle{fancy}
+\author{Don Armstrong}
+\title{OOL Kinetic Formalisms}
+%\date{}
+\onehalfspacing
+\begin{document}
+%\maketitle
+
+<<results=hide,echo=FALSE>>=
+require(lattice)
+require(grid)
+@ 
+
+\section{State Equation}
+% double check this with the bits in the paper
+\begin{equation}
+  \frac{d C^{j}_{i_\mathrm{ves}}}{dt} = k_{fi}k_{fi\mathrm{adj}}\left[C^j_{i_\mathrm{monomer}}\right] -
+  k_{bi}k_{bi\mathrm{adj}}C^j_{i_\mathrm{ves}}
+  \label{eq:state}
+\end{equation}
+
+\subsection{Forward adjustments ($k_{fi\mathrm{adj}}$)}
+
+\begin{equation}
+  k_{fi\mathrm{adj}} = un_f \cdot ch_f \cdot cu_f \cdot l_f \cdot CF1_f
+  \label{eq:kf_adj}
+\end{equation}
+
+\newpage
+\subsubsection{Unsaturation Forward}
+\begin{equation}
+  un_f = 2^{\mathrm{stdev}\left(un_\mathrm{ves}\right)}
+  \label{eq:unsaturation_forward}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=5,height=5>>=
+curve(2^x,from=0,to=sd(c(0,4)),
+      main="Unsaturation forward",
+      xlab="Standard Deviation of Unsaturation of Vesicle",
+      ylab="Unsaturation Forward Adjustment")
+@ 
+
+\newpage
+\subsubsection{Charge Forward}
+\begin{equation}
+  ch_f = 60^{-\left<{ch}_v\right> {ch}_m}
+  \label{eq:charge_forward}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+x <- seq(-1,0,length.out=20)
+y <- seq(-1,0,length.out=20)
+grid <- expand.grid(x=x,y=y)
+grid$z <- as.vector(60^(-outer(x,y)))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab="Average Vesicle Charge",
+          ylab="Component Charge",
+          zlab="Charge Forward"))
+rm(x,y,grid)
+@ 
+
+\newpage
+\subsubsection{Curvature Forward}
+\begin{equation}
+  cu_f = 10^{\mathrm{stdev}\left|\log cu_\mathrm{vesicle}\right|}
+  \label{eq:curvature_forward}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+curve(10^x,from=0,to=sd(c(0.8,1.33)),
+      main="Curvature forward",
+      xlab="Standard Deviation of Curvature of Vesicle",
+      ylab="Curvature Forward Adjustment")
+@ 
+
+\newpage
+\subsubsection{Length Forward}
+\begin{equation}
+  l_f = 3^{\mathrm{stdev}\left|\log l_\mathrm{ves}\right|}
+  \label{eq:length_forward}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+curve(3^x,from=0,to=sd(c(12,24)),
+      main="Length forward",
+      xlab="Standard Deviation of Length of Vesicle",
+      ylab="Length Forward Adjustment")
+@ 
+
+\subsubsection{Complex Formation}
+\begin{equation}
+  CF1_f=1
+  \label{eq:complex_formation_forward}
+\end{equation}
+
+\subsection{Backward adjustments ($k_{bi\mathrm{adj}}$)}
+
+\begin{equation}
+  k_{bi\mathrm{adj}} = un_b \cdot ch_b \cdot cu_b \cdot l_b \cdot CF1_b
+  \label{eq:kf_adj}
+\end{equation}
+
+\newpage
+\subsubsection{Unsaturation Backward}
+\begin{equation}
+  un_b = 10^{\left|3.5^{-\left<un_\mathrm{ves}\right>}-3.5^{-\left<un_\mathrm{monomer}\right>}\right|}
+  \label{eq:unsaturation_backward}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=5,height=5>>=
+grid <- expand.grid(x=seq(0,4,length.out=20),
+                    y=seq(0,4,length.out=20))
+grid$z <- 10^(abs(3.5^-grid$x-3.5^-grid$y))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab="Average Vesicle Unsaturation",
+          ylab="Monomer Unsaturation",
+          zlab="Unsaturation Backward"))
+rm(grid)
+@ 
+
+\newpage
+\subsubsection{Charge Backwards}
+\begin{equation}
+  ch_b = 60^{-\left<{ch}_v\right> {ch}_m}
+  \label{eq:charge_backwards}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+x <- seq(-1,0,length.out=20)
+y <- seq(-1,0,length.out=20)
+grid <- expand.grid(x=x,y=y)
+grid$z <- as.vector(60^(-outer(x,y)))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab="Average Vesicle Charge",
+          ylab="Component Charge",
+          zlab="Charge Backwards"))
+rm(x,y,grid)
+@ 
+
+\newpage
+\subsubsection{Curvature Backwards}
+\begin{equation}
+  cu_f = 4^{\left|\left|\log cu_\mathrm{vesicle}\right|-\left|\log cu_\mathrm{monomer}\right|\right|}
+  \label{eq:curvature_backwards}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+grid <- expand.grid(x=seq(0.8,1.33,length.out=20),
+                    y=seq(0.8,1.33,length.out=20))
+grid$z <- 10^(abs(3.5^-grid$x-3.5^-grid$y))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab="Vesicle Curvature",
+          ylab="Monomer Curvature",
+          zlab="Curvature Backward"))
+rm(grid)
+@ 
+
+\newpage
+\subsubsection{Length Backwards}
+\begin{equation}
+  l_b = 3.2^{\left|l_\mathrm{ves}-l_\mathrm{monomer}\right|}
+  \label{eq:length_backward}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+grid <- expand.grid(x=seq(12,24,length.out=20),
+                    y=seq(12,24,length.out=20))
+grid$z <- 3.2^(abs(grid$x-grid$y))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab="Average Vesicle Length",
+          ylab="Monomer Length",
+          zlab="Length Backward"))
+rm(grid)
+@ 
+
+\newpage
+\subsubsection{Complex Formation Backward}
+\begin{equation}
+  CF1_b=1.5^{CF1_\mathrm{ves} CF1_\mathrm{monomer}-\left|CF1_\mathrm{ves} CF1_\mathrm{monomer}\right|}
+  \label{eq:complex_formation_backward}
+\end{equation}
+
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+grid <- expand.grid(x=seq(-1,3,length.out=20),
+                    y=seq(-1,3,length.out=20))
+grid$z <- 3.2^(grid$x*grid$y-abs(grid$x*grid$y))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab="Vesicle Complex Formation",
+          ylab="Monomer Complex Formation",
+          zlab="Complex Formation Backward"))
+rm(grid)
+@ 
+
+
+
+
+% \bibliographystyle{plainnat}
+% \bibliography{references.bib}
+
+
+\end{document}