X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=kinetic_formalism.Rnw;h=fccc4af7c3a6eb4be8a85ab899b553b8453d4e8c;hb=4ac6dcb5960639dce3d89699983f55a90e022636;hp=4c9222005d0b3bf0e1a5dec7e070e988191186cf;hpb=733fbcf74dd21a8b6b11bb4a28f6487172952099;p=ool%2Flipid_simulation_formalism.git

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index 4c92220..fccc4af 100644
--- a/kinetic_formalism.Rnw
+++ b/kinetic_formalism.Rnw
@@ -59,9 +59,22 @@
 \begin{document}
 %\maketitle
 
-<<results=hide,echo=FALSE>>=
-require(lattice)
-require(grid)
+<<load_libraries,results="hide",message=FALSE,warning=FALSE,echo=FALSE>>=
+require("lattice")
+require("grid")
+require("Hmisc")
+require("gridBase")
+opts_chunk$set(dev="cairo_pdf",
+                  out.width="0.8\\textwidth",
+                  out.height="0.8\\textheight",
+                  out.extra="keepaspectratio")
+opts_chunk$set(cache=TRUE, autodep=TRUE)
+options(device = function(file, width = 6, height = 6, ...) {
+            cairo_pdf(tempfile(), width = width, height = height, ...)
+        })
+to.latex <- function(x){
+  gsub("\\\\","\\\\\\\\",latexSN(x))
+}
 # R in cal / mol K
 to.kcal <- function(k,temp=300) {
   gasconst <- 1.985
@@ -72,19 +85,21 @@ to.kcal <- function(k,temp=300) {
 \section{State Equation}
 % double check this with the bits in the paper
 
-Given a base forward kinetic parameter for the $i$th specie $k_{fi}$
-(which is dependent on lipid type, that is PC, PE, PS, etc.), an
-adjustment parameter $k_{fi\mathrm{adj}}$ based on the vesicle and the
-specific specie (length, unsaturation, etc.) (see~\fref{eq:kf_adj}),
-the molar concentration of monomer of the $i$th specie
-$\left[C_{i_\mathrm{monomer}}\right]$, the surface area of the vesicle
-$S_\mathrm{ves}$, the base backwards kinetic parameter for the $i$th
-specie $k_{bi}$ which is also dependent on lipid type, its adjustment
-parameter $k_{bi\mathrm{adj}}$ (see~\fref{eq:kb_adj}), and the molar
-concentration of the $i$th specie in the vesicle
-$\left[C_{i_\mathrm{ves}}\right]$, the change in concentration of the
-$i$th specie in the vesicle per change in time $\frac{d
-  C_{i_\mathrm{ves}}}{dt}$ can be calculated:
+The base forward kinetic parameter for the $i$th component is
+$k_{\mathrm{f}i}$ and is dependent on the particular lipid type (PC,
+PS, SM, etc.). The forward adjustment parameter,
+$k_{\mathrm{f}i\mathrm{adj}}$, is based on the properties of the
+vesicle and the specific component (type, length, unsaturation, etc.)
+(see Equation~\ref{eq:kf_adj}, and
+Section~\ref{sec:kinetic_adjustments}).
+$\left[C_{i_\mathrm{monomer}}\right]$ is the molar concentration of
+monomer of the $i$th component. $\left[S_\mathrm{vesicle}\right]$ is
+the surface area of the vesicle per volume. The base backwards kinetic
+parameter for the $i$th component is $k_{\mathrm{b}i}$ and its
+adjustment parameter $k_{\mathrm{b}i\mathrm{adj}}$ (see
+Equation~\ref{eq:kb_adj}, and Section~\ref{sec:kinetic_adjustments}).
+$\left[C_{i_\mathrm{vesicle}}\right]$ is the molar concentration of
+the $i$th component in the vesicle.
 
 \begin{equation}
   \frac{d C_{i_\mathrm{ves}}}{dt} = k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{ves} -
@@ -155,14 +170,13 @@ affect the rate of the insertion positively or negatively, so we do
 not include a term for it in this formalism.
 
 
-\setkeys{Gin}{width=3.2in}
-<<fig=TRUE,echo=FALSE,results=hide,width=5,height=5>>=
+<<echo=FALSE,results="hide",fig.width=5,fig.height=5,out.width="3.2in">>=
 curve(2^x,from=0,to=sd(c(0,4)),
       main="Unsaturation Forward",
       xlab="Standard Deviation of Unsaturation of Vesicle",
       ylab="Unsaturation Forward Adjustment")
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=5,height=5>>=
+<<echo=FALSE,results="hide",fig.width=5,fig.height=5,out.width="3.2in">>=
 curve(to.kcal(2^x),from=0,to=sd(c(0,4)),
       main="Unsaturation forward",
       xlab="Standard Deviation of Unsaturation of Vesicle",
@@ -198,7 +212,7 @@ a range of $\Delta \Delta G^\ddagger$ from
 $\Sexpr{format(digits=3,to.kcal(60^(-.165*-1)))}
 \frac{\mathrm{kcal}}{\mathrm{mol}}$ to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$.
 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 x <- seq(-1,0,length.out=20)
 y <- seq(-1,0,length.out=20)
 grid <- expand.grid(x=x,y=y)
@@ -212,7 +226,7 @@ print(wireframe(z~x*y,grid,cuts=50,
                 zlab=list("Charge Forward",rot=93)))
 rm(x,y,grid)
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 x <- seq(-1,0,length.out=20)
 y <- seq(-1,0,length.out=20)
 grid <- expand.grid(x=x,y=y)
@@ -269,9 +283,9 @@ of $\Sexpr{format(digits=3,to.kcal(10^(0.13*0.213)))}
 relatively matched curvatures in our environment.
 
 % 1.5 to 0.75 3 to 0.33
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(0,max(c(sd(abs(log(c(1,3)))),
-y                      sd(abs(log(c(1,0.33)))),sd(abs(log(c(0.33,3)))))),length.out=20),
+                      sd(abs(log(c(1,0.33)))),sd(abs(log(c(0.33,3)))))),length.out=20),
                     y=seq(0,max(c(mean(log(c(1,3)),
                       mean(log(c(1,0.33))),
                       mean(log(c(0.33,3)))))),length.out=20))
@@ -284,7 +298,7 @@ print(wireframe(z~x*y,grid,cuts=50,
           zlab=list("Vesicle Curvature Forward",rot=93)))
 rm(grid)
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(0,max(c(sd(abs(log(c(1,3)))),
                       sd(abs(log(c(1,0.33)))),sd(abs(log(c(0.33,3)))))),length.out=20),
                     y=seq(0,max(c(mean(log(c(1,3)),
@@ -355,13 +369,13 @@ From Nichols85: The association rate constant is independent of acyl
 chain length. {take into account for the formula; rz 8/17/2010}.
 
 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=5>>=
 curve(2^x,from=0,to=sd(c(12,24)),
       main="Length forward",
       xlab="Standard Deviation of Length of Vesicle",
       ylab="Length Forward Adjustment")
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=5>>=
 curve(to.kcal(2^x),from=0,to=sd(c(12,24)),
       main="Length forward",
       xlab="Standard Deviation of Length of Vesicle",
@@ -423,7 +437,7 @@ $\Sexpr{format(digits=3,to.kcal(7^(1-1/(5*(2^-1.7-2^-4)^2+1))))}\frac{\mathrm{kc
 for monomers with 4 unsaturations.
 
 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(0,4,length.out=20),
                     y=seq(0,4,length.out=20))
 grid$z <- (7^(1-1/(5*(2^-grid$x-2^-grid$y)^2+1)))
@@ -435,7 +449,7 @@ print(wireframe(z~x*y,grid,cuts=50,
           zlab=list("Unsaturation Backward",rot=93)))
 rm(grid)
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(0,4,length.out=20),
                     y=seq(0,4,length.out=20))
 grid$z <- to.kcal((7^(1-1/(5*(2^-grid$x-2^-grid$y)^2+1))))
@@ -470,7 +484,7 @@ $0\frac{\mathrm{kcal}}{\mathrm{mol}}$
 for monomers with charge $0$.
 
 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 x <- seq(-1,0,length.out=20)
 y <- seq(-1,0,length.out=20)
 grid <- expand.grid(x=x,y=y)
@@ -483,7 +497,7 @@ print(wireframe(z~x*y,grid,cuts=50,
           zlab=list("Charge Backwards",rot=93)))
 rm(x,y,grid)
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 x <- seq(-1,0,length.out=20)
 y <- seq(-1,0,length.out=20)
 grid <- expand.grid(x=x,y=y)
@@ -527,7 +541,7 @@ $\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.
 
 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(0.8,1.33,length.out=20),
                     y=seq(0.8,1.33,length.out=20))
 grid$z <- 7^(1-1/(20*(log(grid$x)-log(grid$y))^2+1))
@@ -539,7 +553,7 @@ print(wireframe(z~x*y,grid,cuts=50,
           zlab=list("Curvature Backward",rot=93)))
 rm(grid)
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(0.8,1.33,length.out=20),
                     y=seq(0.8,1.33,length.out=20))
 grid$z <- to.kcal(7^(1-1/(20*(log(grid$x)-log(grid$y))^2+1)))
@@ -578,7 +592,7 @@ $\Sexpr{format(digits=3,to.kcal(3.2^abs(24-17.75)))}\frac{\mathrm{kcal}}{\mathrm
 for monomers with length 24 to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with curvature near 18.
 
 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 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$y))
@@ -590,7 +604,7 @@ print(wireframe(z~x*y,grid,cuts=50,
           zlab=list("Length Backward",rot=93)))
 rm(grid)
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(12,24,length.out=20),
                     y=seq(12,24,length.out=20))
 grid$z <- to.kcal(3.2^(abs(grid$x-grid$y)))
@@ -639,7 +653,7 @@ $0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with complex
 formation $0$.
 
 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(-1,3,length.out=20),
                     y=seq(-1,3,length.out=20))
 grid$z <- 1.5^(grid$x*grid$y-abs(grid$x*grid$y))
@@ -651,7 +665,7 @@ print(wireframe(z~x*y,grid,cuts=50,
           zlab=list("Complex Formation Backward",rot=93)))
 rm(grid)
 @ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
 grid <- expand.grid(x=seq(-1,3,length.out=20),
                     y=seq(-1,3,length.out=20))
 grid$z <- to.kcal(1.5^(grid$x*grid$y-abs(grid$x*grid$y)))
@@ -717,6 +731,9 @@ PE 0.45 <- from Nichols82
 PG=PS 
 
 
+kb PC is from table 2 of Wimley90, where we have a half life of 9.6
+hours for DMPC. \Sexpr{log(2)/(9.6*60*60)}.
+
 
 
 \subsubsection{Area for lipid types}