\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
\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} -
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",
$\Sexpr{format(digits=3,to.kcal(60^(-.165*-1)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$ 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)
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)
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))
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)),
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",
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$y)^2+1)))
zlab=list("Unsaturation Backward",rot=93)))
rm(grid)
@
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
grid <- expand.grid(x=seq(0,4,length.out=20),
y=seq(0,4,length.out=20))
grid$z <- to.kcal((7^(1-1/(5*(2^-grid$x-2^-grid$y)^2+1))))
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)
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)
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$y))^2+1))
zlab=list("Curvature Backward",rot=93)))
rm(grid)
@
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
grid <- expand.grid(x=seq(0.8,1.33,length.out=20),
y=seq(0.8,1.33,length.out=20))
grid$z <- to.kcal(7^(1-1/(20*(log(grid$x)-log(grid$y))^2+1)))
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$y))
zlab=list("Length Backward",rot=93)))
rm(grid)
@
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
grid <- expand.grid(x=seq(12,24,length.out=20),
y=seq(12,24,length.out=20))
grid$z <- to.kcal(3.2^(abs(grid$x-grid$y)))
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$y))
zlab=list("Complex Formation Backward",rot=93)))
rm(grid)
@
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+<<echo=FALSE,results="hide",fig.width=7,fig.height=7>>=
grid <- expand.grid(x=seq(-1,3,length.out=20),
y=seq(-1,3,length.out=20))
grid$z <- to.kcal(1.5^(grid$x*grid$y-abs(grid$x*grid$y)))
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}
projects / ool / lipid_simulation_formalism.git / blobdiff