<<results=hide,echo=FALSE>>=
require(lattice)
require(grid)
+# R in cal / mol K
+to.kcal <- function(k,temp=300) {
+ gasconst <- 1.985
+ return(gasconst*temp*log(k)/1000)
+}
@
\section{State Equation}
ylab="Unsaturation Forward Adjustment")
@
+<<fig=TRUE,echo=FALSE,results=hide,width=5,height=5>>=
+curve(to.kcal(2^x),from=0,to=sd(c(0,4)),
+ main="Unsaturation forward",
+ xlab="Standard Deviation of Unsaturation of Vesicle",
+ ylab="Unsaturation Forward (k cal)")
+@
+
+
\newpage
\subsubsection{Charge Forward}
\begin{equation}
rm(x,y,grid)
@
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+x <- seq(-1,0,length.out=20)
+y <- seq(-1,0,length.out=20)
+grid <- expand.grid(x=x,y=y)
+grid$z <- as.vector(to.kcal(60^(-outer(x,y))))
+print(wireframe(z~x*y,grid,cuts=50,
+ drape=TRUE,
+ scales=list(arrows=FALSE),
+ xlab=list("Average Vesicle Charge",rot=30),
+ ylab=list("Component Charge",rot=-35),
+ zlab=list("Charge Forward (k cal)",rot=93)))
+rm(x,y,grid)
+@
+
+
\newpage
\subsubsection{Curvature Forward}
\begin{equation}
ylab="Curvature Forward Adjustment")
@
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+curve(to.kcal(10^x),from=0,to=max(c(sd(abs(log(c(0.8,1.33)))),
+ sd(abs(log(c(1,1.33)))),
+ sd(abs(log(c(0.8,1)))))),
+ main="Curvature forward",
+ xlab="Standard Deviation of Absolute value of the Log of the Curvature of Vesicle",
+ ylab="Curvature Forward Adjustment (kcal)")
+@
+
+
\newpage
\subsubsection{Length Forward}
\begin{equation}
ylab="Length Forward Adjustment")
@
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+curve(to.kcal(3^x),from=0,to=sd(c(12,24)),
+ main="Length forward",
+ xlab="Standard Deviation of Length of Vesicle",
+ ylab="Length Forward Adjustment (kcal)")
+@
+
+
\subsubsection{Complex Formation}
\begin{equation}
CF1_f=1
rm(grid)
@
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(0,4,length.out=20),
+ y=seq(0,4,length.out=20))
+grid$z <- to.kcal(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=list("Average Vesicle Unsaturation",rot=30),
+ ylab=list("Monomer Unsaturation",rot=-35),
+ zlab=list("Unsaturation Backward (kcal)",rot=93)))
+rm(grid)
+@
+
+
\newpage
\subsubsection{Charge Backwards}
\begin{equation}
rm(x,y,grid)
@
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+x <- seq(-1,0,length.out=20)
+y <- seq(-1,0,length.out=20)
+grid <- expand.grid(x=x,y=y)
+grid$z <- to.kcal(as.vector(20^(outer(x,y))))
+print(wireframe(z~x*y,grid,cuts=50,
+ drape=TRUE,
+ scales=list(arrows=FALSE),
+ xlab=list("Average Vesicle Charge",rot=30),
+ ylab=list("Component Charge",rot=-35),
+ zlab=list("Charge Backwards (kcal)",rot=93)))
+rm(x,y,grid)
+@
+
\newpage
\subsubsection{Curvature Backwards}
\begin{equation}
- cu_f = 7^{1-\left(20\left(\log cu_\mathrm{vesicle}-\log cu_\mathrm{monomer}\right)^2+1\right)^{-1}}
+ cu_f = 7^{1-\left(20\left(\log_{e} cu_\mathrm{vesicle}-\log_{e} cu_\mathrm{monomer}\right)^2+1\right)^{-1}}
\label{eq:curvature_backwards}
\end{equation}
rm(grid)
@
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(0.8,1.33,length.out=20),
+ y=seq(0.8,1.33,length.out=20))
+grid$z <- to.kcal(7^(1-1/(20*(log(grid$x)-log(grid$y))^2+1)))
+print(wireframe(z~x*y,grid,cuts=50,
+ drape=TRUE,
+ scales=list(arrows=FALSE),
+ xlab=list("Vesicle Curvature",rot=30),
+ ylab=list("Monomer Curvature",rot=-35),
+ zlab=list("Curvature Backward (kcal)",rot=93)))
+rm(grid)
+@
+
+
\newpage
\subsubsection{Length Backwards}
\begin{equation}
rm(grid)
@
+<<fig=TRUE,echo=FALSE,results=hide,width=7,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$y)))
+print(wireframe(z~x*y,grid,cuts=50,
+ drape=TRUE,
+ scales=list(arrows=FALSE),
+ xlab=list("Average Vesicle Length",rot=30),
+ ylab=list("Monomer Length",rot=-35),
+ zlab=list("Length Backward (kcal)",rot=93)))
+rm(grid)
+@
+
+
\newpage
\subsubsection{Complex Formation Backward}
\begin{equation}
rm(grid)
@
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(-1,3,length.out=20),
+ y=seq(-1,3,length.out=20))
+grid$z <- to.kcal(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=list("Vesicle Complex Formation",rot=30),
+ ylab=list("Monomer Complex Formation",rot=-35),
+ zlab=list("Complex Formation Backward (kcal)",rot=93)))
+rm(grid)
+@
+
+