\begin{equation}
% cu_f = 10^{\mathrm{stdev}\left|\log cu_\mathrm{vesicle}\right|}
- cu_f = 10^{\left<\log cu_\mathrm{vesicle} \right>}
+ cu_f = 10^{\left|\left<\log cu_\mathrm{vesicle} \right>\right|\mathrm{stdev} \log cu_\mathrm{vesicle}}
\label{eq:curvature_forward}
\end{equation}
-The most common $\left<\log {cu}_v\right>$ is around $-0.165$, which leads to
-a range of $\Delta \Delta G^\ddagger$ from
-$\Sexpr{format(digits=3,to.kcal(60^(-.165*-1)))}
-\frac{\mathrm{kcal}}{\mathrm{mol}}$ to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$.
+The most common $\left|\left<\log {cu}_v\right>\right|$ is around $0.013$, which
+with the most common $\mathrm{stdev} \log cu_\mathrm{vesicle}$ of
+$0.213$ leads to a $\Delta \Delta G^\ddagger$ of
+$\Sexpr{format(digits=3,to.kcal(10^(0.13*0.213)))}
+\frac{\mathrm{kcal}}{\mathrm{mol}}$
% 1.5 to 0.75 3 to 0.33
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
-curve(10^x,from=0,to=max(abs(c(mean(log(c(0.8,1.33))),
- mean(log(c(1,1.33))),
- mean(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")
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(0,max(c(sd(log(c(1,3))),
+ sd(log(c(1,0.33))),sd(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))
+grid$z <- 10^(grid$x*grid$y)
+print(wireframe(z~x*y,grid,cuts=50,
+ drape=TRUE,
+ scales=list(arrows=FALSE),
+ xlab=list("Vesicle stdev log curvature",rot=30),
+ ylab=list("Vesicle average log curvature",rot=-35),
+ zlab=list("Vesicle Curvature Forward",rot=93)))
+rm(grid)
@
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
-curve(to.kcal(10^(x^2)),from=0,to=max(abs(c(mean(log(c(0.8,1.33))),
- mean(log(c(1,1.33))),
- mean(log(c(0.8,1)))))),
- main="Curvature forward",
- xlab="Standard Deviation of Absolute value of the Log of the Curvature of Vesicle",
- ylab="Curvature Forward Adjustment (kcal/mol)")
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(0,max(c(sd(log(c(1,3))),
+ sd(log(c(1,0.33))),sd(log(c(0.33,3))))),length.out=20),
+ y=seq(0,max(c(mean(log(c(1,3)),
+ mean(log(c(1,0.33))),
+ mean(log(c(0.33,3)))))),length.out=20))
+grid$z <- to.kcal(10^(grid$x*grid$y))
+print(wireframe(z~x*y,grid,cuts=50,
+ drape=TRUE,
+ scales=list(arrows=FALSE),
+ xlab=list("Vesicle stdev log curvature",rot=30),
+ ylab=list("Vesicle average log curvature",rot=-35),
+ zlab=list("Vesicle Curvature Forward (kcal/mol)",rot=93)))
+rm(grid)
@
-
\newpage
\subsubsection{Length Forward}