From 305d1f2329829911455335dfae94d1b96219739f Mon Sep 17 00:00:00 2001
From: don <don@25fa0111-c432-4dab-af88-9f31a2f6ac42>
Date: Wed, 16 Jun 2010 03:53:55 +0000
Subject: [PATCH] switch to new curvature formalism

git-svn-id: svn+ssh://hemlock.ucr.edu/srv/svn/misc/trunk/origins_of_life@525 25fa0111-c432-4dab-af88-9f31a2f6ac42
---
 kinetic_formalism.Rnw | 54 +++++++++++++++++++++++++++----------------
 1 file changed, 34 insertions(+), 20 deletions(-)

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index c36f6c9..cd55775 100644
--- a/kinetic_formalism.Rnw
+++ b/kinetic_formalism.Rnw
@@ -250,34 +250,48 @@ is $10$, yielding:
 
 \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}
 
-- 
2.39.2