tweak length and complex formation formalisms

[ool/lipid_simulation_formalism.git] / kinetic_formalism.Rnw

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index cd5577541a98cb7541793ba3a7cf8801b51dbb15..cedf6cfdd8f55a3a42eafba12c228523b85e663e 100644 (file)
--- a/kinetic_formalism.Rnw
+++ b/kinetic_formalism.Rnw
@@ -250,7 +250,7 @@ is $10$, yielding:
 
 \begin{equation}
  % cu_f = 10^{\mathrm{stdev}\left|\log cu_\mathrm{vesicle}\right|}
-  cu_f = 10^{\left|\left<\log cu_\mathrm{vesicle} \right>\right|\mathrm{stdev} \log cu_\mathrm{vesicle}}
+  cu_f = 10^{\left|\left<\log cu_\mathrm{vesicle} \right>\right|\mathrm{stdev} \left|\log cu_\mathrm{vesicle}\right|}
   \label{eq:curvature_forward}
 \end{equation}
 
@@ -262,8 +262,8 @@ $\Sexpr{format(digits=3,to.kcal(10^(0.13*0.213)))}
 
 % 1.5 to 0.75 3 to 0.33
 <<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),
+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)),
                       mean(log(c(1,0.33))),
                       mean(log(c(0.33,3)))))),length.out=20))
@@ -277,8 +277,8 @@ print(wireframe(z~x*y,grid,cuts=50,
 rm(grid)
 @ 
 <<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),
+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)),
                       mean(log(c(1,0.33))),
                       mean(log(c(0.33,3)))))),length.out=20))
@@ -488,8 +488,20 @@ rm(grid)
 
 \newpage
 \subsubsection{Length Backwards}
+
+In a model membrane, the dissociation constant decreases by a factor
+of approximately 3.2 per carbon increase in acyl chain length (Nichols
+1985). Unfortunatly, the known experimental data only measures chain
+length less than or equal to the bulk lipid, and does not exceed it,
+and is only known for one bulk lipid species (DOPC).
+
+
+The dissociation constant decreases by approximately 3.2 per carbon
+increase in acyl chain length (Nichols 1985). We assume that this
+decrease is in relationship to the average vesicle length.
+
 \begin{equation}
-  l_b = 3.2^{\left|l_\mathrm{ves}-l_\mathrm{monomer}\right|}
+  l_b = 3.2^{\left|\left<l_\mathrm{ves}\right>-l_\mathrm{monomer}\right|}
   \label{eq:length_backward}
 \end{equation}
 
@@ -522,7 +534,7 @@ rm(grid)
 \newpage
 \subsubsection{Complex Formation Backward}
 \begin{equation}
-  CF1_b=1.5^{CF1_\mathrm{ves} CF1_\mathrm{monomer}-\left|CF1_\mathrm{ves} CF1_\mathrm{monomer}\right|}
+  CF1_b=1.5^{\left<CF1_\mathrm{ves}\right> CF1_\mathrm{monomer}-\left|\left<CF1_\mathrm{ves}right> CF1_\mathrm{monomer}\right|}
   \label{eq:complex_formation_backward}
 \end{equation}