add the length adjustment concerns

[ool/lipid_simulation_formalism.git] / kinetic_formalism.Rnw

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index 8b387e28d27c3ae07b3de4e4235f084dab454267..e52b8380ddbf4395af33f19581ad84dbb344070c 100644 (file)
--- a/kinetic_formalism.Rnw
+++ b/kinetic_formalism.Rnw
@@ -148,6 +148,11 @@ $1.5$, which leads to a $\Delta \Delta G^\ddagger$ of
 $\Sexpr{format(digits=3,to.kcal(2^1.5))}
 \frac{\mathrm{kcal}}{\mathrm{mol}}$.
 
+It is not clear that the unsaturation of the inserted monomer will
+affect the rate of the insertion positively or negatively, so we do
+not include a term for it in this formalism.
+
+
 \setkeys{Gin}{width=3.2in}
 <<fig=TRUE,echo=FALSE,results=hide,width=5,height=5>>=
 curve(2^x,from=0,to=sd(c(0,4)),
@@ -316,6 +321,13 @@ a range of $\Delta \Delta G^\ddagger$ of
 $\Sexpr{format(digits=3,to.kcal(2^(3.4)))}
 \frac{\mathrm{kcal}}{\mathrm{mol}}$.
 
+While it could be argued that increased length of the monomer could
+affect the rate of insertion into the membrane, it's not clear whether
+it would increase (by decreasing the number of available hydrogen
+bonds, for example) or decrease (by increasing the time taken to fully
+insert the acyl chain, for example) the rate of insertion or to what
+degree, so we do not take it into account in this formalism.
+
 
 <<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
 curve(2^x,from=0,to=sd(c(12,24)),
@@ -371,62 +383,6 @@ where $\left<un_\mathrm{ves}\right>$ is the average unsaturation of
 the vesicle, and $un_\mathrm{monomer}$ is the average unsaturation. In
 this equation, as the average unsaturation of the vesicle is larger,
 
-\begin{equation}
-  un_b = 10^{\left(2^{- \left< un_\mathrm{ves} \right> }
-      -2^{-un_\mathrm{monomer}}\right)^2}
-  \label{eq:unsaturation_backward}
-\end{equation}
-
-The most common $\left<un_\mathrm{ves}\right>$ is around $1.7$, which leads to
-a range of $\Delta \Delta G^\ddagger$ from
-$\Sexpr{format(digits=3,to.kcal(10^((2^-1.7-2^-0)^2)))}
-\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with 0 unsaturation
-to
-$\Sexpr{format(digits=3,to.kcal(10^((2^-1.7-2^-4)^2)))}\frac{\mathrm{kcal}}{\mathrm{mol}}$
-for monomers with 4 unsaturations.
-
-
-<<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$z <- 10^((2^-grid$x-2^-grid$y)^2)
-print(wireframe(z~x*y,grid,cuts=50,
-          drape=TRUE,
-          scales=list(arrows=FALSE),
-          xlab=list("Average Vesicle Unsaturation",rot=30),
-          ylab=list("Monomer Unsaturation",rot=-35),
-          zlab=list("Unsaturation Backward",rot=93)))
-rm(grid)
-@ 
-<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
-grid <- expand.grid(x=seq(0,4,length.out=20),
-                    y=seq(0,4,length.out=20))
-grid$z <- to.kcal(10^((2^-grid$x-2^-grid$y)^2))
-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/mol)",rot=93)))
-rm(grid)
-@ 
-
-\subsubsection{Unsaturation Backward II}
-
-Unsaturation also influences the ability of a lipid molecule to leave
-a membrane. If a molecule has an unsaturation level which is different
-from the surrounding membrane, it will be more likely to leave the
-membrane. The more different the unsaturation level is, the greater
-the propensity for the lipid molecule to leave. However, a vesicle
-with some unsaturation is more favorable for lipids with more
-unsaturation than the equivalent amount of less unsatuturation, so the
-difference in energy between unsaturation is not linear. Therefore, an
-equation with the shape
-$x^{\left| y^{-\left< un_\mathrm{ves}\right> }-y^{-un_\mathrm{monomer}} \right| }$
-where $\left<un_\mathrm{ves}\right>$ is the average unsaturation of
-the vesicle, and $un_\mathrm{monomer}$ is the average unsaturation. In
-this equation, as the average unsaturation of the vesicle is larger,
-
 \begin{equation}
   un_b = 7^{1-\left(20\left(2^{-\left<un_\mathrm{vesicle} \right>} - 2^{-un_\mathrm{monomer}} \right)^2+1\right)^{-1}}
   \label{eq:unsaturation_backward}