tweak length and complex formation formalisms

git-svn-id: svn+ssh://hemlock.ucr.edu/srv/svn/misc/trunk/origins_of_life@527 25fa0111-c432-4dab-af88-9f31a2f6ac42

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index a1fa109a5e3f9c7652ef5d1cbbac263af879eb20..cedf6cfdd8f55a3a42eafba12c228523b85e663e 100644 (file)
--- a/kinetic_formalism.Rnw
+++ b/kinetic_formalism.Rnw
@@ -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}