update kinetic formalism and add competion start

git-svn-id: svn+ssh://hemlock.ucr.edu/srv/svn/misc/trunk/origins_of_life@611 25fa0111-c432-4dab-af88-9f31a2f6ac42

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index c7ae0ad9fbd677db74ac6e22f926fe95e38e1864..2b19b6a01884fc9b80bcd64e505c81f1a6d5acf6 100644 (file)
--- a/kinetic_formalism.Rnw
+++ b/kinetic_formalism.Rnw
@@ -641,6 +641,58 @@ rm(grid)
 @ 
 
 
+
+\subsection{Per-Lipid Kinetic Parameters}
+
+Each of the 5 lipid types have different kinetic parameters; to the
+greatest extent possible, we have derived these from literature.
+
+\begin{table}
+  \centering
+  \begin{tabular}{c c c c c c c}
+    Type & $k_f$ & $k_b$ & Area (\r{A}$^2$) & Charge & CF1 & Curvature \\
+    \hline
+    PC   & $3.7\cdot 10^6$ & $2\cdot 10^{-5}$   & 63 & 0  & 2  & 0.8  \\
+    PS   & $3.7\cdot 10^6$ & $1.5\cdot 10^{-5}$ & 54 & -1 & 0  & 1    \\
+    CHOL & $5.1\cdot 10^7$ & $2.8\cdot 10^{-4}$ & 38 & 0  & -1 & 1.21 \\
+    SM   & $3.7\cdot 10^6$ & $3.1\cdot 10^{-3}$ & 51 & 0  & 3  & 0.8  \\
+    PE   & $2.3\cdot 10^6$ & $10^{-5}$          & 55 & 0  & 0  & 1.33 \\
+  \end{tabular}
+  \caption{Kinetic parameters of lipid types}
+  \label{tab:kinetic_parameters_lipid_types}
+\end{table}
+
+\subsubsection{$k_f$ for lipid types}
+For PC, $k_f$ was measured by Nichols85 to be $3.7\cdot 10^6
+\frac{1}{\mathrm{M}\cdot \mathrm{s}}$ by the partitioning of
+P-C$_6$-NBD-PC between DOPC vesicles and water. The method utilized by
+Nichols85 has the weakness of using NBD-PC, with associated label
+perturbations. As similar measures do not exist for SM or PS, we
+assume that they have the same $k_f$. For CHOL, Estronca07 found a
+value for $k_f$ of $5.1\cdot 10^7 \frac{1}{\mathrm{M}\cdot
+  \mathrm{s}}$. For PE, Abreu04 found a value for $k_f$ of $2.3\cdot
+10^6$. \fixme{I'm missing the notes on these last two papers, so this
+  isn't correct yet.}
+
+\subsubsection{$k_b$ for lipid types}
+
+$k_b$ for PC was measured by Wimley90 using a radioactive label and
+large unilammelar vesicles at 30\textdegree C. The other values were
+calculated from the experiments of Nichols82 where the ratio of $k_b$
+of different types was measured to that of PC.
+See~\fref{tab:kinetic_parameters_lipid_types}.
+
+assigned accordingly. kb(PS) was assumed to be the same as kb(PG) given
+by Nichols82 (also ratio from kb(PC)).
+kb(SM) is taken from kb(PC) of Wimley90 (radioactive), and then a ratio of
+kb(PC)/kb(SM) taken from Bai97: = 34/2.2 = 15.45; 2.0 x 10-4 x 15.45 = 3.1 x
+10-3 s -1.
+kb(CHOL) taken from Jones90 (radioactive; POPC LUV; 37°).
+
+
+\subsubsection{Area for lipid types}
+
+
 \section{Simulation Methodology}
 
 \subsection{Overall Architecture}