update kinetic formalism and add competion start

[ool/lipid_simulation_formalism.git] / kinetic_formalism.Rnw

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index c3541f44b57fbf7cb75b290ae7213cb4387140ad..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}
 \section{Simulation Methodology}
 
 \subsection{Overall Architecture}


@@ -750,7 +802,7 @@ many cases as possible, experimentally based)
 (see~\fref{sec:step_duration}), but for a given step is constant. This
 leads to the following:
 
 (see~\fref{sec:step_duration}), but for a given step is constant. This
 leads to the following:
 

-$n_i = k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{ves}dt\mathrm{NA}$
+$n_i = k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{ves}\mathrm{N_A}dt$

 
 In the cases where $n_i > 1$, the integer number of molecules is
 added. Fractional $n_i$ or the fractional remainder after the addition
 
 In the cases where $n_i > 1$, the integer number of molecules is
 added. Fractional $n_i$ or the fractional remainder after the addition


@@ -761,7 +813,7 @@ fractional part of $n_i$, an additional molecule is added.
 
 Molecules leaving the vesicle are handled in a similar manner, with 
 
 
 Molecules leaving the vesicle are handled in a similar manner, with 
 

-$n_i = k_{bi}k_{bi\mathrm{adj}}C_{i_\mathrm{ves}}dt\mathrm{NA}$.
+$n_i = k_{bi}k_{bi\mathrm{adj}}C_{i_\mathrm{ves}}\mathrm{N_A}dt$.

 
 While programatically, the molecule removal happens after the
 addition, the properties that each operates on are the same, so they
 
 While programatically, the molecule removal happens after the
 addition, the properties that each operates on are the same, so they


@@ -807,8 +859,27 @@ to produce later output.
 
 \section{Analyzing output}
 
 
 \section{Analyzing output}
 

+Analyzing of output is handled by a separate perl program which shares
+many common modules with the simulation program. Current output
+includes simulation progress, summary tables, summary statistics, and
+various graphs.
+

 \subsection{PCA plots}
 
 \subsection{PCA plots}
 

+Vesicles have many different axes which contribute to their variation
+between subsequent generations; two major groups of axes are the
+components and properties of vesicles. Each component in a vesicle is
+an axis on its own; it can be measured either as an absolute number of
+molecules in each component, or the fraction of molecules of that
+component over the total number of molecules; the second approach is
+often more convenient, as it allows vesicles of different number of
+molecules to be more directly compared (though it hides any affect of
+vesicle size).
+
+In order to visualize the transition of subsequent generations of
+vesicles from their initial state in the simulation, to their final
+state at the termination of 
+

 \subsection{Carpet plots}
 
 
 \subsection{Carpet plots}