@
+
+\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}
(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
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
\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}
+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}
projects / ool / lipid_simulation_formalism.git / blobdiff