X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=kinetic_formalism.Rnw;h=2b19b6a01884fc9b80bcd64e505c81f1a6d5acf6;hb=41b3edaa39467a2965b467335a481f31a943c695;hp=c3541f44b57fbf7cb75b290ae7213cb4387140ad;hpb=0aaf1bc43b61120a6f93ebc334942780e497e24d;p=ool%2Flipid_simulation_formalism.git diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw index c3541f4..2b19b6a 100644 --- 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} @@ -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: -$n_i = k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{ves}dt\mathrm{NA}$ +$n_i = k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{ves}\mathrm{N_A}dt$ In the cases where $n_i > 1$, the integer number of molecules is added. Fractional $n_i$ or the fractional remainder after the addition @@ -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 -$n_i = k_{bi}k_{bi\mathrm{adj}}C_{i_\mathrm{ves}}dt\mathrm{NA}$. +$n_i = k_{bi}k_{bi\mathrm{adj}}C_{i_\mathrm{ves}}\mathrm{N_A}dt$. While programatically, the molecule removal happens after the addition, the properties that each operates on are the same, so they @@ -807,8 +859,27 @@ to produce later 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} +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}