\usepackage{booktabs}
\usepackage[noblocks]{authblk}
\usepackage[hyperfigures,bookmarks,colorlinks,citecolor=black,filecolor=black,linkcolor=black,urlcolor=black]{hyperref}
+\usepackage[capitalise]{cleveref}
\usepackage[sectionbib,sort&compress,numbers]{natbib}
\usepackage[nomargin,inline,draft]{fixme}
\usepackage[x11names,svgnames]{xcolor}
\renewcommand{\thetable}{S\@arabic\c@table}
\makeatother
-\section{Competition Implementation}
-\subsection{Implementation changes}
-
-\begin{itemize}
-\item settable maximum number of vesicles to track (default $10^4$)
-\item start with 1~L ($10^{-3}$~m$^3$) cube
-\item if at any point the number of vesicles exceeds the maximum
- number, chop the volume and environment molecule number into tenths,
- randomly select one tenth of the vesicles, and continue tracking.
-\item generations will be counted per vesicle, and each progeny
- vesicle will have a generation number one greater than the parental
- vesicle.
-\item 100 generations can result in as many as $2^{100}$
- ($\Sexpr{to.latex(format(digits=3,2^100))}$) vesicles or as few as
- 101 vesicles.
-\item Environment will use a specific number of each component instead
- of a constant concentration; as the number may be larger than
- \texttt{long long} ($2^{64}$), we use libgmp to handle an arbitrary
- precision number of components
-\end{itemize}
-
-\subsection{Infrastructure changes}
-\begin{itemize}
-\item Rewrite core bits in C
-\item Use libgmp for handling large ints
-\item Use openmpi to split the calculations out over multiple
- machines/processors and allow deploying to larger
- clusters/supercomputers
-\end{itemize}
+% \section{Competition Implementation}
+% \subsection{Implementation changes}
+%
+% \begin{itemize}
+% \item settable maximum number of vesicles to track (default $10^4$)
+% \item start with 1~L ($10^{-3}$~m$^3$) cube
+% \item if at any point the number of vesicles exceeds the maximum
+% number, chop the volume and environment molecule number into tenths,
+% randomly select one tenth of the vesicles, and continue tracking.
+% \item generations will be counted per vesicle, and each progeny
+% vesicle will have a generation number one greater than the parental
+% vesicle.
+% \item 100 generations can result in as many as $2^{100}$
+% ($\Sexpr{2^100}$) vesicles or as few as
+% 101 vesicles.
+% \item Environment will use a specific number of each component instead
+% of a constant concentration; as the number may be larger than
+% \texttt{long long} ($2^{64}$), we use libgmp to handle an arbitrary
+% precision number of components
+% \end{itemize}
+%
+% \subsection{Infrastructure changes}
+% \begin{itemize}
+% \item Rewrite core bits in C
+% \item Use libgmp for handling large ints
+% \item Use openmpi to split the calculations out over multiple
+% machines/processors and allow deploying to larger
+% clusters/supercomputers
+% \end{itemize}
and is dependent on the particular lipid type (PC, PS, SM, etc.). The
forward adjustment parameter, $k_{\mathrm{f}i\mathrm{adj}}$, is based on the
properties of the vesicle and the specific component (type, length,
-unsaturation, etc.) (see Equation~\ref{eq:kf_adj}, and
-Section~\ref{sec:kinetic_adjustments}).
+unsaturation, etc.) (see \cref{eq:kf_adj,sec:kinetic_adjustments}).
$\left[C_{i_\mathrm{monomer}}\right]$ is the molar concentration of
monomer of the $i$th component. $\left[S_\mathrm{vesicle}\right]$ is the surface
area of the vesicle per volume. The base backwards kinetic parameter
for the $i$th component is $k_{\mathrm{b}i}$ and its adjustment parameter
-$k_{\mathrm{b}i\mathrm{adj}}$ (see Equation~\ref{eq:kb_adj}, and
-Section~\ref{sec:kinetic_adjustments}).
+$k_{\mathrm{b}i\mathrm{adj}}$ (see \cref{eq:kb_adj,sec:kinetic_adjustments}).
$\left[C_{i_\mathrm{vesicle}}\right]$ is the molar concentration of
the $i$th component in the vesicle.
\subsection{Per-Lipid Kinetic Parameters}
-<<echo=FALSE,results='hide'>>=
+<<kf_prime,echo=FALSE,results='hide'>>=
kf.prime <- c(3.7e6,3.7e6,5.1e7,3.7e6,2.3e6)
kf <- (as.numeric(kf.prime)*10^-3)/(63e-20*6.022e23)
@
% \centering
% \begin{tabular}{c c c c c c c c}
% \toprule
-% Type & $k_\mathrm{f}$ $\left(\frac{\mathrm{m}}{\mathrm{s}}\right)$ & $k'_\mathrm{f}$ $\left(\frac{1}{\mathrm{M} \mathrm{s}}\right)$ & $k_\mathrm{b}$ $\left(\mathrm{s}^{-1}\right)$ & Area $\left({\AA}^2\right)$ & Charge & $\mathrm{CF}1$ & Curvature \\
+% Type & $k_\mathrm{f}$ $\left(\frac{\mathrm{m}}{\mathrm{s}}\right)$ & $k'_\mathrm{f}$ $\left(\frac{1}{\mathrm{M} \mathrm{s}}\right)$ & $k_\mathrm{b}$ $\left(\mathrm{s}^{-1}\right)$ & Area $\left({Å}^2\right)$ & Charge & $\mathrm{CF}1$ & Curvature \\
% \midrule
% PC & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[1]))}$ & $3.7 \times 10^6$ & $2 \times 10^{-5}$ & 63 & 0 & 2 & 0.8 \\
% PS & $\Sexpr{to.latex(format(digits=3,scientific=TRUE,kf[2]))}$ & $3.7 \times 10^6$ & $1.25\times 10^{-5}$ & 54 & -1 & 0 & 1 \\
% \end{table}
%%% \DLA{I think we may just reduce these three sections; area, $k_\mathrm{f}$
-%%% and $k_\mathrm{b}$ to Table~\ref{tab:kinetic_parameters_lipid_types} with
+%%% and $k_\mathrm{b}$ to \cref{tab:kinetic_parameters_lipid_types} with
%%% references.}
%%%
%%% \RZ{Yes, but we also have to have then as comments the numbers that
simulations is around $1.5$, which leads to a $\Delta \Delta
G^\ddagger$ of $\Sexpr{to.latex(format(digits=3,to.kcal(2^1.5)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$, and a total range of possible
-values depicted in Figure~\ref{fig:unf_graph}.
+values depicted in \cref{fig:unf_graph}.
% \RZ{Explain here, or even earlier that the formulas were ad hoc
% adjusted to correspond to ``reasonable'' changes in the Eyring
$\Sexpr{format(digits=3,to.kcal(60^(-.165*-1)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$ to
$0\frac{\mathrm{kcal}}{\mathrm{mol}}$, and the total range of possible
-values seen in Figure~\ref{fig:chf_graph}.
+values seen in \cref{fig:chf_graph}.
\begin{figure}
of $\Sexpr{format(digits=3,to.kcal(10^(0.13*0.213)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$. This is a consequence of the
relatively matched curvatures in our environment. The full range of
-$cu_\mathrm{f}$ values possible are shown in Figure~\ref{fig:cuf_graph}.
+$cu_\mathrm{f}$ values possible are shown in \cref{fig:cuf_graph}.
% 1.5 to 0.75 3 to 0.33
\begin{figure}
\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with 0 unsaturation
to
$\Sexpr{format(digits=3,to.kcal(7^(1-1/(5*(2^-1.7-2^-4)^2+1))))}\frac{\mathrm{kcal}}{\mathrm{mol}}$
-for monomers with 4 unsaturations. See Figure~\ref{fig:unb_graph} for
+for monomers with 4 unsaturations. See \cref{fig:unb_graph} for
the full range of possible values.
$\Sexpr{format(digits=3,to.kcal(20^(-.164*-1)))}
\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with charge $-1$ to
$0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with charge $0$.
-See Figure~\ref{fig:chb_graph} for the full range of possible values
+See \cref{fig:chb_graph} for the full range of possible values
of $ch_\mathrm{b}$.
for monomers with curvature 1.3 to
$0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with curvature near
1. The full range of values possible for $cu_\mathrm{b}$ are shown in
-Figure~\ref{fig:cub_graph}
+\cref{fig:cub_graph}
% \RZ{What about the opposite curvatures that actually do fit to each
% other?}
$\Sexpr{format(digits=3,to.kcal(3.2^abs(24-17.75)))}\frac{\mathrm{kcal}}{\mathrm{mol}}$
for monomers with length 24 to $0\frac{\mathrm{kcal}}{\mathrm{mol}}$
for monomers with length near 18. The full range of possible values of
-$l_\mathrm{b}$ are shown in Figure~\ref{fig:lb_graph}
+$l_\mathrm{b}$ are shown in \cref{fig:lb_graph}
% (for methods? From McLean84LIB: The activation free energies and free
% energies of transfer from self-micelles to water increase by 2.2 and
for monomers with complex formation $2$ to
$0\frac{\mathrm{kcal}}{\mathrm{mol}}$ for monomers with complex
formation $0$. The full range of possible values for $CF1_\mathrm{b}$ are
-depicted in Figure~\ref{fig:cf1b_graph}.
+depicted in \cref{fig:cf1b_graph}.
Determining the number of molecules to add to the lipid membrane
($n_i$) requires knowing $k_{\mathrm{f}i_\mathrm{adj}}$, the surface area of the
-vesicle $S_\mathrm{vesicle}$ (see Section \ref{sec:ves_prop}), the time interval
+vesicle $S_\mathrm{vesicle}$ (see \cref{sec:ves_prop}), the time interval
$dt$ during which lipids are added, the base $k_{\mathrm{f}i}$, and the
concentration of the monomer in the environment
-$\left[C_{i\mathrm{vesicle}}\right]$ (see Equation~\ref{eq:state}).
-$k_{\mathrm{f}i\mathrm{adj}}$ is calculated (see Equation~\ref{eq:kf_adj}) based on the
+$\left[C_{i\mathrm{vesicle}}\right]$ (see \cref{eq:state}).
+$k_{\mathrm{f}i\mathrm{adj}}$ is calculated (see \cref{eq:kf_adj}) based on the
vesicle properties and their hypothesized effect on the rate (in as
many cases as possible, experimentally based)
-(see Section~\ref{sec:kinetic_adjustments} for details). $dt$ can be varied
-(see Section~\ref{sec:step_duration}), but for a given step is constant. This
+(see \cref{sec:kinetic_adjustments} for details). $dt$ can be varied
+(see \cref{sec:step_duration}), but for a given step is constant. This
leads to the following:
$n_i = k_{\mathrm{f}i}k_{\mathrm{f}i_\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{vesicle}\mathrm{N_A}dt$
projects / ool / lipid_simulation_formalism.git / commitdiff