\newcommand{\OM}[1]{\textcolor{red}{\fxnote{OM: #1}}}
-%\SweaveOpts{prefix.string=pub_318_phys_bio_submission_figures_suppl/pub_318_phys_bio_sub_suppl_fig,pdf=TRUE,eps=TRUE}
\oddsidemargin 0.0in
\textwidth 6.5in
\raggedbottom
\begin{document}
\maketitle
-<<results='hide',echo=FALSE>>=
-require(lattice)
-require(grid)
-require(Hmisc)
-require(gridBase)
+<<load.libraries,echo=FALSE,results="hide",warning=FALSE,message=FALSE,error=FALSE,cache=FALSE>>=
+opts_chunk$set(dev="CairoPDF",out.width="\\columnwidth",out.height="0.7\\textheight",out.extra="keepaspectratio")
+opts_chunk$set(cache=TRUE, autodep=TRUE)
+options(scipen = -2, digits = 1)
+library("lattice")
+library("grid")
+library("Hmisc")
+library("gridBase")
to.latex <- function(x){
gsub("\\\\","\\\\\\\\",latexSN(x))
}
to be 9.6 hr. As this is a first order reaction, and the primary
limiting step in exchange is lipid desorption, $k_\mathrm{b}$ for DMPC is
$k_{\mathrm{b}_\mathrm{PC}}=\frac{\log 2}{9.6 \times 60 \times 60} \approx
-\Sexpr{to.latex(format(log(2)/(9.6*60*60),digits=2))}
+\Sexpr{log(2)/(9.6*60*60)}
\mathrm{s}^{-1}$. We assume that $k_\mathrm{b}$ for SM is the same as for PC.
To estimate the $k_\mathrm{b}$ of PE and PS, we used the data from
\citet{Nichols1982:ret_amphiphile_transfer} who measured the rate of
\frac{k_{\mathrm{b}_\mathrm{PC}}\times\mathrm{PE}}{\mathrm{PC}} \approx
\frac{2\times 10^{-5}\,\mathrm{s}^{-1} \times
0.45\,\mathrm{min}^{-1}}{0.89\,\mathrm{min}^{-1}} \approx
-\Sexpr{to.latex(format(log(2)/(9.6*60*60)*0.45/0.89,digits=2))}$~$\mathrm{s}^{-1}$
+\Sexpr{log(2)/(9.6*60*60)*0.45/0.89}$~$\mathrm{s}^{-1}$
and likewise, $k_{\mathrm{b}_\mathrm{PS}}\approx
-\Sexpr{to.latex(format(log(2)/(9.6*60*60)*0.55/0.89,digits=3))}$~$\mathrm{s}^{-1}$.
+\Sexpr{log(2)/(9.6*60*60)*0.55/0.89}$~$\mathrm{s}^{-1}$.
The $k_\mathrm{b}$ of SM was determined using the work of
\citet{Bai1997:lipid_movementbodipy}, who measured spontaneous
transfer of C$_5$-DMB-SM and C$_5$-DMB-PC from donor and acceptor
$2.2\times10^{-3}$~$\mathrm{s}^{-1}$ respectively; using the ratio of
$k_\mathrm{b}$ of C$_5$-DMB-SM to the $k_\mathrm{b}$ of C$_5$-DMB-PC times the $k_\mathrm{b}$ of
PC ($\frac{3.4 \times 10^{-2}\mathrm{s}^{-1}}{2.2 \times
- 10^{-3}\mathrm{s}^{-1}}
-\Sexpr{to.latex(format(log(2)/(9.6*60*60),digits=2))}\mathrm{s}^{-1}$,
+ 10^{-3}\mathrm{s}^{-1}}\approx
+\Sexpr{log(2)/(9.6*60*60)}\mathrm{s}^{-1}$),
we obtain $k_{\mathrm{b}_\mathrm{SM}} \approx
-\Sexpr{to.latex(format(log(2)/(9.6*60*60)*3.4e-2/2.2e-3,digits=2,scientific=TRUE))}$.
+\Sexpr{log(2)/(9.6*60*60)*3.4e-2/2.2e-3}$.
In the case of CHOL, \citet{Jones1990:lipid_transfer} measured the
$t_{1/2}$ of [$^3$H] transfer from POPC vesicles and found it to be 41
minutes, leading to a $k_{\mathrm{b}_\mathrm{CHOL}} = \frac{\log 2}{41\times
60} \approx
-\Sexpr{to.latex(format(log(2)/(41*60),digits=2,scientific=TRUE))}$~$\mathrm{s}^{-1}$.
+\Sexpr{log(2)/(41*60)}$~$\mathrm{s}^{-1}$.
\subsubsection{Headgroup Surface Area for lipid types}
Different lipids have different headgroup surface areas, which contributes to
$\left[S_\mathrm{vesicle}\right]$. \citet{Smaby1997:pc_area_with_chol}
measured the surface area of POPC with a Langmuir film balance, and
-found it to be 63~$\AA^2$ at $30$~$\frac{\mathrm{mN}}{\mathrm{m}}$.
-Molecular dynamic simulations found an area of 54 $\AA^2$ for
+found it to be 63~Å$^2$ at $30$~$\frac{\mathrm{mN}}{\mathrm{m}}$.
+Molecular dynamic simulations found an area of 54 Å$^2$ for
DPPS\citep{Cascales1996:mds_dpps_area,Pandit2002:mds_dpps}, which is
-in agreement with the experimental value of 56~$\AA^2$ found using a
+in agreement with the experimental value of 56~Å$^2$ found using a
Langmuir balance by \citet{Demel1987:ps_area}.
\citet{Shaikh2002:pe_phase_sm_area} measured the area of SM using a
-Langmuir film balance, and found it to be 61~$\AA^2$. Using $^2$H NMR,
+Langmuir film balance, and found it to be 61~Å$^2$. Using $^2$H NMR,
\citet{Thurmond1991:area_of_pc_pe_2hnmr} found the area of
-DPPE-d$_{62}$ to be 55.4 $\AA^2$. \citet{Robinson1995:mds_chol_area}
-found an area for CHOL of 38~$\AA^2$ using molecular dynamic
+DPPE-d$_{62}$ to be 55.4 Å$^2$. \citet{Robinson1995:mds_chol_area}
+found an area for CHOL of 38~Å$^2$ using molecular dynamic
simulations.
% robinson's chol area is kind of crappy; they did it using MDS, but
% not include a term for it in this formalism.
-\setkeys{Gin}{width=6.4in}
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=10,fig.height=5>>=
+<<unf_graph,echo=FALSE,results='hide',fig.width=10,fig.height=5,cache=FALSE>>=
layout(matrix(1:2,nrow=1,ncol=2))
curve(2^x,from=0,to=sd(c(0,4)),
xlab=expression(paste(stdev,group("(",italic(un[vesicle]),")"))),
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
+<<chf_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
% 1.5 to 0.75 3 to 0.33
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
+<<cuf_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=14,fig.height=5>>=
+<<lf_graph,echo=FALSE,results='hide',fig.width=14,fig.height=5>>=
layout(matrix(1:2,nrow=1,ncol=2))
curve(2^x,from=0,to=sd(c(12,24)),
xlab=expression(paste(stdev,group("(",italic(l[vesicle]),")"))),
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
+<<unb_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
+<<chb_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
+<<cub_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
+<<lb_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
\begin{figure}
-<<echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
+<<cf1b_graph,echo=FALSE,results='hide',fig.width=14,fig.height=7>>=
trellis.device(new=F,color=TRUE)
trellis.par.set(list(axis.line =list(col="transparent")))
pushViewport(viewport(layout=grid.layout(nrow=1,ncol=2),clip="off"))
projects / ool / lipid_simulation_formalism.git / blobdiff