\documentclass[english,12pt]{article}
+\usepackage{fontspec}
+\setmainfont{FreeSerif}
+\setsansfont{FreeSans}
+\setmonofont{FreeMono}
+\setmathrm{FreeSerif}
+\setmathsf{FreeSans}
+\setmathtt{FreeSerif}
\usepackage{fancyhdr}
%\usepackage[pdftex]{graphicx}
\usepackage{graphicx}
-\usepackage[bf]{caption2}
+\usepackage[bf]{caption}
\usepackage{rotating}
\usepackage{multirow}
-\usepackage{textcomp}
-\usepackage{mathrsfs}
-\usepackage{amssymb}
+%\usepackage{textcomp}
+%\usepackage{mathrsfs}
+%\usepackage{amssymb}
\usepackage{setspace}
-\usepackage{txfonts}
-\usepackage[light,all]{draftcopy}
-\usepackage{fancyref}
-\usepackage{acronym}
+%\usepackage{txfonts}
+%\usepackage[light,all]{draftcopy}
+\usepackage{acro}
\usepackage{array}
\usepackage{dcolumn}
\usepackage{booktabs}
\usepackage[noblocks]{authblk}
+\usepackage[backend=biber,natbib=true,hyperref=true,citestyle=numeric-comp,style=nature,autocite=inline]{biblatex}
+\addbibresource{references.bib}
\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}
-\usepackage{texshade}
-\newenvironment{narrow}[2]{%
- \begin{list}{}{%
- \setlength{\topsep}{0pt}%
- \setlength{\leftmargin}{#1}%
- \setlength{\rightmargin}{#2}%
- \setlength{\listparindent}{\parindent}%
- \setlength{\itemindent}{\parindent}%
- \setlength{\parsep}{\parskip}}%
- \item[]}{\end{list}}
-\newenvironment{paperquote}{%
- \begin{quote}%
- \it
- }%
- {\end{quote}}
+%\usepackage[sectionbib,sort&compress,numbers]{natbib}
+% \usepackage[nomargin,inline,draft]{fixme}
+%\usepackage[x11names,svgnames]{xcolor}
+%\usepackage{texshade}
\renewcommand{\textfraction}{0.15}
\renewcommand{\topfraction}{0.85}
\renewcommand{\bottomfraction}{0.65}
\renewcommand{\floatpagefraction}{0.60}
%\renewcommand{\baselinestretch}{1.8}
-\newenvironment{enumerate*}%
- {\begin{enumerate}%
- \setlength{\itemsep}{0pt}%
-
- \setlength{\parskip}{0pt}}%
- {\end{enumerate}}
-\newenvironment{itemize*}%
- {\begin{itemize}%
- \setlength{\itemsep}{0pt}%
- \setlength{\parskip}{0pt}}%
- {\end{itemize}}
\newcommand{\DLA}[1]{\textcolor{red}{\fxnote{DLA: #1}}}
\newcommand{\OM}[1]{\textcolor{red}{\fxnote{OM: #1}}}
+\input{acronyms}
\oddsidemargin 0.0in
\textwidth 6.5in
\end{equation}
The base forward kinetic parameter for the $i$th component is $k_{\mathrm{f}i}$
-and is dependent on the particular lipid type (PC, PS, SM, etc.). The
+and is dependent on the particular lipid type (\ac{PC}, \ac{PS}, \ac{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 \cref{eq:kf_adj,sec:kinetic_adjustments}).
$k_{\mathrm{f}_\mathrm{PC}}$ was measured by
\citet{Nichols1985:phospholipid_monomer_vesicle_thermodynamics} and
was found to be $3.7\times 10^6$~$\frac{1}{\mathrm{M}\mathrm{s}}$ by the
-partitioning of P-C$_6$-NBD-PC between DOPC vesicles and water. As
-similar references are not available for SM or PS, we assume that they have
-the same $k_\mathrm{f}$. For CHOL, no direct measurement of $k_\mathrm{f}$ is available,
+partitioning of \ac{NBDPC} between \ac{DOPC} vesicles and water. As
+similar references are not available for \ac{SM} or \ac{PS}, we assume that they have
+the same $k_\mathrm{f}$. For \ac{CHOL}, no direct measurement of $k_\mathrm{f}$ is available,
however, \citet{Estronca2007:dhe_kinetics} measured the transfer of
-DHE from BSA to LUV, and found a $k_\mathrm{f}$ of $5.1\times 10^7$~%
+\ac{DHE} from \ac{BSA} to \acp{LUV}, and found a $k_\mathrm{f}$ of $5.1\times 10^7$~%
$\frac{1}{\mathrm{M} \mathrm{s}}$. We assume that this value is close
-to that of CHOL, and use it for $k_{\mathrm{f}_\mathrm{CHOL}}$. In the case of
-PE, \citet{Abreu2004:kinetics_ld_lo} measured the association of
-NBD-DMPE with POPC LUV found a value for $k_\mathrm{f}$ of $2.3 \times 10^{6}$~%
+to that of \ac{CHOL}, and use it for $k_{\mathrm{f}_\mathrm{\ac{CHOL}}}$. In the case of
+\ac{PE}, \citet{Abreu2004:kinetics_ld_lo} measured the association of
+\ac{NBDDMPE} with \ac{POPC} \acp{LUV} found a value for $k_\mathrm{f}$ of $2.3 \times 10^{6}$~%
$\frac{1}{\mathrm{M} \mathrm{s}}$. These three authors used a slightly
different kinetic formalism ($\frac{d\left[A_v\right]}{dt} =
k'_\mathrm{f}[A_m][L_v] - k_\mathrm{b}[A_v]$), so we correct their values of $k_\mathrm{f}$ by
\subsubsection{$k_\mathrm{b}$ for lipid types}
\citet{Wimley1990:dmpc_exchange} measured the half time for the
-exchange of [$^3$H]DMPC between LUV at 30\textdegree C, and found it
+exchange of [$^3$H]\ac{DMPC} between \acp{LUV} at 30\textdegree C, and found it
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
+limiting step in exchange is lipid desorption, $k_\mathrm{b}$ for \ac{DMPC} is
$k_{\mathrm{b}_\mathrm{PC}}=\frac{\log 2}{9.6 \times 60 \times 60} \approx
\Sexpr{log(2)/(9.6*60*60)}
-\mathrm{s}^{-1}$. 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
+\mathrm{s}^{-1}$. We assume that $k_\mathrm{b}$ for \ac{SM} is the same as for \ac{PC}.
+To estimate the $k_\mathrm{b}$ of \ac{PE} and \ac{PS}, we used the data from
\citet{Nichols1982:ret_amphiphile_transfer} who measured the rate of
-exchange of the fluorescent label C$_6$-NBD attached to different
-lipid species. Although the values of kb are different for the labeled
+exchange of the fluorescent label \ac{C6NBD} attached to different
+lipid species. Although the values of $k_\mathrm{b}$ are different for the labeled
and unlabeled lipids, we assume that the ratios of the kinetics
constants for the lipid types are the same. Furthermore we assume that
-PG behaves similarly to PS. Thus, we can determine the $k_\mathrm{b}$ of PE and
-PS from the already known $k_\mathrm{b}$ of PC. For C$_6$-NBD labeled PC,
+PG behaves similarly to \ac{PS}. Thus, we can determine the $k_\mathrm{b}$ of \ac{PE} and
+\ac{PS} from the already known $k_\mathrm{b}$ of \ac{PC}. For \ac{C6NBD} labeled \ac{PC},
\citet{Nichols1982:ret_amphiphile_transfer} obtained a $k_\mathrm{b}$ of
-$0.89$~$\mathrm{min}^{-1}$, PE of $0.45$~$\mathrm{min}^{-1}$ and PG of
+$0.89$~$\mathrm{min}^{-1}$, \ac{PE} of $0.45$~$\mathrm{min}^{-1}$ and PG of
$0.55$~$\mathrm{min}^{-1}$. Assuming the ratios of the rate of
exchange are the same for unlabeled lipids and labeled lipids, we can
-determine the $k_\mathrm{b}$ of PE and PS from the already known $k_\mathrm{b}$ of
-PC~\citep{Wimley1990:dmpc_exchange}. Calculating the ratio, this leads
+determine the $k_\mathrm{b}$ of \ac{PE} and \ac{PS} from the already known $k_\mathrm{b}$ of
+\ac{PC}~\citep{Wimley1990:dmpc_exchange}. Calculating the ratio, this leads
us to $k_{\mathrm{b}_\mathrm{PE}} =
\frac{k_{\mathrm{b}_\mathrm{PC}}\times\mathrm{PE}}{\mathrm{PC}} \approx
\frac{2\times 10^{-5}\,\mathrm{s}^{-1} \times
\Sexpr{log(2)/(9.6*60*60)*0.45/0.89}$~$\mathrm{s}^{-1}$
and likewise, $k_{\mathrm{b}_\mathrm{PS}}\approx
\Sexpr{log(2)/(9.6*60*60)*0.55/0.89}$~$\mathrm{s}^{-1}$.
-The $k_\mathrm{b}$ of SM was determined using the work of
+The $k_\mathrm{b}$ of \ac{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
vesicles, finding $3.4\times10^{-2}$~$\mathrm{s}^{-1}$ and
$2.2\times10^{-3}$~$\mathrm{s}^{-1}$ 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 ($\frac{3.4 \times 10^{-2}\mathrm{s}^{-1}}{2.2 \times
+\ac{PC} ($\frac{3.4 \times 10^{-2}\mathrm{s}^{-1}}{2.2 \times
10^{-3}\mathrm{s}^{-1}}\approx
\Sexpr{log(2)/(9.6*60*60)}\mathrm{s}^{-1}$),
we obtain $k_{\mathrm{b}_\mathrm{SM}} \approx
\Sexpr{log(2)/(9.6*60*60)*3.4e-2/2.2e-3}$.
-In the case of CHOL, \citet{Jones1990:lipid_transfer} measured the
+In the case of \ac{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 $k_{\mathrm{b}_\mathrm{CHOL}} = \frac{\log 2}{41\times
60} \approx
DPPS\citep{Cascales1996:mds_dpps_area,Pandit2002:mds_dpps}, which is
in agreement with the experimental value of 56~Å$^2$ found using a
Langmuir balance by \citet{Demel1987:ps_area}.
-\citet{Shaikh2002:pe_phase_sm_area} measured the area of SM using a
+\citet{Shaikh2002:pe_phase_sm_area} measured the area of \ac{SM} using a
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 Å$^2$. \citet{Robinson1995:mds_chol_area}
-found an area for CHOL of 38~Å$^2$ using molecular dynamic
+found an area for \ac{CHOL} of 38~Å$^2$ using molecular dynamic
simulations.
% robinson's chol area is kind of crappy; they did it using MDS, but
% vaguely; they don't indicate what it was at the end, and they only
-% had 2 molecules of CHOL.
+% had 2 molecules of \ac{CHOL}.
-% PC: 63 A (Smaby97rd) (Pandit (?)
-% PS: 54 A (Pandit02LIB) (Cascales 1996; J. Chem. Phys 104:2713, Mukhopadhyay2004)
-% CHOL: 38 A (Robinson 1995) (Lundberg 1982)
-% SM: 51 A (Shaikh2002, but 61(?))
+% \ac{PC}: 63 A (Smaby97rd) (Pandit (?)
+% \ac{PS}: 54 A (Pandit02LIB) (Cascales 1996; J. Chem. Phys 104:2713, Mukhopadhyay2004)
+% \ac{CHOL}: 38 A (Robinson 1995) (Lundberg 1982)
+% \ac{SM}: 51 A (Shaikh2002, but 61(?))
% PE: 55 A (Thurmond, 1991) (Pandit2002)
%
% Compare to results by Petrache2004 with DOPC of 72.5, DOPS of 65.3.
\subsubsection{Complex Formation 1}
-\citet{Thomas1988:chol_transfer} found that SM significantly decreases
-the rate of cholesterol transfer from PC, while PE and PS have no
+\citet{Thomas1988:chol_transfer} found that \ac{SM} significantly decreases
+the rate of cholesterol transfer from \ac{PC}, while \ac{PE} and \ac{PS} have no
effect at physiologically significant levels. We attribute this to the
-formation of complexes between SM and CHOL, which retards the rate of
-efflux of CHOL from the membrane. Similar complexes exist between PC
-and CHOL, where it was shown that two CHOL molecules complex with one
-PC~\citep{Huang1999:chol_solubility_model,
+formation of complexes between \ac{SM} and \ac{CHOL}, which retards the rate of
+efflux of \ac{CHOL} from the membrane. Similar complexes exist between \ac{PC}
+and \ac{CHOL}, where it was shown that two \ac{CHOL} molecules complex with one
+\ac{PC}~\citep{Huang1999:chol_solubility_model,
Huang1999:cholesterol_solubility,McConnell2006,McConnell2003}. It
-has also been shown that SM binds more CHOL molecules than
-PC~\citep{Katz1988:pl_packing_chol}. We assume that three CHOL complex
-with one SM, leading to $\mathrm{CF}1$ values of $3$, $2$, and $-1$
-for SM, PC, and CHOL, respectively.
+has also been shown that \ac{SM} binds more \ac{CHOL} molecules than
+\ac{PC}~\citep{Katz1988:pl_packing_chol}. We assume that three \ac{CHOL} complex
+with one \ac{SM}, leading to $\mathrm{CF}1$ values of $3$, $2$, and $-1$
+for \ac{SM}, \ac{PC}, and \ac{CHOL}, respectively.
\subsubsection{Curvature}
$l_c$ is the critical length of the acyl chain, $v$ is the volume of
the lipid, and $a$ is the area of the head group.
\citet{Kumar1991:lipid_packing} found a value for $S$ of 1.33 for PE,
-1.21 for CHOL, and 0.8 for diC$_{16}$ PC. We assume that PS has neutral
-curvature (value of 1), and that SM has the same curvature as PC
+1.21 for \ac{CHOL}, and 0.8 for diC$_{16}$ \ac{PC}. We assume that \ac{PS} has neutral
+curvature (value of 1), and that \ac{SM} has the same curvature as \ac{PC}
(0.8). It should also be noted that in reality the curvature parameter
changes with length, but at longer chain lengths, is effectively
constant; in the current model, curvature is held constant for each
\subsubsection{Charge Forward}
-A charged lipid such as PS approaching a vesicle with an average
+A charged lipid such as \ac{PS} approaching a vesicle with an average
charge of the same sign will experience repulsion, whereas those with
different signs will experience attraction, the degree of which is
dependent upon the charge of the monomer and the average charge of the
\subsubsection{Complex Formation Backward}
-Complex formation ($CF1$) describes the interaction between CHOL and
-PC or SM, where PC or SM protects the hydroxyl group of CHOL from
+Complex formation ($CF1$) describes the interaction between \ac{CHOL} and
+\ac{PC} or \ac{SM}, where \ac{PC} or \ac{SM} protects the hydroxyl group of \ac{CHOL} from
interactions with water %
\citep{Huang1999:chol_solubility_model,
Huang1999:cholesterol_solubility, McConnell2006, McConnell2003}%
-. PC ($CF1=2$) can interact with two CHOL, and SM ($CF1=3$) with three
-CHOL ($CF1=-1$). If the average of $CF1$ is positive (excess of SM and
-PC with regards to complex formation), components with negative $CF1$
-(CHOL) will be retained. If average $CF1$ is negative, components with
+. \ac{PC} ($CF1=2$) can interact with two \ac{CHOL}, and \ac{SM} ($CF1=3$) with three
+\ac{CHOL} ($CF1=-1$). If the average of $CF1$ is positive (excess of \ac{SM} and
+\ac{PC} with regards to complex formation), components with negative $CF1$
+(\ac{CHOL}) will be retained. If average $CF1$ is negative, components with
positive $CF1$ are retained. An equation which has this property is
$CF1_\mathrm{b}=a^{\left<CF1_\mathrm{vesicle}\right>
CF1_\mathrm{monomer}-\left|\left<CF1_\mathrm{vesicle}\right>
\subsubsection{Components}
The environment contains concentrations of components. In the current
set of simulations, there are \Sexpr{1+4*5*7} different possible
-components, consisting of PC, PE, PS, SM, and CHOL, with all lipids
-except for CHOL having 5 possible unsaturations ranging from 0 to 4,
+components, consisting of \ac{PC}, PE, \ac{PS}, \ac{SM}, and \ac{CHOL}, with all lipids
+except for \ac{CHOL} having 5 possible unsaturations ranging from 0 to 4,
and 7 lengths from $12,14,...,22$ ($7\cdot
5\cdot4+1=\Sexpr{1+4*5*7}$). In cases where the environment has less
than the maximum number of components, the components are selected in
order without replacement from a randomly shuffled deck of components
-(with the exception of CHOL) represented once until the desired number
-of unique components is obtained. CHOL is overrepresented
+(with the exception of \ac{CHOL}) represented once until the desired number
+of unique components is obtained. \ac{CHOL} is overrepresented
$\Sexpr{5*7}$ times to be at the level of other lipid types, ensuring
-that the probability of CHOL being absent in the environment is the
-same as the probability of any one of the other lipid types (PS, PE,
+that the probability of \ac{CHOL} being absent in the environment is the
+same as the probability of any one of the other lipid types (\ac{PS}, PE,
etc.) being absent. This reduces the number of simulations with a
-small number of components which are devoid of CHOL.
+small number of components which are devoid of \ac{CHOL}.
\subsubsection{Concentrations}
Once the components of the environment have been selected, their
% clustering~\citep{Shenhav2005:pgard}.
-\bibliographystyle{unsrtnat}
-\bibliography{references.bib}
+%\bibliographystyle{unsrtnat}
+%\bibliography{references.bib}
+
+\printbibliography
\end{document}
projects / ool / lipid_simulation_formalism.git / commitdiff