https://github.com/davidcsterratt/KappaNEURON
Revision 6a88c934b3f78ff0a213b88a04e6e7e6efa6df3d authored by David C Sterratt on 06 January 2017, 14:37:31 UTC, committed by David C Sterratt on 06 January 2017, 14:37:31 UTC
1 parent 9aa8f57
Tip revision: 6a88c934b3f78ff0a213b88a04e6e7e6efa6df3d authored by David C Sterratt on 06 January 2017, 14:37:31 UTC
Added pulling of aclocal
Added pulling of aclocal
Tip revision: 6a88c93
units.tex
\documentclass{article}
\usepackage{tabularx}
\usepackage[amssymb]{SIunits}
\addunit{\molar}{M}
\newcommand{\cS}{[\mathrm{S}]}
\newcommand{\NA}{N_\mathrm{A}}
\newcommand{\convfac}{10^{-18}N_\mathrm{A}}
\usepackage[left=1in,right=1in]{geometry}
\begin{document}
\section{Units and conversions}
\begin{table}
\centering
\begin{tabularx}{\linewidth}{l>{$}l<{$}>{\ttfamily}lll}
Quantity & \mathrm{Symbol} & \textrm{NEURON varible names} & Units \\
\hline
Species concentration & \cS & states & mM \\
Species number & S & Stot,DeltaStot & \\
Current density & I & & mA\per\centi\meter\squared\\
Absolute current & & rhs & \\
Faraday's constant & F & h.FARADAY & C\per\mole \\
Compartment volume & v & volumes[] & \micro\meter\cubed \\
Compartment area & a & surface\_area[] & \micro\meter\squared \\
Avogadro's constant & \NA & & \per\mole \\
Molecules\per mM\per\micro\meter\cubed & \convfac &
molecules\_per\_mM\_um3 \\
Rate of change of concentration & \cS/dt & b & \milli\molar\per\milli\second \\
\hline
\end{tabularx}
\caption{Quantities}
\label{tab:quantities}
\end{table}
\subsection{Number of molecules to concentration}
\label{units:sec:numb-molec-conc}
\begin{equation}
\label{units:eq:1}
\cS = \frac{S}{\NA v}
\end{equation}
\begin{equation}
\label{units:eq:2}
\cS \milli\molar = \frac{S}{\NA\per\mole v\micro\meter\cubed}
= \frac{S}{\NA v}
\frac{\mole}{\micro\meter\cubed}
= \frac{S}{\NA v}
\frac{\mole}{\deci\meter\cubed}\frac{\deci\meter\cubed}{\micro\meter\cubed}
= \frac{S}{\NA v}
10^{15} \molar
= \frac{S}{\NA v}
10^{15} 10^3 \milli\molar
= \frac{S}{10^{-18}\NA v}
\milli\molar
\end{equation}
\subsection{Rate of change of concentration to absolute current}
\label{units:sec:numb-molec-conc}
\begin{equation}
\label{units:eq:3}
I = \frac{d\cS}{dt} z F v
\end{equation}
\begin{equation}
\label{units:eq:3}
I = \frac{d\cS}{dt} \frac{\milli\molar}{\milli\second} z F
\frac{C}{\mole} v \micro\meter\cubed
= \frac{d\cS}{dt} z F v \frac{\mole}{\deci\meter\cubed}
\frac{C}{\mole} \micro\meter\cubed
= \frac{d\cS}{dt} z F v \frac{\mole}{\second\deci\meter\cubed}
\frac{C}{\mole} \micro\meter\cubed
= \frac{d\cS}{dt} z F v
\frac{C}{\second} 10^{-15}
= \frac{d\cS}{dt} z F v
10^{-15} \ampere = 10^{-6} \frac{d\cS}{dt} z F v
\nano\ampere
\end{equation}
\end{document}
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