\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}