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\Section{Life from a Bacterium's Perspective}
\label{sec:Life from a Bacterium's Perspective}

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Bacteria are so small that they are affected by natural forces in ways we are unaccustomed to. For instance, unlike us, bacteria do not coast when they stop swimming; they stop almost instantaneously (0.004 nm) \cite{berg}. The Reynolds number ($\frac{inertial forces}{viscous forces}$ = $\frac{Size \cdot Velocity \cdot Density}{Viscosity}$) is used as a measure of which of the two types of force, inertia (arising from the object's momentum) or viscosity (the amount of resistance the fluid exerts on the object), is the dominant factor that limits movement through fluids.\footnote{An excellent informal paper, \href{http://dx.doi.org/10.1119/1.10903}{Life at Low Reynolds Number (Purcell, 1976)}, is available online at http://dx.doi.org/10.1119/1.10903} Examples of some characteristic Reynolds numbers for self-propelled organisms are shown in Table ~\ref{tab:reynolds_number}.

\begin{table}[htbp]
	\centering
		\begin{tabular}{l r @{.} l}
		\textbf{Organism type}																&
		\multicolumn{2}{c}{\textbf{Reynolds number}} \\
		\hline
		A large whale swimming at 10 m/s											& 300,000,000&0 \\
		A large dragon fly going 7 m/s												&	30,000&0 \\
		Flapping wings of the smallest flying insects 				&	30&0 \\
		A sea urchin sperm swimming at 0.2 mm/s 							&	0&03 \\
		A bacterium, swimming at 0.01 mm/s 										& 0&00001 \\
		\end{tabular}
	\caption{A spectrum of Reynolds numbers for self-propelled organisms taken from \cite{vogel1994lmf}. The Reynolds numbers range from very large values, for a swimming whale, to extremely small values for swimming bacteria. That means that a whale, where inertial effects dominate, will continue to `coast' for a substantial distance and time after it has stopped actively swimming. For a bacterium on the other hand, inertial effects are irrelevant and viscous effects dominate, so that a bacterium will stop almost instantaneously.}
		\label{tab:reynolds_number}
\end{table}

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\end{itemize}

\Section{Motility and Taxis in Model Species}
\label{sec:Motility and Taxis in Model Species}

\Subsection{Motilty}
\label{ssec:Motility}
Unlike swimming animals  \cite{trachtenberg1987tds, block:89}. 

\newpage
\Subsection{The Bacterial Flagellar Motor}
\label{ssec:The Bacterial Flagellar Motor}
The motor, shown in Figure ~\ref{fig:bfm_structure}, is formed from the products of $\sim$40 genes, which are expressed in a particular sequence that results in self-assembly across the cell membrane (reviewed in \cite{macnab03}). The motor consists of a central rotor surrounded (in \ec{} at least) by approximately eleven stator complexes \cite{reid2006mnt}. Torque is generated at the periphery of the rotor by the translocation of ions into the cytoplasm through the stator complexes.

\begin{figure}[htbp]
	\centering
		\includegraphics[scale=0.9]{chapter1/figs1/bfm_structure.jpg}
		\caption{A schematic of the bacterial flagellar motor based on an electron micrograph (EM) (adapted from \cite{berg2008bfm} and \cite{thomas01}). The core of the motor is called the `basal body' that spans the cell envelope.	The L and P rings are thought to be embedded in the outer lipopolysaccharide membrane and peptidoglycan cell wall, respectively. They may work as a bushing between the rotor and the outer parts of the cell envelope. The flow of ions from the periplasm into the cytoplasm through channels in the stator complexes, drives the rotation of the motor. The switch complex (FliG, FliM, and FliN) is responsible for generating torque of the appropriate sign, dependent on cytoplasmic CheY-P levels. See \cite{berg03} and \cite{sowa2008bfm} for full flagellar motor reviews.}
	\label{fig:bfm_structure}
\end{figure}

\Subsubsection{Torque-Generating Units}
\Subsubsection{Motor `Fuel'}
\Subsubsection{Torque-Speed Relationship}