400 9.2  Systems Biology and Biophysics: “Systems Biophysics”

all distances between data points must be less than a predetermined threshold, if not

then remove these points from the putative cluster, which, after several iterations,

may result in eroding that cluster entirely).

In biological applications, network theory has been applied to interactions between

biomolecules, especially protein–​protein interactions and metabolic interactions, including

cell signaling and gene regulation in particular, as well as networks that model the organ­

ization of cellular components, disease states such as cancer, and species evolution models.

Many aspects of systems biology can be explored using network theory.

Bacterial chemotaxis again is an ideal system for aligning systems biology and biophys­

ical experimentation for the study of biomolecular interaction networks. Bacteria live in a

dynamic, often harsh environment in which other cells compete for finite food resources.

Sensory systems have evolved for highly efficient detection of external chemicals. The manner

in which this is achieved is fundamentally different from the general operating principles of

many biological systems in that no genetic regulation (see Chapter 7) as such appears to be

involved. Signal detection and transduction does not involve any direct change in the amount

or type of proteins that are made from the genes, but rather utilizes a network of proteins

and protein complexes in situ to bring about this end. In essence, when one views a typical

bacterium such as E. coli under the microscope, we see that its swimming consists of smooth

runs of perhaps a few seconds mixed with cell tumbling events that last on the order of a few

hundred milliseconds (see Chapter 8).

After each tumble, the cell swimming direction is randomized, so in effect each cell

performs a 3D random walk. However, the key feature to bacterial chemotaxis is that if a

chemical attractant is added to the solution, then the rate of tumbling drops off—​the overall

effect is that the cell swimming, although still essentially randomized by tumbling, is then

biased in the direction of an increasing concentration of the attractant; in other words, this

imparts an ability to move closer to a food source. The mechanisms behind this have been

studied using optical microscopy on active, living cells, and single-​molecule experiments are

now starting to offer enormous insight into systems-​level behavior.

Much of our experimental knowledge comes from the chemosensory system exhibited

by the bacteria E. coli and Salmonella enterica, and it is worth discussing this para­

digm system in reasonable depth since it illustrates some remarkable general features of

signal transduction regulation that are applicable to several different systems. Figure 9.1b

illustrates a cartoon of our understanding to date based on these species in terms of the

approximate spatial locations and key interactions of the various molecular components

of the complete system. Traveling in the direction of the signal, that is, from the out­

side of the cell in the first subsystem we encounter concerns the primary detection of

chemicals outside the cell. Here, we find many thousands of tightly packed copies of

a protein complex, which forms a chemoreceptor spanning the cell membrane (these

complexes can undergo chemical modification by methyl groups and are thus described

as methyl-​accepting chemotaxis proteins [MCPs]).

The MCPs are linked via the protein CheW to the CheA protein. This component has a

phosphate group bound to it, which can be shifted to another part of the same molecule.

This process is known as transautophosphorylation, and it was found that the extent of this

transautophosphorylation is increased in response to a decrease in local chemoattractant

binding to the MCPs. Two different proteins known as CheB and CheY compete in binding

specifically to this transferred phosphoryl group. Phosphorylated CheB (CheB-​P) catalyzes

demethylation of the MCPs and controls receptor adaptation in coordination with CheR that

catalyzes MCP methylation, which thus serves as a negative feedback system to adapt the

chemoreceptors to the size of the external chemical attractant signal, while phosphorylated

CheY-​P binds to the protein FliM on the rotary motor and causes the direction of rotation to

reverse with CheZ being required for signal termination by catalyzing dephosphorylation of

CheY-​P back to CheY.

Biochemical reactions in molecular interaction networks can be solved computation­

ally using the Gillespie algorithm. The Gillespie algorithm (or the Doob–​Gillespie algo­

rithm) generates a statistically optimized solution to a stochastic mathematical equation,