Biology Reference
In-Depth Information
1982). Also, the presence of the enzymes that are involved in a certain path-
way may be controlled by regulation of the expression of the related genes by
a transcriptional regulatory network. Most prominent among genetic network
models is the
lac
operon of
Escherichia coli
. Here, the transcription of genes
for enzymes that are part of a catabolic pathway is regulated by the carbon and
free-energy sources lactose and glucose; in short, lactose upregulates and glu-
cose suppresses the expression of the
lac
operon (Pardee et al., 1959; Jacob &
Monod, 1961; see Weber, 2005 and Richardson & Stephan, this volume). Sig-
naling systems are the other domain of pathway modeling.
4
Among these are
the visual cascade (Chabre & Deterre, 1989) and other instances of G-protein
signaling (Dohlman & Thorner, 2001). Often rhythms on a short time scale
were under investigation, e.g., in the regulation of the swimming behavior and
chemotactic response of
E. coli
(Spudich & Koshland 1975; Bourret & Stock,
2002). All these systems are conceived as networks that process some kind of
signal or stimulus that elicits a specific response. In chemotaxis of
E. coli
, the
stimulus is a change in the concentration of certain chemicals, mostly nutrients
like glucose and amino acids; the response is a modification of the swimming
behavior, enabling the bacterium to swim, by means of a modulated random
walk, along a chemical gradient. In the G-protein cascades, a photon or a trans-
mitter molecule may act as stimulus or as signal, respectively. The response is
a change in the conductivity of certain ion channels leading to a transient depo-
larization of the cell membrane or activation of other enzymes. These cascades
are self-regulated. In many cases, the response decays even if the changed con-
ditions pertain, allowing so-called perfect adaptation to the background stimulus
level.
3.2. Modeling regulatory networks and gathering data
Mathematical models of metabolic pathways usually rely on the kinetic parame-
ters of the enzymes, determined with isolated active enzyme, and on estimates of
enzyme and metabolite concentrations. Other regulatory networks include param-
eters also for, e.g., protein-protein interaction. Most models are based on basic
chemical reaction kinetics and enzyme kinetics of the Michaelis-Menten kind.
They may be given in terms of a set of ordinary differential equations that take into
account the main in- and outflows of metabolites, including intermediate products
of the pathway. Models of this kind often describe the smallest system that qualita-
tively shows the same dynamics as the biological pathway. As suchmodels proceed
from data about components to a description of a complex system, pathway mod-
eling can be characterized as bottom-up. This makes it a candidate for an important
4
Both domains are not clearly separated, since any regulation of a metabolic pathway may be regarded as
signal processing as well.
