Biology Reference
In-Depth Information
transitions, meaningless
T
-invariants arise. For example, in the scheme shown in Fig. 6, the
T
-invariant
{
}
occurs. In order to avoid the cancellation of such
T
-invariants after their computation, it will
be worthwhile extending Petri net theory by allowing for reversible transitions.
A property that can be checked for Petri nets is boundedness. As biochemical networks are open
systems, they are not usually covered by semi-positive
P
-invariants; that is, they are not conservative.
Nevertheless, subnets are often covered by such invariants and are, therefore, bounded. For example,
if the conservation relation ATP
+
ADP
=
const. holds, one can deduce that the energy currency
metabolite ATP cannot exceed a certain limit. If negative coefficients exist in the conservation relation,
boundedness cannot be guaranteed even for the corresponding subnet. Beside conservative subnets,
there may be superconservative subnets. Obviously, they imply unboundedness. First, there may be
metabolites that are only produced by irreversible reactions but not consumed by any reaction (Fig. 8).
Second, if consuming reactions exist, the catalysing enzymes may have such a low maximal velocity
(saturation level) that the rate of production is higher than the rate of consumption.
Here, we have focussed on topological analysis, which deals with the properties that occur from the
static construction of the network. For many biological applications, such as the assignment of the
metabolic function to an enzyme gene (functional genomics) [Dandekar
et al.
, 1999; F orster
et al.
, 2002;
Selkov
et al.
, 1997], it is sufficient to analyse these properties rather than the dynamics. The structural
properties are the most representative features that one should look for. Compared to kinetic parameters
of enzymes, they are constant in time and often much better known. Thus, reaction stoichiometries are
easier to get from databases [Kanehisa and Goto, 2000; Selkov
et al.
, 1996]. Topological analysis, (in
particular, the computation of invariants) constitutes the basis for the simulation of the dynamics of the
system.
T
1
,
t
2
ACKNOWLEDGEMENTS
We would like to thank Dr. Barbara Bakker (Amsterdam) for drawing our attention to the special
properties of TPI mutants in
T. brucei
and Drs. I. Koch and P. H. Starke (Berlin) for helpful discussions.
Financial support by the DFG to both authors is gratefully acknowledged.
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