Biology Reference
In-Depth Information
CONCLUSIONS
This paper applies higher-level Petri nets to the design, qualitative analysis, and execution of metabolic
steady state system models. Compared to low-level Petri nets and to algebraic methods and tools from
biochemistry, this approach renders important new results about the invariants and the processes of
(sufficiently complex) metabolic pathways. The crucial point of using high-level nets is the ability
to discriminate metabolites, if necessary, according to their topological environment, i.e., the reaction
chains in which they are involved. On this basis, models can be developped which can be simulated
smoothly and can be subjected to a rigorous symbolic analysis. This has been demonstrated for the rather
complex sample of the combined glycolysis and pentose phosphate pathways. Our main results are the
following.
Firstly, some full S-invariant of the sample net were found that represent interesting, non-trivial
preservation laws for the total amounts of certain atoms or molecules in the system. Additionally, their
incremental construction may reveal inconsistencies or deficiencies of the examinated model.
Secondly, the elementary modes (and the corresponding T-invariants) and their overall reaction equa-
tions as computed by METATOOL have been verified. These three T-invariants have been represented as
one parameterized vector. Moreover, not only the number of reaction occurrences related to a T-invariant,
but also their partial order has been determined.
Thirdly, the sample net model can be simulated cyclically, restoring the initial system state at the end
of each cycle, avoiding deadlocks, and respecting the inherent concurrency.
Fourthly, a biochemical interpretation of high-level Petri net models of steady state pathways and their
invariants may enhance the understanding of metabolic processes.
A most interesting topic for further research is the question whether or to which extent the search
for and the construction of S- and T-invariants can be automated. Moreover, the significance of (full)
S-invariants and defects deserves an increased attention. Finally, the application of symbolic analysis to
less understood metabolic systems is expected to lead to valuable new results.
ACKNOWLEDGEMENTS
We thank for the financial support by the BMBF (Federal Ministry of Education and Research of
Germany), BCB project number 0312705D. Further we would like to thank Hartmann Genrich and
Stefan Schuster for fruitful discussions.
Abbreviations
Metabolites/Compounds
ADP
Adenosine diphosphate
ATP
Adenosine triphosphate
BPS
1,3-Biphosphoglycerate
DHAP
Dihydroxyacetone phosphate
DPG
2-Phosphoglycerate
E4P
Erythose-phosphate
FBP
Fructose biphosphate
F6P
Fructose-phosphate
GAP
Glyceraldehyde-phosphate
Gluc
Glucose
GSH
Glutathione
GSSG
Glutathionedisulfide
G6P
Glucose-phosphate
Lac
Lactate
Search WWH ::




Custom Search