Biological Petri Nets - Volume 162 Studies in Health by E. Wingender

By E. Wingender

It was once advised a few years in the past that Petri nets could be compatible to modeling metabolic networks, overcoming a few of the obstacles encountered via platforms making use of ODEs (ordinary differential equations). a lot paintings has been performed on the grounds that then which confirms this and demonstrates the usefulness of this idea for structures biology. Petri internet know-how isn't just intuitively understood by means of scientists expert within the existence sciences, it additionally has a powerful mathematical origin and offers the mandatory measure of flexibleness. therefore it sounds as if to be a really promising method of modeling organic platforms. matters lined contain a precis of crucial subject matters, easy requisites and constraints; quantitative modeling of metabolic networks, gene regulatory and cell-cell communique strategies; the concept that of hybrid Petri nets; modeling sign transduction pathways; internet types of metabolic regular states in addition to a few extra functions of Petri web dependent modeling. The booklet is helping to demonstrate the price of Petri internet method of sleek lifestyles sciences. it truly is devoted to the reminiscence of Prof. Dr. Carl Adam Petri.IOS Press is a world technological know-how, technical and clinical writer of high quality books for teachers, scientists, and execs in all fields. a few of the parts we submit in: -Biomedicine -Oncology -Artificial intelligence -Databases and knowledge platforms -Maritime engineering -Nanotechnology -Geoengineering -All elements of physics -E-governance -E-commerce -The wisdom economic climate -Urban stories -Arms keep an eye on -Understanding and responding to terrorism -Medical informatics -Computer Sciences

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Biological Petri Nets - Volume 162 Studies in Health Technology and Informatics

It used to be recommended a few years in the past that Petri nets may be compatible to modeling metabolic networks, overcoming many of the obstacles encountered by way of structures applying ODEs (ordinary differential equations). a lot paintings has been performed considering the fact that then which confirms this and demonstrates the usefulness of this idea for structures biology.

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However, one should be aware that this generates self-loops, so that the Petri net is no longer pure. Thus, as far as the external metabolites are concerned, the incidence matrix does not equal the stoichiometry matrix. This is no problem since the external metabolites are not usually included in the stoichiometry matrix [Heinrich and Schuster, 1996]. I. Zevedei-Oancea and S. Schuster / Topological Analysis of Metabolic Networks Based on Petri Net Theory 24 INVARIANTS IN PETRI NETS When studying a system, it is always appropriate to begin with the study of its structural invariants.

9. Petri net representation of the glycolysis metabolism of Trypanosoma brucei. T1 = {NADH, NAD+ } is simultaniously a P -invariant, a trap and a siphon. In the absence of TPI1 and TPI2 , t2 = {DHAPg, DHAPc, GLY3Pg, GLY3Pc, Gly} is a trap. If TPI1 and TPI2 act, t2 is not a trap any more, but t3 = {DHAPC, DHAPg, GLY3Pc, GLY3Pg, Gly, GA3P, BPGA, 3PGK, 2PGK, PEP, Pyr} forms a trap. We consider the case where the flux through t2 is positive and ALD is product-inhibited by DHAPg. 32 Places Firing ATP Glu F16P DHAPg DHAPc GA3P NADH NAD + GLY3Pg GLY3Pc BPGA 3PGA 2PGA PEP Pyr Gly sequence ADP 2 0 ∞ 0 0 0 0 1 0 0 0 0 0 0 0 0 e1 0 2 ∞ 1 0 0 0 1 0 0 0 0 0 0 0 0 ALD 0 2 ∞ 0 1 0 1 1 0 0 0 0 0 0 0 0 GPDH 0 2 ∞ 0 0 0 1 0 1 1 0 0 0 0 0 0 GAPDH 0 2 ∞ 0 0 0 0 1 0 1 0 1 0 0 0 0 PGK 1 1 ∞ 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 ∞ 0 0 0 0 1 0 1 0 0 0 1 0 0 t3 e2 1 1 ∞ 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 ∞ 0 0 0 0 1 0 1 0 0 0 0 0 1 e3 t2 1 1 ∞ 0 0 0 0 1 0 0 1 0 0 0 0 1 GPO 1 1 ∞ 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 ∞ 0 1 0 0 1 0 0 0 0 0 0 0 1 t1 GPDH 1 1 ∞ 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 ∞ 0 0 0 0 0 1 0 1 0 0 0 0 1 t2 GPO 1 1 ∞ 0 0 1 0 0 1 0 0 0 0 0 0 1 t1 1 1 ∞ 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 m0 .

Schuster / Topological Analysis of Metabolic Networks Based on Petri Net Theory 33 Petri net (Fig. 7B) and then, analysed it using the program INA. For modelling the external metabolites, we have chosen to introduce a self-loop for each source and each sink and to keep the same firing rule (2) independently of the metabolite’s type. If we do not impose capacities for the internal metabolites, the net is unbounded because uridine, for example, can accumulate more and more tokens if Cdd keeps firing while Urk1 is not.

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