By E. Wingender
It was once urged a few years in the past that Petri nets could be compatible to modeling metabolic networks, overcoming a few of the barriers encountered by way of platforms applying ODEs (ordinary differential equations). a lot paintings has been performed in view that then which confirms this and demonstrates the usefulness of this idea for platforms biology. Petri internet know-how isn't just intuitively understood through scientists proficient within the existence sciences, it additionally has a powerful mathematical beginning and gives the necessary measure of suppleness. therefore it sounds as if to be a really promising method of modeling organic structures. topics coated comprise a precis of crucial themes, simple necessities and constraints; quantitative modeling of metabolic networks, gene regulatory and cell-cell verbal exchange approaches; the idea that of hybrid Petri nets; modeling sign transduction pathways; web versions of metabolic regular states in addition to a couple of extra purposes of Petri web established modeling. The booklet is helping to demonstrate the price of Petri web method of smooth lifestyles sciences. it's devoted to the reminiscence of Prof. Dr. Carl Adam Petri.IOS Press is a world technological know-how, technical and clinical writer of top of the range books for lecturers, scientists, and execs in all fields. a few of the parts we submit in: -Biomedicine -Oncology -Artificial intelligence -Databases and knowledge structures -Maritime engineering -Nanotechnology -Geoengineering -All points of physics -E-governance -E-commerce -The wisdom financial system -Urban reports -Arms keep an eye on -Understanding and responding to terrorism -Medical informatics -Computer Sciences
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Extra info for Biological Petri Nets - Volume 162 Studies in Health Technology and Informatics
5. Petri net representation of autocatalysis. enzyme as a parameter (as usually done in biochemical modelling, see Heinrich and Schuster, 1996) rather than explicitly as a substrate. Second, for each loop, one may introduce another place and another transition. If all weights equal unity, the number of tokens in the new place is the difference between the capacity of the old place and the number of tokens that this old place contains already (Fig. 4b). By this construction, the new place corresponds to the enzyme-substrate complex, and the so-called overall reaction (old transition) has been decomposed into half-reactions (the new transitions).
Schuster / Topological Analysis of Metabolic Networks Based on Petri Net Theory 29 concepts of liveness, deadlocks, siphons and traps are connected with each other. A net satisﬁes the deadlock-trap property if each non-empty siphon includes a trap and the maximal trap in each minimal deadlock is sufﬁciently marked. In this case, no dead marking is reachable. So, the net is deadlock-free. A further special class of Petri nets is made up of the free-choice nets. In these nets, each place has at most one output transition or the input places of the output transitions of p consist only of p for any place p belonging to the net.
6). So, for each reversible reaction, we should consider only one ﬂux direction and for the opposite one, we should introduce another transition. So, metabolic networks can be transformed into pure ones. Alternatively, 22 I. Zevedei-Oancea and S. Schuster / Topological Analysis of Metabolic Networks Based on Petri Net Theory Fig. 6. Treatment of reversible reactions. To model a reversible reaction A + B ←→ C + D, one usually introduces a transition for each direction. one might think of deﬁning reversible transitions.
Biological Petri Nets - Volume 162 Studies in Health Technology and Informatics by E. Wingender