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title:
Hybrid models as a strategy for tackling high dimensional Bio-Chemical reaction networks. |
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name:
Jahnke |
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first name:
Tobias
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location/conference:
SPP-JT13
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WWW-link:
.math.kit.edu/ianm3/~sunkara/en |
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event_NEW/dateien/SPP-JT13/talks/Jahnke_JT13.pdf |
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abstract:
Modern systems biology is working towards describing processes in Bio-Chemical Reaction Networks by Markov jump processes.The probability of observing any particular state the network is in at a particular point in time evolves according to the Chemical Master Equation (CME). Unfortunately, the CME of a realisitic bio-chemical system cannot be solved with standard methods due to the high dimension of the underlying state space. We discuss using hybrid models to make the CME more computationally tractable for large bio-chemical systems. The hybrid framework imposes that certain interactions in the network behave deterministically and other stochastically. This has motivated the development of hybrid models which are computationally much cheaper but nevertheless approximate the dynamics of the full CME in a certain sense. In this talk, we consider a hybrid model where a low-dimensional CME (describing the time evolution of species with low copy numbers) is coupled to a set of ordinary differential equations (representing the abundant species). We prove an error bound for the approximation given by the hybrid model and introduce a new numerical technique for computing bio-chemical systems with a large number of interacting species. |
