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Multi-level modelling via stochastic multi-level multiset rewriting†

Published online by Cambridge University Press:  28 February 2013

NICOLAS OURY  and
GORDON PLOTKIN
NICOLAS OURY
Affiliation:
University of Edinburgh, Edinburgh, United Kingdom Email: Gordon.Plotkin@ed.ac.uk, Nicolas.Oury@ed.ac.uk
GORDON PLOTKIN
Affiliation:
University of Edinburgh, Edinburgh, United Kingdom Email: Gordon.Plotkin@ed.ac.uk, Nicolas.Oury@ed.ac.uk
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Abstract

We present a simple stochastic rule-based approach to multi-level modelling for computational systems biology. Populations are modelled using multi-level multisets; these contain both species and agents, with the latter possibly containing further such multisets. Rules are pairs of such multisets, but they may now also include variables (as well as species and agents), together with an associated stochastic rate.

We give two illustrative examples. The first is an extracellular model of virus infection, coupled with an intracellular model of viral reproduction; this model can demonstrate successive waves of infection. The second is a model of cell division in which a repressor protein is diluted in successive generations, so eventually repression no longer occurs. The multi-level multiset approach can also be seen in terms of stochastic term rewriting for the theory of a commutative monoid equipped with extra constants (for the species) and unary operations (for the agents). We further discuss the relationship of this approach with two others: Krivine et al.'s stochastic bigraphs, restricted to Milner's place graphs, and Coppo et al.'s Stochastic Calculus of Wrapped Compartments. These various relationships provide evidence for the fundamental nature of the approach.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Special Issue 2: Developments In Computational Models 2010 , April 2013 , pp. 471 - 503
Copyright
Copyright © Cambridge University Press 2013

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Footnotes

†

This work was supported by BBSRC/EPSRC Grant BB/D019621/1, and by a Royal Society–Wolfson Award.

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