Abstract
Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction events. Since they often involve a large number of interactions, it can be difficult to construct such a model for a system, and since the resulting state-level model can involve a huge number of states, model analysis can be difficult or impossible. Here, we describe methods for the high-level specification of a system using hypergraphs, for the automated generation of a state-level model from a high-level model, and for the exact reduction of a state-level model using information from the high-level model. Exact reduction is achieved through the automated application to the high-level model of the symmetry reduction technique and reduction by decomposition by independent subsystems, allowing potentially significant reductions without the need to generate a full model. The application of the method to biochemical reaction systems is illustrated by models describing a hypothetical ion-channel at several levels of complexity. The method allows for the reduction of the otherwise intractable example models to a manageable size.
Highlights
A system model aims to predict the integrated behavior of a number of interacting system components
The qualitative behavior of a biochemical network may be modeled as a labeled transition system (LTS), consisting of a set of states and labeled transitions between the states, where the transitions correspond to biochemical reaction events
The basic approach used by many of these tools to deal with exploding state-spaces is to define a high-level model (HLM) describing the reaction rules according to some high-level specification method (HLSM), and to use the HLM along with a kinetic Monte Carlo (KMC) algorithm to simulate sample trajectories of a reaction
Summary
A system model aims to predict the integrated behavior of a number of interacting system components. Of several tools designed for this purpose.[1–4] The basic approach used by many of these tools to deal with exploding state-spaces is to define a high-level model (HLM) describing the reaction rules according to some high-level specification method (HLSM), and to use the HLM along with a kinetic Monte Carlo (KMC) algorithm to simulate sample trajectories of a reaction. A large focus on the rule-based modeling of biochemical systems has been geared toward simulation using KMC algorithms, there exists a variety of powerful numerical approaches for the analysis of a HLM that have been developed and applied to many different problems ( in the field of operations) over the last few decades These approaches may be divided into two major classes: (1) those designed to tolerate largeness; and (2) those designed to avoid largeness.
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