Dynamical complexity reduction of biochemical reaction networks: time scale decomposition
The simulation of the dynamical behavior of increasingly large cellular systems is hampered by the size and complexity of the underlying biochemical reaction network models. In order to reduce the computational demand of the simulations, and also in order to facilitate the identification of the key features of the dynamical systems, the availability of a suitable complexity reduction method must be considered as an indispensable prerequisite. Such a complexity reduction method should allow for a systematic and automated decomposition of the network model into weakly or non-interacting subsystems, each of them representing a well-defined subset of the properties of the dynamical system under investigation. However, existing complexity reduction approaches are either based on the evaluation of structural network properties only or rely on specific assumptions - namely the system operating under steady state conditions.
With the aim of providing a complexity reduction tool for biochemical reaction networks that works independent of the assumption of a specific dynamical behavior of the system, we have designed and implemented a method based on a time scale decomposition of the reaction network. This dynamical complexity reduction method relies on the fact that the processes responsible for the dynamics of the biochemical reaction network typically take place on time scales differing by up to several orders of magnitude. Based on this finding the system is decomposed in a dynamical way. Processes being sufficiently fast compared to the actual time scale of interest - which of course changes within the course of the dynamical simulation - are assumed to be relaxed and are therefore neglected. The number of ordinary differential equations which need to be solved in order to obtain the time evolution of the reaction network in the context of a deterministic, spatially homogeneous modeling formalism is reduced accordingly. In addition, the analysis of the species participating in the active processes provides valuable insight into the nature of the processes and interactions responsible for the dynamical properties of the reaction network on a specific time scale.
As a first non-trivial testcase our dynamical complexity reduction tool has been successfully applied to the simulation of the dynamics of a Peroxidase-Oxidase reaction network model comprising 15 individual reactions. As a result we managed to reduce the dimension n of the active space in the course of the simulation substantially (n = 3 - 5) - even in the demanding case of the system showing a complex oscillatory behavior.
Future work in the project will focus mainly on improving the efficiency and analytical capabilities of the prototype implementation as well as increasing the usability of the tool by implementing appropriate user interfaces. Additionally, alternative reduction methods will be evaluated.
Dr. Dirk Lebiedz , Anton Ishmurzin, Julia Kammerer, IWR, University of Heidelberg, Heidelberg, Germany