A New Time-Dependent Complexity Reduction Method for Biochemical Systems

Systems biology aims at an understanding of increasingly large and complex cellular systems making use of computational approaches, e.g. numerical simulations. The size and complexity of the underlying biochemical reaction networks call for methods to speed up simulations and/or dissect the biochemical network into smaller subsystems which can be studied independently. Both goals can be achieved by so-called complexity reduction algorithms. However, existing complexity reduction approaches for biochemical reaction networks are mostly based on studying the steady state behavior of a system and/or are based on heuristics. Given the fact that many complex biochemical systems display highly nonlinear dynamics and that this dynamics plays a crucial role in the functioning of the organism, a new methodology has to be developed. Therefore, we present a new complexity reduction method which is time-dependent and suited not only for steady states, but for all possible dynamics of a biochemical system. It makes use of the evolution of the different time–scales in the system, allowing to reduce the number of equations necessary to describe the system which is speeding up the computation time. In addition, it is possible to study the way different variables/metabolites contribute to the reduced equation system which indicates how strongly they interact and couple. In the extreme case of variables decoupling in a specific state, the method allows the complete dissection of the system resulting in subsystems that can be studied in isolation. The whole method provides a systematic tool for an automated complexity reduction of arbitrary biochemical reaction networks. With the aid of a specific example, the oscillatory peroxidase-oxidase system, we show that coupling of time–scales depends heavily on the specific dynamics of the system. Therefore, neither computational improvement nor systematic understanding can be achieved by studying these aspects solely under steady state conditions.