(383a) Model-Reduction by Simultaneous Determination of Network Topology and Parameters: Application to Modules in Biochemical Networks

Biochemical reaction networks are composed of numerous chemical species with complex reactions and interactions spanning multiple timescales and spatial domains, making the networks complicated non-linear systems. To understand these complex networks they can be depicted as biochemical reaction schemes (mechanisms) which can be formulated mathematically and analyzed computationally. However, computational analysis of large biochemical networks is impractical due to unavailability of data and the computational complexity of simulation. To simplify, the networks can be broken down into distinct modules. However, the modules themselves can be quite complex. Hence, there is a need for development of methods to reduce the size and complexity of computational models for the modules themselves while retaining predictive accuracy. In this paper, with a brief discussion on recent work on reduction of reaction-networks, a new algorithm is presented in which both the network topology of the reduced network and the parameters are determined simultaneously.

Optimization-based approaches have been successfully applied to reduce reaction networks. Edwards et al. (1998) used genetic-algorithm (GA)-based optimization approach to identify reactions that could be eliminated. Bhattacharjee et al. (2003) used an integer programming approach to solve the optimization problem. These methods assume that the rate parameters are known which is seldom true about biological systems. Hence, a methodology in which both the parameters and the reduced-network topology can be identified using the available data is needed. Recently, Maurya et al. (2005) presented an iterative procedure to reduce reaction networks using an implicit multidimensional sensitivity analysis (MDSA) approach. In each-iteration first the network topology was determined followed by the estimation of the unknown parameters. In this paper a new algorithm is presented where both the reduced-network topology and the unknown parameters are determined simultaneously (mixed-integer nonlinear optimization) using a GA. Thus, no iterations are needed. Succinct details and the important results are presented below.

In this approach, binary variables are used to indicate whether or not a parameter is retained in the model. Complex expressions in which some parameters should be retained or be eliminated simultaneously can be handled by introducing appropriate constraints. The key idea is to substitute each parameter, say, k, by the expression k_ret*k, and then to optimize with respect to both k and k_ret to minimize the fit error between experimental data and model predictions. The relevant constraints also are reformulated appropriately. k_ret = 1 or 0 mean that parameter is retained or eliminated, respectively. The computational complexity of the overall process is about only twice of the complexity of parameter estimation for the detailed model. Thus, this approach is much faster than the MDSA approach.

The proposed approach is used to develop a reduced-order model (ROM) of the GTPase cycle module of m1 muscarinic acetylcholine receptor, Gq, and regulator of G-protein signaling 4 (RGS4, a GTPase activating protein or GAP) starting from a detailed model proposed by Bornheimer et al. (2004). The detailed model has 48 reaction-rate parameters. The reduced-order model obtained using the proposed method has only 14 parameters, and is better than the model obtained using the MDSA method. Further, the methodology is about an order-of-magnitude faster than the MDSA method (Maurya et al., 2005).

Key words: model-reduction, parameter-estimation, topology, signal-transduction, GTPase cycle, mixed-integer nonlinear optimization, genetic-algorithm.

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