A Hybrid Parameter Estimation Algorithm for S-System Model of Gene Regulatory Networks

The reconstruction of a gene regulatory network expressed in terms of a S-system model may be accomplished by a simple task of parameter estimation. Empirical data indicate that biological gene networks are sparsely connected and the average number of upstream-regulators per gene is less than two, implying that most of parameter variables in the S-system model are zero. It is thus desired to search for a parameter estimation algorithm that is capable of identifying the connectivity of the gene network and determining its reduced number of non-zero parameters. A hybrid algorithm is presented for identification and parameter estimation of gene network structure described by a S-system model. It combines an optimization process with a system identification method commonly used in the aerospace community. Constraint equations in a matrix form are formulated to deal with the steady state and the network connectivity conditions. The system parameter vector resides in the null space of the constraint matrix. The resulting network structure and system parameters are optimally tuned by minimizing the error of state time history. A numerical experiment is given to illustrate the hybrid parameter estimation algorithm.