Genetic regulatory network identification using multivariate monotone functions

We present a method for identification of gene regulatory network topology using a time series of gene expression data. The underlying assumption is that the regulatory effects of a set of regulators to a gene can be described by a multivariate function. The multivariate function is constrained to be continuous, nonnegative and monotonic in each variable. We present necessary and sufficient conditions for the validity of the regulation hypothesis. Checking these conditions can be expressed as a Linear Programming feasibility problem. This paper builds on our previous work, where the regulation is described by a summation of multiple regulator functions, one function for each gene in the regulator set. Our procedure is two phased; the first identifies the correct set of regulators, the second uses the data and the regulator set to generate an appropriate regulator function. This paper focuses on the identification of the correct regulator set. As demonstration, we run our main algorithm on some experimental data from a synthetic gene network in yeast. We are able to show that the correct set of regulators is picked by the algorithm.