Data from:A method for estimating Hill function-based dynamic models of gene regulatory networks

Gene regulatory networks (GRNs) are quite large and complex. To better understand and analyze GRNs, mathematical models are being employed. Different types of models, such as logical, continuous, and stochastic models, can be used to describe GRNs. In this paper, we present a new approach to identify continuous models, since they are more suitable for large number of genes and quantitative analysis. One of the most promising techniques for identifying continuous models of GRNs is based on Hill functions and generalized profiling method (GPM). The advantage of this approach is low computational cost and insensitivity to initial conditions. In the GPM, a constrained nonlinear optimization problem has to be solved that is usually under-determined. In this paper, we propose a new optimization approach in which we reformulate the optimization problem such that constraints are embedded implicitly in the cost function. Moreover, we propose to split the unknown parameter in two sets based on the structure of Hill functions. These two sets are estimated separately to resolve the issue of under-determined problem. As a case study, we apply the proposed technique on the SOS response in Escherichia coli and compare the results with the existing literature.