Error Bound for Hill-Function Approximations in a Class of Stochastic Transcriptional Network Models

Abstract

Hill functions are often used in stochastic models of gene regulation to approximate the dependence of gene activity on the concentration of the transcription factor which regulates the gene. It is incompletely known, however, how much error one may incur from this approximation. We investigate this question in the context of transcriptional networks (TN). In particular, under the assumption of rapid binding and unbinding of transcription factors with their gene targets, we bound the approximation error associated with Hill functions for TNs in which each transcription factor regulates a gene in a one-to-one fashion and each regulated gene produces a single transcription factor. We also assume that transcription factors do not homodimerize or heterodimerize and that each gene only has a single transcription factor binding site. These results are pertinent for the modeling of TNs and may also carry relevance for more general biological processes.