Mutual information and the fidelity of response of gene regulatory models

We investigate cellular response to extracellular signals by using information theory techniques motivated by recent experiments. We present results for the steady state of the following gene regulatory models found in both prokaryotic and eukaryotic cells: a linear transcription-translation model and a positive or negative auto-regulatory model. We calculate both the information capacity and the mutual information exactly for simple models and approximately for the full model. We find that (1) small changes in mutual information can lead to potentially important changes in cellular response and (2) there are diminishing returns in the fidelity of response as the mutual information increases. We calculate the information capacity using Gillespie simulations of a model for the TNF-alpha-NF-kappa B network and find good agreement with the measured value for an experimental realization of this network. Our results provide a quantitative understanding of the differences in cellular response when comparing experimentally measured mutual information values of different gene regulatory models. Our calculations demonstrate that Gillespie simulations can be used to compute the mutual information of more complex gene regulatory models, providing a potentially useful tool in synthetic biology.