Channel Capacity Computations for Unregulated and Autoregulated Gene Expression

How living cells can reliably process biochemical cues in the presence of molecular noise is not fully understood. Here we investigate the fidelity of information transfer in the expression of a single gene. We use the established model of gene expression to examine how precisely the protein levels can be controlled by two distinct mechanisms: (i) the transcription rate of the gene, or (ii) the translation rate for the corresponding mRNA. The fidelity of gene expression is quantified with the information-theoretic notion of information capacity. Derived information capacity formulae reveal that transcriptional control generally provides a tangibly higher capacity as compared to the translational control. We next introduce negative feedback regulation in gene expression, where the protein directly inhibits its own transcription. While negative feedback reduces noise in the level of the protein for a given input signal, it also decreases the input-to-output sensitivity. Our results show that the combined effect of these two opposing forces is a reduced capacity in the presence of feedback. In summary, our analysis presents the first analytical quantification of information transfer in simple gene expression models, which provides insight into the fidelity of basic gene expression control mechanisms.