Hill kinetics as a noise filter: the role of transcription factor autoregulation in gene cascades

An intuition based on deterministic models of chemical kinetics is that population heterogeneity of transcription factor levels in cells is transmitted unchanged downstream to the target genes. We use a stochastic model of a two-gene cascade with a self-regulating upstream gene to show that, counter to the intuition, there is no simple mapping (bimodal to bimodal, unimodal to unimodal) between the shapes of the distributions of transcription factor numbers and target protein numbers in cells. Due to the presence of the two regulations, the system contains two nonlinear transfer functions, defined by the Hill kinetics of transcription factor binding. The transfer function of the regulator can "interfere" with the transfer function of the target, converting the bimodal input into a unimodal output or vice versa. We show that this effect can be predicted by a geometric construction. As an example application of the method, we present a case study of a system of several downstream genes of different sensitivities, controlled by a common transcription factor which also regulates its own transcription. We show that a single regulator can induce qualitatively different patterns (binary or graded) of responses to a signal in different downstream genes, depending on whether the sensitivity regions of the transfer functions of the upstream and downstream genes overlap or not. Alternatively, the same model can be interpreted as describing a single downstream gene that has different sensitivities in different cell lines due to mutations. Our model shows, therefore, a possible kinetic mechanism by which different genes can interpret the same biological signal in a different manner.