Fig. 2

Mechanisms for metabolite bimodality. a We evaluated the Poisson Mixture Model across a broad range of promoter switching timescale and promoter activity. Unimodal distributions for enzyme and metabolite (similar to those shown in Fig. 1c) cover a large fraction of the parameter space. We identified two regimes in which metabolites are bimodal: in the switching-induced regime, bimodality propagates from the enzyme to the metabolite. In the catalytically-induced regime, bimodality originates from a lowly abundant enzyme and the strong separation of timescales between expression and catalysis. The small panels show model predictions for a fixed kinetic parameter K = 0.1333 molecules, and increasing λ_∞ = {300, 3000, 30000} molecules, obtained by increasing the turnover rate constant k_cat. b Exact simulations for two parameter sets verify the predictions drawn from the PMM approximation. We simulated over a long time horizon to obtain accurate estimates for stationary distributions; insets show only a small portion of the time courses. The parameter values for the promoter switching rates are indicated in panel (a) and we fixed λ_∞ = 500 molecules. Both types of bimodality can be clearly distinguished in the time courses, but we note that they lead to almost identical distributions for the metabolite. In both cases, the PMM provides an accurate approximation for the stationary distributions