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Environmental Statistics and Optimal Regulation

Figure 5

In a rapidly changing environment, the value of memory peaks at intermediate measurement noise.

For a quadratic cost function and environmental changes on timescales comparable to cellular response, the dimensionless ratio determines the preference among different regulatory strategies [see Eq. (11)]. High relative measurement noise (, right column) leads to a preference for constitutive response; low relative measurement noise (, left column) produces a preference for naive response to the present measurements; and the intermediate case (, middle column) produces a preference for dynamic Bayesian inference that takes into account both present and past measurements. In the heat maps (bottom row), blue represents high levels of enzyme and green represents low.

doi: https://doi.org/10.1371/journal.pcbi.1003826.g005