Environmental Statistics and Optimal Regulation
Figure 3
Increasing measurement noise shifts the optimal strategy from naive response to constitutive response.
For a quadratic cost function () and relatively slow environmental dynamics, the dimensionless ratio
of the measurement imprecision
(middle row) and the environmental variation
(top row) determines the preference for different regulatory strategies [see Eq. (5)]. Low relative measurement noise (
, left column) leads to a preference for naive response; high relative measurement noise (
, right column) produces a preference for constitutive response; and the intermediate case (
, middle column) leads to a preference for more sophisticated inference incorporating both prior knowledge and the current measurement of the environment. Top row: distribution of possible environmental nutrient concentrations around the mean
. Middle row: distribution of cellular readouts given a particular nutrient concentration (red dotted line).