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Environmental Statistics and Optimal Regulation

Figure 2

Cost convexity relative to benefit produces preference for either thresholding or for graded response.

For a benefit function that is linear in nutrient concentration (purple curves in top panel) and a simple polynomial cost function , concave cost (, left column) implies an optimal enzyme expression level of either zero or the maximal enzyme level (thresholding), whereas convex cost (, right column) implies an optimal enzyme expression level that varies continuously with the cellular readout (graded response). Top row: costs (green curves) and benefits (purple curves) associated with an enzyme expression level for a given nutrient concentration. Bottom row: optimal regulatory strategy specifying a enzyme expression level for a given cellular readout.

doi: https://doi.org/10.1371/journal.pcbi.1003826.g002