Accurate Encoding and Decoding by Single Cells: Amplitude Versus Frequency Modulation
Fig 5
First three moments of the protein distribution in concentration sensing from the master equation.
Averages (A,B), variance (C,D), and skewness (E,F) as a function of the frequency of binding events, f = k+ c0/(1+k+ c0/k−). (Insets) Magnification of small-noise approximation region (fast switching). Analytical results for CM (blue) and numerical results for BM (red) as function of the frequency of binding events (logarithmic scale). Two regimes are shown: k− = 10 k+ c0 (α = 100s−1, γ = 1s−1, ζ from 1000 to 1) (left column) and k− = 0.1 k+ c0 (α = 10s−1, γ = 1s−1, ζ from 1000 to 1) (right column). Averages from CM and BM are constrained to be equal, i.e. . Variances of CM and BM exhibit two different regimes for fast switching: for k+ c0 < k− BM is more accurate than CM (inset in C), while for k+ c0 > k− CM is generally more accurate (inset in D), except for ζ = 1. Third moments show that, for large noise, the probability distributions become asymmetric.