Fig 1.
Probabilities of correct discrimination between two inputs, xi and xj.
The input distribution, P(X) = (1/2, 1/2), visualized in (A), and the conditional output probabilities P(Y|X), presented in (B), can be translated, via the Bayes formula, into conditional input distributions, P(X|Y), visualized in (C). The conditional input distribution, P(X|Y), serves to calculate the probability of correct discrimination of the observation y, as shown in (D). Precisely, for any fixed output, y, vertical line in (B), the conditional input probability, in (C), P(X|Y = y), quantifies how likely it is that y was generated by each of the inputs. The probability of correct discrimination of the observation, y is given as the maximum of P(xi|Y = y) and P(xj|Y = y). Completely overlapping conditional output probabilities P(Y|X), left column, yield random discrimination as opposed to non-overlapping distributions yielding perfect discrimination, right column. The use of the conditional input distribution, P(X|Y), enables quantification of intermediate scenarios, middle column.
Fig 2.
Information-theoretic analysis of the NF-κB responses to TNF-α stimulation.
(A) Temporally resolved responses of individual cells to selected concentrations of TNF-α. The panel corresponds to Fig. IV in S1 Text. (B) The information capacity as a function of time for time-point responses. (C) As in (B) but for time-series responses. (D) Probabilities of the correct pairwise discrimination between TNF-α concentrations for time-point responses at 21 minutes. The color filled fraction of the circle marks the probability of correct discrimination. (E) The same as in (D) but for time-series responses. (F) Differences between probabilities in (D) and (E). Modeling details: Uncertainties of estimates (grey ribbons in B and C) were obtained by bootstrapping 80% of data (repeated 100 times). Probabilities in (D) and (E) present mean of 50 bootstrap re-sampling.
Fig 3.
(A) A violin plot representation of the conditional output distribution Y|xi for 11 considered inputs. (B) Information capacity estimates as the function of the sample size N. Blue and red lines correspond to SLEMI and KNN estimates, respectively. The bold black line marks the true value of the capacity. For the KNN estimation, k = 10 was assumed. (C) Information capacity estimates of the KNN method as a function of k compared with the true value (bold black line). The error-bars in B and C show the standard deviation of capacity estimates from 40 repeated samplings. N = 1000 was assumed. (D) Computation time of SLEMI and KNN method as the function of the sample size N. (E) Computation time of SLEMI (blue) and the KNN method as the function of the number of considered input values. Input values were subsequently added starting with x1 and x2, only, and ending up with all 11 considered input values. The times reported in panels (D) and (E) correspond to computations performed by a single core on a workstation with Intel Xeon E5-1650 3.50 GHz processor and 32 GB RAM.