Intrinsic noise can increase or decrease information transfer in threshold genetic systems.

<p>(A) Any transmission of signals (<i>x</i>) that could lead to an error in the output (<i>y</i>) can be framed as a noisy information channel. The mutual information (MI) quantifies the dependence between input and output distributions, <i>P</i>(<i>x</i>) and <i>P</i>(<i>y</i>), respectively, and can discriminate some associations not detected by the correlation coefficient. For instance, the cartoon illustrates two cases with the same correlation (represented by the eccentricity of the ellipses) but different MI. (B) The channel can describe a gene autoactivating its own expression (<i>y</i>) in a bistable OFF/ON manner, i.e., a simple example of threshold regulatory circuit. Information transfer depends on the relationship between <i>x</i> and the threshold value of activation (<i>x</i> and <i>y</i> in arbitrary units). Three instances of <i>P</i>(<i>x</i>) are shown (uniform distributions with different means; the blue one corresponds to a mean equal to the threshold value). When the signal is always beyond the threshold (red distribution) the circuit exhibit a nonzero MI only when it works stochastically (note the output distributions). Here we considered a binary response (OFF if <i>y</i> < 1, ON otherwise). (C) Resonance in MI as a function of intrinsic noise for the red <i>P</i>(<i>x</i>) in (B). MI values computed with the responses of the device to 10⁴ different signals drawn from the described distribution. Responses are shown explicitly for three noise strengths (inset figures, black dots), together with its averaged stimulus-response profile (red curve). The maximum in MI occurs when the averaged stimulus-response profile is more linear (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005156#pcbi.1005156.s002" target="_blank">S1 Fig</a>). (D) Other signal distributions, in which intrinsic noise always reduces MI, can nevertheless exhibit a resonance when the combined response of several units is considered (we show here the case of duplicated threshold devices; <i>N</i> = 2). Colors correspond to those distributions shown in (B). See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005156#sec010" target="_blank">Materials and Methods</a> for details.