Optimal Information Processing in Small Stochastic Biochemical Networks

Etay Ziv, Columbia University

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We argue that the functional quality of a biochemical signaling pathway or a regulatory circuit should be measured in terms of the amount of information (in bits) between the copy numbers of the input and the output signaling molecules that is attainable by the circuit. Treating stochastic effects by the linear noise (semiclassical) expansion around a deterministic solution of a biochemical dynamical system (which we verify by direct Gillespie simulations), we systematically analyze this mutual information in many small biochemical circuits, including various feedback loops, that can be built out of 3 chemical species coupled by Hill-type interactions as a function of ~15 chemical kinetics parameters. We study this information for a certain distribution of the input signals and maximize it over biologically realistic ranges of the parameters. Surprisingly, all the circuits manage to attain almost the maximum information possible (which we calculate analytically) for the given mean molecular copy numbers and integration times. Additionally, these high information solutions are robust to rather large fluctuations in the parameters. These findings suggest potential explanations for the “cross-talk” paradox and other molecular information processing phenomena. Furthermore, they lead us to question an assumption behind many recent publications that naturally occurring biochemical networks are special in their information processing properties.

Abstract Author(s): Etay Ziv<br />Ilya Nemenman <br />Chris Wiggins