Information transmission in biological signaling circuits has often beendescribed using the metaphor of a noise filter. Cellular systems need accurate,real-time data about their environmental conditions, but the biochemicalreaction networks that propagate, amplify, and process signals work with noisyrepresentations of that data. Biology must implement strategies that not onlyfilter the noise, but also predict the current state of the environment basedon information delayed due to the finite speed of chemical signaling. The ideaof a biochemical noise filter is actually more than just a metaphor: wedescribe recent work that has made an explicit mathematical connection betweensignaling fidelity in cellular circuits and the classic theories of optimalnoise filtering and prediction that began with Wiener, Kolmogorov, Shannon, andBode. This theoretical framework provides a versatile tool, allowing us toderive analytical bounds on the maximum mutual information between theenvironmental signal and the real-time estimate constructed by the system. Ithelps us understand how the structure of a biological network, and the responsetimes of its components, influences the accuracy of that estimate. The theoryalso provides insights into how evolution may have tuned enzyme kineticparameters and populations to optimize information transfer.
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