  Information transmission in biological signaling circuits has often been
described using the metaphor of a noise filter. Cellular systems need accurate,
real-time data about their environmental conditions, but the biochemical
reaction networks that propagate, amplify, and process signals work with noisy
representations of that data. Biology must implement strategies that not only
filter the noise, but also predict the current state of the environment based
on information delayed due to the finite speed of chemical signaling. The idea
of a biochemical noise filter is actually more than just a metaphor: we
describe recent work that has made an explicit mathematical connection between
signaling fidelity in cellular circuits and the classic theories of optimal
noise filtering and prediction that began with Wiener, Kolmogorov, Shannon, and
Bode. This theoretical framework provides a versatile tool, allowing us to
derive analytical bounds on the maximum mutual information between the
environmental signal and the real-time estimate constructed by the system. It
helps us understand how the structure of a biological network, and the response
times of its components, influences the accuracy of that estimate. The theory
also provides insights into how evolution may have tuned enzyme kinetic
parameters and populations to optimize information transfer.
