Biological cells encode information about their environment through biochemical signaling networks that control their internal state and response. This information is often encoded in the dynamical patterns of the signaling molecules, rather than just their instantaneous concentrations. Here, we analytically calculate the information contained in these dynamics for a number of paradigmatic cases in the linear regime, for both static and time-dependent input signals. When considering oscillatory output dynamics, we report on the emergence of synergy between successive measurements, meaning that the joint information in two measurements exceeds the sum of the individual information. We extend our analysis numerically beyond the scope of linear input encoding to reveal synergetic effects in the cases of frequency or damping modulation, both of which are relevant to classical biochemical signaling systems.

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• Calcium signaling
• Cell signaling
• Intracellular signalling
• Signal transduction
• Stochastic processes
• Signaling networks
• Information theory