  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 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.
