  Cells use temporal dynamical patterns to transmit information via signaling
pathways. As optimality with respect to the environment plays a fundamental
role in biological systems, organisms have evolved optimal ways to transmit
information. Here, we use optimal control theory to obtain the dynamical signal
patterns for the optimal transmission of information, in terms of efficiency
(low energy) and reliability (low uncertainty). Adopting an
activation-deactivation decoding network, we reproduce several dynamical
patterns found in actual signals, such as steep, gradual, and overshooting
dynamics. Notably, when minimizing the energy of the input signal, the optimal
signals exhibit overshooting, which is a biphasic pattern with transient and
steady phases; this pattern is prevalent in actual dynamical patterns. We also
identify conditions in which these three patterns (steep, gradual, and
overshooting) confer advantages. Our study shows that cellular signal
transduction is governed by the principle of minimizing free energy dissipation
and uncertainty; these constraints serve as selective pressures when designing
dynamical signaling patterns.
