Thermodynamic Limits on Reliable Signaling by Biochemical Traveling Waves

Biochemical traveling waves transmit signals across cells and tissues, but the thermodynamic cost of reliable propagation remains unclear.

We develop a stochastic thermodynamic framework for reaction--diffusion systems with stable traveling waves and show that diffusion of the wave position is bounded by the dissipation specifically associated with propagation.

The bound follows by projecting noisy field dynamics onto the adjoint translational mode, which maps the wave position to an effective biased random walk.

Its tightness is controlled by the non-self-adjoint part of the linearized dynamics, with finite wave speed and antisymmetric reaction dynamics generically producing deviations from equality.

For excitable trigger waves in a FitzHugh--Nagumo model, we show that the slow inhibitor dominates the propagation cost, yielding a trade-off among wave speed, inhibitor amplitude, and dissipation.

We test these predictions in stochastic simulations of a microscopic Belousov--Zhabotinsky reaction--diffusion system and find consistent signatures in mitotic trigger-wave experiments in \textit{Xenopus} egg extracts.

The same relation further imposes an annihilation-limited bound on the reliable signaling rate of wave trains.