Fluctuation Theorems from a Continuous-Time Markov Model of Information-Thermodynamic Capacity in Biochemical Signal Cascades

TL;DR

This paper models biochemical signal cascades as continuous-time Markov processes to quantify their information transmission capacity and energy dissipation, deriving fluctuation theorems and connecting thermodynamics with information theory.

Contribution

It introduces a rigorous stochastic-thermodynamic framework for biochemical signaling, linking capacity, entropy production, and fluctuation theorems using Markov models.

Findings

Derived fluctuation theorems for biochemical signaling

Connected information capacity to energy dissipation rates

Applied theory to MAPK/ERK signaling timescales

Abstract

Biochemical signaling cascades transmit intracellular information while dissipating energy under nonequilibrium conditions. We model a cascade as a code string and apply information-entropy ideas to quantify an optimal transmission rate. A time-normalized entropy functional is maximized to define a capacity-like quantity governed by a conserved multiplier. To place the theory on a rigorous stochastic-thermodynamic footing, we formulate stepwise signaling as a continuous-time Markov jump process with forward and reverse competing rates. The embedded jump chain yields well-defined transition probabilities that justify time-scale-based expressions. Under local detailed balance, the log ratio of forward and reverse rates can be interpreted as entropy production per event, enabling a trajectory-level derivation of detailed and integral fluctuation theorems. We further connect the information-theoretic capacity to the mean dissipation rate and outline finite-time fluctuation structure via the scaled cumulant generating function (SCGF) and Gallavotti--Cohen symmetry, including a worked example using MAPK/ERK timescales.