Optimal Allocation of Dissipation to Maximize Flux, Analytically

Biological processes are inherently stochastic, and to achieve directionality, consume free energy. In most cases, the total free energy for a single cycle is fixed. We investigate how this fixed free energy can be allocated throughout different states to maximize the probability flux. We adopt a formalism based on the master equation to find exact solutions to the probability distribution for a specific state at a given time in Laplace space. With this analytical expression for probability distributions, we can calculate the probability flux for a 2-state and 3-state systems using two different energy landscapes, forward=labile, and reverse-labile schemes. We find the optimal allocation of free energy is unevenly distributed to compensate for slower transitions rates in the cycle.