Measuring dissipation in biochemical processes remains largely uncharted territory. Dissipation of free energy for small systems with a discrete number of species has been proposed, and successfully applied to the same family of problems, namely quantifying dissipation in the actomyosin network. The goal was to understand the connection between dissipation of energy and the information created by sequence generation during polymerization. Theory predicts that dissipation depends on the polymerization mechanism, as well as on the number of different monomers present in the simulation, even if the rates of polymerization and depolymerization of those monomers are the same. We use the free energy associated with the formation of polymer sequences, as proposed by T. Ouldridge (Ouldridge, T.E. 2021. New Journal of Physics), to quantify the free energy associated with dimer formation. Additionally, we focus primarily on the dimerization reaction, which is a good proxy for polymer synthesis where the rate of monomer addition on the chain depends only on the monomer at the end, and where the sequence does not affect the polymerization rate (Bernoulli chain). The reactions are performed in an open reactor, where two monomer types are continuously added at every time step, and where reactor content is diluted by deleting monomer compounds with a uniform rate.
Figure 1. shows the results for two non-equilibrium systems, in the first case, the rate of homodimer formation is different compared to the rate of heterodimer formation, while in the second case, the two monomers are injected at different sites. In both cases, the free energy of information is computed as a function of varying simulation parameters, and we find that the quantity is positive due to the intrinsic dependence of the distributions of dimers, fluxes, and monomers in these systems. In addition, the quantity is bound by an upper and lower value for the parameter regimes that are explored.
