Nonequilibrium free-energetics of confined active filaments from variational time reversal

Chromatin, a macromolecular filament packed inside the eukaryotic cell nucleus, dynamically mediates gene expression through conformational fluctuations and thereby controls essential biological functions including memory map formation in the brain and the mechanoelastic properties of musculoskeletal tissue throughout the body. Experimental observation and theoretical modeling link the epigenetic regulatory functions of chromatin to activity-driven processes operating far from thermodynamic equilibrium that carefully tailor the multiscale organization of chromatin. To elucidate a clearer picture of this interplay between activity and structure, we develop a quantitative understanding of how active forces drive the steady state nonequilibrium fluxes between metastable structural-dynamic motifs of a confined active filament. Combining stochastic thermodynamics and path-integral optimal control theory, we derive a method that variationally estimates the nonequilibrium free-energy density of an active diffusive polymeric system relative to its passive counterpart along an arbitrary order parameter. We show that the unique optimal control policy that saturates our variational bound for the free-energy density difference is that which achieves a non-dissipative time reversal of the driven process at its steady state, and we use this knowledge to design physically-motivated control policy parameterizations that converge rapidly in an online reinforcement learning implementation of our method. Applying our method to the active filament allows us to map out nonequilibrium free-energy profiles as functions of mean active force amplitude, nucleosome repeat length, and filament rigidity to quantify the relative populations of, and flux intensities between, structural-dynamic motifs that in qualitative agreement with those identified using previous coarse-grained polymer models of confined active chromatin.