Beyond structural cycles: computational mechanisms of biomolecular machines.

Understanding biomolecular machines requires more than determining their structures; it requires identifying the dynamical principles that couple chemical or electrochemical free energy to function. Recent advances in cryo-EM, single-molecule spectroscopy, high-speed atomic force microscopy, and deep mutational scanning provide unprecedented experimental constraints for computational models, while developments in molecular simulation and kinetic modeling increasingly allow mechanistic interpretation of these observations. Here, we discuss recent computational advances that exemplify this transition from structural characterization toward predictive dynamical modeling, focusing on atomistic mechanisms of mechanochemical coupling, identification of slow collective variables and transition states, construction of branched kinetic networks, and emerging descriptions of memory effects arising from reduced dynamical representations. We conclude by discussing several pressing challenges, including the integration of physics-based simulations with machine learning, rigorous descriptions of nonequilibrium dynamics, and the computational design of dynamic proteins as an emerging test of our mechanistic understanding of biomolecular machines.