Coarse-Grained Directed Simulation.

Many free-energy sampling and quantum mechanics/molecular mechanics (QM/MM) computations on protein complexes have been performed where, by necessity, a single component is studied isolated in solution while its overall configuration is kept in the complex-like state by either rigid restraints or harmonic constraints. A drawback in these studies is that the system's native fluctuations are lost, both due to the change of environment and the imposition of the extra potential. Yet, we know that having both accurate structure and fluctuations is likely crucial to achieving correct simulation estimates for the subsystem within its native larger protein complex context. In this work, we provide a new approach to this problem by drawing on ideas developed to incorporate experimental information into a molecular simulation by relative entropy minimization to a target system. We show that by using linear biases on coarse-grained (CG) observables (such as distances or angles between large subdomains within a protein), we can maintain the protein in a particular target conformation while also preserving the correct equilibrium fluctuations of the subsystem within its larger biomolecular complex. As an application, we demonstrate this algorithm by training a bias that causes an actin monomer (and trimer) in solution to sample the same average structure and fluctuations as if it were embedded within a much larger actin filament. Additionally, we have developed a number of algorithmic improvements that accelerate convergence of the on-the-fly relative entropy minimization algorithms for this type of application. Finally, we have contributed these methods to the PLUMED open source free energy sampling software library.