Coarse-Grained Directed Simulation

In the field of molecular simulation, there are many situations where we might like to do extensive and expensive sampling procedures on a subsystem within a larger macromolecular context, e.g., on one or a few proteins from within a many-protein assembly (such as an actin filament or a virus capsid), or on a region of a polymer within a mesoscopic assembly of such polymers. In such cases, we might want to study, e.g., the free-energetics of a small molecule binding to a protein that is contained in a large complex or embedded within a membrane, or the conformational motions of one of the proteins within the larger many-protein assembly. This kind of situation is typically modeled by putting the subsystem into solution and either fixing some of its conformations or by constraining it via harmonic potentials. A drawback of either approach is that they lose the system’s native fluctuations due to changing the environment and the imposition of the extra potential, and these fluctuations may be crucial to achieving correct simulation estimates for a model within the larger assembly. Moreover, such constraints do not minimize the relative entropy of the constrained subsystem to the unconstrained one in the larger assembly. In this study, we provide a new approach to this problem by drawing on ideas developed to incorporate experimental information into a molecular simulation. We show that by using linear biases on coarse-grained 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.