Polarizable Amoeba Force Field Metadynamics With Minimization Predicts Missing Protein Loops

Computational methods developed to find the global free energy minimum of amino acid sequences are increasingly successful, but limitations in both accuracy and efficiency remain. Optimization algorithms are typically focused on proteins of modest size (i.e. of approximately 100 residues) and utilize potential energy functions based on fixed charged force fields, statistical or knowledge based potentials, and/or potentials incorporating experimental data. Although the aforementioned methods are widely used, known limitations include 1) search protocols that are inefficient or not deterministic due to rough energy landscapes characterized by large energy barriers between multiple minima and 2) use of a target function whose global minimum does not correspond to the actual free energy minimum. To overcome the first limitation, this work describes a global optimization approach based on metadynamics to drive the search of conformational space toward unexplored regions by adding a time-dependent bias to the objective function. To overcome the second limitation, a hybrid objective function is defined as the sum of the polarizable AMOEBA polarizable force field and an experimental X-ray crystallography target. As metadynamics drives the search, periodic quenching via local minimization is used to access structure quality via evaluation of Rwork. Thus, the overall method is called AMOEBA Metadynamics with Minimization (AMM), and is suitable for optimization of side-chains, ligand binding poses, protein loops or even protein complexes. Here we focus on characterizing the ability of AMM to elucidate the structural details of missing protein loops, which are often excluded from experimental X-ray crystallography structures due to conformational heterogeneity and/or limitations in the resolution of the data. We first show that the correlation between experimental data and AMOEBA structural minima is stronger than that for OPLS-AA/L (i.e. a fixed charge force field). Next, missing protein loops are optimized using 5 nsec of sampling for both AMM and simulated annealing with OPLS-AA/L. The AMM procedure provides more accurate structures in terms of both experimental (i.e. lower Rfree values) and structural metrics (i.e. MolProbity). In addition to providing more accurate loop conformations, AMM converged faster than the simulated annealing protocol. Overall, this work suggests that AMM is well-suited to refine or predict the coordinates of missing amino acid residues and/or protein loops due to both the increased accuracy of the target function relative to OPLS-AA/L and more rapid convergence of the metadynamics driven search compared to simulation annealing.