RESUMO
Our ability to calculate rate constants of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant free-energy barrier heights. In this work, we improve upon a recently proposed rate estimator that allows us to predict transition times with molecular dynamics simulations biased to rapidly explore one or several collective variables (CVs). This approach relies on the idea that not all bias goes into promoting transitions, and along with the rate, it estimates a concomitant scale factor for the bias termed the "CV biasing efficiency" γ. First, we demonstrate mathematically that our new formulation allows us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when using a perfect CV, where γ = 1. After testing it on a model potential, we then study the unfolding behavior of a previously well characterized coarse-grained protein, which is sufficiently complex that we can choose many different CVs to bias, but which is sufficiently simple that we are able to compute the unbiased rate directly. For this system, we demonstrate that predictions from our new Exponential Average Time-Dependent Rate (EATR) estimator converge to the true rate constant more rapidly as a function of bias deposition time than does the previous iMetaD approach, even for bias deposition times that are short. We also show that the γ parameter can serve as a good metric for assessing the quality of the biasing coordinate. We demonstrate that these results hold when applying the methods to an atomistic protein folding example. Finally, we demonstrate that our approach works when combining multiple less-than-optimal bias coordinates, and adapt our method to the related "OPES flooding" approach. Overall, our time-dependent rate approach offers a powerful framework for predicting rate constants from biased simulations.
RESUMO
Aggregates of misfolded α-synuclein proteins (asyn) are key markers of Parkinson's disease. Asyn proteins have three domains: an N-terminal domain, a hydrophobic NAC core implicated in aggregation, and a proline-rich C-terminal domain. Proteins with truncated C-terminal domains are known to be prone to aggregation and suggest that studying domain-domain interactions in asyn monomers could help elucidate the role of the flanking domains in modulating protein structure. To this end, we used Gaussian accelerated molecular dynamics (GAMD) to simulate wild-type (WT), N-terminal truncated (DN), C-terminal truncated (ΔC), and isolated NAC domain variants (isoNAC). Using clustering and contact analysis, we found that N- and C-terminal domains interact via electrostatic interactions, while the NAC and N-terminal domains interact through hydrophobic contacts. Our work also suggests that the C-terminal domain does not interact directly with the NAC domain but instead interacts with the N-terminal domain. Removal of the N-terminal domain led to increased contacts between NAC and C-terminal domains and the formation of interdomain ß-sheets. Removal of either flanking domain also resulted in increased compactness of every domain. We also found that the contacts between flanking domains results in an electrostatic potential (ESP) that could possibly lead to favorable interactions with anionic lipid membranes. Removal of the C-terminal domain disrupts the ESP in a way that is likely to over-stabilize protein-membrane interactions. All of this suggests that one of the roles of the flanking domains may be to modulate the protein structure in a way that helps maintain elongation, hide hydrophobic residue from the solvent, and maintain an ESP that aids favorable interactions with the membrane.
