Quantifying Macromolecular Conformational Transition Pathways

Abstract

Diverse classes of proteins such as molecular motors, enzymes, and active transmembrane transporters function through large-scale conformational changes. Computer simulations of these conformational transitions are challenging. A range of coarse-grained and biased simulation techniques have been used to generate individual transitions or ensembles of transition pathways but it has been difficult to compare pathways produced by different methods and so to assess their relative strengths. We introduce a comprehensive method (pathway similarity analysis, PSA) for quantitatively characterizing and comparing macromolecular pathways. The Hausdorff and Frechet metrics (known from computational geometry) are used to quantify the degree of similarity between piecewise-linear curves in configuration space. We tested PSA on a toy system to study the effect of temperature fluctuations (path roughness) and dimensionality. We compare a sample of publicly accessible transition pathway simulation servers and our own dynamic importance sampling (DIMS) MD method for the closed-to-open transitions of the apo enzyme adenylate kinase (AdK). PSA was applied to ensembles of hundreds of trajectories of the conformational transitions of the transporter Mhp1 and of AdK and diphtheria toxin, which were produced by DIMS MD and the Geometrical Pathways algorithm. Clustered PSA enabled the selection of a small subset of representative trajectories for further analysis. A strength of PSA is its use of the full information available from the 3N-dimensional configuration space trajectory, without requiring additional specific knowledge about the system. We show how trajectory analysis methods relying on pre-defined collective variables such as native contacts or geometric quantities can be used synergistically with PSA. We discuss the method's potential to enhance our understanding of transition path sampling methods, validate them, and ultimately help guide future research toward deeper physical insights into conformational transitions.