Uncovering One-Dimensional Reaction Coordinate that Underlies Structure-Function Relationship of Proteins

Understanding the mechanism of functional protein dynamics is critical to understanding protein functions. Reaction coordinates is a central topic in protein dynamics and the grail is to find the one-dimensional reaction coordinate that can fully determine the value of committor (i.e. the reaction probability in configuration space) for any protein configuration. We present a powerful new method that can, for the first time, identify the rigorous one-dimensional reaction coordinate in complex molecules. This one-dimensional reaction coordinate is determined by a fundamental mechanical operator--the generalized work functional. This method only requires modest computational cost and can be readily applied to large molecules. Most importantly, the generalized work functional is the physical origin of the collectivity in functional protein dynamics and provides a tentative roadmap that connects the structure of a protein to its function.

Optimizing reaction coordinate by flux maximization in the transition path ensemble

Transition path ensemble is a collection of reactive trajectories, all of which largely keep going forward along the transition channel from the reactant state to the product one, and is believed to possess the information necessary for the identification of reaction coordinate. Previously, the full coordinates (both position and momentum) of the snapshots in the transition path ensemble were utilized to obtain the reaction coordinate (J. Chem. Phys. 2016, 144, 114103; J. Chem. Phys. 2018, 148, 084105). Here, with the conformational (or position) coordinates alone, it is demonstrated that the reaction coordinate can be optimized by maximizing the flux of a given coordinate in the transition path ensemble. In the application to alanine dipeptide in vacuum, dihderal angles ϕ and θ were identified to be the two best reaction coordinates, which was consistent with the results in existing studies. A linear combination of these two coordinates gave a better reaction coordinate, which is highly correlated with committor. Most importantly, the method obtained a linear combination of pairwise distances between heavy atoms, which was highly correlated with committor as well. The standard deviation of committor at the transition region defined by the optimized reaction coordinate is as small as 0.08. In addition, the effects of practical factors, such as the choice of transition path sub-ensembles and saving interval between frames in transition paths, on reaction coordinate optimization were also considered.

Transiently increased intercommunity regulation characterizes concerted cell phenotypic transition

Phenotype transition takes place in many biological processes such as differentiation and reprogramming. A fundamental question is how cells coordinate switching of expressions of clusters of genes. Through analyzing single cell RNA sequencing data in the framework of transition path theory, we studied how such a genome-wide expression program switching proceeds in three different cell transition processes. For each process we reconstructed a reaction coordinate describing the transition progression, and inferred the gene regulation network (GRN) along the reaction coordinate. In all three processes we observed common pattern that the effective number and strength of regulation between different communities increase first and then decrease. The change accompanies with similar change of the GRN frustration, defined as overall confliction between the regulation received by genes and their expression states, and GRN heterogeneity. While studies suggest that biological networks are modularized to contain perturbation effects locally, our analyses reveal a general principle that during a cell phenotypic transition intercommunity interactions increase to concertedly coordinate global gene expression reprogramming, and canalize to specific cell phenotype as Waddington visioned.

Non-Markovian modeling of protein folding

We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide alanine9 for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote–Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.