Toward a quantitative description of microscopic pathway heterogeneity in protein folding.

How many structurally different microscopic routes are accessible to a protein molecule while folding? This has been a challenging question to address experimentally as single-molecule studies are constrained by the limited number of observed folding events while ensemble measurements, by definition, report only an average and not the distribution of the quantity under study. Atomistic simulations, on the other hand, are restricted by sampling and the inability to reproduce thermodynamic observables directly. We overcome these bottlenecks in the current work and provide a quantitative description of folding pathway heterogeneity by developing a comprehensive, scalable and yet experimentally consistent approach combining concepts from statistical mechanics, physical kinetics and graph theory. We quantify the folding pathway heterogeneity of five single-domain proteins under two thermodynamic conditions from an analysis of 100 000 folding events generated from a statistical mechanical model incorporating the detailed energetics from more than a million conformational states. The resulting microstate energetics predicts the results of protein engineering experiments, the thermodynamic stabilities of secondary-structure segments from NMR studies, and the end-to-end distance estimates from single-molecule force spectroscopy measurements. We find that a minimum of ∼3-200 microscopic routes, with a diverse ensemble of transition-path structures, are required to account for the total folding flux across the five proteins and the thermodynamic conditions. The partitioning of flux amongst the numerous pathways is shown to be subtly dependent on the experimental conditions that modulate protein stability, topological complexity and the structural resolution at which the folding events are observed. Our predictive methodology thus reveals the presence of rich ensembles of folding mechanisms that are generally invisible in experiments, reconciles the contradictory observations from experiments and simulations and provides an experimentally consistent avenue to quantify folding heterogeneity.

A General Mechanism for the Propagation of Mutational Effects in Proteins.

Mutations in the hydrophobic interior of proteins are generally thought to weaken the interactions only in their immediate neighborhood. This forms the basis of protein engineering-based studies of folding mechanism and function. However, mutational work on diverse proteins has shown that distant residues are thermodynamically coupled, with the network of interactions within the protein acting as signal conduits, thus raising an intriguing paradox. Are mutational effects localized, and if not, is there a general rule for the extent of percolation and the functional form of this propagation? We explore these questions from multiple perspectives in this work. Perturbation analysis of interaction networks within proteins and microsecond long molecular dynamics simulations of several aliphatic mutants of ubiquitin reveal strong evidence of the distinct alteration of distal residue-residue communication networks. We find that mutational effects consistently propagate into the second shell of the altered site (even up to 15-20 Å) in proportion to the perturbation magnitude and dissipate exponentially with a decay distance constant of ∼4-5 Å. We also report evidence for this phenomenon from published experimental nuclear magnetic resonance data that strikingly resemble predictions from network theory and molecular dynamics simulations. Reformulating these observations onto a statistical mechanical model, we reproduce the stability changes of 375 mutations from 19 single-domain proteins. Our work thus reveals a robust energy dissipation-cum-signaling mechanism in the interaction network within proteins, quantifies the partitioning of destabilization energetics around the mutation neighborhood, and presents a simple theoretical framework for modeling the allosteric effects of point mutations.

Are protein folding intermediates the evolutionary consequence of functional constraints?

High-resolution experiments on several apparently two-state proteins point to the existence of partially structured excited- or intermediate-states in dynamic equilibrium with native states. Are these intermediate states the byproducts of functional constraints that are by necessity evolutionarily conserved or are they merely the hidden imprints of evolutionary processes? To investigate this, we characterize the folding of Barstar that has a rich history of complex conformational behavior employing a combination of methods-statistical-mechanical model, electrostatic calculations, MD simulations and multiple-sequence alignment-that provide a detailed yet consistent view of its landscape in agreement with experiments. We find that the multistate folding in Barstar is the direct consequence of a strong evolutionary pressure to maintain its binding affinity with Barnase through a large negative electrostatic potential on one face. A single mutation (E76K or E80K) at the binding site is shown to not only enhance the native-state stability but also alter the Barstar folding mechanism to resemble an unfrustrated two-state-like system. Our results argue that though natural proteins are expected to be minimally frustrated, functional constraints can singularly determine the folding mechanism even if it occurs at the expense of frustrated multistate folding.