Toward a quantitative description of microscopic pathway heterogeneity in protein folding

Abstract

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.

Reversible two-state folding of the ultrafast protein gpW under mechanical force

“…The mechanical unfolding of the + protein gpW is thus very different from that of the all- CspB, in which the 6 -strands unravel one by one stochastically 21 . Similar mechanistic differences have been found for these two proteins on a recent computational analysis of folding pathways 37 . It is interesting to note that the mechanical unfolding transition state of gpW that we find here and the thermal unfolding transition state inferred from the folding interaction networks obtained by NMR experiments and MD simulations 16 appear to be quite similar.…”

Reversible two-state folding of the ultrafast protein gpW under mechanical force

“…The mechanical unfolding of the α + β protein gpW is thus very different from that of the all-β CspB, in which the six β-strands unravel one by one stochastically 21 . Similar mechanistic differences have been found for these two proteins on a recent computational analysis of folding pathways 39 . It is interesting to note that the mechanical unfolding transition state of gpW that we find here and the thermal unfolding transition state inferred from the folding interaction networks obtained by NMR experiments and MD simulations 16 appear to be quite similar.…”

Thermodynamics and folding landscapes of large proteins from a statistical mechanical model

“…The Wako-Saitô-Muñoz-Eaton (WSME) model is one such statistical mechanical model that was first developed by Wako and Saitô ( Wako and Saito, 1978a , Wako and Saito, 1978b ), discussed in detail by Gō and Abe ( Go and Abe, 1981 , Abe and Go, 1981 ), and then later independently developed by Muñoz and Eaton (1999) . Originally seen as a physical tool to predict the folding rates of proteins from three-dimensional structures ( Muñoz and Eaton, 1999 , Henry and Eaton, 2004 ), the model has expanded its scope to quantitatively analyze folding behaviors of folded globular domains ( Bruscolini and Naganathan, 2011 , Garcia-Mira et al., 2002 , Narayan and Naganathan, 2014 , Narayan and Naganathan, 2017 , Narayan and Naganathan, 2018 , Naganathan and Muñoz, 2014 , Naganathan et al., 2015 , Munshi and Naganathan, 2015 , Rajasekaran et al., 2016 , Narayan et al., 2017 , Itoh and Sasai, 2006 ), repeat proteins ( Faccin et al., 2011 , Sivanandan and Naganathan, 2013 , Hutton et al., 2015 ), disordered proteins (with appropriate controls) ( Naganathan and Orozco, 2013 , Gopi et al., 2015 , Munshi et al., 2018a ), predict and engineer thermodynamic stabilities of proteins via mutations ( Naganathan, 2012 , Naganathan, 2013b , Rajasekaran et al., 2017 ) and entropic effects ( Rajasekaran et al., 2016 ), model allosteric transitions ( Itoh and Sasai, 2011 , Sasai et al., 2016 ), protein-DNA binding ( Munshi et al., 2018b ), quantifying folding pathways at different levels of resolution ( Henry et al., 2013 , Kubelka et al., 2008 , Gopi et al., 2017 ), force-spectroscopic measurements ( Imparato et al., 2007 ) and even crowding effects ( Caraglio and Pelizzola, 2012 ).

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“…While this approach reduces the number of microstates drastically (compared to the 2 N states), it has been successful in predicting the folding mechanism of the Villin head-piece domain in quantitative agreement with experiments and all-atom MD simulations ( Henry et al., 2013 ). A similar model but with more detailed energetics (van der Waals interactions, electrostatics, implicit solvation and excess conformational entropy) has been instrumental in providing a detailed description of folding pathway heterogeneity in five different proteins in quantitative agreement with ensemble and single-molecule data ( Gopi et al., 2017 ).…”