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

Abstract

Statistical mechanical models that afford an intermediate resolution between macroscopic chemical models and all-atom simulations have been successful in capturing folding behaviors of many small single-domain proteins. However, the applicability of one such successful approach, the Wako-Saitô-Muñoz-Eaton (WSME) model, is limited by the size of the protein as the number of conformations grows exponentially with protein length. In this work, we surmount this size limitation by introducing a novel approximation that treats stretches of 3 or 4 residues as blocks, thus reducing the phase space by nearly three orders of magnitude. The performance of the ‘bWSME’ model is validated by comparing the predictions for a globular enzyme (RNase H) and a repeat protein (IκBα), against experimental observables and the model without block approximation. Finally, as a proof of concept, we predict the free-energy surface of the 370-residue, multi-domain maltose binding protein and identify an intermediate in good agreement with single-molecule force-spectroscopy measurements. The bWSME model can thus be employed as a quantitative predictive tool to explore the conformational landscapes of large proteins, extract the structural features of putative intermediates, identify parallel folding paths, and thus aid in the interpretation of both ensemble and single-molecule experiments.

Weakening of interaction networks with aging in tip-link protein induces hearing loss

“…A mutation can have complex effects on the folding conformational landscape modulating the number and nature of the intermediates, apart from effects on the folded and unfolded ensembles [ 25 ]. To probe for such effects we employed the block description of the Ising-like bWSME model to generate a minimal 105 316 microstate representation of the folding conformational landscape of WT and the mutant S47P [ 37 , 38 ]. The model contributions from van der Waals interactions, electrostatics, and differences in backbone conformational entropy (see Methods).…”

“…To do so, we employ the recent block approximation (i.e. the bWSME model [ 37 ]) that considers stretches of residues as blocks thus further coarse-graining the landscape but that is still physically realistic to capture multiple thermodynamic and kinetic features. For the 102 residue Cadherin and considering 3-residue blocks, the protein chain would be reduced to just 34 blocks while the total number of microstates would be brought down to 105 316, thus enabling rapid and automated fitting of DSC profiles and free-energy surface generation.…”

The metal cofactor zinc and interacting membranes modulate SOD1 conformation-aggregation landscape in an in vitro ALS model

“…To overcome this challenge and to obtain a simple physical picture of how the energetics of folding is governed by metal ions, we resort to constructing the folding landscape of reduced SOD1 variants through the statistical mechanical Wako-Saitô-Muñoz-Eaton (WSME) model (see Methods for model description and parametrization) 15,16 . Here, we employ the bWSME model where stretches of three consecutive residues are considered as a block (b) that reduces the total number of microstates from 42.7 million to just ~450,000 17 .…”

“…31 Wako-Saitô-Muñoz-Eaton (WSME) Model. We employ the Ising-like WSME model 15, with the block approximation 17 to predict the conformational landscape of SOD1 oxidized monomer and its variants using the PDB structure 4FF9 as the reference. Briefly, the model assigns binary variables of 1 or 0 for folded or unfolded status of residues, respectively.…”

Combining ancestral reconstruction with folding-landscape simulations to engineer heterologous protein expression

“…as a single block or unit). This model has been validated against the residue-level approximations and enables rapid predictions 53 . In addition, we include contributions from van der Waals interactions, all-to-all electrostatics 57 , simplified solvation terms and sequence and structure specific conformational entropy.…”