Cooperative folding near the downhill limit determined with amino acid resolution by hydrogen exchange

How hydrophobicity, side chains, and salt affect the dimensions of disordered proteins

Despite the generally accepted role of the hydrophobic effect as the driving force for folding, many intrinsically disordered proteins (IDPs), including those with hydrophobic content typical of foldable proteins, behave nearly as self-avoiding random walks (SARWs) under physiological conditions. Here, we tested how temperature and ionic conditions influence the dimensions of the N-terminal domain of pertactin (PNt), an IDP with an amino acid composition typical of folded proteins. While PNt contracts somewhat with temperature, it nevertheless remains expanded over 10-58°C, with a Flory exponent, ν, >0.50. Both low and high ionic strength also produce contraction in PNt, but this contraction is mitigated by reducing charge segregation. With 46% glycine and low hydrophobicity, the reduced form of snow flea anti-freeze protein (red-sfAFP) is unaffected by temperature and ionic strength and persists as a near-SARW, ν ~ 0.54, arguing that the thermal contraction of PNt is due to stronger interactions between hydrophobic side chains. Additionally, red-sfAFP is a proxy for the polypeptide backbone, which has been thought to collapse in water. Increasing the glycine segregation in red-sfAFP had minimal effect on ν. Water remained a good solvent even with 21 consecutive glycine residues (ν > 0.5), and red-sfAFP variants lacked stable backbone hydrogen bonds according to hydrogen exchange. Similarly, changing glycine segregation has little impact on ν in other glycine-rich proteins. These findings underscore the generality that many disordered states can be expanded and unstructured, and that the hydrophobic effect alone is insufficient to drive significant chain collapse for typical protein sequences.

Engineered Metal-Binding Sites to Probe Protein Folding Transition States: Psi Analysis

The formation of the transition state ensemble (TSE) represents the rate-limiting step in protein folding. The TSE is the least populated state on the pathway, and its characterization remains a challenge. Properties of the TSE can be inferred from the effects on folding and unfolding rates for various perturbations. A difficulty remains on how to translate these kinetic effects to structural properties of the TSE. Several factors can obscure the translation of point mutations in the frequently used method, "mutational Phi analysis." We take a complementary approach in "Psi analysis," employing rationally inserted metal binding sites designed to probe pairwise contacts in the TSE. These contacts can be confidently identified and used to construct structural models of the TSE. The method has been applied to multiple proteins and consistently produces a considerably more structured and native-like TSE than Phi analysis. This difference has significant implications to our understanding of protein folding mechanisms. Here we describe the application of the method and discuss how it can be used to study other conformational transitions such as binding.

Prediction and Validation of a Protein's Free Energy Surface Using Hydrogen Exchange and (Importantly) Its Denaturant Dependence

The denaturant dependence of hydrogen-deuterium exchange (HDX) is a powerful measurement to identify the breaking of individual H-bonds and map the free energy surface (FES) of a protein including the very rare states. Molecular dynamics (MD) can identify each partial unfolding event with atomic-level resolution. Hence, their combination provides a great opportunity to test the accuracy of simulations and to verify the interpretation of HDX data. For this comparison, we use Upside, our new and extremely fast MD package that is capable of folding proteins with an accuracy comparable to that of all-atom methods. The FESs of two naturally occurring and two designed proteins are so generated and compared to our NMR/HDX data. We find that Upside's accuracy is considerably improved upon modifying the energy function using a new machine-learning procedure that trains for proper protein behavior including realistic denatured states in addition to stable native states. The resulting increase in cooperativity is critical for replicating the HDX data and protein stability, indicating that we have properly encoded the underlying physiochemical interactions into an MD package. We did observe some mismatch, however, underscoring the ongoing challenges faced by simulations in calculating accurate FESs. Nevertheless, our ensembles can identify the properties of the fluctuations that lead to HDX, whether they be small-, medium-, or large-scale openings, and can speak to the breadth of the native ensemble that has been a matter of debate.

Water as a Good Solvent for Unfolded Proteins: Folding and Collapse are Fundamentally Different

The argument that the hydrophobic effect is the primary effect driving the folding of globular proteins is nearly universally accepted (including by the authors). But does this view also imply that water is a "poor" solvent for the unfolded states of these same proteins? Here we argue that the answer is "no," that is, folding to a well-packed, extensively hydrogen-bonded native structure differs fundamentally from the nonspecific chain collapse that defines a poor solvent. Thus, the observation that a protein folds in water does not necessitate that water is a poor solvent for its unfolded state. Indeed, chain-solvent interactions that are marginally more favorable than nonspecific intrachain interactions are beneficial to protein function because they destabilize deleterious misfolded conformations and inter-chain interactions.

A protein interaction free energy model based on amino acid residue contributions: Assessment of point mutation stability of T4 lysozyme

Here we present a model to estimate the interaction free energy contribution of each amino acid residue of a given protein. Protein interaction energy is described in terms of per-residue interaction factors, μ. Multibody interactions are implicitly captured in μ through the combination of amino acid terms (γ) guided by local conformation indices (σ). The model enables construction of an interaction factor heat map for a protein in a given fold, allows prima facie assessment of the degree of residue-residue interaction, and facilitates a qualitative and quantitative evaluation of protein association properties. The model was used to compute thermal stability of T4 bacteriophage lysozyme mutants across seven sites. Qualitative assessment of mutational effects provides a straightforward rationale regarding whether a particular site primarily perturbs native or non-native states, or both. The presented model was found to be in good agreement with experimental mutational data (R 2 = 0.73) and suggests an approach by which to convert structure space into energy space.

Choice of Adaptive Sampling Strategy Impacts State Discovery, Transition Probabilities, and the Apparent Mechanism of Conformational Changes

Interest in atomically detailed simulations has grown significantly with recent advances in computational hardware and Markov state modeling (MSM) methods, yet outstanding questions remain that hinder their widespread adoption. Namely, how do alternative sampling strategies explore conformational space and how might this influence predictions generated from the data? Here, we seek to answer these questions for four commonly used sampling methods: (1) a single long simulation, (2) many short simulations run in parallel, (3) adaptive sampling, and (4) our recently developed goal-oriented sampling algorithm, FAST. We first develop a theoretical framework for analytically calculating the probability of discovering select states on simple landscapes, where we uncover the drastic effects of varying the number and length of simulations. We then use kinetic Monte Carlo simulations on a variety of physically inspired landscapes to characterize the probability of discovering particular states and transition pathways for each of the four methods. Consistently, we find that FAST simulations discover each target state with the highest probability, while traversing realistic pathways. Furthermore, we uncover the potential pathology that short parallel simulations sometimes predict an incorrect transition pathway by crossing large energy barriers that long simulations would typically circumnavigate. We refer to this pathology as "pathway tunneling". To protect against this phenomenon when using adaptive-sampling and FAST simulations, we introduce the FAST-string method. This method enhances sampling along the highest-flux transition paths to refine an MSMs transition probabilities and discriminate between competing pathways. Additionally, we compare the performance of a variety of MSM estimators in describing accurate thermodynamics and kinetics. For adaptive sampling, we recommend simply normalizing the transition counts out of each state after adding small pseudocounts to avoid creating sources or sinks. Lastly, we evaluate whether our insights from simple landscapes hold for all-atom molecular dynamics simulations of the folding of the λ-repressor protein. Remarkably, we find that FAST-contacts predicts the same folding pathway as a set of long simulations but with orders of magnitude less simulation time.

pH-Dependent cooperativity and existence of a dry molten globule in the folding of a miniprotein BBL

Solution pH plays an important role in protein dynamics, stability, and folding; however, detailed mechanisms remain poorly understood. Here we use continuous constant pH molecular dynamics in explicit solvent with pH replica exchange to describe the pH profile of the folding cooperativity of a miniprotein BBL, which has drawn intense debate in the past. Our data reconciled the two opposing hypotheses (downhill vs. two-state) and uncovered a sparsely populated unfolding intermediate. As pH is lowered from 7 to 5, the folding barrier vanishes. As pH continues to decrease, the unfolding barrier lowers and denaturation is triggered by the protonation of Asp162, consistent with experimental evidence. Interestingly, unfolding proceeded via an intermediate, with intact secondary structure and a compact, unlocked hydrophobic core shielded from solvent, lending support to the recent hypothesis of a universal dry molten globule in protein folding. Our work demonstrates that constant pH molecular dynamics is a unique tool for testing this and other hypotheses to advance the knowledge in protein dynamics, stability, and folding.