Temperature-dependent downhill unfolding of ubiquitin. II. Modeling the free energy surface

Unlocking the unfolded structure of ubiquitin: Combining time-resolved x-ray solution scattering and molecular dynamics to generate unfolded ensembles

The unfolding dynamics of ubiquitin were studied using a combination of x-ray solution scattering (XSS) and molecular dynamics (MD) simulations. The kinetic analysis of the XSS ubiquitin signals showed that the protein unfolds through a two-state process, independent of the presence of destabilizing salts. In order to characterize the ensemble of unfolded states in atomic detail, the experimental XSS results were used as a constraint in the MD simulations through the incorporation of x-ray scattering derived potential to drive the folded ubiquitin structure toward sampling unfolded states consistent with the XSS signals. We detail how biased MD simulations provide insight into unfolded states that are otherwise difficult to resolve and underscore how experimental XSS data can be combined with MD to efficiently sample structures away from the native state. Our results indicate that ubiquitin samples unfolded in states with a high degree of loss in secondary structure yet without a collapse to a molten globule or fully solvated extended chain. Finally, we propose how using biased-MD can significantly decrease the computational time and resources required to sample experimentally relevant nonequilibrium states.

The Wako-Saitô-Muñoz-Eaton Model for Predicting Protein Folding and Dynamics

Despite the recent advances in the prediction of protein structures by deep neutral networks, the elucidation of protein-folding mechanisms remains challenging. A promising theory for describing protein folding is a coarse-grained statistical mechanical model called the Wako-Saitô-Muñoz-Eaton (WSME) model. The model can calculate the free-energy landscapes of proteins based on a three-dimensional structure with low computational complexity, thereby providing a comprehensive understanding of the folding pathways and the structure and stability of the intermediates and transition states involved in the folding reaction. In this review, we summarize previous and recent studies on protein folding and dynamics performed using the WSME model and discuss future challenges and prospects. The WSME model successfully predicted the folding mechanisms of small single-domain proteins and the effects of amino-acid substitutions on protein stability and folding in a manner that was consistent with experimental results. Furthermore, extended versions of the WSME model were applied to predict the folding mechanisms of multi-domain proteins and the conformational changes associated with protein function. Thus, the WSME model may contribute significantly to solving the protein-folding problem and is expected to be useful for predicting protein folding, stability, and dynamics in basic research and in industrial and medical applications.

Uncovering the Early Stages of Domain Melting in Calmodulin with Ultrafast Temperature-Jump Infrared Spectroscopy

The signaling protein calmodulin (CaM) undergoes a well-known change in secondary structure upon binding Ca²⁺, but the structural plasticity of the Ca²⁺-free apo state is linked to CaM functionality. Variable temperature studies of apo-CaM indicate two structural transitions at 46 and 58 °C that are assigned to melting of the C- and N-terminal domains, respectively, but the molecular mechanism of domain unfolding is unknown. We report temperature-jump time-resolved infrared (IR) spectroscopy experiments designed to target the first steps in the C-terminal domain melting transition of human apo-CaM. A comparison of the nonequilibrium relaxation of apo-CaM with the more thermodynamically stable holo-CaM, with 4 equiv of Ca²⁺ bound, shows that domain melting of apo-CaM begins on microsecond time scales with α-helix destabilization. These observations enable the assignment of previously reported dynamics of CaM on hundreds of microsecond time scales to thermally activated melting, producing a complete mechanism for thermal unfolding of CaM.

Protein unfolding from free-energy calculations: integration of the Gaussian network model with bond binding energies

Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate kinase we find three major partial unfolding states, which is consistent with single molecule FRET experiments [Pirchi et al., Nat. Commun. 2, 493 (2011)] for which hidden Markov analysis reveals between three and five such states. Such states can play a major role in enzymatic activity.

Atomic-level description of ubiquitin folding

Equilibrium molecular dynamics simulations, in which proteins spontaneously and repeatedly fold and unfold, have recently been used to help elucidate the mechanistic principles that underlie the folding of fast-folding proteins. The extent to which the conclusions drawn from the analysis of such proteins, which fold on the microsecond timescale, apply to the millisecond or slower folding of naturally occurring proteins is, however, unclear. As a first attempt to address this outstanding issue, we examine here the folding of ubiquitin, a 76-residue-long protein found in all eukaryotes that is known experimentally to fold on a millisecond timescale. Ubiquitin folding has been the subject of many experimental studies, but its slow folding rate has made it difficult to observe and characterize the folding process through all-atom molecular dynamics simulations. Here we determine the mechanism, thermodynamics, and kinetics of ubiquitin folding through equilibrium atomistic simulations. The picture emerging from the simulations is in agreement with a view of ubiquitin folding suggested from previous experiments. Our findings related to the folding of ubiquitin are also consistent, for the most part, with the folding principles derived from the simulation of fast-folding proteins, suggesting that these principles may be applicable to a wider range of proteins.

Thermodynamics of protein folding using a modified Wako-Saitô-Muñoz-Eaton model

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model's thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.

Single-shot NMR measurement of protein unfolding landscapes

The transient unfolding events from the native state of a protein towards higher energy states can be closely investigated by studying the process of hydrogen exchange. Here, we present BLUU-Tramp (Biophysics Laboratory University of Udine-Temperature ramp), a new method to measure the rates for the exchange process and the underlying equilibrium thermodynamic parameters, using just a single sample preparation, in a single experiment that lasts some 20 to 60h depending on the protein thermal stability, to record hundreds of points over a virtually continuous temperature window. The method is suitable also in presence of other proteins in the sample, if only the target protein is (15)N-labelled. This allows the complete thermodynamic description of the unfolding landscape at an atomic level in the presence of small or macromolecular ligands or cosolutes, or in physiological environments. The method was successfully tested with human ubiquitin. Then the unfolding thermodynamic parameters were satisfactorily determined for the amyloidogenic protein β(2)-microglobulin, in aqueous buffer and in synovial liquid, that is the natural medium of amyloid deposition in joints.

Long-lived states to monitor protein unfolding by proton NMR

The relaxation of long-lived states (LLS) corresponds to the slow return to statistical thermal equilibrium between symmetric and antisymmetric proton spin states. This process is remarkably sensitive to the presence of external spins and can be used to obtain information about partial unfolding of proteins. We detected the appearance of a destabilized conformer of ubiquitin when urea is added to the protein in its native state. This conformer shows increased mobility in the C-terminus, which significantly extends the lifetimes of proton LLS magnetisation in Ser-65. These changes could not be detected by conventional measurements of T(1) and T(2) relaxation times of protons, and would hardly be sensed by carbon-13 or nitrogen-15 relaxation measurements. Conformers with similar dynamic and structural features, as revealed by LLS relaxation times, could be observed, in the absence of urea, in two ubiquitin mutants, L67S and L69S.

Analysis of the equilibrium and kinetics of the ankyrin repeat protein myotrophin

We apply the Wako-Saito-Muñoz-Eaton model to the study of myotrophin, a small ankyrin repeat protein, whose folding equilibrium and kinetics have been recently characterized experimentally. The model, which is a native-centric with binary variables, provides a finer microscopic detail than the Ising model that has been recently applied to some different repeat proteins, while being still amenable for an exact solution. In partial agreement with the experiments, our results reveal a weakly three-state equilibrium and a two-state-like kinetics of the wild-type protein despite the presence of a nontrivial free-energy profile. These features appear to be related to a careful "design" of the free-energy landscape, so that mutations can alter this picture, stabilizing some intermediates and changing the position of the rate-limiting step. Also, the experimental findings of two alternative pathways, an N-terminal and a C-terminal one, are qualitatively confirmed, even if the variations in the rates upon the experimental mutations cannot be quantitatively reproduced. Interestingly, the folding and unfolding pathways appear to be different, even if closely related: a property that is not generally considered in the phenomenological interpretation of the experimental data.

Quantitative prediction of protein folding behaviors from a simple statistical model

The statistical nature of the protein folding process requires the use of equally detailed yet simple models that lend themselves to characterize experiments. One such model is the Wako-Saitô-Muñoz-Eaton model, that we extend here to include solvation effects (WSME-S), introduced via empirical terms. We employ the novel version to analyze the folding of two proteins, gpW and SH3, that have similar size and thermodynamic stability but with the former folding 3 orders of magnitude faster than SH3. A quantitative analysis reveals that gpW presents at most marginal barriers, in contrast to SH3 that folds following a simple two-state approximation. We reproduce the observed experimental differences in melting temperature in gpW as seen by different experimental spectroscopic probes and the shape of the rate-temperature plot. In parallel, we predict the folding complexity expected in gpW from the analysis of both the residue-level thermodynamics and kinetics. SH3 serves as a stringent control with neither folding complexity nor dispersion in melting temperatures being observed. The extended model presented here serves as an ideal tool not only to characterize folding data but also to make experimentally testable predictions.

Nearly symmetrical proteins: folding pathways and transition states

The folding pathways of the B domain of protein A have been the subject of many experimental and computational studies. Based on a statistical mechanical model, it has been suggested that the native state symmetry leads to multiple pathways, highly dependent on temperature and denaturant concentration. Experiments, however, have not confirmed this scenario. By considering four nearly symmetrical proteins, one of them being the above molecule, here we show that, if contact energies are properly taken into account, a different picture emerges from kinetic simulations of the above-mentioned model. This is characterized by a dominant folding pathway, which is consistent with the most recent experimental results. Given the simplicity of the model, we also report on a direct sampling of the transition state.

Direct evidence for a dry molten globule intermediate during the unfolding of a small protein

Little is known about how proteins begin to unfold. In particular, how and when water molecules penetrate into the protein interior during unfolding, thereby enabling the dissolution of specific structure, is poorly understood. The hypothesis that the native state expands initially into a dry molten globule, in which tight packing interactions are broken, but whose hydrophobic core has not expanded sufficiently to be able to absorb water molecules, has very little experimental support. Here, we report our analysis of the earliest observable events during the unfolding of single chain monellin (MNEI), a small plant protein. Far- and near-UV circular dichroism measurements of GdnHCl-induced unfolding indicate that a molten globule intermediate forms initially, before the major slow unfolding reaction commences. Steady-state fluorescence resonance energy transfer measurements show that the C-terminal end of the single helix of MNEI initially moves rapidly away from the single tryptophan residue that is close to the N-terminal end of the helix. The average end-to-end distance of the protein also expands during unfolding to the molten globule intermediate. At this time, water has yet to penetrate the protein core, according to the evidence from intrinsic tryptophan fluorescence and 8-anilino-1-naphthalenesulfonic acid fluorescence-monitored kinetic unfolding measurements. Our results therefore provide direct evidence for a dry molten globule intermediate at the initial stage of unfolding. Our results further suggest that the structural transition between the native and dry molten globule states could be an all-or-none transition, whereas further swelling of the globule appears to occur gradually.

Probing the folding transition state of ubiquitin mutants by temperature-jump-induced downhill unfolding

Crucial to revealing mechanistic details of protein folding is a characterization of the transition state ensemble and its structural dynamics. To probe the transition state of ubiquitin thermal unfolding, we examine unfolding dynamics and kinetics of wild-type and mutant ubiquitin using time-resolved nonlinear infrared spectroscopy after a nanosecond temperature jump. We observe spectral changes on two different time scales. A fast nonexponential microsecond phase is attributed to downhill unfolding from the transition state region, which is induced by a shift of the barrier due to the rapid temperature change. Slow millisecond changes arise from thermally activated folding and unfolding kinetics. Mutants that stabilize or destabilize beta strands III-V lead to a decreased or increased amplitude of the microsecond phase, indicating that the disruption or weakening of these strands occurs in the transition state. Unfolding features from microseconds to milliseconds can be explained by temperature-dependent changes of a two-dimensional free energy surface constructed by the native contacts between beta strands of the protein. In addition, the results support the possibility of an intermediate state in thermal unfolding.