Collapse Precedes Folding in Denaturant-Dependent Assembly of Ubiquitin

SOP-MULTI: A Self-Organized Polymer-Based Coarse-Grained Model for Multidomain and Intrinsically Disordered Proteins with Conformation Ensemble Consistent with Experimental Scattering Data

Multidomain proteins with long flexible linkers and full-length intrinsically disordered proteins (IDPs) are best defined as an ensemble of conformations rather than a single structure. Determining high-resolution ensemble structures of such proteins poses various challenges by using tools from experimental structural biophysics. Integrative approaches combining available low-resolution ensemble-averaged experimental data and in silico biomolecular reconstructions are now often used for the purpose. However, extensive Boltzmann weighted conformation sampling for large proteins, especially for ones where both the folded and disordered domains exist in the same polypeptide chain, remains a challenge. In this work, we present a 2-site per amino-acid resolution SOP-MULTI force field for simulating coarse-grained models of multidomain proteins. SOP-MULTI combines two well-established self-organized polymer models─: (i) SOP-SC models for folded systems and (ii) SOP-IDP for IDPs. For the SOP-MULTI, we introduce cross-interaction terms between the beads belonging to the folded and disordered regions to generate conformation ensembles for full-length multidomain proteins such as hnRNP A1, TDP-43, G3BP1, hGHR-ECD, TIA1, HIV-1 Gag, polyubiquitin, and FUS. When back-mapped to all-atom resolution, SOP-MULTI trajectories faithfully recapitulate the scattering data over the range of the reciprocal space. We also show that individual folded domains preserve native contacts with respect to solved folded structures, and root-mean-square fluctuations of residues in folded domains match those obtained from all-atom molecular dynamics simulation trajectories of the same folded systems. SOP-MULTI force field is made available as a LAMMPS-compatible user package along with setup codes for generating the required files for any full-length protein with folded and disordered regions.

Slow Conformational Exchange between Partially Folded and Near-Native States of Ubiquitin: Evidence for a Multistate Folding Model

The mechanism by which small proteins fold, i.e., via intermediates or via a two-state mechanism, is a subject of intense investigation. Intermediate states in the folding pathways of these proteins are sparsely populated due to transient lifetimes under normal conditions rendering them transparent to a majority of the biophysical methods employed for structural, thermodynamic, and kinetic characterization, which attributes are essential for understanding the cooperative folding/unfolding of such proteins. Dynamic NMR spectroscopy has enabled the characterization of folding intermediates of ubiquitin that exist in equilibrium under conditions of low pH and denaturants. At low pH, an unlocked state defined as N' is in fast exchange with an invisible state, U″, as observed by CEST NMR. Addition of urea to ubiquitin at pH 2 creates two new states F' and U', which are in slow exchange (kF'→U' = 0.14 and kU'→F' = 0.28 s-1) as indicated by longitudinal ZZ-magnetization exchange spectroscopy. High-resolution solution NMR structures of F' show it to be in an "unlocked" conformation with measurable changes in rotational diffusion, translational diffusion, and rotational correlational times. U' is characterized by the presence of just the highly conserved N-terminal β1-β2 hairpin. The folding of ubiquitin is cooperative and is nucleated by the formation of an N-terminal β-hairpin followed by significant hydrophobic collapse of the protein core resulting in the formation of bulk of the secondary structural elements stabilized by extensive tertiary contacts. U' and F' may thus be described as early and late folding intermediates in the ubiquitin folding pathway.

Brewing COFFEE: A Sequence-Specific Coarse-Grained Energy Function for Simulations of DNA-Protein Complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription and gene expression to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse-grained Force Field for Energy Estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the self-organized polymer model with side-chains for proteins and the three interaction site model for DNA in a modular fashion, without recalibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a data set of high-resolution crystal structures. The only parameter in COFFEE is the strength (λDNAPRO) of the DNA-protein contact potential. For an optimal choice of λDNAPRO, the crystallographic B-factors for DNA-protein complexes with varying sizes and topologies are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts scattering profiles that are in quantitative agreement with small-angle X-ray scattering experiments, as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which do not alter the balance of electrostatic interactions but affect chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

Brewing COFFEE: A sequence-specific coarse-grained energy function for simulations of DNA-protein complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription, gene expression, to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse grained force field for energy estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the Self-Organized Polymer model with Side Chains for proteins and the Three Interaction Site model for DNA in a modular fashion, without re-calibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a dataset of high-resolution crystal structures. The only parameter in COFFEE is the strength (λ D N A P R O ) of the DNA-protein contact potential. For an optimal choice of λ D N A P R O , the crystallographic B-factors for DNA-protein complexes, with varying sizes and topologies, are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts the scattering profiles that are in quantitative agreement with SAXS experiments as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which does not alter the balance of electrostatic interactions, but affects chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

The Action of Chemical Denaturants: From Globular to Intrinsically Disordered Proteins

Proteins perform their many functions by adopting either a minimal number of strictly similar conformations, the native state, or a vast ensemble of highly flexible conformations. In both cases, their structural features are highly influenced by the chemical environment. Even though a plethora of experimental studies have demonstrated the impact of chemical denaturants on protein structure, the molecular mechanism underlying their action is still debated. In the present review, after a brief recapitulation of the main experimental data on protein denaturants, we survey both classical and more recent interpretations of the molecular basis of their action. In particular, we highlight the differences and similarities of the impact that denaturants have on different structural classes of proteins, i.e., globular, intrinsically disordered (IDP), and amyloid-like assemblies. Particular attention has been given to the IDPs, as recent studies are unraveling their fundamental importance in many physiological processes. The role that computation techniques are expected to play in the near future is illustrated.

Conformational Features and Hydration Dynamics of Proteins in Cosolvents: A Perspective from Computational Approaches

The importance of solvent in stabilizing protein structures has long been recognized. Water is the common solvent for proteins, and hydration is elemental in governing protein stability, flexibility, and function through various interactions. The addition of small organic molecules known as cosolvents may deploy stabilization (folding) or destabilization (unfolding) effects on native protein conformations. Despite exhaustive literature, the molecular mechanism by which cosolvents regulate protein conformations and dynamics is controversial. Specifically, the cosolvent behavior has been unpredictable with the nature and concentrations that lead to protein stabilizing/destabilizing effects as it changes in water content near the vicinity of proteins. With the massive development of computational resources, advancement of computational methods, and the availability of numerous experimental techniques, various theoretical and computational studies of proteins in a mixture of solvents have been instigated. The growing interest in such studies has been to unravel the underlying mechanism of protein folding and cosolvent/solvent-protein interactions that have significant implications in biomedical and biotechnological applications. In this mini-review, apart from the brief overview of important theories and force-field model-based cosolvent effects on proteins, we present the current state of knowledge and recent advances in the field to describe cosolvent-guided conformational features of proteins and hydration dynamics from computational approaches. The mini-review further explains the mechanistic details of protein stability in various popularly used cosolvents, including limitations of present studies and future outlooks. The counteracting effects of cosolvent on the proteins in the mixture of stabilizing and destabilizing cosolvents are also presented and discussed.

Salt-Induced Transitions in the Conformational Ensembles of Intrinsically Disordered Proteins

Salts modulate the behavior of intrinsically disordered proteins (IDPs) and influence the formation of membraneless organelles through liquid-liquid phase separation (LLPS). In low ionic strength solutions, IDP conformations are perturbed by the screening of electrostatic interactions, independent of the salt identity. In this regime, insight into the IDP behavior can be obtained using the theory for salt-induced transitions in charged polymers. However, salt-specific interactions with the charged and uncharged residues, known as the Hofmeister effect, influence IDP behavior in high ionic strength solutions. There is a lack of reliable theoretical models in high salt concentration regimes to predict the salt effect on IDPs. We propose a simulation methodology using a coarse-grained IDP model and experimentally measured water to salt solution transfer free energies of various chemical groups that allowed us to study the salt-specific transitions induced in the IDPs conformational ensemble. We probed the effect of three different monovalent salts on five IDPs belonging to various polymer classes based on charged residue content. We demonstrate that all of the IDPs of different polymer classes behave as self-avoiding walks (SAWs) at physiological salt concentration. In high salt concentrations, the transitions observed in the IDP conformational ensembles are dependent on the salt used and the IDP sequence and composition. Changing the anion with the cation fixed can result in the IDP transition from a SAW-like behavior to a collapsed globule. An important implication of these results is that a suitable salt can be identified to induce condensation of an IDP through LLPS.

Monitoring Protein Global and Local Parameters in Unfolding and Binding Studies: The Extended Applicability of the Diffusion Coefficient─Molecular Size Empirical Relations

Protein unfolding and denaturation are main issues in biochemical and pharmaceutical research. Using a global parameter, the translational diffusion coefficient D, folded, unfolded, and intrinsically disordered proteins of a given molar mass M can be distinguished based on their distinct hydrodynamic properties. For broader applications, we provide generalized, PFG-NMR-based empirical D-M relations validated at different temperatures and ready to use with the corresponding corrections in different media. We demonstrate that these relations enable a more accurate molecular mass determination and show fewer potential errors than those of the common methods based on small-molecular diffusion standards. We monitor unfolding of three model proteins using 8 M urea and dimethyl sulfoxide (DMSO)-water mixtures as denaturing agents, highlighting the effect of disulfide bonds. Denaturation in 8 M urea is pH-dependent; in addition, for proteins with highly stable disulfide bonds, a reducing agent (TCEP) is required to achieve complete unfolding. Regarding the effect of local parameters, we show that at low DMSO concentrations─common conditions in pharmaceutical binding studies─the PFG-NMR-derived global parameters are not significantly affected. Still, the atomic environments can change, and the bound solvent molecule can inhibit the binding of a partner molecule. Using proteins with natural isotopic abundance, this effect can be proven by fast ¹H-¹⁵N 2D correlation spectra. Our results enable fast and easy estimation of protein molecular mass and the degree of folding in various media; moreover, the effect of the cosolvent on the atomic-level structure can be traced without the need of isotope labeling.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Effects of alignment activity on the collapse kinetics of a flexible polymer

The dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following quenching from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. The results from our MD simulations reveal that though the globular state is also the typical final state in the active case, the nonequilibrium pathways to arrive at such a state differ from the picture for the passive case due to the alignment interaction among the beads. We notice that deviations from the intermediate "pearl-necklace"-like arrangement, which is observed in the passive case, and the formation of more elongated dumbbell-like structures increase with increasing activity. Furthermore, it appears that while a small active force on the beads certainly makes the coarsening process much faster, there exists a nonmonotonic dependence of the collapse time on the strength of active interaction. We quantify these observations by comparing the scaling laws for the collapse time and growth of pearls with the passive case.

Energy Landscape of Ubiquitin Is Weakly Multidimensional

Single molecule pulling experiments report time-dependent changes in the extension (X) of a biomolecule as a function of the applied force (f). By fitting the data to one-dimensional analytical models of the energy landscape, we can extract the hopping rates between the folded and unfolded states in two-state folders as well as the height and the location of the transition state (TS). Although this approach is remarkably insightful, there are cases for which the energy landscape is multidimensional (catch bonds being the most prominent). To assess if the unfolding energy landscape in small single domain proteins could be one-dimensional, we simulated force-induced unfolding of ubiquitin (Ub) using the coarse-grained self-organized polymer-side chain (SOP-SC) model. Brownian dynamics simulations using the SOP-SC model reveal that the Ub energy landscape is weakly multidimensional (WMD), governed predominantly by a single barrier. The unfolding pathway is confined to a narrow reaction pathway that could be described as diffusion in a quasi-1D X-dependent free energy profile. However, a granular analysis using the P_fold analysis, which does not assume any form for the reaction coordinate, shows that X alone does not account for the height and, more importantly, the location of the TS. The f-dependent TS location moves toward the folded state as f increases, in accord with the Hammond postulate. Our study shows that, in addition to analyzing the f-dependent hopping rates, the transition state ensemble must also be determined without resorting to X as a reaction coordinate to describe the unfolding energy landscapes of single domain proteins, especially if they are only WMD.

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.

Pearl-Necklace-Like Local Ordering Drives Polypeptide Collapse

The collapse of the polypeptide backbone is an integral part of protein folding. Using polyglycine as a probe, we explore the nonequilibrium pathways of protein collapse in water. We find that the collapse depends on the competition between hydration effects and intrapeptide interactions. Once intrapeptide van der Waal interactions dominate, the chain collapses along a nonequilibrium pathway characterized by formation of pearl-necklace-like local clusters as intermediates that eventually coagulate into a single globule. By describing this coarsening through the contact probability as a function of distance along the chain, we extract a time-dependent length scale that grows in a linear fashion. The collapse dynamics is characterized by a dynamical critical exponent z ≈ 0.5 that is much smaller than the values of z = 1–2 reported for nonbiological polymers. This difference in the exponents is explained by the instantaneous formation of intrachain hydrogen bonds and local ordering that may be correlated with the observed fast folding times of proteins.

Unfolded states under folding conditions accommodate sequence-specific conformational preferences with random coil-like dimensions

Proteins are marginally stable molecules that fluctuate between folded and unfolded states. Here, we provide a high-resolution description of unfolded states under refolding conditions for the N-terminal domain of the L9 protein (NTL9). We use a combination of time-resolved Förster resonance energy transfer (FRET) based on multiple pairs of minimally perturbing labels, time-resolved small-angle X-ray scattering (SAXS), all-atom simulations, and polymer theory. Upon dilution from high denaturant, the unfolded state undergoes rapid contraction. Although this contraction occurs before the folding transition, the unfolded state remains considerably more expanded than the folded state and accommodates a range of local and nonlocal contacts, including secondary structures and native and nonnative interactions. Paradoxically, despite discernible sequence-specific conformational preferences, the ensemble-averaged properties of unfolded states are consistent with those of canonical random coils, namely polymers in indifferent (theta) solvents. These findings are concordant with theoretical predictions based on coarse-grained models and inferences drawn from single-molecule experiments regarding the sequence-specific scaling behavior of unfolded proteins under folding conditions.

Thermally versus Chemically Denatured Protein States

Protein unfolding thermodynamic parameters are conventionally extracted from equilibrium thermal and chemical denaturation experiments. Despite decades of work, the degree of structure and the compactness of denatured states populated in these experiments are still open questions. Here, building on previous works, we show that thermally and chemically denatured protein states are distinct from the viewpoint of far-ultraviolet circular dichroism experiments that report on the local conformational status of peptide bonds. The differences identified are independent of protein length, structural class, or experimental conditions, highlighting the presence of two sub-ensembles within the denatured states. The sub-ensembles, U_T and U_D for thermally induced and denaturant-induced unfolded states, respectively, can exclusively exchange populations as a function of temperature at high chemical denaturant concentrations. Empirical analysis suggests that chemically denatured states are ∼50% more expanded than the thermally denatured chains of the same protein. Our observations hint that the strength of protein backbone-backbone interactions and identity versus backbone-solvent/co-solvent interactions determine the conformational distributions. We discuss the implications for protein folding mechanisms, the heterogeneity in relaxation rates, and folding diffusion coefficients.

Sequence Effects on Size, Shape, and Structural Heterogeneity in Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) lack well-defined three-dimensional structures, thus challenging the archetypal notion of structure-function relationships. Determining the ensemble of conformations that IDPs explore under physiological conditions is the first step toward understanding their diverse cellular functions. Here, we quantitatively characterize the structural features of IDPs as a function of sequence and length using coarse-grained simulations. For diverse IDP sequences, with the number of residues ( NT) ranging from 20 to 441, our simulations not only reproduce the radii of gyration ( Rg) obtained from experiments, but also predict the full scattering intensity profiles in excellent agreement with small-angle X-ray scattering experiments. The Rg values are well-described by the standard Flory scaling law, Rg = Rg0 NTν, with ν ≈ 0.588, making it tempting to assert that IDPs behave as polymers in a good solvent. However, clustering analysis reveals that the menagerie of structures explored by IDPs is diverse, with the extent of heterogeneity being highly sequence-dependent, even though ensemble-averaged properties, such as the dependence of Rg on chain length, may suggest synthetic polymer-like behavior in a good solvent. For example, we show that for the highly charged Prothymosin-α, a substantial fraction of conformations is highly compact. Even if the sequence compositions are similar, as is the case for α-Synuclein and a truncated construct from the Tau protein, there are substantial differences in the conformational heterogeneity. Taken together, these observations imply that metrics based on net charge or related quantities alone cannot be used to anticipate the phases of IDPs, either in isolation or in complex with partner IDPs or RNA. Our work sets the stage for probing the interactions of IDPs with each other, with folded protein domains, or with partner RNAs, which are critical for describing the structures of stress granules and biomolecular condensates with important cellular functions.

Commonly used FRET fluorophores promote collapse of an otherwise disordered protein

The dimensions that unfolded proteins, including intrinsically disordered proteins (IDPs), adopt in the absence of denaturant remain controversial. We developed an analysis procedure for small-angle X-ray scattering (SAXS) profiles and used it to demonstrate that even relatively hydrophobic IDPs remain nearly as expanded in water as they are in high denaturant concentrations. In contrast, as demonstrated here, most fluorescence resonance energy transfer (FRET) measurements have indicated that relatively hydrophobic IDPs contract significantly in the absence of denaturant. We use two independent approaches to further explore this controversy. First, using SAXS we show that fluorophores employed in FRET can contribute to the observed discrepancy. Specifically, we find that addition of Alexa-488 to a normally expanded IDP causes contraction by an additional 15%, a value in reasonable accord with the contraction reported in FRET-based studies. Second, using our simulations and analysis procedure to accurately extract both the radius of gyration (R_g) and end-to-end distance (R_ee) from SAXS profiles, we tested the recent suggestion that FRET and SAXS results can be reconciled if the R_g and R_ee are "uncoupled" (i.e., no longer simply proportional), in contrast to the case for random walk homopolymers. We find, however, that even for unfolded proteins, these two measures of unfolded state dimensions remain proportional. Together, these results suggest that improved analysis procedures and a correction for significant, fluorophore-driven interactions are sufficient to reconcile prior SAXS and FRET studies, thus providing a unified picture of the nature of unfolded polypeptide chains in the absence of denaturant.

The Sensitivity of Computational Protein Folding to Contact Map Perturbations: The Case of Ubiquitin Folding and Function

Ubiquitin is a small model protein, commonly used in protein folding experiments and simulations. We simulated ubiquitin using a well-tested structure-based model coarse-grained to a C_α level (C_α-SBM) and found that the simulated folding route did not agree with the experimentally observed one. Simulating the C_α-SBM with a cutoff contact map, instead of a screened contact map, switched the folding route with the new route matching the experimental route. Thus, the simulated folding of ubiquitin is sensitive to contact map definition. The screened contact map, which is used in folding simulations because it captures protein folding cooperativity, removes contacts in which the atoms in contact are occluded by a third atom and is less sensitive to the value of the cutoff distance in well-packed regions of the protein. In sparsely packed regions, the larger cutoff distance creates bridging contacts between atoms which are separated by voids. Such contacts do not seem to affect the folding of most proteins, including those of the ubiquitin fold. However, the surface of ubiquitin has several protruding functional side chains which naturally create bridging contacts. Together, our results show that subtle structural features of a protein that may not be apparent by mere observation can be identified by comparing folding simulations of SBMs in which these features are differently encoded. When such structural features are preserved for functional reasons, differences in computational folding can be leveraged to identify functional features. Notably, such features are accessible to a gradation of SBMs even in commonly studied proteins such as ubiquitin.

Interrupted Pressure-Jump NMR Experiments Reveal Resonances of On-Pathway Protein Folding Intermediate

Previous pressure-jump NMR experiments on a pressure-sensitized double mutant of ubiquitin showed evidence that its folding occurs via two parallel, comparably efficient pathways: a single barrier and a two-barrier pathway. An interrupted folding NMR experiment is introduced, where for a brief period the pressure is dropped to atmospheric conditions (1 bar), followed by a jump back to high pressure for signal detection. Conventional, forward sampling of the indirect dimension during the low-pressure period correlates the ¹⁵N or ¹³C' chemical shifts of the unfolded protein at 1 bar to the ¹H frequencies of both the unfolded and folded proteins at high pressure. Remarkably, sampling the data of the same experiment in the reverse direction yields the frequencies of proteins present at the end of the low-pressure interval, which include unfolded, intermediate, and folded species. Although the folding intermediate ¹⁵N shifts differ strongly from natively folded protein, its ¹³C' chemical shifts, which are more sensitive probes for secondary structure, closely match those of the folded protein and indicate that the folding intermediate must have a structure that is quite similar to the native state.

Monitoring 15N Chemical Shifts During Protein Folding by Pressure-Jump NMR

Pressure-jump hardware permits direct observation of protein NMR spectra during a cyclically repeated protein folding process. For a two-state folding protein, the change in resonance frequency will occur nearly instantaneously when the protein clears the transition state barrier, resulting in a monoexponential change of the ensemble-averaged chemical shift. However, protein folding pathways can be more complex and contain metastable intermediates. With a pseudo-3D NMR experiment that utilizes stroboscopic observation, we measure the ensemble-averaged chemical shifts, including those of exchange-broadened intermediates, during the folding process. Such measurements for a pressure-sensitized mutant of ubiquitin show an on-pathway kinetic intermediate whose ¹⁵N chemical shifts differ most from the natively folded protein for strands β5, its preceding turn, and the two strands that pair with β5 in the native structure.

Collapse Transitions of Proteins and the Interplay Among Backbone, Sidechain, and Solvent Interactions

Proteins can collapse into compact globules or form expanded, solvent-accessible, coil-like conformations. Additionally, they can fold into well-defined three-dimensional structures or remain partially or entirely disordered. Recent discoveries have shown that the tendency for proteins to collapse or remain expanded is not intrinsically coupled to their ability to fold. These observations suggest that proteins do not have to form compact globules in aqueous solutions. They can be intrinsically disordered, collapsed, or expanded, and even form well-folded, elongated structures. This ability to decouple collapse from folding is determined by the sequence details of proteins. In this review, we highlight insights gleaned from studies over the past decade. Using a polymer physics framework, we explain how the interplay among sidechains, backbone units, and solvent determines the driving forces for collapsed versus expanded states in aqueous solvents.

Study of protein folding under native conditions by rapidly switching the hydrostatic pressure inside an NMR sample cell

Development of specialized instrumentation enables rapid switching of the hydrostatic pressure inside an operating NMR spectrometer. This technology allows observation of protein signals during the repeated folding process. Applied to ubiquitin, a previously extensively studied model of protein folding, the methodology reveals an initially highly dynamic state that deviates relatively little from random coil behavior but also provides evidence for numerous repeatedly failed folding events, previously only observed in computer simulations. Above room temperature, direct NMR evidence shows a ∼50% fraction of proteins folding through an on-pathway kinetic intermediate, thereby revealing two equally efficient parallel folding pathways.

In general, small proteins rapidly fold on the timescale of milliseconds or less. For proteins with a substantial volume difference between the folded and unfolded states, their thermodynamic equilibrium can be altered by varying the hydrostatic pressure. Using a pressure-sensitized mutant of ubiquitin, we demonstrate that rapidly switching the pressure within an NMR sample cell enables study of the unfolded protein under native conditions and, vice versa, study of the native protein under denaturing conditions. This approach makes it possible to record 2D and 3D NMR spectra of the unfolded protein at atmospheric pressure, providing residue-specific information on the folding process. ¹⁵N and ¹³C chemical shifts measured immediately after dropping the pressure from 2.5 kbar (favoring unfolding) to 1 bar (native) are close to the random-coil chemical shifts observed for a large, disordered peptide fragment of the protein. However, ¹⁵N relaxation data show evidence for rapid exchange, on a ∼100-μs timescale, between the unfolded state and unstable, structured states that can be considered as failed folding events. The NMR data also provide direct evidence for parallel folding pathways, with approximately one-half of the protein molecules efficiently folding through an on-pathway kinetic intermediate, whereas the other half fold in a single step. At protein concentrations above ∼300 μM, oligomeric off-pathway intermediates compete with folding of the native state.

Denaturants Alter the Flux through Multiple Pathways in the Folding of PDZ Domain

Although we understand many aspects of how small proteins (number of residues less than about hundred) fold, it is a major challenge to quantitatively describe how large proteins self-assemble. To partially overcome this challenge, we performed simulations using the self-organized polymer model with side chains (SOP-SC) in guanidinium chloride (GdmCl), using the molecular transfer model (MTM), to describe the folding of the 110-residue PDZ3 domain. The simulations reproduce the folding thermodynamics accurately including the melting temperature (T_m), the stability of the folded state with respect to the unfolded state. We show that the calculated dependence of ln k_obs (k_obs is the relaxation rate) has the characteristic chevron shape. The slopes of the chevron plots are in good agreement with experiments. We show that PDZ3 folds by four major pathways populating two metastable intermediates, in accord with the kinetic partitioning mechanism. The structure of one of the intermediates, populated after polypeptide chain collapse, is structurally similar to an equilibrium intermediate. Surprisingly, the connectivities between the intermediates and hence, the fluxes through the pathways depend on the concentration of GdmCl. The results are used to predict possible outcomes for unfolding of PDZ domain subject to mechanical forces. Our study demonstrates that, irrespective of the size or topology, simulations based on MTM and SOP-SC offer a theoretical framework for describing the folding of proteins, mimicking precisely the conditions used in experiments.

Innovative scattering analysis shows that hydrophobic disordered proteins are expanded in water

A substantial fraction of the proteome is intrinsically disordered, and even well-folded proteins adopt non-native geometries during synthesis, folding, transport, and turnover. Characterization of intrinsically disordered proteins (IDPs) is challenging, in part because of a lack of accurate physical models and the difficulty of interpreting experimental results. We have developed a general method to extract the dimensions and solvent quality (self-interactions) of IDPs from a single small-angle x-ray scattering measurement. We applied this procedure to a variety of IDPs and found that even IDPs with low net charge and high hydrophobicity remain highly expanded in water, contrary to the general expectation that protein-like sequences collapse in water. Our results suggest that the unfolded state of most foldable sequences is expanded; we conjecture that this property was selected by evolution to minimize misfolding and aggregation.