ProtSA: a web application for calculating sequence specific protein solvent accessibilities in the unfolded ensemble

Background  

The stability of proteins is governed by the heat capacity, enthalpy and entropy changes of folding, which are strongly correlated to the change in solvent accessible surface area experienced by the polypeptide. While the surface exposed in the folded state can be easily determined, accessibilities for the unfolded state at the atomic level cannot be obtained experimentally and are typically estimated using simplistic models of the unfolded ensemble. A web application providing realistic accessibilities of the unfolded ensemble of a given protein at the atomic level will prove useful.     

Residue solvent accessibilities in the unfolded polypeptide chain.

The difference of solvent accessibilities in the native and unfolded states of the protein is used as a measure of the hydrophobic contribution to the free energy of folding. We present a new approximation of amino acids solvent accessibilities in the unfolded state based on the 1-ns molecular dynamics simulation of Ala-X-Ala tripeptides at a temperature of 368 K. The standard accessibility values averaged from the molecular dynamics study are significantly lower from those previously obtained by considering only selected conformations of Ala-X-Ala tripeptides.     

Dimensions,energetics, and denaturant effects of the protein unstructured state

Determining the energetics of the unfolded state of a protein is essential for understanding the folding mechanics of ordered proteins and the structure–function relation of intrinsically disordered proteins. Here, we adopt a coil‐globule transition theory to develop a general scheme to extract interaction and free energy information from single‐molecule fluorescence resonance energy transfer spectroscopy. By combining protein stability data, we have determined the free energy difference between the native state and the maximally collapsed denatured state in a number of systems, providing insight on the specific/nonspecific interactions in protein folding. Both the transfer and binding models of the denaturant effects are demonstrated to account for the revealed linear dependence of inter‐residue interactions on the denaturant concentration, and are thus compatible under the coil‐globule transition theory to further determine the dimension and free energy of the conformational ensemble of the unfolded state. The scaling behaviors and the effective θ‐state are also discussed.     

Native-like mean structure in the unfolded ensemble of small proteins

The nature of the unfolded state plays a great role in our understanding of proteins. However, accurately studying the unfolded state with computer simulation is difficult, due to its complexity and the great deal of sampling required. Using a supercluster of over 10,000 processors we have performed close to 800 micros of molecular dynamics simulation in atomistic detail of the folded and unfolded states of three polypeptides from a range of structural classes: the all-alpha villin headpiece molecule, the beta hairpin tryptophan zipper, and a designed alpha-beta zinc finger mimic. A comparison between the folded and the unfolded ensembles reveals that, even though virtually none of the individual members of the unfolded ensemble exhibits native-like features, the mean unfolded structure (averaged over the entire unfolded ensemble) has a native-like geometry. This suggests several novel implications for protein folding and structure prediction as well as new interpretations for experiments which find structure in ensemble-averaged measurements.     

Prediction of natively unfolded regions in protein chain

We have shown that the ability of a protein to be in globular or in natively unfolded state (under native conditions) may be determined (besides low overall hydrophobicity and a large net charge) by such a property as the average environment density, the average number of residues enclosed at the given distance. A statistical scale of the average number of residues enclosed at the given distance for 20 types of amino acid residues in globular state has been created on the basis of 6626 protein structures. Using this scale for separation of 80 globular and 90 natively unfolded proteins we fail only in 11% of proteins (compared with 17% of errors which are observed if to use hydrophobicity scale). The present scale may be used both for prediction of form (folded or unfolded) of the native state of protein and for prediction of natively unfolded regions in protein chains. The results of comparison of our method of predicting natively unfolded regions with the other known methods show that our method has the highest fraction of correctly predicted natively unfolded regions (that is 87% and 77% if to make averaging over residues and over proteins correspondingly).     

Determination of ultrafast protein folding rates from loop formation dynamics

Quenching of the triplet state of tryptophan by contact with cysteine can be used to measure the kinetics of loop formation in unfolded proteins. Here we show that cysteine quenching dynamics also provide a novel method for measuring folding rates when the exchange between folded and unfolded states is faster than the unquenched triplet lifetime (approximately 100 micros). We use this technique to investigate folding/unfolding kinetics of the 35 residue headpiece subdomain of the protein villin, which contains a single tryptophan residue and was engineered to contain a cysteine residue at the N terminus. At intermediate concentrations of denaturant the time-course of the triplet decay consists of two relaxations, the rates and amplitudes of which reveal the fast kinetics for folding and unfolding of this protein. The folding rates extracted using a simple kinetic model are close to those reported previously from laser-induced temperature-jump experiments that employ the change in tryptophan fluorescence as a probe. However, the results differ significantly from those reported from dynamic NMR line shape analysis on a variant with methionine at the N terminus, an issue that remains to be resolved. The analysis of the triplet quenching kinetics also shows that the quenching rates in the unfolded state increase with decreasing denaturant concentration, indicating a compaction of the unfolded protein.     

High-pressure SAXS study of folded and unfolded ensembles of proteins

A structural interpretation of the thermodynamic stability of proteins requires an understanding of the structural properties of the unfolded state. High-pressure small-angle x-ray scattering was used to measure the effects of temperature, pressure, denaturants, and stabilizing osmolytes on the radii of gyration of folded and unfolded state ensembles of staphylococcal nuclease. A set of variants with the internal Val-66 replaced with Ala, Tyr, or Arg was used to examine how changes in the volume and polarity of an internal microcavity affect the dimensions of the native state and the pressure sensitivity of the ensemble. The unfolded state ensembles achieved for these proteins with high pressure were more compact than those achieved at high temperature, and were all very sensitive to the presence of urea and glycerol. Substitutions at the hydrophobic core detectably altered the conformation of the protein, even in the folded state. The introduction of a charged residue, such as Arg, inside the hydrophobic interior of a protein could dramatically alter the structural properties, even those of the unfolded state. The data suggest that a charge at an internal position can interfere with the formation of transient hydrophobic clusters in the unfolded state, and ensure that the pressure-unfolded form of a protein occupies the maximum volume possible. Only at high temperatures does the radius of gyration of the unfolded state ensemble approach the value for a statistical random coil.     

The effect of a DeltaK280 mutation on the unfolded state of a microtubule-binding repeat in Tau

Tau is a natively unfolded protein that forms intracellular aggregates in the brains of patients with Alzheimer's disease. To decipher the mechanism underlying the formation of tau aggregates, we developed a novel approach for constructing models of natively unfolded proteins. The method, energy-minima mapping and weighting (EMW), samples local energy minima of subsequences within a natively unfolded protein and then constructs ensembles from these energetically favorable conformations that are consistent with a given set of experimental data. A unique feature of the method is that it does not strive to generate a single ensemble that represents the unfolded state. Instead we construct a number of candidate ensembles, each of which agrees with a given set of experimental constraints, and focus our analysis on local structural features that are present in all of the independently generated ensembles. Using EMW we generated ensembles that are consistent with chemical shift measurements obtained on tau constructs. Thirty models were constructed for the second microtubule binding repeat (MTBR2) in wild-type (WT) tau and a DeltaK280 mutant, which is found in some forms of frontotemporal dementia. By focusing on structural features that are preserved across all ensembles, we find that the aggregation-initiating sequence, PHF6*, prefers an extended conformation in both the WT and DeltaK280 sequences. In addition, we find that residue K280 can adopt a loop/turn conformation in WT MTBR2 and that deletion of this residue, which can adopt nonextended states, leads to an increase in locally extended conformations near the C-terminus of PHF6*. As an increased preference for extended states near the C-terminus of PHF6* may facilitate the propagation of beta-structure downstream from PHF6*, these results explain how a deletion at position 280 can promote the formation of tau aggregates.     

Energetics of protein structure and folding

The available experimental date on the kinetics of unfolding and refolding of small proteins are reviewed. Excluding slow transitions in the unfolded protein due to cis–trans isomerization of peptide bonds, the rate-limiting transition state in both unfolding and refolding is concluded to be a high-energy distortion of the fully folded state. Partially folded intermediates are undoubtedly important for folding, but their formation is normally not rate limiting. A simple model is used to illustrate some of the aspects of protein-folding energetics.     

Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

The Effect of a ΔK280 Mutation on the Unfolded State of a Microtubule-Binding Repeat in Tau

Tau is a natively unfolded protein that forms intracellular aggregates in the brains of patients with Alzheimer''s disease. To decipher the mechanism underlying the formation of tau aggregates, we developed a novel approach for constructing models of natively unfolded proteins. The method, energy-minima mapping and weighting (EMW), samples local energy minima of subsequences within a natively unfolded protein and then constructs ensembles from these energetically favorable conformations that are consistent with a given set of experimental data. A unique feature of the method is that it does not strive to generate a single ensemble that represents the unfolded state. Instead we construct a number of candidate ensembles, each of which agrees with a given set of experimental constraints, and focus our analysis on local structural features that are present in all of the independently generated ensembles. Using EMW we generated ensembles that are consistent with chemical shift measurements obtained on tau constructs. Thirty models were constructed for the second microtubule binding repeat (MTBR2) in wild-type (WT) tau and a ΔK280 mutant, which is found in some forms of frontotemporal dementia. By focusing on structural features that are preserved across all ensembles, we find that the aggregation-initiating sequence, PHF6*, prefers an extended conformation in both the WT and ΔK280 sequences. In addition, we find that residue K280 can adopt a loop/turn conformation in WT MTBR2 and that deletion of this residue, which can adopt nonextended states, leads to an increase in locally extended conformations near the C-terminus of PHF6*. As an increased preference for extended states near the C-terminus of PHF6* may facilitate the propagation of β-structure downstream from PHF6*, these results explain how a deletion at position 280 can promote the formation of tau aggregates.     

Shortening a loop can increase protein native state entropy

Protein loops are essential structural elements that influence not only function but also protein stability and folding rates. It was recently reported that shortening a loop in the AcP protein may increase its native state conformational entropy. This effect on the entropy of the folded state can be much larger than the lower entropic penalty of ordering a shorter loop upon folding, and can therefore result in a more pronounced stabilization than predicted by polymer model for loop closure entropy. In this study, which aims at generalizing the effect of loop length shortening on native state dynamics, we use all‐atom molecular dynamics simulations to study how gradual shortening a very long or solvent‐exposed loop region in four different proteins can affect their stability. For two proteins, AcP and Ubc7, we show an increase in native state entropy in addition to the known effect of the loop length on the unfolded state entropy. However, for two permutants of SH3 domain, shortening a loop results only with the expected change in the entropy of the unfolded state, which nicely reproduces the observed experimental stabilization. Here, we show that an increase in the native state entropy following loop shortening is not unique to the AcP protein, yet nor is it a general rule that applies to all proteins following the truncation of any loop. This modification of the loop length on the folded state and on the unfolded state may result with a greater effect on protein stability. Proteins 2015; 83:2137–2146. © 2015 Wiley Periodicals, Inc.     

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.     

Using the Unfolded State as the Reference State Improves the Performance of Statistical Potentials

Distance-dependent statistical potentials are an important class of energy functions extensively used in modeling protein structures and energetics. These potentials are obtained by statistically analyzing the proximity of atoms in all combinatorial amino-acid pairs in proteins with known structures. In model evaluation, the statistical potential is usually subtracted by the value of a reference state for better selectivity. An ideal reference state should include the general chemical properties of polypeptide chains so that only the unique factors stabilizing the native structures are retained after calibrating on reference state. However, reference states available as of this writing rarely model specific chemical constraints of peptide bonds and therefore poorly reflect the behavior of polypeptide chains. In this work, we proposed a statistical potential based on unfolded state ensemble (SPOUSE), where the reference state is summarized from the unfolded state ensembles of proteins produced according to the statistical coil model. Due to its better representation of the features of polypeptides, SPOUSE outperforms three of the most widely used distance-dependent potentials not only in native conformation identification, but also in the selection of close-to-native models and correlation coefficients between energy and model error. Furthermore, SPOUSE shows promising possibility of further improvement by integration with the orientation-dependent side-chain potentials.     

Glucosylation of beta-lactoglobulin lowers the heat capacity change of unfolding; a unique way to affect protein thermodynamics

Chemical glycosylation of proteins occurs in vivo spontaneously, especially under stress conditions, and has been linked in a number of cases to diseases related to protein denaturation and aggregation. It is the aim of this work to study the origin of the change in thermodynamic properties due to glucosylation of the folded beta-lactoglobulin A. Under mild conditions Maillard products can be formed by reaction of epsilon-amino groups of lysines with the reducing group of, in this case, glucose. The formed conjugates described here have an average degree of glycosylation of 82%. No impact of the glucosylation on the protein structure is detected, except that the Stokes radius was increased by approximately 3%. Although at ambient temperatures the change in Gibbs energy of unfolding is reduced by 20%, the denaturation temperature is increased by 5 degrees C. Using a combination of circular dichroism, fluorescence, and calorimetric approaches, it is shown that the change in heat capacity upon denaturation is reduced by 60% due to the glucosylation. Since in the denatured state the Stokes radius of the protein is not significantly smaller for the glucosylated protein, it is suggested that the nonpolar residues associate to the covalently linked sugar moiety in the unfolded state, thereby preventing their solvent exposure. In this way coupling of small reducing sugar moieties to solvent exposed groups of proteins offers an efficient and unique tool to deal with protein stability issues, relevant not only in nature but also for technological applications.     

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1–3 above, because a hard-sphere solvent acts as a protecting osmolyte.     

Kinetic analysis of folding and unfolding the 56 amino acid IgG-binding domain of streptococcal protein G.

The 56 amino acid B domain of protein G (GB) is a stable globular folding unit with no disulfide cross-links. The physical properties of GB offer extraordinary flexibility for evaluating the energetics of the folding reaction. The protein is monomeric and very soluble in both folded and unfolded forms. The folding reaction has been previously examined by differential scanning calorimetry (Alexander et al., 1992) and found to exhibit two-state unfolding behavior over a wide pH range with an unfolding transition near 90 degrees C (GB1) at neutral pH. Here, the kinetics of folding and unfolding two naturally occurring versions of GB have been measured using stopped-flow mixing methods and analyzed according to transition-state theory. GB contains no prolines, and the kinetics of folding and unfolding can be fit to a single, first-order rate constant over the temperature range of 5-35 degrees C. The major thermodynamic changes going from the unfolded state to the transition state are (1) a large decrease in heat capacity (delta Cp), indicating that the transition state is compact and solvent inaccessible relative to the unfolded state; (2) a large loss of entropy; and (3) a small increase in enthalpy. The most surprising feature of the folding of GB compared to that of previously studied proteins is that its folding approximates a rapid diffusion controlled process with little increase in enthalpy going from the unfolded to the transition state.     

Microscopic reversibility of protein folding in molecular dynamics simulations of the engrailed homeodomain

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.     

Prediction of natively unfolded regions in protein chains

Analysis showed that the globular or natively unfolded state of a protein can be inferred not only from a lower hydrophobicity or a higher charge, but also from the average environment density (average number of close residues located within a certain distance of a given one) of its residues. A database of 6626 protein structures was used to construct a statistical scale of the average number of close residues in globular structures for the 20 amino acids. The portion of false predictions in distinguishing between 80 globular and 90 natively unfolded proteins was 11% with the new scale and 17% with a hydrophobicity scale. The new scale proved suitable for predicting the folded or unfolded state for native proteins or the natively unfolded regions for protein chains. In comparisons with the available algorithms, the new method yielded the highest portion of true predictions (87 and 77% with averaging over residues and over proteins, respectively).