Thermodynamics and folding kinetics analysis of the SH3 domain form discrete molecular dynamics

We perform a detailed analysis of the thermodynamics and folding kinetics of the SH3 domain fold with discrete molecular dynamic simulations. We propose a protein model that reproduces some of the experimentally observed thermodynamic and folding kinetic properties of proteins. Specifically, we use our model to study the transition state ensemble of the SH3 fold family of proteins, a set of unstable conformations that fold to the protein native state with probability 1/2. We analyze the participation of each secondary structure element formed at the transition state ensemble. We also identify the folding nucleus of the SH3 fold and test extensively its importance for folding kinetics. We predict that a set of amino acid contacts between the RT-loop and the distal hairpin are the critical folding nucleus of the SH3 fold and propose a hypothesis that explains this result.     

Intermediates and the folding of proteins L and G

We use a minimalist protein model, in combination with a sequence design strategy, to determine differences in primary structure for proteins L and G, which are responsible for the two proteins folding through distinctly different folding mechanisms. We find that the folding of proteins L and G are consistent with a nucleation-condensation mechanism, each of which is described as helix-assisted beta-1 and beta-2 hairpin formation, respectively. We determine that the model for protein G exhibits an early intermediate that precedes the rate-limiting barrier of folding, and which draws together misaligned secondary structure elements that are stabilized by hydrophobic core contacts involving the third beta-strand, and presages the later transition state in which the correct strand alignment of these same secondary structure elements is restored. Finally, the validity of the targeted intermediate ensemble for protein G was analyzed by fitting the kinetic data to a two-step first-order reversible reaction, proving that protein G folding involves an on-pathway early intermediate, and should be populated and therefore observable by experiment.     

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.     

Transition state contact orders correlate with protein folding rates

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.     

Effects of the difference in the unfolded-state ensemble on the folding of Escherichia coli dihydrofolate reductase

The unfolded state of a protein is an ensemble of a large number of conformations ranging from fully extended to compact structures. To investigate the effects of the difference in the unfolded-state ensemble on protein folding, we have studied the structure, stability, and folding of "circular" dihydrofolate reductase (DHFR) from Escherichia coli in which the N and C-terminal regions are cross-linked by a disulfide bond, and compared the results with those of disulfide-reduced "linear" DHFR. Equilibrium studies by circular dichroism, difference absorption spectra, solution X-ray scattering, and size-exclusion chromatography show that whereas the native structures of both proteins are essentially the same, the unfolded state of circular DHFR adopts more compact conformations than the unfolded state of the linear form, even with the absence of secondary structure. Circular DHFR is more stable than linear DHFR, which may be due to the decrease in the conformational entropy of the unfolded state as a result of circularization. Kinetic refolding measurements by stopped-flow circular dichroism and fluorescence show that under the native conditions both proteins accumulate a burst-phase intermediate having the same structures and both fold by the same complex folding mechanism with the same folding rates. Thus, the effects of the difference in the unfolded state of circular and linear DHFRs on the refolding reaction are not observed after the formation of the intermediate. This suggests that for the proteins with close termini in the native structure, early compaction of a protein molecule to form a specific folding intermediate with the N and C-terminal regions in close proximity is a crucial event in folding. If there is an enhancement in the folding reflecting the reduction in the breadth of the unfolded-state ensemble for circular DHFR, this acceleration must occur in the sub-millisecond time-range.     

Sequence of events in folding mechanism: beyond the Gō model

Simplified Gō models, where only native contacts interact favorably, have proven useful to characterize some aspects of the folding of small proteins. The success of these models is limited by the fact that all residues interact in the same way so that the folding features of a protein are determined only by the geometry of its native conformation. We present an extended version of a Calpha-based Gō model where different residues interact with different energies. The model is used to calculate the thermodynamics of three small proteins (Protein G, Src-SH3, and CI2) and the effect of mutations (DeltaDeltaGU-N, DeltaDeltaGdouble dagger-N, DeltaDeltaGdouble dagger-U, and phi-values) on the wild-type sequence. The model allows us to investigate some of the most controversial areas in protein folding, such as its earliest stages and the nature of the unfolded state, subjects that have lately received particular attention.     

Multiple parallel-pathway folding of proline-free Staphylococcal nuclease

When a protein exhibits complex kinetics of refolding, we often ascribe the complexity to slow isomerization events in the denatured protein, such as cis/trans isomerization of peptidyl prolyl bonds. Does the complex folding kinetics arise only from this well-known reason? Here, we have investigated the refolding of a proline-free variant of staphylococcal nuclease by stopped-flow, double-jump techniques, to examine the folding reactions without the slow prolyl isomerizations. As a result, the protein folds into the native state along at least two accessible parallel pathways, starting from a macroscopically single denatured-state ensemble. The presence of intermediates on the individual folding pathways has revealed the existence of multiple parallel pathways, and is characterized by multi-exponential folding kinetics with a lag phase. Therefore, a "single" amino acid sequence can fold along the multiple parallel pathways. This observation in staphylococcal nuclease suggests that the multiple folding may be more general than we have expected, because the multiple parallel-pathway folding cannot be excluded from proteins that show simpler kinetics.     

Folding of the yeast prion protein Ure2: kinetic evidence for folding and unfolding intermediates.

The Saccharomyces cerevisiae non-Mendelian factor [URE3] propagates by a prion-like mechanism, involving aggregation of the chromosomally encoded protein Ure2. The N-terminal prion domain (PrD) of Ure2 is required for prion activity in vivo and amyloid formation in vitro. However, the molecular mechanism of the prion-like activity remains obscure. Here we measure the kinetics of folding of Ure2 and two N-terminal variants that lack all or part of the PrD. The kinetic folding behaviour of the three proteins is identical, indicating that the PrD does not change the stability, rates of folding or folding pathway of Ure2. Both unfolding and refolding kinetics are multiphasic. An intermediate is populated during unfolding at high denaturant concentrations resulting in the appearance of an unfolding burst phase and "roll-over" in the denaturant dependence of the unfolding rate constants. During refolding the appearance of a burst phase indicates formation of an intermediate during the dead-time of stopped-flow mixing. A further fast phase shows second-order kinetics, indicating formation of a dimeric intermediate. Regain of native-like fluorescence displays a distinct lag due to population of this on-pathway dimeric intermediate. Double-jump experiments indicate that isomerisation of Pro166, which is cis in the native state, occurs late in refolding after regain of native-like fluorescence. During protein refolding there is kinetic partitioning between productive folding via the dimeric intermediate and a non-productive side reaction via an aggregation prone monomeric intermediate. In the light of this and other studies, schemes for folding, aggregation and prion formation are proposed.     

Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains

Langevin dynamics is used with our physics-based united-residue (UNRES) force field to study the folding pathways of the B-domain of staphylococcal protein A (1BDD (alpha; 46 residues)). With 400 trajectories of protein A started from the extended state (to gather meaningful statistics), and simulated for more than 35 ns each, 380 of them folded to the native structure. The simulations were carried out at the optimal folding temperature of protein A with this force field. To the best of our knowledge, this is the first simulation study of protein-folding kinetics with a physics-based force field in which reliable statistics can be gathered. In all the simulations, the C-terminal alpha-helix forms first. The ensemble of the native basin has an average RMSD value of 4 A from the native structure. There is a stable intermediate along the folding pathway, in which the N-terminal alpha-helix is unfolded; this intermediate appears on the way to the native structure in less than one-fourth of the folding pathways, while the remaining ones proceed directly to the native state. Non-native structures persist until the end of the simulations, but the native-like structures dominate. To express the kinetics of protein A folding quantitatively, two observables were used: (i) the average alpha-helix content (averaged over all trajectories within a given time window); and (ii) the fraction of conformations (averaged over all trajectories within a given time window) with Calpha RMSD values from the native structure less than 5 A (fraction of completely folded structures). The alpha-helix content grows quickly with time, and its variation fits well to a single-exponential term, suggesting fast two-state kinetics. On the other hand, the fraction of folded structures changes more slowly with time and fits to a sum of two exponentials, in agreement with the appearance of the intermediate, found when analyzing the folding pathways. This observation demonstrates that different qualitative and quantitative conclusions about folding kinetics can be drawn depending on which observable is monitored.     

Identifying folding nucleus based on residue contact networks of proteins

In the native structure of a protein, all the residues are tightly parked together in a specific order following its folding and every residue contacts with some spatially neighbor residues. A residue contact network can be constructed by defining the residues as nodes and the native contacts as edges. During the folding of small single-domain proteins, there is a set of contacts (or bonds), defined as the folding nucleus (FN), which is formed around the transition state, i.e., a rate-limiting barrier located at about the middle between the unfolded states and the native state on the free energy landscape. Such a FN plays an essential role in the folding dynamics and the residues, which form the related contacts called as folding nucleus residues (FNRs). In this work, the FNRs in proteins are identified by using quantities which characterize the topology of residue contact networks of proteins. By comparing the specificities of residues with the network quantities K(R), L(R), and D(R), up to 90% FNRs of six typical proteins found experimentally are identified. It is found that the FNRs behave the full-closeness centrals rather than degree or closeness centers in the residue contact network, implying that they are important to the folding cooperativity of proteins. Our study shows that the FNRs can be identified solely from the native structures of proteins based on the analysis of residue contact network without any knowledge of the transition state ensemble.     

Trapping the on-pathway folding intermediate of Im7 at equilibrium

The four-helical protein Im7 folds via a rapidly formed on-pathway intermediate (k(UI)=3000 s(-1) at pH 7.0, 10 degrees C) that contains three (helices I, II and IV) of the four native alpha-helices. The relatively slow (k(IN)=300 s(-1)) conversion of this intermediate into the native structure is driven by the folding and docking of the six residue helix III onto the developing hydrophobic core. Here, we describe the structural properties of four Im7* variants designed to trap the protein in the intermediate state by disrupting the stabilising interactions formed between helix III and the rest of the protein structure. In two of these variants (I54A and L53AI54A), hydrophobic residues within helix III have been mutated to alanine, whilst in the other two mutants the sequence encompassing the native helix III was replaced by a glycine linker, three (H3G3) or six (H3G6) residues in length. All four variants were shown to be monomeric, as judged by analytical ultracentrifugation, and highly helical as measured by far-UV CD. In addition, all the variants denature co-operatively and have a stability (DeltaG(UF)) and buried hydrophobic surface area (M(UF)) similar to those of the on-pathway kinetic intermediate. Structural characterisation of these variants using 1-anilino-8-napthalene sulphonic acid (ANS) binding, near-UV CD and 1D (1)H NMR demonstrate further that the trapped intermediate ensemble is highly structured with little exposed hydrophobic surface area. Interestingly, however, the structural properties of the variants I54A and L53AI54A differ in detail from those of H3G3 and H3G6. In particular, the single tryptophan residue, located near the end of helix IV, and distant from helix III, is in a distinct environment in the two sets of mutants as judged by fluorescence, near-UV CD and the sensitivity of tryptophan fluorescence to iodide quenching. Overall, the results confirm previous kinetic analysis that demonstrated the hierarchical folding of Im7 via an on-pathway intermediate, and show that this species is a highly helical ensemble with a well-formed hydrophobic core. By contrast with the native state, however, the intermediate ensemble is flexible enough to change in response to mutation, its structural properties being tailored by residues in the sequence encompassing the native helix III.     

Three topologically equivalent core residues affect the transition state ensemble in a protein folding reaction

The single domain protein, interleukin-1beta, is representative of a distinct class of proteins characterized by their beta-trefoil topology. Each subdomain of this structural class is composed of a beta beta beta loop beta (betabetabetaLbeta) motif comprised of approximately 50 residues and gives the protein a pseudo- 3-fold axis of symmetry. A common feature of proteins in this topological family appears to be that they are slow folders, which reach the native state on the order of tens to 100s of seconds. Sequence analysis of interleukin-1beta indicates that three phenylalanine residues located at positions 42, 101, and 146 are well conserved, separated by approximately 50 residues in the primary sequence, located in similar positions in the pseudo-symmetric units of the trefoil, and are juxtaposed to one another in conformational space. These residues surround the hydrophobic cavity and "pin" the hairpin triplet cap to the core beta-barrel. To determine if cap-barrel interactions are involved in maintaining the structural stability and cooperativity or in controlling the slow formation of the native state, we performed a series of mutational studies. The results indicate that interleukin-1beta tolerates large increases in side-chain volume at these three topologically conserved sites with little effect on stability, while the kinetics show significant differences in both the unfolding and refolding rates. Taken together, our results indicate that these conserved core residues are essential contacts in the transition-state ensemble for folding.     

Commitment and nucleation in the protein G transition state

An accurate characterization of the transition state ensemble (TSE) is central to furthering our understanding of the protein folding reaction. We have extensively tested a recently reported method for studying a protein's TSE, utilizing phi-value data from protein engineering experiments and computational studies as restraints in all-atom Monte Carlo (MC) simulations. The validity of interpreting experimental phi-values as the fraction of native contacts made by a residue in the TSE was explored, revealing that this definition is unable to uniquely specify a TSE. The identification of protein G's second hairpin, in both pre and post-transition conformations demonstrates that high experimental phi-values do not guarantee a residue's importance in the TSE. An analysis of simulations based on structures restrained by experimental phi-values is necessary to yield this result, which is not obvious from a simplistic interpretation of individual phi-values. The TSE that we obtain corresponds to a single, specific nucleation event, characterized by six residues common to all three observed, convergent folding pathways. The same specific nucleus was independently identified from computational and experimental data, and "Conservation of Conservation" analysis in the protein G fold. When associated strictly with complete nucleus formation and concomitant chain collapse, folding is a well-defined two state event. Once the nucleus has formed, the folding reaction enters a slow relaxation process associated with side-chain packing and small, local backbone rearrangements. A detailed analysis of phi-values and their relationship to the transition state ensemble allows us to construct a unified theoretical model of protein G folding.     

On the role of some conserved and nonconserved amino acid residues in the transitional state and intermediate of apomyoglobin folding

The contributions of some amino acid residues in the A, B, G, and H helices to the formation of the folding nucleus and folding intermediate of apomyoglobin were estimated. The effects of point substitutions of Ala for hydrophobic amino acid residues on the structural stability of the native (N) protein and its folding intermediate (I), as well as on the folding/unfolding rates for four mutant apomyoglobin forms, were studied. The equilibrium and kinetic studies of the folding/unfolding rates of these mutant proteins in a wide range of urea concentrations demonstrated that their native state was considerably destabilized as compared with the wild-type protein, whereas the stability of the intermediate state changed moderately. It was shown that the amino acid residues in the A, G, and H helices contributed insignificantly to the stabilization of the apomyoglobin folding nucleus in the rate-limiting I ? N transition, taking place after the formation of the intermediate, whereas the residue of the B helix was of great importance in the formation of the folding nucleus in this transition.     

Folding/Unfolding Kinetics of Apomyoglobin

The equilibrium and kinetic folding/unfolding of apomyoglobin (ApoMb) were studied at pH 6.2, 11 °C by recording tryptophan fluorescence. The equilibrium unfolding of ApoMb in the presence of urea was shown to involve accumulation of an intermediate state, which had a higher fluorescence intensity as compared with the native and unfolded states. The folding proceeded through two kinetic phases, a rapid transition from the unfolded to the intermediate state and a slow transition from the intermediate to the native state. The accumulation of the kinetic intermediate state was observed in a wide range of urea concentrations. The intermediate was detected even in the region corresponding to the unfolding limb of the chevron plot. Urea concentration dependence was obtained for the observed folding/unfolding rate. The shape of the dependence was compared with that of two-state proteins characterized by a direct transition from the unfolded to the native state.     

On the Prediction of Folding Nuclei in Globular Proteins

An approach to predicting folding nuclei in globular proteins with known three-dimensional structures is proposed. This approach is based on the pinpointing of the lowest saddle points on the barrier between the unfolded state and native structure on the free-energy landscape of a protein chain; the proposed technique uses the dynamic programming method. A comparison of calculation results with experimental data on the folding nuclei of 21 proteins shows that the model provides good Φ value predictions for protein structures determined by X-ray analysis and, less successfully, in structures determined by nuclear magnetic resonance. Consideration of the whole ensemble of transition states provides a better prediction of folding nuclei than consideration of only transition states with lowest free energies. In addition, we predict the location of folding nuclei in three-dimensional structures of some proteins whose folding kinetics is being studied, but there is no experimental evidence concerning their folding nuclei.     

Kinetic consequences of native state optimization of surface-exposed electrostatic interactions in the Fyn SH3 domain

Optimization of surface exposed charge-charge interactions in the native state has emerged as an effective means to enhance protein stability; but the effect of electrostatic interactions on the kinetics of protein folding is not well understood. To investigate the kinetic consequences of surface charge optimization, we characterized the folding kinetics of a Fyn SH3 domain variant containing five amino acid substitutions that was computationally designed to optimize surface charge-charge interactions. Our results demonstrate that this optimized Fyn SH3 domain is stabilized primarily through an eight-fold acceleration in the folding rate. Analyses of the constituent single amino acid substitutions indicate that the effects of optimization of charge-charge interactions on folding rate are additive. This is in contrast to the trend seen in folded state stability, and suggests that electrostatic interactions are less specific in the transition state compared to the folded state. Simulations of the transition state using a coarse-grained chain model show that native electrostatic contacts are weakly formed, thereby making the transition state conducive to nonspecific, or even nonnative, electrostatic interactions. Because folding from the unfolded state to the folding transition state for small proteins is accompanied by an increase in charge density, nonspecific electrostatic interactions, that is, generic charge density effects can have a significant contribution to the kinetics of protein folding. Thus, the interpretation of the effects of amino acid substitutions at surface charged positions may be complicated and consideration of only native-state interactions may fail to provide an adequate picture.     

Predicting protein folding rates from geometric contact and amino acid sequence

Protein folding speeds are known to vary over more than eight orders of magnitude. Plaxco, Simons, and Baker (see References) first showed a correlation of folding speed with the topology of the native protein. That and subsequent studies showed, if the native structure of a protein is known, its folding speed can be predicted reasonably well through a correlation with the "localness" of the contacts in the protein. In the present work, we develop a related measure, the geometric contact number, N (alpha), which is the number of nonlocal contacts that are well-packed, by a Voronoi criterion. We find, first, that in 80 proteins, the largest such database of proteins yet studied, N (alpha) is a consistently excellent predictor of folding speeds of both two-state fast folders and more complex multistate folders. Second, we show that folding rates can also be predicted from amino acid sequences directly, without the need to know the native topology or other structural properties.     

Charge-charge interactions in the denatured state influence the folding kinetics of ribonuclease Sa

Gaining a better understanding of the denatured state ensemble of proteins is important for understanding protein stability and the mechanism of protein folding. We studied the folding kinetics of ribonuclease Sa (RNase Sa) and a charge-reversal variant (D17R). The refolding kinetics are similar, but the unfolding rate constant is 10-fold greater for the variant. This suggests that charge-charge interactions in the denatured state and the transition state ensembles are more favorable in the variant than in RNase Sa, and shows that charge-charge interactions can influence the kinetics and mechanism of protein folding.