Two-state Proteins Research Articles

Topological complexity, contact order, and protein folding rates

Monte Carlo simulations of protein folding show the emergence of a strong correlation between the relative contact order parameter, CO, and the folding time, t, of two-state folding proteins for longer chains with number of amino acids N⩾54, and higher contact order, CO>0.17. The correlation is particularly strong for N=80 corresponding to slow and more complex folding kinetics. These results are qualitatively compatible with experimental data where a general trend towards increasing t with CO is indeed observed in a set of proteins with chain length ranging from 41 to 154 amino acids.

Complete change of the protein folding transition state upon circular permutation.

Reversing the loop lengths of the small protein S6 by circular permutation has a dramatic effect on the transition state structure: it changes from globally diffuse to locally condensed. The phenomenon arises from a biased dispersion of the contact energies. Stability data derived from point mutations throughout the S6 structure show that interactions between residues that are far apart in sequence are stronger than those that are close. This entropy compensation drives all parts of the protein to fold simultaneously and produces the diffuse transition-state structure typical for two-state proteins. In the circular permutant, where strong contacts and short sequence separations are engineered to concur, the transition state becomes atypically condensed and polarized. Taken together with earlier findings that S6 may also fold by a 'collapsed' trajectory with an intermediate, the results suggest that this protein may fold by a multiplicity of mechanisms. The observations indicate that the diffuse transition state of S6 is not required for folding but could be an evolutionary development to optimize cooperativity.

Important amino acid properties for determining the transition state structures of two-state protein mutants

Understanding the mechanism in the folding pathways of proteins is an important problem in molecular biology. The Φ-value analysis provides insight into the transition state structures during protein folding. In this work, we have analyzed the relationship between the observed Φ values upon mutations in two-state proteins (FK506 binding protein, chymotrypsin inhibitor and src SH3 domain) and the changes in 48 various physico-chemical, energetic and conformational properties. We found that the classification of mutations based on solvent accessibility improved the correlation significantly. The relationship between conformational properties and Φ values determines the presence/absence of secondary structures in the transition state. In buried mutations, the physical properties volume, shape and flexibility, and the thermodynamic properties enthalpy, entropy and free-energy change have significant correlation with Φ. The short and medium-range non-bonded energy in partially buried mutations and average long-range contacts in exposed mutations showed a strong correlation with Φ values. Multiple regression analysis incorporating combinations of three properties from among all possible combinations of the 48 properties increased the correlation coefficient up to 0.99, by an average rise of 20% for all the data sets. Information about local sequence and structure is more important in surface mutations than those in buried mutations for explaining the transition state structures of two-state proteins. Further, the implications of our results for understanding the process of protein folding have been discussed.

Fast-folding protein kinetics, hidden intermediates, and the sequential stabilization model.

Do two-state proteins fold by pathways or funnels? Native-state hydrogen exchange experiments show discrete nonnative structures in equilibrium with the native state. These could be called hidden intermediates (HI) because their populations are small at equilibrium, and they are not detected in kinetic experiments. HIs have been invoked as disproof of funnel models, because funnel pictures appear to indicate (1) no specific sequences of events in folding; (2) a continuum, rather than a discrete ladder, of structures; and (3) smooth landscapes. In the present study, we solve the exact dynamics of a simple model. We find, instead, that the present microscopic model is indeed consistent with HIs and transition states, but such states occur in parallel, rather than along the single pathway predicted by the sequential stabilization model. At the microscopic level, we observe a huge multiplicity of trajectories. But at the macroscopic level, we observe two pathways of specific sequences of events that are relatively traditional except that they are in parallel, so there is not a single reaction coordinate. Using singular value decomposition, we show an accurate representation of the shapes of the model energy landscapes. They are highly complex funnels.

Time‐resolved backbone desolvation and mutational hot spots in folding proteins

A method is presented to identify hot mutational spots and predict the extent of surface burial at the transition state relative to the native fold in two-state folding proteins. The method is based on ab initio simulations of folding histories in which transitions between coarsely defined conformations and pairwise interactions are dependent on the solvent environments created by the chain. The highly conserved mammalian ubiquitin is adopted as a study case to make predictions. The evolution in time of the chain topology suggests a nucleation process with a critical point signaled by a sudden quenching of structural fluctuations. The occurrence of this nucleus is shown to be concurrent with a sudden escalation in the number of three-body correlations whereby hydrophobic units approach residue pairs engaged in amide-carbonyl hydrogen bonding. These correlations determine a pattern designed to structure the surrounding solvent, protecting intramolecular hydrogen bonds from water attack. Such correlations are shown to be required to stabilize the nucleus, with kinetic consequences for the folding process. Those nuclear residues that adopt the dual role of protecting and being protected while engaged in hydrogen bonds are predicted to be the hottest mutational spots. Some such residues are shown not to retain the same protecting role in the native fold. This kinetic treatment of folding nucleation is independently validated vis-a-vis a Φ-value analysis on chymotrypsin inhibitor 2, a protein for which extensive mutational data exists. Proteins 2002;47:447–457. © 2002 Wiley-Liss, Inc.

Exploring protein aggregation and self-propagation using lattice models: phase diagram and kinetics.

Many seemingly unrelated neurodegenerative disorders, such as amyloid and prion diseases, are associated with propagating fibrils whose structures are dramatically different from the native states of the corresponding monomers. This observation, along with the experimental demonstration that any protein can aggregate to form either fibrils or amorphous structures (inclusion bodies) under appropriate external conditions, suggest that there must be general principles that govern aggregation mechanisms. To probe generic aspects of prion-like behavior we use the model of Harrison, Chan, Prusiner, and Cohen. In this model, aggregation of a structure, that is conformationally distinct from the native state of the monomer, occurs by three parallel routes. Kinetic partitioning, which leads to parallel assembly pathways, occurs early in the aggregation process. In all pathways transient unfolding precedes polymerization and self-propagation. Chain polymerization is consistent with templated assembly, with the dimer being the minimal nucleus. The kinetic effciency of R(n-1) + G --> R(n) (R is the aggregation prone state and G is either U, the unfolded state, or N, the native state of the monomer) is increased when polymerization occurs in the presence of a "seed" (a dimer). These results support the seeded nucleated-polymerization model of fibril formation in amyloid peptides. To probe generic aspects of aggregation in two-state proteins, we use lattice models with side chains. The phase diagram in the (T,C) plane (T is the temperature and C is the polypeptide concentration) reveals a bewildering array of "phases" or structures. Explicit computations for dimers show that there are at least six phases including ordered structures and amorphous aggregates. In the ordered region of the phase diagram there are three distinct structures. We find ordered dimers (OD) in which each monomer is in the folded state and the interaction between the monomers occurs via a well-defined interface. In the domain-swapped structures a certain fraction of intrachain contacts are replaced by interchain contacts. In the parallel dimers the interface is stabilized by favorable intermolecular hydrophobic interactions. The kinetics of folding to OD shows that aggregation proceeds directly from U in a dynamically cooperative manner without populating partially structured intermediates. These results support the experimental observation that ordered aggregation in the two-state folders U1A and CI2 takes place from U. The contrasting aggregation processes in the two models suggest that there are several distinct mechanisms for polymerization that depend not only on the polypeptide sequence but also on external conditions (such as C, T, pH, and salt concentration).

Time-resolved backbone desolvation and mutational hot spots in folding proteins.

A method is presented to identify hot mutational spots and predict the extent of surface burial at the transition state relative to the native fold in two-state folding proteins. The method is based on ab initio simulations of folding histories in which transitions between coarsely defined conformations and pairwise interactions are dependent on the solvent environments created by the chain. The highly conserved mammalian ubiquitin is adopted as a study case to make predictions. The evolution in time of the chain topology suggests a nucleation process with a critical point signaled by a sudden quenching of structural fluctuations. The occurrence of this nucleus is shown to be concurrent with a sudden escalation in the number of three-body correlations whereby hydrophobic units approach residue pairs engaged in amide-carbonyl hydrogen bonding. These correlations determine a pattern designed to structure the surrounding solvent, protecting intramolecular hydrogen bonds from water attack. Such correlations are shown to be required to stabilize the nucleus, with kinetic consequences for the folding process. Those nuclear residues that adopt the dual role of protecting and being protected while engaged in hydrogen bonds are predicted to be the hottest mutational spots. Some such residues are shown not to retain the same protecting role in the native fold. This kinetic treatment of folding nucleation is independently validated vis-a-vis a Phi-value analysis on chymotrypsin inhibitor 2, a protein for which extensive mutational data exists.

Maximal Stabilities of Reversible Two-State Proteins

The hydrophobic effect is the major force driving protein folding. Around room temperature, small organic solutes and hydrophobic amino acids have low solubilities in water and the hydrophobic effect is the strongest. These facts suggest that globular proteins should be maximally stable around room temperature. While this fundamental paradigm has been expected, it has not actually been shown to hold. Toward this goal, we have collected and analyzed experimental thermodynamic data for 31 proteins that show reversible two-state folding <--> unfolding transitions at or near neutral pH. Twenty-six of these are unique, and 20 of the 26 are maximally stable around room temperature irrespective of their structural properties, the melting temperature, or the living temperatures of their source organisms. Their average temperature of maximal stability is 293 +/- 8 K (20 +/- 8 degrees C). These proteins differ in size, fold, and number of domains, hydrophobic folding units, and oligomeric states. They derive from the cold-loving psychrophiles, from mesophiles, and from thermophiles. Analysis of the single-domain proteins present in this set shows that the variations in their thermodynamic parameters are correlated in a way which may explain the adaptation of the proteins to the living temperatures of the organisms from which they derive. The average energetic contribution of the individual amino acids toward protein stability decreases with an increase in protein size, suggesting that there may be an upper limit for protein maximal thermodynamic stability. For the remaining proteins, deviation of the maximal stability temperatures from room temperature may be due to greater uncertainties in their heat capacity change (DeltaC(p)) values, a weaker hydrophobic effect, and/or a stronger electrostatic contribution.

Conformational plasticity in folding of the split β-α-β protein S6: evidence for burst-phase disruption of the native state

An increasing number of folding studies of two-state proteins shows that point mutations sometimes change the kinetic m-values, leading to kinks and curves in the chevron plots. The molecular origin of these changes is yet unclear although it is speculated that they are linked to structural rearrangement of the transition state or to accumulation of meta-stable intermediates. To shed more light on this issue, we present here a combined m and φ-value analysis of the split β-α-β protein S6. Wild-type S6 displays classical two-state kinetics with v-shaped chevron plot, but a majority of its mutants display distinct m-value changes or curved chevrons. We observe that this kinetic aberration of S6 is linked to mutations that are clustered in distinct regions of the native structure. The most pronounced changes, i.e. decrease in the m-value for the unfolding rate constant, are seen upon truncation of interactions between the N and C termini, whereas mutations in the centre of the hydrophobic core show smaller or even opposed effects. As a consequence, the calculated φ-values display a systematic increase upon addition of denaturant. In the case of S6, the phenomenon seems to arise from a general plasticity of the different species on the folding pathway. That is, the structure of the denatured ensemble, the transition state, and the native ground-state for unfolding seem to change upon mutation. From these changes, it is concluded that interactions spanning the centre of the hydrophobic core form early in folding, whereas the entropically disfavoured interactions linking the N and C termini consolidate very late, mainly on the down-hill-side of the folding barrier. Copyright 2002 Elsevier Science Ltd.

Importance of Long-Range Interactions for Determining the Folding Rate and Transition State Structures of Two-state Proteins

Elucidating the mechanism of protein folding is an intriguing and challenging task. Currently, tremen-dous advances have been explored and the combination of experimental and theoretical approachesprovides new insights to protein folding [3]. The formation of stable secondary structures and a uniquetertiary structure of a protein is mainly dictated by interactions between amino acid residues alongthe polypeptide chain. Consequently, medium and long-range interactions play an active role in thefolding and stability of proteins. In this article, we discuss about the development of a novel param-eter, long-range order (LRO) and its application for predicting the protein folding rates of two-stateproteins. Further, we revealed the important amino acid properties for determining the transitionstate structures of two-state protein mutants.

Folding of circular permutants with decreased contact order: general trend balanced by protein stability

To examine the influence of contact order and stability on the refolding rate constant for two-state proteins, we have analysed the folding kinetics of the small β-α-β protein S6 and two of its circular permutants with relative contact orders of 0.19, 0.15 and 0.12. Data reveal a small but significant increase of the refolding rate constant (log kf) with decreasing contact order. At the same time, the decreased contact order is correlated to losses in global stability and alterations of the folding nucleus. When the differences in stability are accounted for by addition of Na2SO4 or by comparison of the folding kinetics at the transition mid-point, the dependence between log kf and contact order becomes stronger and follows the general correlation for two-state proteins. The observation emphasizes the combined action of topology and stability in controlling the rate constant of protein folding.

Is there a unique melting temperature for two-state proteins?

Thermal unfolding (or folding) in many proteins occurs in an apparent two-state manner, suggesting that only two states, unfolded and folded, are populated. At the melting temperature, Tm, the two states coexist. Using lattice models with side chains we show that individual residues become structured at temperatures that deviate from Tm, which implies that partially folded conformations make substantial contribution to thermodynamic properties of two-state proteins. We also find that the folding cooperativity for a given residue is linked to its accessible surface area. These results are consistent with the experiments on GCN4-like zipper peptide, which showed that local melting temperatures differ from Tm. Analysis of thermal unfolding of six proteins shows that deltaT/Tm approximately N(-1), where deltaT is the transition width and N is the number of residues. This scaling allows us to conclude that, when corrected for finite size effects, folding cooperativity can be captured using coarse grained models.

The building block folding model and the kinetics of protein folding.

Here we show that qualitatively, the building blocks folding model accounts for three-state versus the two-state protein folding. Additionally, it is consistent with the faster versus slower folding rates of the two-state proteins. Specifically, we illustrate that the building blocks size, their mode of associations in the native structure, the number of ways they can combinatorially assemble, their population times and the way they are split in the iterative, step-by-step structural dissection which yields the anatomy trees, explain a broad range of folding rates. We further show that proteins with similar general topologies may have different folding pathways, and hence different folding rates. On the other hand, the effect of mutations resembles that of changes in conditions, shifting the population times and hence the energy landscapes. Hence, together with the secondary structure type and the extent of local versus non-local interactions, a coherent, consistent rationale for folding kinetics can be outlined, in agreement with experimental results. Given the native structure of a protein, these guidelines enable a qualitative prediction of the folding kinetics. We further describe these in the context of the protein folding energy landscape. Quantitatively, in principle, the diffusion-collision model for the building block association can be used. However, the folding rates of the building blocks and traps in their formation and association, need to be considered.

Transition states and the meaning of Phi-values in protein folding kinetics.

What is the mechanism of two-state protein folding? The rate-limiting step is typically explored through a Phi-value, which is the mutation-induced change in the transition state free energy divided by the change in the equilibrium free energy of folding. Phi-values ranging from 0 to 1 have been interpreted as meaning the transition state is denatured-like (0), native-like (1) or in-between. But there is no classical interpretation for the experimental Phi-values that are negative or >1. Using a rigorous method to identity transition states via an exact lattice model, we find that nonclassical Phi-values can arise from parallel microscopic flow processes, such as those in funnel-shaped energy landscapes. Phi < 0 results when a mutation destabilizes a slow flow channel, causing a backflow into a faster flow channel. Phi > 1 implies the reverse: a backflow from a fast channel into a slow one. Using a 'landscape mapping' method, we find that Phi correlates with the acceleration/deceleration of folding induced by mutations, rather than with the degree of nativeness of the transition state.

Validation of protein-unfolding transition states identified in molecular dynamics simulations.

Experimental and simulation studies can complement each other nicely in the area of protein folding. Experiment reports on the average properties of a large ensemble (approx. 10(17)-10(19) molecules), typically over time. Molecular dynamics simulations, on the other hand, provide detailed information for a single molecule, a component of the ensemble. By combining these approaches we can obtain not only a more complete picture of folding, but we can also take advantage of the strengths of different methods. For example, experiment cannot provide molecular structures. Molecular dynamics simulations can provide such information, but the simulations are meaningless without a linked experiment. Thus, the interrelated nature of simulation in assessing experimental assumptions and in providing structures to augment energetic descriptions, and experiment in judging whether the simulations are reasonable, provides more confidence in the resulting information about folding. This combination yields tested and testable molecular models of states that evade characterization by conventional methods. Therefore, we have explored the combined use of these methods to map folding/unfolding pathways at atomic resolution, in collaboration with Alan Fersht. Here we focus on chymotrypsin inhibitor 2, a small single-domain, two-state folding protein.

Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction

The contact order is believed to be an important factor for understanding protein folding mechanisms. In our earlier work, we have shown that the long-range interactions play a vital role in protein folding. In this work, we analyzed the contribution of long-range contacts to determine the folding rate of two-state proteins. We found that the residues that are close in space and are separated by at least ten to 15 residues in sequence are important determinants of folding rates, suggesting the presence of a folding nucleus at an interval of approximately 25 residues. A novel parameter “long-range order” has been proposed to predict protein folding rates. This parameter shows as good a relationship with the folding rate of two-state proteins as contact order. Further, we examined the minimum limit of residue separation to determine the long-range contacts for different structural classes. We observed an excellent correlation between long-range order and folding rate for all classes of globular proteins. We suggest that in mixed-class proteins, a larger number of residues can serve as folding nuclei compared to all-α and all-β proteins. A simple statistical method has been developed to predict the folding rates of two-state proteins using the long-range order that produces an agreement with experimental results that is better or comparable to other methods in the literature.

Two-state protein model with water interactions: influence of temperature on the intrinsic viscosity of myoglobin.

We describe a single-domain protein as a two-state system with water interactions. Around the unfolded apolar parts of the protein we incorporate the hydration effect by introducing hydrogen bonds between the water molecules in order to mimic the "icelike" shell structure. Intrinsic viscosity, proportional to the effective hydrodynamic volume, for sperm whale metmyoglobin is assigned from experimental data in the folded and in the denaturated state. By weighing statistically the two states against the degree of folding, we express the total intrinsic viscosity. The temperature dependence of the intrinsic viscosity, for different chemical potentials, is in good correspondence with experimental data [P. L. Privalov et al., J. Mol. Biol. 190, 487 (1986)]. Cold and warm unfolding, common to small globular proteins, is also a result of the model.

Multiple protein folding nuclei and the transition state ensemble in two-state proteins.

Using exhaustive simulations of lattice models with side-chains, we show that optimized two-state folders reach the native state by a nucleation-collapse mechanism with multiple folding nuclei (MFN). For both the full model and the Go version, there are certain contacts that on an average participate in the critical nuclei with higher probability than the others. The high- (> or = 0.5) probability contacts are largely determined by the structure of the native state. Comparison of the results for the full sequence and the Go model shows that non-native interactions compromise the degree of cooperativity and stability of the native state. From an extremely detailed analysis of the folding kinetics, we find that non-native interactions are present in the folding nuclei. The folding times decrease if the non-native interactions in the folding nuclei are made neutral or repulsive. Using cluster analysis and making no prior assumption about reaction coordinate, we show that both full and Go models have three distinct transition states that give a structural description for the MFN. In the transition states, on an average, about two-thirds of the sequence is structured, whereas the rest is disordered, reminiscent of the polarized transition state in the SH3 domain. Our studies show that Go models cannot describe the transition state characteristics of two-state folders at the molecular level. As a byproduct of our investigations, we establish that our method of computing the transition state ensemble is numerically equivalent to the technique based on the stochastic separatrix, which also does not require a priori knowledge of the folding reaction coordinate.

Pathways in Two-State Protein Folding

Thermodynamic measurements of proteins indicate that the folding to the native state takes place either through stable intermediates or through a two-state process without intermediates. The rather short folding times of proteins indicate that folding is guided through some sequence of contact bindings. We discuss the possibility of reconciling a two-state folding event with a sequential folding process in a schematic model of protein folding. We propose a new dynamical transition temperature that is lower than the temperature at which proteins in equilibrium unfold. This is in qualitative agreement with observations of in vivo protein folding activity quantified by chaperone concentration in Escherichia coli. Finally, we discuss our framework in connection with the unfolding of proteins at low temperatures.

Formation of hydrogen bonds precedes the rate-limiting formation of persistent structure in the folding of ACBP

A burst phase in the early folding of the four-helix two-state folder protein acyl-coenzyme A binding protein (ACBP) has been detected using quenched-flow in combination with site-specific NMR-detected hydrogen exchange. Several of the burst phase structures coincide with a structure consisting of eight conserved hydrophobic residues at the interface between the two N and C-terminal helices. Previous mutation studies have shown that the formation of this structure is rate limiting for the final folding of ACBP. The burst phase structures observed in ACBP are different from the previously reported collapsed types of burst phase intermediates observed in the folding of other proteins.