Protein folding kinetics provides a context-independent assessment of beta-strand propensity in the Fyn SH3 domain

Structural database-derived propensities for amino acids to adopt particular local protein structures, such as alpha-helix and beta-strand, have long been recognized and effectively exploited for the prediction of protein secondary structure. However, the experimental verification of database-derived propensities using mutagenesis studies has been problematic, especially for beta-strand propensities, because local structural preferences are often confounded by non-local interactions arising from formation of the native tertiary structure. Thus, the overall thermodynamic stability of a protein is not always altered in a predictable manner by changes in local structural propensity at a single position. In this study, we have undertaken an investigation of the relationship between beta-strand propensity and protein folding kinetics. By characterizing the effects of a wide variety of amino acid substitutions at two different beta-strand positions in an SH3 domain, we have found that the observed changes in protein folding rates are very well correlated to beta-strand propensities for almost all of the substitutions examined. In contrast, there is little correlation between propensities and unfolding rates. These data indicate that beta-strand conformation is well formed in the structured portion of the SH3 domain transition state, and that local structure propensity strongly influences the stability of the transition state. Since the transition state is known to be packed more loosely than the native state and likely lacks many of the non-local stabilizing interactions seen in the native state, we suggest that folding kinetics studies may generally provide an effective means for the experimental validation of database-derived local structural propensities.     

Identification and ab initio simulations of early folding units in proteins

The location of protein subunits that form early during folding, constituted of consecutive secondary structure elements with some intrinsic stability and favorable tertiary interactions, is predicted using a combination of threading algorithms and local structure prediction methods. Two folding units are selected among the candidates identified in a database of known protein structures: the fragment 15-55 of 434 cro, an all-alpha protein, and the fragment 1-35 of ubiquitin, an alpha/beta protein. These units are further analyzed by means of Monte Carlo simulated annealing using several database-derived potentials describing different types of interactions. Our results suggest that the local interactions along the chain dominate in the first folding steps of both fragments, and that the formation of some of the secondary structures necessarily occurs before structure compaction. These findings led us to define a prediction protocol, which is efficient to improve the accuracy of the predicted structures. It involves a first simulation with a local interaction potential only, whose final conformation is used as a starting structure of a second simulation that uses a combination of local interaction and distance potentials. The root mean square deviations between the coordinates of predicted and native structures are as low as 2-4 A in most trials. The possibility of extending this protocol to the prediction of full proteins is discussed. Proteins 2001;42:164-176.     

Peptide fragment studies on the folding elements of dihydrofolate reductase from Escherichia coli

One of the necessary conditions for a protein to be foldable is the presence of a complete set of “folding elements” (FEs) that are short, contiguous peptide segments distributed over an amino acid sequence. The FE‐assembly model of protein folding has been proposed, in which the FEs play a role in guiding structure formation through FE–FE interactions early in folding. However, two major issues remain to be clarified regarding the roles of the FEs in determining protein foldability. Are the FEs AFUs that can form nativelike structures in isolation? Is the presence of only the FEs without mutual connections a sufficient condition for a protein to be foldable? Here, we address these questions using peptide fragments corresponding to the FEs of DHFR from Escherichia coli. We show by CD measurement that the FE peptides are unfolded under the native conditions, and some of them have the propensities toward non‐native helices. MD simulations also show the non‐native helical propensities of the peptides, and the helix contents estimated from the simulations are well correlated with those estimated from the CD in TFE. Thus, the FEs of DHFR are not AFUs, suggesting the importance of the FEs in nonlocal interactions. We also show that equimolar mixtures of the FE peptides do not induce any structural formation. Therefore, mutual connections between the FEs, which should strengthen the nonlocal FE–FE interactions, are also one of the necessary conditions for a protein to be foldable. Proteins 2006. © 2005 Wiley‐Liss, Inc.     

Stability and folding kinetics of a ubiquitin mutant with a strong propensity for nonnative beta-hairpin conformation in the unfolded state

A F45W mutant of yeast ubiquitin has been used as a model system to examine the effects of nonnative local interactions on protein folding and stability. Mutating the native TLTGK G-bulged type I turn in the N-terminal beta-hairpin to NPDG stabilizes a nonnative beta-strand alignment in the isolated peptide fragment. However, NMR structural analysis of the native and mutant proteins shows that the NPDG mutant is forced to adopt the native beta-strand alignment and an unfavorable type I NPDG turn. The mutant is significantly less stable (approximately 9 kJ mol(-1)) and folds 30 times slower than the native sequence, demonstrating that local interactions can modulate protein stability and that attainment of a nativelike beta-hairpin conformation in the transition state ensemble is frustrated by the turn mutations. Surprising, alcoholic cosolvents [5-10% (v/v) TFE] are shown to accelerate the folding rate of the NPDG mutant. We conclude, backed-up by NMR data on the peptide fragments, that even though nonnative states in the denatured ensemble are highly populated and their stability further enhanced in the presence of cosolvents, the simultaneous increase in the proportion of nativelike secondary structure (hairpin or helix), in rapid equilibrium with nonnative states, is sufficient to accelerate the folding process. It is evident that modulating local interactions and increasing nonnative secondary structure propensities can change protein stability and folding kinetics. However, nonlocal contacts formed in the global cooperative folding event appear to determine structural specificity.     

Local interactions and the optimization of protein folding

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig's simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of energy functions in which the energy of the native structure is fixed, but the relative contributions of local and nonlocal interactions to this energy are varied over a broad range. For funnel shaped energy landscapes, we find that 1) the rate of folding increases, but the stability of the folded state decreases, as the contribution of local interactions to the energy of the native structure increases, and 2) the amount of native structure in the unfolded state and the transition state vary considerably with the local interaction strength. Simple exponential kinetics and a well-defined free energy barrier separating folded and unfolded states are observed when nonlocal interactions make an appreciable contribution to the energy of the native structure; in such cases a transition state theory type approximation yields reasonably accurate estimates of the folding rate. Bumps in the folding funnel near the native state, which could result from desolvation effects, side chain freezing, or the breaking of nonnative contacts, significantly alter the dependence of the folding rate on the local interaction strength: the rate of folding decreases when the local interaction strength is increased beyond a certain point. A survey of the distribution of strong contacts in the protein structure database suggests that evolutionary optimization has involved both kinetics and thermodynamics: strong contacts are enriched at both very short and very long sequence separations. Proteins 29:282–291, 1997. © 1997 Wiley-Liss, Inc.     

Composites of local structure propensities: Evidence for local encoding of long-range structure

To estimate how extensively the ensemble of denatured-state conformations is constrained by local side-chain–backbone interactions, propensities of each of the 20 amino acids to occur in mono- and dipeptides mapped to discrete regions of the Ramachandran map are computed from proteins of known structure. In addition, propensities are computed for the trans, gauche−, and gauche+ rotamers, with or without consideration of the values of phi and psi. These propensities are used in scoring functions for fragment threading, which estimates the energetic favorability of fragments of protein sequence to adopt the native conformation as opposed to hundreds of thousands of incorrect conformations. As finer subdivisions of the Ramachandran plot, neighboring residue phi/psi angles, and rotamers are incorporated, scoring functions become better at ranking the native conformation as the most favorable. With the best composite propensity function, the native structure can be distinguished from 300,000 incorrect structures for 71% of the 2130 arbitrary protein segments of length 40, 48% of 2247 segments of length 30, and 20% of 2368 segments of length 20. A majority of fragments of length 30–40 are estimated to be folded into the native conformation a substantial fraction of the time. These data suggest that the variations observed in amino acid frequencies in different phi/psi/chi1 environments in folded proteins reflect energetically important local side-chain–backbone interactions, interactions that may severely restrict the ensemble of conformations populated in the denatured state to a relatively small subset with nativelike structure.     

Structure of a folding intermediate reveals the interplay between core and peripheral elements in RNA folding

Though the molecular architecture of many native RNA structures has been characterized, the structures of folding intermediates are poorly defined. Here, we present a nucleotide-level model of a highly structured equilibrium folding intermediate of the specificity domain of the Bacillus subtilis RNase P RNA, obtained using chemical and nuclease mapping, circular dichroism spectroscopy, small-angle X-ray scattering and molecular modeling. The crystal structure indicates that the 154 nucleotide specificity domain is composed of several secondary and tertiary structural modules. The structure of the intermediate contains modules composed of secondary structures and short-range tertiary interactions, implying a sequential order of tertiary structure formation during folding. The intermediate lacks the native core and several long-range interactions among peripheral regions, such as a GAAA tetraloop and its receptor. Folding to the native structure requires the local rearrangement of a T-loop in the core in concert with the formation of the GAAA tetraloop-receptor interaction. The interplay of core and peripheral structure formation rationalizes the high degree of cooperativity observed in the folding transition leading to the native structure.     

Structure-approximating inverse protein folding problem in the 2D HP model.

The inverse protein folding problem is that of designing an amino acid sequence which has a particular native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein-protein interactions. In this paper, we show that in the 2D HP model of Dill it is possible to solve this problem for a broad class of structures. These structures can be used to closely approximate any given structure. One of the most important properties of a good protein (in drug design) is its stability--the aptitude not to fold simultaneously into other structures. We show that for a number of basic structures, our sequences have a unique fold.     

A consistent set of statistical potentials for quantifying local side-chain and backbone interactions

The frequencies of occurrence of atom arrangements in high-resolution protein structures provide some of the most accurate quantitative measures of interaction energies in proteins. In this report we extend our development of a consistent set of statistical potentials for quantifying local interactions between side-chains and the polypeptide backbone, as well as nearby side-chains. Starting with phi/psi/chi1 propensities that select for optimal interactions of the 20 amino acid side-chains with the 2 flanking peptide bonds, the following 3 new terms are added: (1) a distance-dependent interaction between the side-chain at i and the carbonyl oxygens and amide protons of the peptide units at i +/- 2, i +/- 3, and i +/- 4; (2) a distance-dependent interaction between the side-chain at position i and side-chains at positions i + 1 through i + 4; and (3) an orientation-dependent interaction between the side-chain at position i and side-chains at i + 1 through i + 4. The relative strengths of these 4 pseudo free energy terms are estimated by the average information content of each scoring matrix and by assessing their performance in a simple fragment threading test. They vary from -0.4 - -0.5 kcal/mole per residue for phi/psi/chi1 propensities to a range of -0.15 - -0.6 kcal/mole per residue for each of the other 3 terms. The combined energy function, containing no interactions between atoms more than 4 residues apart, identifies the correct structural fragment for randomly selected 15 mers over 40% of the time, after searching through 232,000 alternative conformations. For 14 out of 20 sets of all-atom Rosetta decoys analyzed, the native structure has a combined score lower than any of the 1700-1900 decoy conformations. The ability of this energy function to detect energetically important details of local structure is demonstrated by its power to distinguish high-resolution crystal structures from NMR solution structures.     

A tale of two secondary structure elements: when a beta-hairpin becomes an alpha-helix.

In this work, we have analyzed the relative importance of secondary versus tertiary interactions in stabilizing and guiding protein folding. For this purpose, we have designed four different mutants to replace the alpha-helix of the GB1 domain by a sequence with strong beta-hairpin propensity in isolation. In particular, we have chosen the sequence of the second beta-hairpin of the GB1 domain, which populates the native conformation in aqueous solution to a significant extent. The resulting protein has roughly 30 % of its sequence duplicated and maintains the 3D-structure of the wild-type protein, but with lower stability (up to -5 kcal/mol). The loss of intrinsic helix stability accounts for about 80 % of the decrease in free energy, illustrating the importance of local interactions in protein stability. Interestingly enough, all the mutant proteins, included the one with the duplicated beta-hairpin sequence, fold with similar rates as the GB1 domain. Essentially, it is the nature of the rate-limiting step in the folding reaction that determines whether a particular interaction will speed up, or not, the folding rates. While local contacts are important in determining protein stability, residues involved in tertiary contacts in combination with the topology of the native fold, seem to be responsible for the specificity of protein structures. Proteins with non-native secondary structure tendencies can adopt stable folds and be as efficient in folding as those proteins with native-like propensities.     

Inter-residue interactions in protein folding and stability

During the process of protein folding, the amino acid residues along the polypeptide chain interact with each other in a cooperative manner to form the stable native structure. The knowledge about inter-residue interactions in protein structures is very helpful to understand the mechanism of protein folding and stability. In this review, we introduce the classification of inter-residue interactions into short, medium and long range based on a simple geometric approach. The features of these interactions in different structural classes of globular and membrane proteins, and in various folds have been delineated. The development of contact potentials and the application of inter-residue contacts for predicting the structural class and secondary structures of globular proteins, solvent accessibility, fold recognition and ab initio tertiary structure prediction have been evaluated. Further, the relationship between inter-residue contacts and protein-folding rates has been highlighted. Moreover, the importance of inter-residue interactions in protein-folding kinetics and for understanding the stability of proteins has been discussed. In essence, the information gained from the studies on inter-residue interactions provides valuable insights for understanding protein folding and de novo protein design.     

Exploring the Levinthal limit in protein folding

According to the thermodynamic hypothesis, the native state of proteins is uniquely defined by their amino acid sequence. On the other hand, according to Levinthal, the native state is just a local minimum of the free energy and a given amino acid sequence, in the same thermodynamic conditions, can assume many, very different structures that are as thermodynamically stable as the native state. This is the Levinthal limit explored in this work. Using computer simulations, we compare the interactions that stabilize the native state of four different proteins with those that stabilize three non-native states of each protein and find that the nature of the interactions is very similar for all such 16 conformers. Furthermore, an enhancement of the degree of fluctuation of the non-native conformers can be explained by an insufficient relaxation to their local free energy minimum. These results favor Levinthal’s hypothesis that protein folding is a kinetic non-equilibrium process.     

The consistency principle in protein structure and pathways of folding

• 1.i) It is pointed out that various energy terms contributing to stabilize the native state of globular proteins are consistent in the first approximation with each other in the native state. This means that each energy term is individually minimized at the minimum point of the total energy. I proposed (1) to call this fact “the consistency principle in protein structure.”
• 2.ii) The fair success of various methods of prediction of the secondary structures in globular proteins from their amino acid sequence is often interpreted as indicating the dominance of the short-range interactions in determining the local structures of the polypeptide chains. Partly from such a point of view, the hierarchic condensation model has been popular for the process of protein folding. However the consistency principle indicates that the short-range interactions are just one type of intramolecular interaction which contributes to stabilization of the native structure together with other mutually consistent types of intramolecular interactions. Therefore the hierarchic condensation model is not necessarily a unique model of protein folding.
• 3.iii) Roles of a possible nonspecific globular state, stabilized by nonspecific long-range intramolecular interactions, in the folding process are discussed. It is expected that this nonspecific globular state is observed either as an equilibrium or a kinetic intermediate state between the unfolded and the folded native states. Observation as a kinetic intermediate state is expected to occur in experiments done under strongly refolding conditions. In this case the polypeptide chain in the unfolded state collapses into a nonspecific globule by the action of nonspecific long-range intramolecular interactions. Two possible mechanisms of the transition from the nonspecific globular state to the specific native folded state are discussed.
• 4.iv) In an experiment done under weakly refolding conditions, folding is expected to occur according to the embryo-nucleus model. This model is a refined version of the hierarchic condensation model. Refinement is done by taking into account the fact that the intermediate structures assumed in the hierarchic condensation model are unstable against both the native folded state and the unfolded state. A nucleus is an ordered structure of a certain size. Ordered structures of a size larger than a nucleus tend to fold further to become the native specific globule. Ordered structures of a size smaller than a nucleus tend to unfold. Embryos are intrinsically unstable ordered structures smaller than a nucleus. Folding occurs when embryos grow in size to become a nucleus. The intrinsic instability of embryos is the built-in mechanism to overcome the low resolving power of the short-range interactions in determining local conformations of the polypeptide chain.

     

An empirical energy function for threading protein sequence through the folding motif

In this paper we present a new residue contact potantial derived by statistical analysis of protein crystal structures. This gives mean hydrophobic and pairwise contact energies as a function of residue type and distance interval. To test the accuracy of this potential we generate model structures by “threading” different sequences through backbone folding motifs found in the structural data base. We find that conformational energies calculated by summing contact potentials show perfect specificity in matching the correct sequences with each globular folding motif in a 161-protcin data set. They also identify correct models with the core folding motifs of heme-rythrin and immunoglobulin McPC603 V₁-do- main, among millions of alternatives possible when we align subsequences with α-helices and β-strands, and allow for variation in the lengths of intervening loops. We suggest that contact potentials reflect important constraints on nonbonded interaction in native proteins, and that “threading” may be useful for structure prediction by recognition of folding motif. © 1993 Wiley-Liss, Inc.     

Protein folding and misfolding: mechanism and principles

Two fundamentally different views of how proteins fold are now being debated. Do proteins fold through multiple unpredictable routes directed only by the energetically downhill nature of the folding landscape or do they fold through specific intermediates in a defined pathway that systematically puts predetermined pieces of the target native protein into place? It has now become possible to determine the structure of protein folding intermediates, evaluate their equilibrium and kinetic parameters, and establish their pathway relationships. Results obtained for many proteins have serendipitously revealed a new dimension of protein structure. Cooperative structural units of the native protein, called foldons, unfold and refold repeatedly even under native conditions. Much evidence obtained by hydrogen exchange and other methods now indicates that cooperative foldon units and not individual amino acids account for the unit steps in protein folding pathways. The formation of foldons and their ordered pathway assembly systematically puts native-like foldon building blocks into place, guided by a sequential stabilization mechanism in which prior native-like structure templates the formation of incoming foldons with complementary structure. Thus the same propensities and interactions that specify the final native state, encoded in the amino-acid sequence of every protein, determine the pathway for getting there. Experimental observations that have been interpreted differently, in terms of multiple independent pathways, appear to be due to chance misfolding errors that cause different population fractions to block at different pathway points, populate different pathway intermediates, and fold at different rates. This paper summarizes the experimental basis for these three determining principles and their consequences. Cooperative native-like foldon units and the sequential stabilization process together generate predetermined stepwise pathways. Optional misfolding errors are responsible for 3-state and heterogeneous kinetic folding.     

NMR elucidation of early folding hierarchy in HIV-1 protease

Folding studies on proteases by the conventional hydrogen exchange experiments are severely hampered because of interference from the autolytic reaction in the interpretation of the exchange data. We report here NMR identification of the hierarchy of early conformational transitions (folding propensities) in HIV-1 protease by systematic monitoring of the changes in the state of the protein as it is subjected to different degrees of denaturation by guanidine hydrochloride. Secondary chemical shifts, HN-Halpha coupling constants, 1H-15N nuclear Overhauser effects, and 15N transverse relaxation parameters have been used to report on the residual structural propensities, motional restrictions, conformational transitions, etc., and the data suggest that even under the strongest denaturing conditions (6 m guanidine) hydrophobic clusters as well as different native and non-native secondary structural elements are transiently formed. These constitute the folding nuclei, which include residues spanning the active site, the hinge region, and the dimerization domain. Interestingly, the proline residues influence the structural propensities, and the small amino acids, Gly and Ala, enhance the flexibility of the protein. On reducing the denaturing conditions, partially folded forms appear. The residues showing high folding propensities are contiguous along the sequence at many locations or are in close proximity on the native protein structure, suggesting a certain degree of local cooperativity in the conformational transitions. The dimerization domain, the flaps, and their hinges seem to exhibit the highest folding propensities. The data suggest that even the early folding events may involve many states near the surface of the folding funnel.     

A new protein folding recognition potential function

On the study of protein inverse folding problem, one goal is to find simple and efficient potential to evaluate the compatibility between structure and a given sequence. We present here a novo empirical mean force potential to address the importance of electrostatic interactions in protein inverse folding study. It is based on protein main chain polar fraction and constructed in a way similar with Sippl's from a database of 64 known independent three-dimensional protein structures. This potential was applied to recognize the protein native conformations among a conformation pool. Calculated results show that this potential is powerful in picking out native conformations, in addition it can also find structure similarity between proteins with low sequence similarity. The success of this new potential clearly shows the importance of electrostatic factors in protein inverse folding studies. © 1995 Wiley-Liss, Inc.     

Non‐native α‐helix formation is not necessary for folding of lipocalin: Comparison of burst‐phase folding between tear lipocalin and β‐lactoglobulin

Tear lipocalin and β‐lactoglobulin are members of the lipocalin superfamily. They have similar tertiary structures but unusually low overall sequence similarity. Non‐native helical structures are formed during the early stage of β‐lactoglobulin folding. To address whether the non‐native helix formation is found in the folding of other lipocalin superfamily proteins, the folding kinetics of a tear lipocalin variant were investigated by stopped‐flow methods measuring the time‐dependent changes in circular dichroism (CD) spectrum and small‐angle X‐ray scattering (SAXS). CD spectrum showed that extensive secondary structures are not formed during a burst‐phase (within a measurement dead time). The SAXS data showed that the radius of gyration becomes much smaller than in the unfolded state during the burst‐phase, indicating that the molecule is collapsed during an early stage of folding. Therefore, non‐native helix formation is not general for folding of all lipocalin family members. The non‐native helix content in the burst‐phase folding appears to depend on helical propensities of the amino acid sequence. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Exploring local and non-local interactions for protein stability by structural motif engineering

In order to probe the relative contribution of local and non-local interactions to the thermodynamic stability of proteins, we have devised an experimental approach based on a combination of motif engineering and sequence shuffling. Candidate chain segments in an immunoglobulin V(L) domain were identified whose conformation is proposed to be dominated by non-local interactions. Locally interacting structural motifs of a different conformation were then constructed as replacements, by introducing motif consensus sequences. We find that all nine replacements we constructed systematically reduce the folding cooperativity. By comparing this destabilising effect with the folding transitions of shuffled sequences for three of these motifs, we estimate the contribution of local, native interactions to the free energy of folding. Our results suggest that local and non-local interactions contribute to stability by an approximately equal amount, but that local interactions stabilise by increasing the resistance to denaturation while non-local interactions increase folding cooperativity. The systematic loss of stability by sequence shuffling in these host-guest experiments suggests that the designed interactions indeed are present in the native state, thus consensus sequence engineering may be a useful tool in structure design, but non-local interactions must be taken into account for global stability engineering. Statistical approaches are powerful tools for engineering protein structure and stability, but an analysis based on local sequence propensities alone does not adequately represent the balance of sequence and context in protein structures.     

Noninteracting local-structure model of folding and unfolding transition in globular proteins. I. Formulation

A statistical-mechanical model (a noninteracting local structure model) of folding and unfolding transition in globular proteins is described and a formulation is given to calculate the partition function. The process of transition is discussed in this model within the framework of equilibrium statistical mechanics. In order to clarify the range of applicability of such an approach, the characteristics of the folding and unfolding transition in globular proteins are analyzed from the statistical-physical point of view. A theoretical advantage is pointed out in studying folding and unfolding processes taking place as conformational fluctuations in individual protein molecules under macroscopic equilibrium at the melting temperature. In this case, paths of folding and unfolding are shown to be identical in the statistical sense. A key to the noninteracting local structure model lies in the concept of local structures and the assumption of the absence of interactions between local structures. A local structure is defined as a continuous section of the chain which takes the same or similar local conformation as in the native conformation. The assumption of the absence of inter-actions between local structures endows the model with the remarkable character that its partition function can be calculated exactly; thereby the equilibrium population of various conformations along the folding and unfolding paths can be discussed only by a knowledge of the folded native conformation.