Cooperativity in protein-folding kinetics

Reduced BPTI is collapsed. A pulsed field gradient NMR study of unfolded and partially folded bovine pancreatic trypsin inhibitor

Pulsed field gradient NMR was used to measure the hydrodynamic behavior of unfolded variants of bovine pancreatic trypsin inhibitor (BPTI). The unfolded BPTI species studied were [R]Abu, at pH 4.5 and pH 2.5, and unfolded [14-38]Abu, at pH 2.5. These were prepared by chemical synthesis. [R]Abu is a model for reduced BPTI; all cysteine residues are replaced by alpha-amino-n-butyric acid (Abu). [14-38]Abu retains cysteines 14 and 38, which form a disulfide bond, while the other cysteine residues are replaced by Abu. In the PFG experiments, the diffusion coefficient is measured as a function of protein concentration, and the value of D degree -the diffusion coefficient extrapolated to infinite dilution-is determined. From D degree, a value of the hydrodynamic radius. Rh, is computed from the Stokes-Einstein relationship. At pH 4.5, [R]Abu has an Rh value significantly less than the value calculated for a random coil, while at pH 2.5 the experimental Rh value is the same as for a random coil. In view of the changes in NMR detected structure of [R]Abu at pH 4.5 versus pH 2.5 (Pan H, Barbar E, Barany G, Woodward C. 1995. Extensive non-random structure in reduced and unfolded bovine pancreatic trypsin inhibitor. Biochemistry 34:13974-13981), the collapse of reduced BPTI at pH 4.5 may be associated with the formation of non-native hydrophobic clusters of pairs of side chains one to three amino acids apart in sequence. The diffusion constant of [14-38]Abu was also measured at pH 4.5, where the protein is partially folded. An increase in hydrodynamic radius of partially folded [14-38]Abu, relative to native BPTI, is similar to the increase in radius of gyration measured for other proteins under "molten globule" conditions.

Ultrafast signals in protein folding and the polypeptide contracted state

To test the significance of ultrafast protein folding signals (<<1 msec), we studied cytochrome c (Cyt c) and two Cyt c fragments with major C-terminal segments deleted. The fragments remain unfolded under all conditions and so could be used to define the unfolded baselines for protein fluorescence and circular dichroism (CD) as a function of denaturant concentration. When diluted from high to low denaturant in kinetic folding experiments, the fragments readjust to their new baseline values in a "burst phase" within the mixing dead time. The fragment burst phase reflects a contraction of the polypeptide from a more extended unfolded condition at high denaturant to a more contracted unfolded condition in the poorer, low denaturant solvent. Holo Cyt c exhibits fluorescence and CD burst phase signals that are essentially identical to the fragment signals over the whole range of final denaturant concentrations, evidently reflecting the same solvent-dependent, relatively nonspecific contraction and not the formation of a specific folding intermediate. The significance of fast folding signals in Cyt c and other proteins is discussed in relation to the hypothesis of an initial rate-limiting search-nucleation-collapse step in protein folding [Sosnick, T. R., Mayne, L. & Englander, S. W. (1996) Proteins Struct. Funct. Genet. 24, 413-426].

Following co-operative formation of secondary and tertiary structure in a single protein module

We have prepared a family of peptide fragments of the 64 amino acid protein chymotrypsin inhibitor (CI2), corresponding to progressive elongation from the N terminus, in order to elucidate the basis of conformational preferences in single-domain proteins and to obtain insights into their conformational pathway. Structural analysis of the fragment comprising the first 50 residues, CI2(1-50), indicates that it is mainly disordered, with patches of hydrophobic residues exposed to the solvent. Structural characterisation of the fragment CI2(1-63) which lacks only the C-terminal glycine, Gly64, shows native-like structure in all regions of the fragment. The study provides insights into the contribution of specific residues to the stability and co-operativity of the intact protein. We define a phiNMR value, derived from chemical shift analysis, which describes the build-up of structure at the level of individual residues (protons). All the macroscopic probes used to study the growth of structure in CI2 on elongation of the chain (circular dichroism, fluorescence and gel filtration) are in agreement with the residue-by-residue description by NMR. It is seen that secondary and tertiary structure build up in parallel in the fragments and show similar structures to those developed in the transition state for folding of the intact protein.

Protein folding: optimized sequences obtained by simulated breeding in a minimalist model

For a minimalist model of protein folding, which we introduced recently, we investigate various methods to obtain folding sequences. A detailed study of random sequences shows that, for this model, such sequences usually do not fold to their ground states during simulations. Straight-forward techniques for the construction of folding sequences, based solely on the target structure, fail. We describe in detail an optimization algorithm, based on genetic algorithms, for the "simulated breeding" of folding sequences in this model. We find that, for any target structure studied, there is not only a single folding sequence but a patch of sequences in sequence space that fold to this structure. In addition, we show that, much as in real proteins, nonhomologous sequences may fold to the same target structure.

Direct conversion of an oligopeptide from a beta-sheet to an alpha-helix: a model for amyloid formation

A 16-amino acid oligopeptide forms a stable beta-sheet structure in water. In physiological solutions it is able to self-assemble to form a macroscopic matrix that stains with Congo red. On raising the temperature of the aqueous solution above 70 degrees C, an abrupt structural transition occurs in the CD spectra from a beta-sheet to a stable alpha-helix without a detectable random-coil intermediate. With cooling, it retained the alpha-helical form and took several weeks at room temperature to partially return to the beta-sheet form. Slow formation of the stable beta-sheet structure thus shows kinetic irreversibility. Such a formation of very stable beta-sheet structures is found in the amyloid of a number of neurological diseases. This oligopeptide could be a model system for studying the protein conformational changes that occurs in scrapie or Alzheimer disease. The abrupt and direct conversion from a beta-sheet to an alpha-helix may also be found in other processes, such as protein folding and protein-protein interaction. Furthermore, such drastic structure changes may also be exploited in biomaterials designed as sensors to detect environmental changes.

From Levinthal to pathways to funnels

While the classical view of protein folding kinetics relies on phenomenological models, and regards folding intermediates in a structural way, the new view emphasizes the ensemble nature of protein conformations. Although folding has sometimes been regarded as a linear sequence of events, the new view sees folding as parallel microscopic multi-pathway diffusion-like processes. While the classical view invoked pathways to solve the problem of searching for the needle in the haystack, the pathway idea was then seen as conflicting with Anfinsen's experiments showing that folding is pathway-independent (Levinthal's paradox). In contrast, the new view sees no inherent paradox because it eliminates the pathway idea: folding can funnel to a single stable state by multiple routes in conformational space. The general energy landscape picture provides a conceptual framework for understanding both two-state and multi-state folding kinetics. Better tests of these ideas will come when new experiments become available for measuring not just averages of structural observables, but also correlations among their fluctuations. At that point we hope to learn much more about the real shapes of protein folding landscapes.

Properties of the protein matrix revealed by the free energy of cavity formation

BACKGROUND

The classical picture of the hydrophobic stabilization of proteins invokes a resemblance between the protein interior and nonpolar solvents, but the extent to which this is the case has often been questioned. The protein interior is believed to be at least as tightly packed as organic crystals, and was shown to have very low compressibility. There is also evidence that these properties are not uniform throughout the protein, and conflicting views exist on the nature of sidechain packing and on its influence on the properties of the protein.

RESULTS

In order to probe the physical properties of the protein, the free energy associated with the formation of empty cavities has been evaluated for two proteins: barnase and T4 lysozyme. To this end, the likelihood of encountering such cavities was computed from room temperature molecular dynamics trajectories of these proteins in water. The free energy was evaluated in each protein taken as a whole and in submolecular regions. The computed free energies yielded information on the manner in which empty space is distributed in the system, while the latter undergoes thermal motion, a property hitherto not analyzed in heterogeneous media such as proteins. Our results showed that the free energy of cavity formation is higher in proteins than in both water and hexane, providing direct evidence that the native protein medium differs in fundamental ways from the two liquids. Furthermore, although the packing density was found to be higher in nonpolar regions of the protein than in polar ones, the free energy cost of forming atomic size cavities is significantly lower in nonpolar regions, implying that these regions contain larger chunks of empty space, thereby increasing the likelihood of containing atomic size packing defects. These larger empty spaces occur preferentially where buried hydrophobic sidechains belonging to secondary structures meet one another. These particular locations also appear to be more compressible than other parts of the core or surface of the protein.

CONCLUSIONS

The cavity free energy calculations described here provide a much more detailed physical picture of the protein matrix than volume and packing calculations. According to this picture, the packing of hydrophobic sidechains is tight in the interior of the protein, but far from uniform. In particular, the packing is tighter in regions where the backbone forms less regular hydrogen-bonding interactions than at interfaces between secondary structure elements, where such interactions are fully developed. This may have important implications on the role of sidechain packing in protein folding and stability.

Protein fold recognition and dynamics in the space of contact maps

We introduce an energy function for contact maps of proteins. In addition to the standard term, that takes into account pair-wise interactions between amino acids, our potential contains a new hydrophobic energy term. Parameters of the energy function were obtained from a statistical analysis of the contact maps of known structures. The quality of our energy function was tested extensively in a variety of ways. In particular, fold recognition experiments revealed that for a fixed sequence the native map is identified correctly in an overwhelming majority of the cases tested. We succeeded in identifying the structure of some proteins that are known to pose difficulties for such tests (BPTI, spectrin, and cro-protein). In addition, many known pairs of homologous structures were correctly identified, even when the two sequences had relatively low sequence homology. We also introduced a dynamic Monte Carlo procedure in the space of contact maps, taking topological and polymeric constraints into account by restrictive dynamic rules. Various aspects of protein dynamics, including high-temperature melting and refolding, were simulated. Perspectives of application of the energy function and the method for structure checking and fold prediction are discussed.

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.

Diffusion-limited contact formation in unfolded cytochrome c: estimating the maximum rate of protein folding

How fast can a protein fold? The rate of polypeptide collapse to a compact state sets an upper limit to the rate of folding. Collapse may in turn be limited by the rate of intrachain diffusion. To address this question, we have determined the rate at which two regions of an unfolded protein are brought into contact by diffusion. Our nanosecond-resolved spectroscopy shows that under strongly denaturing conditions, regions of unfolded cytochrome separated by approximately 50 residues diffuse together in 35-40 microseconds. This result leads to an estimate of approximately (1 microsecond)-1 as the upper limit for the rate of protein folding.

A fast conformational search strategy for finding low energy structures of model proteins

We describe a new computer algorithm for finding low-energy conformations of proteins. It is a chain-growth method that uses a heuristic bias function to help assemble a hydrophobic core. We call it the Core-directed chain Growth method (CG). We test the CG method on several well-known literature examples of HP lattice model proteins [in which proteins are modeled as sequences of hydrophobic (H) and polar (P) monomers], ranging from 20-64 monomers in two dimensions, and up to 88-mers in three dimensions. Previous nonexhaustive methods--Monte Carlo, a Genetic Algorithm, Hydrophobic Zippers, and Contact Interactions--have been tried on these same model sequences. CG is substantially better at finding the global optima, and avoiding local optima, and it does so in comparable or shorter times. CG finds the global minimum energy of the longest HP lattice model chain for which the global optimum is known, a 3D 88-mer that has only been reachable before by the CHCC complete search method. CG has the potential advantage that it should have nonexponential scaling with chain length. We believe this is a promising method for conformational searching in protein folding algorithms.

The folding mechanism of larger model proteins: role of native structure

The folding mechanism of a 125-bead heteropolymer model for proteins is investigated with Monte Carlo simulations on a cubic lattice. Sequences that do and do not fold in a reasonable time are compared. The overall folding behavior is found to be more complex than that of models for smaller proteins. Folding begins with a rapid collapse followed by a slow search through the semi-compact globule for a sequence-dependent stable core with about 30 out of 176 native contacts which serves as the transition state for folding to a near-native structure. Efficient search for the core is dependent on structural features of the native state. Sequences that fold have large amounts of stable, cooperative structure that is accessible through short-range initiation sites, such as those in anti-parallel sheets connected by turns. Before folding is completed, the system can encounter a second bottleneck, involving the condensation and rearrangement of surface residues. Overly stable local structure of the surface residues slows this stage of the folding process. The relation of the results from the 125-mer model studies to the folding of real proteins is discussed.

Protein folding for realists: a timeless phenomenon

Future research on protein folding must confront two serious dilemmas. (1) It may never be possible to observe at high resolution the very important structures that form in the first few milliseconds of the refolding reaction. (2) The energy functions used to predict structure from sequence will always be approximations of the true energy function. One strategy to resolve both dilemmas is to view protein folding from a different perspective, one that no longer emphasizes time and unique trajectories through conformation space. Instead, free energy replaces time as the reaction coordinate, and ensembles of equilibrium states of partially folded proteins are analyzed in place of trajectories of one protein chain through conformation space, either in vitro or in silico. Initial characterization of the folding of staphylococcal nuclease within this alternative conceptual framework has led to an equilibrium folding pathway with several surprising features. In addition to the finding of two bundles of four hydrophobic segments containing both native and non-native interactions, a gradient in relative stability of different substructures has been identified, with the most stable interactions located toward the amino terminus and the least stable toward the carboxy terminus. Hydrophobic bundles with up-down topology and stability gradients may be two examples of numerous tactics used by proteins to facilitate rapid folding and minimize aggregation. As NMR methods for structural analysis of partially folded proteins are refined, higher resolution descriptions of the structure and dynamics of the polypeptide chain outside the native state may provide many insights into the processes and energetics underlying the self-assembly of folded structure.

Why are some proteins structures so common?

Many biological proteins are observed to fold into one of a limited number of structural motifs. By considering the requirements imposed on proteins by their need to fold rapidly, and the ease with which such requirements can be fulfilled as a function of the native structure, we can explain why certain structures are repeatedly observed among proteins with negligible sequence similarity. This work has implications for the understanding of protein sequence structure relationships as well as protein evolution.

Molecular dynamics simulations of N-terminal peptides from a nucleotide binding protein

Molecular dynamics (MD) simulations of N-terminal peptides from lactate dehydrogenase (LDH) with increasing length and individual secondary structure elements were used to study their stability in relation to folding. Ten simulations of 1-2 ns of different peptides in water starting from the coordinates of the crystal structure were performed. The stability of the peptides was compared qualitatively by analyzing the root mean square deviation (RMSD) from the crystal structure, radius of gyration, secondary and tertiary structure, and solvent accessible surface area. In agreement with earlier MD studies, relatively short (< 15 amino acids) peptides containing individual secondary structure elements were generally found to be unstable; the hydrophobic alpha 1-helix of the nucleotide binding fold displayed a significantly higher stability, however. Our simulations further showed that the first beta alpha beta supersecondary unit of the characteristic dinucleotide binding fold (Rossmann fold) of LDH is somewhat more stable than other units of similar length and that the alpha 2-helix, which unfolds by itself, is stabilized by binding to this unit. This finding suggests that the first beta alpha beta unit could function as an N-terminal folding nucleus, upon which the remainder of the polypeptide chain can be assembled. Indeed, simulations with longer units (beta-alpha-beta-alpha and beta-alpha-beta-alpha beta-beta) showed that all structural elements of these units are rather stable. The outcome of our studies is in line with suggestions that folding of the N-terminal portion of LDH in vivo can be a cotranslational process that takes place during the ribosomal peptide synthesis.

Analysis of the effect of local interactions on protein stability

BACKGROUND

Protein stability appears to be governed by non-covalent interactions. These can be local (between residues close in sequence) or non-local (medium-range and long-range interactions). The specific role of local interactions is controversial. Statistical mechanics arguments point out that local interactions must be weak in stable folded proteins. However, site-directed mutagenesis has revealed that local interactions make a significant contribution to protein stability. Finally, computer simulations suggest that correctly folded proteins require a delicate balance between local and non-local contributions to protein stability.

RESULT

To analyze experimentally the effect of local interactions on protein stability, each of the five Che Y alpha-helices was enhanced in its helical propensity. alpha-Helix-promoting mutations have been designed, using a helix/coil transition algorithm tuned for heteropolypeptides, that do not alter the overall hydrophobicity or protein packing. The increase in helical propensity has been evaluated by far-UV CD analysis of the corresponding peptides. Thermodynamic analysis of the five Che Y mutants reveals, in all cases, an increase in half urea ([urea]1/2) and in Tm, and a decrease in the sensitivity to chemical denaturants (m). ANS binding assays indicate that the changes in m are not due to the stabilization of an intermediate, and the kinetic analysis of the mutants shows that their equilibrium unfolding transition can be considered as following a two-state model, while the change in m is found in the refolding reaction (m(k)f).

CONCLUSIONS

These results are explained by a variable two-state model in which the changes in half urea and Tm arise from the stabilization of the native state and the decrease in m from the compaction of the denatured state. Therefore, the net change in protein stability in aqueous solution produced by increasing the contribution of native-like local interactions in Che Y is the balance between these two conflicting effects. Our results support the idea that optimization of protein stability and cooperativity involve a specific ratio of local versus non-local interactions.

Contact interactions method: a new algorithm for protein folding simulations

Computer simulations of simple exact lattice models are an aid in the study of protein folding process; they have sometimes resulted in predictions experimentally proved. The contact interactions (CI) method is here proposed as a new algorithm for the conformational search in the low-energy regions of protein chains modeled as copolymers of hydrophobic and polar monomers configured as self-avoiding walks on square or cubic lattices. It may be regarded as an extension of the standard Monte Carlo method improved by the concept of cooperativity deriving from nonlocal contact interactions. A major difference with respect to other algorithms is that criteria for the acceptance of new conformations generated during the simulations are not based on the energy of the entire molecule, but cooling factors associated with each residue define regions of the model protein with higher or lower mobility. Nine sequences of length ranging from 20 to 64 residues were used on the square lattice and 15 sequences of length ranging from 46 to 136 residues were used on the cubic lattice. The CI algorithm proved very efficient both in two and three dimensions, and allowed us to localize energy minima not localized by other searching algorithms described in the literature. Use of this algorithm is not limited to the conformational search, because it allows the exploration of thermodynamic and kinetic behavior of model protein chains.

Unfolded BPTI variants with a single disulfide bond have diminished non-native structure distant from the crosslink

BACKGROUND

NMR studies of denatured states, both fully unfolded and partially folded, give insight into the conformations and interactions favored in initial stages of folding, and in early intermediates formed during folding. We have characterized non-random structures favored in unfolded, reduced BPTI [1], and in partially folded BPTI [2]. Here, we report NMR-detected structure of two analogs of unfolded BPTI with one native 14-38 disulfide bond.

RESULTS

Analogs Y21A[14-38]Abu and Y23A[14-38]Abu, obtained by chemical synthesis of [14-38]Abu with Y21 or Y23 replaced by alanine, are models for unfolded BPTI with 14-38 the only disulfide. Compared to unfolded BPTI with all three disulfides broken, the unfolded 14-38 BPTI analogs have numerous differences, including loss of non-native, turn-like conformations for beta 2 residues, diminished non-native aromatic-aliphatic NOEs, and increased intermediate chemical exchange of residues that have native-like conformations in partially folded BPTI. Although the Y21A and Y23A analogs have similar CD and NMR properties, specific differences in NOE patterns and in exchange broadening are observed.

CONCLUSIONS

Changes in unfolded BPTI associated with formation of the 14-38 disulfide bond are consistent with less non-native structure, and more native-like structure, in residues composing the stable core of antiparallel beta-sheet in partially folded BPTI. Specific differences between Y21A[14-38]Abu and Y23A[14-38]Abu indicate that replacement of Y23 results in less ordered structure than replacement of Y21.

Experimental investigation of sidechain interactions in early folding intermediates

Kinetic studies of folding sometimes reveal very rapid spectroscopic changes that may indicate the population of intermediates, but it is difficult to elucidate in detail the nature of the interactions involved. In this review, we focus on one important aspect of this problem: how to probe the nature and extent of clustering of hydrophobic sidechains. As the information obtainable from different experimental approaches is outlined, it becomes clear that a combination of methods is likely to be necessary to build up a reasonable picture of early folding events.

Fast protein folding in the hydrophobic-hydrophilic model within three-eighths of optimal

We present performance-guaranteed approximation algorithms for the protein folding problem in the hydrophobic-hydrophilic model (Dill, 1985). Our algorithms are the first approximation algorithms in the literature with guaranteed performance for this model (Dill, 1994). The hydrophobic-hydrophilic model abstracts the dominant force of protein folding: the hydrophobic interaction. The protein is modeled as a chain of amino acids of length n that are of two types; H (hydrophobic, i.e., nonpolar) and P (hydrophilic, i.e., polar). Although this model is a simplification of more complex protein folding models, the protein folding structure prediction problem is notoriously difficult for this model. Our algorithms have linear (3n) or quadratic time and achieve a three-dimensional protein conformation that has a guaranteed free energy no worse than three-eighths of optimal. This result answers the open problem of Ngo et al. (1994) about the possible existence of an efficient approximation algorithm with guaranteed performance for protein structure prediction in any well-studied model of protein folding. By achieving speed and near-optimality simultaneously, our algorithms rigorously capture salient features of the recently proposed framework of protein folding by Sali et al. (1994). Equally important, the final conformations of our algorithms have significant secondary structure (antiparallel sheets, beta-sheets, compact hydrophobic core). Furthermore, hypothetical folding pathways can be described for our algorithms that fit within the framework of diffusion-collision protein folding proposed by Karplus and Weaver (1979). Computational limitations of algorithms that compute the optimal conformation have restricted their applicability to short sequences (length < or = 90). Because our algorithms trade computational accuracy for speed, they can construct near-optimal conformations in linear time for sequences of any size.

Synthesis and characterization of the human elastin W4 sequence

Following the nomenclature of Sandberg, the W4 sequence of human elastin, [sequence: see text], has been synthesized by solid-phase methods and characterized by carbon-13 nuclear magnetic resonance, amino-acid analysis, mass spectra and elemental analysis. This sequence was then polymerized to greater than 50 kDa as determined by retention in 50 kDa molecular weight cut-off dialysis tubing. It has been successfully cross-linked by gamma-irradiation (20 Mrad) to form an elastomeric matrix, designated as X20-poly(W4). Physical characterizations such as stress/strain, thermolelasticity, acid-base titration and inverse temperature transition studies have been carried out on this elastomer, which is homologous to the striking, poly(VPGVG), W4 sequence of bovine and porcine elastins. These results are compared with previous results on the polypentapeptide of elastin, (VPGVG)n, and it has been demonstrated that X20-poly(W4) also is a dominantly entropic elastomer. Finally, the working model for the structure of this human elastin sequence was derived computationally using molecular mechanics and dynamics calculations. Thus the human W4 sequence appears to be structurally and functionally equivalent to the bovine and porcine W4 sequences in spite of the less regular repeating pentamer sequence.

Addition of side chain interactions to modified Lifson-Roig helix-coil theory: application to energetics of phenylalanine-methionine interactions

We introduce here i, i + 3 and i, i + 4 side chain interactions into the modified Lifson-Roig helix-coil theory of Doig et al. (1994, Biochemistry 33:3396-3403). The helix/coil equilibrium is a function of initiation, propagation, capping, and side chain interaction parameters. If each of these parameters is known, the helix content of any isolated peptide can be predicted. The model considers every possible conformation of a peptide, is not limited to peptides with only a single helical segment, and has physically meaningful parameters. We apply the theory to measure the i, i + 4 interaction energies between Phe and Met side chains. Peptides with these residues spaced i, i + 4 are significantly more helical than controls where they are spaced i, i + 5. Application of the model yields delta G for the Phe-Met orientation to be -0.75 kcal.mol-1, whereas that for the Met-Phe orientation is -0.54 kcal.mol-1. These orientational preferences can be explained, in part, by rotamer preferences for the interacting side chains. We place Phe-Met i, i + 4 at the N-terminus, the C-terminus, and in the center of the host peptide. The model quantitatively predicts the observed helix contents using a single parameter for the side chain-side chain interaction energy. This result indicates that the model works well even when the interaction is at different locations in the helix.

Interactions between the GroE chaperonins and rhodanese. Multiple intermediates and release and rebinding

Efficient renaturation of urea-denatured rhodanese using the chaperonin GroE system requires GroEL, GroES, and ATP. At high concentrations this renaturation also requires the substrate thiosulfate to have been present during GroEL-rhodanese complex formation. When thiosulfate is present the GroEL-rhodanese complex can be concentrated to greater than 1 mg/ml rhodanese with little effect on the efficiency of renaturation. However, if complex is formed in the absence of thiosulfate, renaturation of rhodanese in the presence of thiosulfate shows a critical concentration of approximately 0.4 mg/ml, above which renaturation yields drop dramatically. This critical concentration appears to be related to an aggregation event in the refolding of rhodanese. The nucleotide free or ADP-bound form of GroEL also binds to rhodanese that has been either already renatured or never denatured. The bound rhodanese has no activity but can be released from GroEL with ATP recovering 90% of control activity. The data presented herein support a release and rebinding mechanism for the GroE-assisted refolding of rhodanese. It also suggests GroEL binds several protein folding intermediates along the entire refolding pathway.

On constructing folding heteropolymers

Simplified models of the protein-folding process have led to valuable insights into the generic properties of the folding of heteropolymers. On the basis of theoretical arguments, Shakhnovich and Gutin [(1993) Proc. Natl. Acad. Sci. USA 90, 7195-7199] have proposed a specific method to generate folding sequences for one of these. Here we present a model of folding in heteropolymers that is comparable in simplicity but different in spirit to the one studied by Shakhnovich and Gutin. In our model, the proposed recipe for constructing folding sequence fails. We find that, as a rule, the construction of folding sequences is impossible to achieve by looking at the native conformation only. Rather, competing conformations have to be taken into account too. An evolutionary algorithm that generates folding sequences by optimizing both stability of the native state and folding time is described. Remarkably, this algorithm produces, among others, sequences that fold reproducibly to metastable states.

Local moves: an efficient algorithm for simulation of protein folding

We have enhanced genetic algorithms and Monte Carlo methods for simulation of protein folding by introducing "local moves" in dihedral space. A local move consists of changes in backbone dihedral angles in a sequential window while the positions of all atoms outside the window remain unchanged. We find three advantages of local moves: (1) For some energy functions, protein conformations of lower energy are found; (2) these low energy conformations are found in fewer steps; and (3) the simulations are less sensitive to the details of the annealing protocol. To distinguish the effectiveness of local move algorithm from the complexity of the energy function, we have used several different energy functions. These energy functions include the Profile score (Bowie et al., Science 253:164-170, 1991), the knowledge-based energy function used by Bowie and Eisenberg 1994 (Proc. Natl. Acad. Sci. U.S.A. 91:4434-4440, 1994), two energy terms developed as suggested by Sippl and coworkers (Hendlich et al., J. Mol. Biol. 216:167-180, 1990), and AMBER (Weiner and Kollman, J. Comp. Chem. 2:287-303, 1981). Besides these energy functions we have used three energy functions that include knowledge of the native structures: the RMSD from the native structure, the distance matrix error, and an energy term based on the distance between different residue types called DBIN. In some of these simulations the main advantage of local moves is the reduced dependence on the details of the annealing schedule. In other simulations, local moves are superior to other algorithms as structures with lower energy are found.

Conformation, energy, and folding ability of selected amino acid sequences

Evolutionary selection of sequences is studied with a knowledge-based Hamiltonian to find the design principle for folding to a model protein structure. With sequences selected by naive energy minimization, the model structure tends to be unstable and the folding ability is low. Sequences with high folding ability have only the low-lying energy minimum but also an energy landscape which is similar to that found for the native sequence over a wide region of the conformation space. Though there is a large fluctuation in foldable sequences, the hydrophobicity pattern and the glycine locations are preserved among them. Implications of the design principle for the molecular mechanism of folding are discussed.

Optimal local propensities for model proteins

Lattice models of proteins were used to examine the role of local propensities in stabilizing the native state of a protein, using techniques drawn from spin-glass theory to characterize the free-energy landscapes. In the strong evolutionary limit, optimal conditions for folding are achieved when the contributions from local interactions to the stability of the native state is small. Further increasing the local interactions rapidly decreases the foldability.

Design and characterization of a model alpha beta peptide

CD and nmr spectroscopy were used to compare the conformational properties of two related peptides. One of the peptides, Model AB, was designed to adopt a helix-turn-extended strand (alpha beta) tertiary structure in water that might be stabilized by hydrophobic interactions between two leucine residues in the amino-terminal segment and two methionine residues in the carboxyl terminal segment. The other peptide, AB Helix, has the same amino acid sequence as Model AB except that it lacks the -Pro-Met-Thr-Met-Thr-Gly segment at the carboxyl-terminus. Although the carboxyl-terminal segment of Model AB was found to be unstructured, its presence increases the number of residues in a helical conformation, shifts the pKas of three ionizable side chains by 1 pH unit or more compared to an unstructured peptide, stabilizes the peptide as a monomer in high concentrations of ammonium sulfate, increases the conformational stability of residues at the terminal ends of the helix, and results in many slowly exchanging amide protons throughout the entire backbone of the peptide. These results suggest that interactions between adjacent segments in a small peptide can have significant structure organizing effects. Similar kinds of interactions may be important in determining the structure of early intermediates in protein folding and may be useful in the de novo design of independently folding peptides.

Folding of beta-sheet proteins

In the past year, interesting new information concerning various aspects of the folding process of beta-sheet proteins has been gleaned. Kinetic and equilibrium folding intermediates have been characterized. Studies of extensively denatured states and of model peptide fragments have enabled important steps to be taken towards an understanding of the initiation of the folding process of beta-sheet proteins. Site-directed mutagenesis has been used in combination with various probes to monitor folding events.

Periodicity of polar and nonpolar amino acids is the major determinant of secondary structure in self-assembling oligomeric peptides

The tendency of a polypeptide chain to form alpha-helical or beta-strand secondary structure depends upon local and nonlocal effects. Local effects reflect the intrinsic propensities of the amino acid residues for particular secondary structures, while nonlocal effects reflect the positioning of the individual residues in the context of the entire amino acid sequence. In particular, the periodicity of polar and nonpolar residues specifies whether a given sequence is consistent with amphiphilic alpha-helices or beta-strands. The importance of intrinsic propensities was compared to that of polar/nonpolar periodicity by a direct competition. Synthetic peptides were designed using residues with intrinsic propensities that favored one or the other type of secondary structure. The polar/nonpolar periodicities of the peptides were designed either to be consistent with the secondary structure favored by the intrinsic propensities of the component residues or in other cases to oppose these intrinsic propensities. Characterization of the synthetic peptides demonstrated that in all cases the observed secondary structure correlates with the periodicity of the peptide sequence--even when this secondary structure differs from that predicted from the intrinsic propensities of the component amino acids. The observed secondary structures are concentration dependent, indicating that oligomerization of the amphiphilic peptides is responsible for the observed secondary structures. Thus, for self-assembling oligomeric peptides, the polar/nonpolar periodicity can overwhelm the intrinsic propensities of the amino acid residues and serves as the major determinant of peptide secondary structure.

Interactions between hydrophobic side chains within alpha-helices

The thermodynamic basis of helix stability in peptides and proteins is a topic of considerable interest. Accordingly, we have computed the interactions between side chains of all hydrophobic residue pairs and selected triples in a model helix, using Boltzmann-weighted exhaustive modeling. Specifically, all possible pairs from the set Ala, Cys, His, Ile, Leu, Met, Phe, Trp, Tyr, and Val were modeled at spacings of (i, i + 2), (i, i + 3), and (i, i + 4) in the central turn of a model poly-alanyl alpha-helix. Significant interactions--both stabilizing and destabilizing-- were found to occur at spacings of (i, i + 3) and (i, i + 4), particularly in side chains with rings (i.e., Phe, Tyr, Trp, and His). In addition, modeling of leucine triples in a helix showed that the free energy can exceed the sum of pairwise interactions in certain cases. Our calculated interaction values both rationalize recent experimental data and provide previously unavailable estimates of the constituent energies and entropies of interaction.

Automatic recognition of hydrophobic clusters and their correlation with protein folding units

A method is described to objectively identify hydrophobic clusters in proteins of known structure. Clusters are found by examining a protein for compact groupings of side chains. Compact clusters contain seven or more residues, have an average of 65% hydrophobic residues, and usually occur in protein interiors. Although smaller clusters contain only side-chain moieties, larger clusters enclose significant portions of the peptide backbone in regular secondary structure. These clusters agree well with hydrophobic regions assigned by more intuitive methods and many larger clusters correlate with protein domains. These results are in striking contrast with the clustering algorithm of J. Heringa and P. Argos (1991, J Mol Biol 220:151-171). That method finds that clusters located on a protein's surface are not especially hydrophobic and average only 3-4 residues in size. Hydrophobic clusters can be correlated with experimental evidence on early folding intermediates. This correlation is optimized when clusters with less than nine hydrophobic residues are removed from the data set. This suggests that hydrophobic clusters are important in the folding process only if they have enough hydrophobic residues.

The nature of the initial step in the conformational folding of disulphide-intact ribonuclease A

Here we investigate conformational folding reaction of disulphide-intact ribonuclease A in the absence of the complicating effects due to non-native interactions (such as cis/trans proline isomerization) in the unfolded state. The conformational folding process is found to be intrinsically very fast occurring on the milliseconds time scale. The kinetic data indicate that the conformational folding of ribonuclease A proceeds through the formation of a hydrophobically collapsed intermediate with properties similar to those of equilibrium molten-globules. Furthermore, the data suggest that the rate-limiting transition states on the unfolding and refolding pathways are substantially different with the refolding transition state having non-native-like properties.

LINUS: a hierarchic procedure to predict the fold of a protein

We describe LINUS, a hierarchic procedure to predict the fold of a protein from its amino acid sequence alone. The algorithm, which has been implemented in a computer program, was applied to large, overlapping fragments from a diverse test set of 7 X-ray-elucidated proteins, with encouraging results. For all proteins but one, the overall fragment topology is well predicted, including both secondary and supersecondary structure. The algorithm was also applied to a molecule of unknown conformation, groES, in which X-ray structure determination is presently ongoing. LINUS is an acronym for Local Independently Nucleated Units of Structure. The procedure ascends the folding hierarchy in discrete stages, with concomitant accretion of structure at each step. The chain is represented by simplified geometry and folds under the influence of a primitive energy function. The only accurately described energetic quantity in this work is hard sphere repulsion--the principal force involved in organizing protein conformation [Richards, F. M. Ann. Rev. Biophys. Bioeng. 6:151-176, 1977]. Among other applications, the method is a natural tool for use in the human genome initiative.

The hydrophobic-staple motif and a role for loop-residues in alpha-helix stability and protein folding

A recurrent local structural motif is described at the amino terminus of alpha-helices, that consists of a specific hydrophobic interaction between a residue located before the N-cap, with a residue within the helix (i,i+5 interaction). NMR and CD analysis of designed peptides demonstrate its presence in aqueous solution, its contribution to alpha-helix stability and its role in defining the alpha-helix N terminus limit. Comparison between the N-terminal structures of the peptide and those in proteins with the same fingerprint sequence, shows striking similarities. The change in the polypeptide chain direction produced by the motif suggests an important role in protein folding for residues located in polypeptide segments between secondary structure elements.

Insights into protein folding using physical techniques: studies of lysozyme and alpha-lactalbumin

Understanding the process of protein folding, during which a disordered polypeptide chain is converted into a compact well-defined structure, is one of the major challenges of modern structural biology. In this article we discuss how a combination of physical techniques can provide a structural description of the events which occur during the folding of a protein. First, we discuss how the rapid kinetic events which take place during in vitro folding can be monitored and deciphered in structural terms. Then we consider how more detailed structural descriptions of intermediates may be obtained from NMR studies of stable, partly folded states. Finally, we discuss how these experimental strategies may be extended to relate the findings of in vitro studies to the events occurring during folding in vivo. The approaches will be illustrated using results primarily from our own studies of the c-type lysozymes and the homologous alpha-lactalbumins. The conclusions from these studies are also related to those from other systems to highlight their unifying features. On the basis of these results we identify some of the determinants of the events in folding and we speculate on the importance of these in driving folding molecules to their native states.

Models of cooperativity in protein folding

What is the basis for the two-state cooperativity of protein folding? Since the 1950s, three main models have been put forward. 1. In 'helix-coil' theory, cooperativity is due to local interactions among near neighbours in the sequence. Helix-coil cooperativity is probably not the principal basis for the folding of globular proteins because it is not two-state, the forces are weak, it does not account for sheet proteins, and there is no evidence that helix formation precedes the formation of a hydrophobic core in the following pathways. 2. In the 'sidechain packing' model, cooperativity is attributed to the jigsaw-puzzle-like complementary fits of sidechains. This too is probably not the basis of folding cooperativity because exact models and experiments on homopolymers with sidechains give no evidence that sidechain freezing is two-state, sidechain complementarities in proteins are only weak trends, and the molten globule model predicted by this model is far more native-like than experiments indicate. 3. In the 'hydrophobic core collapse' model, cooperativity is due to the assembly of non-polar residues into a good core. Exact model studies show that this model gives two-state behaviour for some sequences of hydrophobic and polar monomers. It is based on strong forces. There is considerable experimental evidence for the kinetics this model predicts: the development of hydrophobic clusters and cores is concurrent with secondary structure formation. It predicts compact denatured states with sizes and degrees of disorder that are in reasonable agreement with experiments.

Computer determination of peptide conformations in water: different roads to structure

Fragments of proteins (short peptides) that "fold" suggest a mechanism of how complete conformational search in protein folding is avoided. We used a computational method to determine structures of two foldable peptides in explicit water: RVEW and CSVTC. The optimization starts from random structures and no experimental constraints are used. In agreement with NMR data, the simulations find a hydrophobic pair (Val/Trp) in REVW. The structure of CSVTC is induced by a surface water that bridges two amide hydrogens, a drive to structure hypothesized by Ben-Naim [Ben-Naim, A. (1990) J. Chem. Phys. 93, 8196-8210] that is largely ignored in studies of folding. Tendency to structure in short peptide chains suggests a mechanism for the formation of short-range nucleation sites in protein folding.

Principles of protein folding--a perspective from simple exact models

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.

Partially folded, molten globule and molten coil states of bovine pancreatic trypsin inhibitor

Three denatured states of bovine pancreatic trypsin inhibitor have been characterized, using two chemically synthesized analogues designed for study of folding intermediates. One analogue, [14-38]Abu, retains only the 14-38 disulphide. At pH 4.5-6 and 1-7 degrees C, [14-38]Abu is a highly ordered beta-sheet molten globule; it has the circular dichroism (CD), ANS-binding and folding kinetics of a molten globule; is partially folded by NMR analysis; and undergoes cooperative thermal denaturation. At low temperature [14-38]Abu also forms an acid state at pH 1.5, as well as a denatured state at pH 2.5. A second BPTI analogue with all three disulphide bridges eliminated, [R]Abu, lacks detectable secondary and tertiary structure but has stable hydrophobic surfaces and is collapsed. We term this species a 'molten coil'.