Folding funnels and binding mechanisms.

The long-held views on lock-and-key versus induced fit in binding arose from the notion that a protein exists in a single, most stable conformation, dictated by its sequence. However, in solution proteins exist in a range of conformations, which may be described by statistical mechanical laws and their populations follow statistical distributions. Upon binding, the equilibrium will shift in favor of the bound conformation from the ensemble of conformations around the bottom of the folding funnel. Hence here we extend the implications and the usefulness of the folding funnel concept to explain fundamental binding mechanisms.     

Statistical mechanics of protein folding by exhaustive enumeration

It is hard to construct theories for the folding of globular proteins because they are large and complicated molecules having enormous numbers of nonnative conformations and having native states that are complicated to describe. Statistical mechanical theories of protein folding are constructed around major simplifying assumptions about the energy as a function of conformation and/or simplifications of the representation of the polypeptide chain, such as one point per residue on a cubic lattice. It is not clear how the results of these theories are affected by their various simplifications. Here we take a very different simplification approach where the chain is accurately represented and the energy of each conformation is calculated by a not unreasonable empirical function. However, the set of amino acid sequences and allowed conformations is so restricted that it becomes computationally feasible to examine them all. Hence we are able to calculate melting curves for thermal denaturation as well as the detailed kinetic pathway of refolding. Such calculations are based on a novel representation of the conformations as points in an abstract 12-dimensional Euclidean conformation space. Fast folding sequences have relatively high melting temperatures, native structures with relatively low energies, small kinetic barriers between local minima, and relatively many conformations in the global energy minimum's watershed. In contrast to other folding theories, these models show no necessary relationship between fast folding and an overall funnel shape to the energy surface, or a large energy gap between the native and the lowest nonnative structure, or the depth of the native energy minimum compared to the roughness of the energy landscape. Proteins 32:425–437, 1998. © 1998 Wiley-Liss, Inc.     

Identification and Characterization of a Misfolded Monomeric Serpin Formed at Physiological Temperature

The native serpin state is kinetically trapped. However, under mildly destabilizing conditions, the conformational landscape changes, and a number of nonnative conformations with increased stability can be readily formed. The ability to undergo structural change is due to intrinsic strain within the serpin's tertiary fold, which is utilized for proteinase inhibition but renders the protein susceptible to aberrant folding and self-association. The relationship between these various conformations is poorly understood. Antichymotrypsin (ACT) is an inhibitory serpin that readily forms a number of inactive conformations, induced via either environmental stress or interaction with proteinases. Here we have used a variety of biophysical and structural techniques to characterize the relationship between some of these conformations. Incubation of ACT at physiological temperature results in the formation of a range of conformations, including both polymer and misfolded monomer. The ability to populate these nonnative states and the native conformation reflects an energy landscape that is very sensitive to the solution conditions. X-ray crystallography reveals that the misfolded monomeric conformation is in the delta conformation. Further polymerization and seeding experiments show that the delta conformation is an end point in the misfolding pathway of ACT and not an on-pathway intermediate formed during polymerization. The observation that ACT readily forms this inactive conformation at physiological temperature and pH suggests that it may have a role in both health and disease.     

Hydrophobic Core Formation and Dehydration in Protein Folding Studied by Generalized-Ensemble Simulations

Despite its small size, chicken villin headpiece subdomain HP36 folds into the native structure with a stable hydrophobic core within several microseconds. How such a small protein keeps up its conformational stability and fast folding in solution is an important issue for understanding molecular mechanisms of protein folding. In this study, we performed multicanonical replica-exchange simulations of HP36 in explicit water, starting from a fully extended conformation. We observed at least five events of HP36 folding into nativelike conformations. The smallest backbone root mean-square deviation from the crystal structure was 1.1 Å. In the nativelike conformations, the stably formed hydrophobic core was fully dehydrated. Statistical analyses of the simulation trajectories show the following sequential events in folding of HP36: 1), Helix 3 is formed at the earliest stage; 2), the backbone and the side chains near the loop between Helices 2 and 3 take nativelike conformations; and 3), the side-chain packing at the hydrophobic core and the dehydration of the core side chains take place simultaneously at the later stage of folding. This sequence suggests that the initial folding nucleus is not necessarily the same as the hydrophobic core, consistent with a recent experimental ϕ-value analysis.     

Functional analysis of propeptide as an intramolecular chaperone for in vivo folding of subtilisin nattokinase

Here, we show that during in vivo folding of the precursor, the propeptide of subtilisin nattokinase functions as an intramolecular chaperone (IMC) that organises the in vivo folding of the subtilisin domain. Two residues belonging to β-strands formed by conserved regions of the IMC are crucial for the folding of the subtilisin domain through direct interactions. An identical protease can fold into different conformations in vivo due to the action of a mutated IMC, resulting in different kinetic parameters. Some interfacial changes involving conserved regions, even those induced by the subtilisin domain, blocked subtilisin folding and altered its conformation. Insight into the interaction between the subtilisin and IMC domains is provided by a three-dimensional structural model.     

Stereochemistry of peptides containing 1-aminocycloheptane-1-carboxylic acid (Ac7c).

The crystal structures of four peptides incorporating 1-aminocycloheptane-1-carboxylic acid (Ac7c) are described. Boc-Aib-Ac7c-NHMe and Boc-Pro-Ac7c-Ala-OMe adopt beta-turn conformations stabilized by an intramolecular 4----1 hydrogen bond, the former folding into a type-I/III beta-turn and the latter into a type-II beta-turn. In the dipeptide esters, Boc-Aib-Ac7c-OMe and Boc-Pro-Ac7c-OMe, the Ac7c and Aib residues adopt helical conformations, while the Pro residue remains semi-extended in both the molecules of Boc-Pro-Ac7c-OMe found in the asymmetric unit. The cycloheptane ring of Ac7c residues adopts a twist-chair conformation in all the peptides studied. 1H-NMR studies in CDCl3 and (CD3)2SO and IR studies in CDCl3 suggest that Boc-Aib-Ac7c-NHMe and Boc-Pro-Ac7c-Ala-OMe maintain the beta-turn conformations in solution.     

Cotranslational folding promotes beta-helix formation and avoids aggregation in vivo

Newly synthesized proteins must form their native structures in the crowded environment of the cell, while avoiding non-native conformations that can lead to aggregation. Yet, remarkably little is known about the progressive folding of polypeptide chains during chain synthesis by the ribosome or of the influence of this folding environment on productive folding in vivo. P22 tailspike is a homotrimeric protein that is prone to aggregation via misfolding of its central β-helix domain in vitro. We have produced stalled ribosome:tailspike nascent chain complexes of four fixed lengths in vivo, in order to assess cotranslational folding of newly synthesized tailspike chains as a function of chain length. Partially synthesized, ribosome-bound nascent tailspike chains populate stable conformations with some native-state structural features even prior to the appearance of the entire β-helix domain, regardless of the presence of the chaperone trigger factor, yet these conformations are distinct from the conformations of released, refolded tailspike truncations. These results suggest that organization of the aggregation-prone β-helix domain occurs cotranslationally, prior to chain release, to a conformation that is distinct from the accessible energy minimum conformation for the truncated free chain in solution.     

The native metastability and misfolding of serine protease inhibitors

The native metastability of serine protease inhibitors (serpins) is believed to facilitate the conformational change required for biological function. However, energetically unfavorable structural features that contribute to metastability of the native serpin conformation, such as buried polar groups, cavities, and over-packing of side-chains, also appear to hinder proper folding. Hence, folding of serpin polypeptides appears prone to error; in particular, the folding polypeptides are readily diverted toward a non-productive folding pathway culminating in a more stable but inactive conformation. In a survey of deficient serpin mutants, various folding defects, such as retarded protein folding, destabilized native conformation, and spontaneous conversion into more stable, inactive conformations such as the latent form and loop-sheet polymers, have been discovered.     

Free-energy landscape of the villin headpiece in an all-atom force field

We investigate the landscape of the internal free-energy of the 36 amino acid villin headpiece with a modified basin hopping method in the all-atom force field PFF01, which was previously used to predictively fold several helical proteins with atomic resolution. We identify near native conformations of the protein as the global optimum of the force field. More than half of the twenty best simulations started from random initial conditions converge to the folding funnel of the native conformation, but several competing low-energy metastable conformations were observed. From 76,000 independently generated conformations we derived a decoy tree which illustrates the topological structure of the entire low-energy part of the free-energy landscape and characterizes the ensemble of metastable conformations. These emerge as similar in secondary content, but differ in tertiary arrangement.     

Failures of inverse folding and threading with gapped alignment

To calculate the tertiary structure of a protein from its amino acid sequence, the thermodynamic approach requires a potential function of sequence and conformation that has its global minimum at the native conformation for many different proteins. Here we study the behavior of such functions for the simplest model system that still has some of the features of the protein folding problem, namely two-dimensional square lattice chain configurations involving two residue types. First we show that even the given contact potential, which by definition is used to identify the folding sequences and their unique native conformations, cannot always correctly select which sequences will fold to a given structure. Second, we demonstrate that the given contact potential is not always able to favor the native alignment of a native sequence on its own native conformation over other gapped alignments of different folding sequences onto that same conformation. Because of these shortcomings, even in this simple model system in which all conformations and all native sequences are known and determined directly by the given potential, we must reexamine our expectations for empirical potentials used for inverse folding and gapped alignment on more realistic representations of proteins. © 1996 Wiley-Liss, Inc.     

Folding-unfolding thermodynamics of a beta-heptapeptide from equilibrium simulations

The thermodynamics of folding and unfolding of a beta-heptapeptide in methanol solution has been studied at four different temperatures, 298 K, 340 K, 350 K, and 360 K, by molecular dynamics simulation. At each of these temperatures, the 50-ns simulations were sufficient to generate an equilibrium distribution between a relatively small number of conformations (approximately 10(2)), showing that, even above the melting temperature (approximately 340 K), the peptide does not randomly sample conformational space. The free energy of folding and the free energy difference between pairs of conformations have been calculated from their relative populations. The experimentally determined folded conformation at 298 K, a left-handed 3(1)-helix, is at each of the four temperatures the predominant conformation, with its probability and average lifetime decreasing with increasing temperature. The most common intermediates of folding and unfolding are also the same at the four temperatures. Paths and rates of interconversion between different conformations have been determined. It has been found that folding can occur through multiple pathways, not necessarily downhill in free energy, although the final step involves a reduced number of intermediates.     

Folding of alpha(r)beta and epsilonbeta reverse turns; a nanosecond molecular dynamics simulation of the hexapeptide MSALNT and the octapeptide NMSALNTL in water.

Folding of the hexapeptide MSALNT and the octapeptide NMSALNTL were investigated using 2.8 ns molecular dynamics (MD) simulations in aqueous solution. In the simulation, the central sequence SALN of the hexapeptide folded rapidly within 200 ps into an alpha(r)beta turn conformation (type VIII conformation) and remained in this conformation for the rest of the trajectory. The sequence SALN of the octapeptide needed 2 ns to fold via epsilonbeta conformations into a similar conformation. The results join the sequences into a growing group of sequences which have a tendency to form secondary structures and thereby to direct protein folding. The structures of the reverse turn conformations were in accordance with the experimental results (Hakalehto et al., Eur J. Biochem. 250, 19-29 (1997)). The main driving force of folding seems to be the hydrophobic interaction between the side chains of Ala and Leu at the i+1 and i+2 positions of the beta-turn.     

Use of machine learning algorithms to classify binary protein sequences as highly-designable or poorly-designable

Background

By using a standard Support Vector Machine (SVM) with a Sequential Minimal Optimization (SMO) method of training, Naïve Bayes and other machine learning algorithms we are able to distinguish between two classes of protein sequences: those folding to highly-designable conformations, or those folding to poorly- or non-designable conformations.

Results

First, we generate all possible compact lattice conformations for the specified shape (a hexagon or a triangle) on the 2D triangular lattice. Then we generate all possible binary hydrophobic/polar (H/P) sequences and by using a specified energy function, thread them through all of these compact conformations. If for a given sequence the lowest energy is obtained for a particular lattice conformation we assume that this sequence folds to that conformation. Highly-designable conformations have many H/P sequences folding to them, while poorly-designable conformations have few or no H/P sequences. We classify sequences as folding to either highly – or poorly-designable conformations. We have randomly selected subsets of the sequences belonging to highly-designable and poorly-designable conformations and used them to train several different standard machine learning algorithms.

Conclusion

By using these machine learning algorithms with ten-fold cross-validation we are able to classify the two classes of sequences with high accuracy – in some cases exceeding 95%.

     

Understanding the Role of Three-Dimensional Topology in Determining the?Folding Intermediates of Group I Introns

Many RNA molecules exert their biological function only after folding to unique three-dimensional structures. For long, noncoding RNA molecules, the complexity of finding the native topology can be a major impediment to correct folding to the biologically active structure. An RNA molecule may fold to a near-native structure but not be able to continue to the correct structure due to a topological barrier such as crossed strands or incorrectly stacked helices. Achieving the native conformation thus requires unfolding and refolding, resulting in a long-lived intermediate. We investigate the role of topology in the folding of two phylogenetically related catalytic group I introns, the Twort and Azoarcus group I ribozymes. The kinetic models describing the Mg²⁺-mediated folding of these ribozymes were previously determined by time-resolved hydroxyl (⋅OH) radical footprinting. Two intermediates formed by parallel intermediates were resolved for each RNA. These data and analytical ultracentrifugation compaction analyses are used herein to constrain coarse-grained models of these folding intermediates as we investigate the role of nonnative topology in dictating the lifetime of the intermediates. Starting from an ensemble of unfolded conformations, we folded the RNA molecules by progressively adding native constraints to subdomains of the RNA defined by the ⋅OH time-progress curves to simulate folding through the different kinetic pathways. We find that nonnative topologies (arrangement of helices) occur frequently in the folding simulations despite using only native constraints to drive the reaction, and that the initial conformation, rather than the folding pathway, is the major determinant of whether the RNA adopts nonnative topology during folding. From these analyses we conclude that biases in the initial conformation likely determine the relative flux through parallel RNA folding pathways.     

Loop propensity of the sequence YKGQP from staphylococcal nuclease: implications for the folding of nuclease.

Recently we performed molecular dynamics (MD) simulations on the folding of the hairpin peptide DTVKLMYKGQPMTFR from staphylococcal nuclease in explicit water. We found that the peptide folds into a hairpin conformation with native and nonnative hydrogen-bonding patterns. In all the folding events observed in the folding of the hairpin peptide, loop formation involving the region YKGQP was an important event. In order to trace the origins of the loop propensity of the sequence YKGQP, we performed MD simulations on the sequence starting from extended, polyproline II and native type I' turn conformations for a total simulation length of 300 ns, using the GROMOS96 force field under constant volume and temperature (NVT) conditions. The free-energy landscape of the peptide YKGQP shows minima corresponding to loop conformation with Tyr and Pro side-chain association, turn and extended conformational forms, with modest free-energy barriers separating the minima. To elucidate the role of Gly in facilitating loop formation, we also performed MD simulations of the mutated peptide YKAQP (Gly --> Ala mutation) under similar conditions starting from polyproline II conformation for 100 ns. Two minima corresponding to bend/turn and extended conformations were observed in the free-energy landscape for the peptide YKAQP. The free-energy barrier between the minima in the free-energy landscape of the peptide YKAQP was also modest. Loop conformation is largely sampled by the YKGQP peptide, while extended conformation is largely sampled by the YKAQP peptide. We also explain why the YKGQP sequence samples type II turn conformation in these simulations, whereas the sequence as part of the hairpin peptide DTVKLMYKGQPMTFR samples type I' turn conformation both in the X-ray crystal structure and in our earlier simulations on the folding of the hairpin peptide. We discuss the implications of our results to the folding of the staphylococcal nuclease.     

Identifying the protein folding nucleus using molecular dynamics

Molecular dynamics simulations of folding in an off-lattice protein model reveal a nucleation scenario, in which a few well-defined contacts are formed with high probability in the transition state ensemble of conformations. Their appearance determines folding cooperativity and drives the model protein into its folded conformation. Amino acid residues participating in those contacts may serve as "accelerator pedals" used by molecular evolution to control protein folding rate.     

Ubiquitin folds via a flip-twist-lock mechanism

To perform specific functional activities, the majority of proteins should fold into their distinct three-dimensional conformations. However, the biologically active conformation of a protein is generally found to be marginally stable than the other conformations that the chain can adopt. How a protein finds its native conformation from its post-synthesis unfolded structure in a complex conformational landscape is the unsolved question that still drives the protein folding community. Here, we report the folding mechanism of a globular protein, ubiquitin, from its chemically denatured state using all-atom molecular dynamics simulations. From the kinetic analysis of the simulated trajectories we show that the folding process can be described by the hydrophobic collapse mechanism, initiated by the “dewetting transition”, and subsequently assisted by the origination of an N-terminal folding nucleus, and finally supported by a native salt-bridge interaction between K11 and E34. We show that ubiquitin folds via an intermediate. Finally, we confirm the presence of “biological water” and explain its role to the folding process.     

Analysis of the code relating sequence to conformation in globular proteins. Theory and application of expected information

1. An information theory analysis of the folding of a globular protein is proposed. 2. The folding is seen as a transfer of information between two messages, the primary sequence and the biologically active conformation. 3. It is shown how the information transferred was estimated by inspection of proteins of known primary sequence and conformation. 4. In this estimation, concerted use of subjective (Bayesian) probabilities leads to a more robust approach which can be employed whether the number of proteins of known sequence and conformation is large or small. 5. Further, it is demonstrated that the problem then becomes a very simple algebraic formulation for information estimates. 6. Finally, it is shown how this process of information theory analysis can be reversed to predict the conformation of a protein by using its primary sequence and the above information estimates obtained from other proteins. 7. The present paper provides the theoretical basis for the derivation and application of a stereochemical alphabet (Robson & Pain, 1974a,c), and for an investigation of the effects of residues on the conformations of their neighbours (Robson & Pain, 1974b).     

Two peptide fragments G55-I72 and K97-A109 from staphylococcal nuclease exhibit different behaviors in conformational preferences for helix formation

Two synthetic peptides, SNasealpha1 and SNasealpha2, corresponding to residues G55-I72 and K97-A109, respectively, of staphylococcal nuclease (SNase), are adopted for detecting the role of helix alpha1 (E57-A69) and helix alpha2 (M98-Q106) in the initiation of folding of SNase. The helix-forming tendencies of the two SNase peptide fragments are investigated using circular dichroism (CD) and two-dimensional (2D) nuclear magnetic resonance (NMR) methods in water and 40% trifluoroethanol (TFE) solutions. The coil-helix conformational transitions of the two peptides in the TFE-H2O mixture are different from each other. SNasealpha1 adopts a low population of localized helical conformation in water, and shows a gradual transition to helical conformation with increasing concentrations of TFE. SNasealpha2 is essentially unstructured in water, but undergoes a cooperative transition to a predominantly helical conformation at high TFE concentrations. Using the NMR data obtained in the presence of 40% TFE, an ensemble of alpha-helical structures has been calculated for both peptides in the absence of tertiary interactions. Analysis of all the experimental data available indicates that formation of ordered alpha-helical structures in the segments E57-A69 and M98-Q106 of SNase may require nonlocal interactions through transient contact with hydrophobic residues in other parts of the protein to stabilize the helical conformations in the folding. The folding of helix alpha1 is supposed to be effective in initiating protein folding. The formation of helix alpha2 depends strongly on the hydrophobic environment created in the protein folding, and is more important in the stabilization of the tertiary conformation of SNase.     

Conformational aspects of polypeptides. XXV. Solvent and temperature effects on the conformations of copolymers of benzyl and methyl L-aspartate with nitrobenzyl L-aspartate

A series of copolymers of β-p-nitrobenzyl L -aspartate with β-benzyl L -aspartate and with β-mcthyl L -aspartatc in helix-supporting and helix-breaking conditions have been reexamined by using ultraviolet isotropic, absorption, optical rotatory dispersion, and circular dichroism techniques. Many different conformations are apparent, depending on solvent and temperature. Chloroform, trifluoroethanol, and methylene dichloride support the left-handed helical conformation of the copolymers containing less than about 20 mole-% nitroaromatic residues and the right-handed helical conformation of the copolymers containing more than approximately 30 mole-% nitroaromatic residues. In trifluoroacetic acid all the copolymers are in a random-coil conformation. In hexa-fluoroacetone trihydrate and in trimethyl phosphate, the copolypeptides with low nitroaromatic residues content are predominantly in a disordered conformation, while those with high nitroaromatic residues content show a right-handed helical array. Reversible helix-ramlom-coil transitions are observed with increasing temperature in trimethyl phosphate. An example of right-handed-left-handed helix reversible transition with temperature is reported in a chloroform-trimethyl phosphate (2:1) mixture. Nitrobenzyl-nilrobenzyl side-chain interactions in chloroform, but not in trifluoroacetic acid or in trimethyl phosphate, have been confirmed. For the first time we report the circular dichroism spectra in which the n-π* peptide band of a left-handed helical conformation is almost completely evident.