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.     

新型平均势函数在蛋白质反向折叠中的应用

利用蛋白质主链的极性分数及主链二面角为参量,构建了一种基于蛋白质结构数据库的势函数。将该势函数应用于蛋白质反向折叠研究中,发现该函数可成功地将蛋白质分子的天然构象从构建的构象库中识别出来;将一目标序列与构象库的每一可能的构象匹配,并用该势函数计算相应的能量,结果表明对绝大多数蛋白质分子来说,天然的构象的能量值总是最低。此外,该函数还将一些序列相似性较低,而结构相似性较高的蛋白质分子识别出来。我们认     

Learning about protein folding via potential functions

Over the last few years we have developed an empirical potential function that solves the protein structure recognition problem: given the sequence for an n-residue globular protein and a collection of plausible protein conformations, including the native conformation for that sequence, identify the correct, native conformation. Having determined this potential on the basis of only some 6500 native/nonnative pairs of structures for 58 proteins, we find it recognizes the native conformation for essentially all compact, soluble, globular proteins having known native conformations in comparisons with 10⁴ to 10⁶ reasonable alternative conformations apiece. In this sense, the potential encodes nearly all the essential features of globular protein conformational preference. In addition it “knows” about many additional factors in protein folding, such as the stabilization of multimeric proteins, quaternary structure, the role of disulfide bridges and ligands, proproteins vs. processed proteins, and minimal strand lengths in globular proteins. Comparisons are made with other sorts of protein folding problems, and applications in protein conformational determination and prediction are discussed. © 1994 Wiley-Liss, Inc.     

A heteropolymer model study for the mechanism of protein folding

A heteropolymer model of randomly self-interacting chains in two dimensions is studied with numerical simulations in order to elucidate the folding mechanism of protein. We find that the model occasionally shows folding propensity depending on the sequence of random numbers given to the chain. We study the thermodynamic and kinematic roles in the folding mechanism by grouping the local energy minima found in the simulations into clusters according to the similarity of their conformations. It is suggested that the local minima to which some heteropolymers show a folding tendency are always the lowest energy states of the energy spectrum within a cluster, though which cluster is selected depends on the sequence. For the eight random sequences we study, we find that the energy gap between the ground state and excited states is little correlated with folding or nonfolding. We rather find that folding propensities are correlated with the global structure of the average energy surface, implying a dominant kinetic role in the folding mechanism, although thermal factors cannot be ignored as the mechanism of choosing the ground state within a cluster of states connected by small deformations. We suggest that a hierarchical cluster structure plays an important role in selecting a unique folded state out of the huge number of local minima of heteropolymers. © 1997 John Wiley & Sons, Inc.     

Analysis on folding of misgurin using two-dimensional HP model

Misgurin is an antimicrobial peptide from the loach, while the hydrophobic-polar (HP) model is a way to study the folding conformations and native states in peptide and protein although several amino acids cannot be classified either hydrophobic or polar. Practically, the HP model requires extremely intensive computations, thus it has yet to be used widely. In this study, we use the two-dimensional HP model to analyze all possible folding conformations and native states of misgurin with conversion of natural amino acids according to the normalized amino acid hydrophobicity index as well as the shortest benchmark HP sequence. The results show that the conversion of misgurin into HP sequence with glycine as hydrophobic amino acid at pH 2 has 1212 folding conformations with the same native state of minimal energy -6; the conversion of glycine as polar amino acid at pH 2 has 13,386 folding conformations with three native states of minimal energy -5; the conversion of glycine as hydrophobic amino acid at pH 7 has 2538 folding conformations with three native states of minimal energy -5; and the conversion of glycine as polar amino acid at pH 7 has 12,852 folding conformations with three native states of minimal energy -4. Those native states can be ranked according to the normalized amino acid hydrophobicity index. The detailed discussions suggest two ways to modify misgurin.     

Discrimination of the native from misfolded protein models with an energy function including implicit solvation.

An essential requirement for theoretical protein structure prediction is an energy function that can discriminate the native from non-native protein conformations. To date most of the energy functions used for this purpose have been extracted from a statistical analysis of the protein structure database, without explicit reference to the physical interactions responsible for protein stability. The use of the statistical functions has been supported by the widespread belief that they are superior for such discrimination to physics-based energy functions. An effective energy function which combined the CHARMM vacuum potential with a Gaussian model for the solvation free energy is tested for its ability to discriminate the native structure of a protein from misfolded conformations; the results are compared with those obtained with the vacuum CHARMM potential. The test is performed on several sets of misfolded structures prepared by others, including sets of about 650 good decoys for six proteins, as well as on misfolded structures of chymotrypsin inhibitor 2. The vacuum CHARMM potential is successful in most cases when energy minimized conformations are considered, but fails when applied to structures relaxed by molecular dynamics. With the effective energy function the native state is always more stable than grossly misfolded conformations both in energy minimized and molecular dynamics-relaxed structures. The present results suggest that molecular mechanics (physics-based) energy functions, complemented by a simple model for the solvation free energy, should be tested for use in the inverse folding problem, and supports their use in studies of the effective energy surface of proteins in solution. Moreover, the study suggests that the belief in the superiority of statistical functions for these purposes may be ill founded.     

Statistical mechanics of protein folding by cluster distance geometry

This is our second type of model for protein folding where the configurational parameters and the effective potential energy function are chosen in such a way that all conformations are described and the canonical partition function can be evaluated analytically. Structure is described in terms of distances between pairs of sequentially contiguous blocks of eight residues, and all possible conformations are grouped into 71 subsets in terms of bounds on these distances. The energy is taken to be a sum of pairwise interactions between such blocks. The 210 energy parameters were adjusted so that the native folds of 32 small proteins are favored in free energy over the denatured state. We then found 146 proteins having negligible sequence similarity to any of the training proteins, yet the free energy of the respective correct native states were favored over the denatured state.     

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.     

Refolding simulations of an isolated fragment of barnase into a native-like β hairpin: Evidence for compactness and hydrogen bonding as concurrent stabilizing factors

Experimental evidence and theoretical models both suggest that protein folding is initiated within specific fragments intermittently adopting conformations close to that found in the protein native structure. These folding initiation sites encompassing short portions of the protein are ideally suited for study in isolation by computational methods aimed at peering into the very early events of folding. We have used Molecular Dynamics (MD) technique to investigate the behavior of an isolated protein fragment formed by residues 85 to 102 of barnase that folds into a β hairpin in the protein native structure. Three independent MD simulations of 1.3 to 1.8 ns starting from unfolded conformations of the peptide portrayed with an all-atom model in water were carried out at gradually decreasing temperature. A detailed analysis of the conformational preferences adopted by this peptide in the course of the simulations is presented. Two of the unfolded peptide conformations fold into a hairpin characterized by native and a larger bulk of nonnative interactions. Both refolding simulations substantiate the close relationship between interstrand compactness and hydrogen bonding network involving backbone atoms. Persistent compactness witnessed by side-chain interactions always occurs concomitantly with the formation of backbone hydrogen bonds. No highly populated conformations generated in a third simulation starting from the remotest unfolded conformer relative to the native structure are observed. However, nonnative long-range and medium-range contacts with the aromatic moiety of Trp94 are spotted, which are in fair agreement with a former nuclear magnetic resonance study of a denaturing solution of an isolated barnase fragment encompassing the β hairpin. All this lends reason to believe that the 85–102 barnase fragment is a strong initiation site for folding. Proteins 29:212–227, 1997. © 1997 Wiley-Liss, Inc.     

Xylanase homology modeling using the inverse protein folding approach.

Xylanase has been used in wood pulp bleaching in an effort to reduce chlorine release into the environment and pollution associated with paper production. The three-dimensional structure of xylanase is important to enable better understanding of the enzyme mechanism and to help design a more thermostable xylanase mutant. At the time this work was begun, there was no sequence homologous protein available for traditional sequence-based homology modeling. In order to circumvent this problem, the inverse protein folding approach was undertaken to find a suitable template structure. Model structures of Bacillus circulans xylanase were built based on the data-base search results of related proteins. The model structures were refined and compared to the recently solved xylanase X-ray crystal structure. The overall structural similarity between the theoretical model and experimental structure demonstrate the usefulness of this approach. Disagreement in folding topology, however, warrants further research into the inverse protein folding approach.     

The fastest global events in RNA folding: electrostatic relaxation and tertiary collapse of the Tetrahymena ribozyme

Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved small-angle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.     

Searching for foldable protein structures using optimized energy functions

During evolution, the effective interactions between residues in a protein can be adjusted through mutations to allow the protein to fold to its native structure on an adequate time scale. We seek to address the question: Are there some structures that can be better optimized than others? Using exhaustive enumeration of the compact conformations of short proteins confined to simple lattices, we find that the best structures are those that contain contacts rare in random structures, indicating the importance of nonlocal contacts for assisting the folding process. Certain structural motifs such as long β-hairpins, Greek-key motifs, and jelly rolls, commonly found in proteins of known structure, have a high degree of optimizability. Contrary to what might be expected, positive correlations between the various interactions reduce optimizability. The optimization procedure produces a correlated energy landscape, which might assist folding. © 1995 John Wiley & Sons, Inc.     

Coupling between conformation and proton binding in proteins

Interest centers here on whether the use of a fixed charge distribution of a protein solute, or a treatment that considers proton-binding equilibria by solving the Poisson equation, is a better approach to discriminate native from non-native conformations of proteins. In this analysis of the charge distribution of 7 proteins, we estimate the solvation free energy contribution to the total free energy by exploring the 2(zeta) possible ionization states of the whole molecule, with zeta being the number of ionizable groups in the amino acid sequence, for every conformation in the ensembles of 7 proteins. As an additional consideration of the role of electrostatic interactions in determining the charge distribution of native folds, we carried out a comparison of alternative charge assignment models for the ionizable residues in a set of 21 native-like proteins. The results of this work indicate that (1) for 6 out of 7 proteins, estimation of solvent polarization based on the Generalized Born model with a fixed charge distribution provides the optimal trade-off between accuracy, with respect to the Poisson equation, and speed when compared to the accessible surface area model; for the seventh protein, consideration of all possible ionization states of the whole molecule appears to be crucial to discriminate the native from non-native conformations; (2) significant differences in the degree of ionization and hence the charge distribution for native folds are found between the different charge models examined; (3) the stability of the native state is determined by a delicate balance of all the energy components, and (4) conformational entropy, and hence the dynamics of folding, may play a crucial role for a successful ab initio protein folding prediction.     

Salt contribution to RNA tertiary structure folding stability

Accurate quantification of the ionic contribution to RNA folding stability could greatly enhance our ability to understand and predict RNA functions. Recently, motivated by the potential importance of ion correlation and fluctuation in RNA folding, we developed the tightly bound ion (TBI) model. Extensive experimental tests showed that the TBI model can lead to better treatment of multivalent ions than the Poisson-Boltzmann equation. In this study, we use the model to quantify the contribution of salt (Na⁺ and Mg²⁺) to the RNA tertiary structure folding free energy. Folding of the RNA tertiary structure often involves intermediates. We focus on the folding transition from an intermediate state to the native state, and compute the electrostatic folding free energy of the RNA. Based on systematic calculations for a variety of RNA molecules, we derive a set of formulas for the electrostatic free energy for tertiary structural folding as a function of the sequence length and compactness of the RNA and the Na⁺ and Mg²⁺ concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Downhill versus Barrier-Limited Folding of BBL: 3. Heterogeneity of the Native State of the BBL Peripheral Subunit Binding Domain and Its Implications for Folding Mechanisms

Protein folding studies are generally predicated on Anfinsen's dogma that there is a unique native state of a protein. However, this is not always the case. NMR measurements of BBL, for example, find a decrease in helicity of helix 2 surrounding His166 on its protonation, which, with other experimental data, suggests that the native state can occupy two or more conformations. Here, we analysed the native structure of BBL as a function of pH, temperature and ionic strength, along with a truncated BBL construct, by extensive all-atom molecular dynamics simulations in explicit solvent, corresponding to at least 400 ns of trajectories collected for each set of conditions. The native state was heterogeneous under a variety of conditions, consisting of two predominant conformations. This equilibrium changed with conditions: protonation of His166 at low pH shifted the equilibrium in favour of a less ordered conformer, while high ionic strength at neutral pH shifted the equilibrium to a more ordered conformer. Furthermore, high temperature and truncation of the sequence also shifted the equilibrium toward the less ordered conformer. Importantly, conformational heterogeneity in a native structure that changes with conditions will lead to deviations from the classic two-state behaviour during the barrier-limited unfolding of a protein. In particular, some regions of the protein will appear to unfold asynchronously and some residues will have anomalous thermal titration curves and unusual baseline behaviour monitored microscopically by NMR spectroscopy and macroscopically by calorimetry and other techniques. Such data could otherwise be interpreted as evidence for barrier-free downhill folding. Any biological significance of downhill folding of BBL appears to be ruled out by recent crystallographic studies on the reaction cycle of the BBL-equivalent domain in a pyruvate dehydrogenase multienzyme complex in which the domain remains of constant structure.     

The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation

We present a novel Monte Carlo simulation of protein folding, in which all heavy atoms are represented as interacting hard spheres. This model includes all degrees of freedom relevant to folding, all side-chain and backbone torsions, and uses a Go potential. In this study, we focus on the 46 residue alpha/beta protein crambin and two of its structural components, the helix and helix hairpin. For a wide range of temperatures, we recorded multiple folding events of these three structures from random coils to native conformations that differ by less than 1 A C(alpha) dRMS from their crystal structure coordinates. The thermodynamics and kinetic mechanism of the helix-coil transition obtained from our simulation shows excellent agreement with currently available experimental and molecular dynamics data. Based on insights obtained from folding its smaller structural components, a possible folding mechanism for crambin is proposed. We observed that the folding occurs via a cooperative, first order-like process, and that many folding pathways to the native state exist. One particular sequence of events constitutes a "fast-folding" pathway where kinetic traps are avoided. At very low temperatures, a kinetic trap arising from the incorrect packing of side-chains was observed. These results demonstrate that folding to the native state can be observed in a reasonable amount of time on desktop computers even when an all-atom representation is used, provided the energetics sufficiently stabilize the native state.     

An evolutionary strategy for all-atom folding of the 60-amino-acid bacterial ribosomal protein l20

We have investigated an evolutionary algorithm for de novo all-atom folding of the bacterial ribosomal protein L20. We report results of two simulations that converge to near-native conformations of this 60-amino-acid, four-helix protein. We observe a steady increase of "native content" in both simulated ensembles and a large number of near-native conformations in their final populations. We argue that these structures represent a significant fraction of the low-energy metastable conformations, which characterize the folding funnel of this protein. These data validate our all-atom free-energy force field PFF01 for tertiary structure prediction of a previously inaccessible structural family of proteins. We also compare folding simulations of the evolutionary algorithm with the basin-hopping technique for the Trp-cage protein. We find that the evolutionary algorithm generates a dynamic memory in the simulated population, which leads to faster overall convergence.     

A polar, solvent-exposed residue can be essential for native protein structure

BACKGROUND: A large energy gap between the native state and the non-native folded states is required for folding into a unique three-dimensional structure. The features that define this energy gap are not well understood, but can be addressed using de novo protein design. Previously, alpha(2)D, a dimeric four-helix bundle, was designed and shown to adopt a native-like conformation. The high-resolution solution structure revealed that this protein adopted a bisecting U motif. Glu7, a solvent-exposed residue that adopts many conformations in solution, might be involved in defining the unique three-dimensional structure of alpha(2)D. RESULTS: A variety of hydrophobic and polar residues were substituted for Glu7 and the dynamic and thermodynamic properties of the resulting proteins were characterized by analytical ultracentrifugation, circular dichroism spectroscopy, and nuclear magnetic resonance spectroscopy. The majority of substitutions at this solvent-exposed position had little affect on the ability to fold into a dimeric four-helix bundle. The ability to adopt a unique conformation, however, was profoundly modulated by the residue at this position despite the similar free energies of folding of each variant. CONCLUSIONS: Although Glu7 is not involved directly in stabilizing the native state of alpha(2)D, it is involved indirectly in specifying the observed fold by modulating the energy gap between the native state and the non-native folded states. These results provide experimental support for hypothetical models arising from lattice simulations of protein folding, and underscore the importance of polar interfacial residues in defining the native conformations of proteins.