A method for predicting protein structure from sequence

BACKGROUND: The ability to predict the native conformation of a globular protein from its amino-acid sequence is an important unsolved problem of molecular biology. We have previously reported a method in which reduced representations of proteins are folded on a lattice by Monte Carlo simulation, using statistically-derived potentials. When applied to sequences designed to fold into four-helix bundles, this method generated predicted conformations closely resembling the real ones. RESULTS: We now report a hierarchical approach to protein-structure prediction, in which two cycles of the above-mentioned lattice method (the second on a finer lattice) are followed by a full-atom molecular dynamics simulation. The end product of the simulations is thus a full-atom representation of the predicted structure. The application of this procedure to the 60 residue, B domain of staphylococcal protein A predicts a three-helix bundle with a backbone root mean square (rms) deviation of 2.25-3 A from the experimentally determined structure. Further application to a designed, 120 residue monomeric protein, mROP, based on the dimeric ROP protein of Escherichia coli, predicts a left turning, four-helix bundle native state. Although the ultimate assessment of the quality of this prediction awaits the experimental determination of the mROP structure, a comparison of this structure with the set of equivalent residues in the ROP dime- crystal structure indicates that they have a rms deviation of approximately 3.6-4.2 A. CONCLUSION: Thus, for a set of helical proteins that have simple native topologies, the native folds of the proteins can be predicted with reasonable accuracy from their sequences alone. Our approach suggest a direction for future work addressing the protein-folding problem.     

Prediction of the three-dimensional structure of proteins using the electrostatic screening model and hierarchic condensation

We describe a method for predicting the three-dimensional (3-D) structure of proteins from their sequence alone. The method is based on the electrostatic screening model for the stability of the protein main-chain conformation. The free energy of a protein as a function of its conformation is obtained from the potentials of mean force analysis of high-resolution x-ray protein structures. The free energy function is simple and contains only 44 fitted coefficients. The minimization of the free energy is performed by the torsion space Monte Carlo procedure using the concept of hierarchic condensation. The Monte Carlo minimization procedure is applied to predict the secondary, super-secondary, and native 3-D structures of 12 proteins with 28–110 amino acids. The 3-D structures of the majority of local secondary and super-secondary structures are predicted accurately. This result suggests that control in forming the native-like local structure is distributed along the entire protein sequence. The native 3-D structure is predicted correctly for 3 of 12 proteins composed mainly from the α-helices. The method fails to predict the native 3-D structure of proteins with a predominantly β secondary structure. We suggest that the hierarchic condensation is not an appropriate procedure for simulating the folding of proteins made up primarily from β-strands. The method has been proved accurate in predicting the local secondary and super-secondary structures in the blind ab initio 3-D prediction experiment. Proteins 31:74–96, 1998. © 1998 Wiley-Liss, Inc.     

Autonomous subdomains in protein folding.

Proteolytic dissection of native trp repressor and horse heart cytochrome c has been used to infer some of the steps in the folding pathways of the intact proteins. For both proteins, small fragments are capable of undergoing spontaneous noncovalent association to form subdomains with native-like secondary and/or tertiary structural features, suggesting that dissection/reassembly may be a general method to gain insight into the structures of folding intermediates. The importance of this approach is its simplicity and potential applicability to studying the folding pathways of a wide range of proteins. The proteases report on the structure and dynamics of the native state, circumventing the need for prior knowledge of the structures of folding intermediates. The observation that small fragments of proteins can associated noncovalently suggests that protein folding can be viewed as an intramolecular "recognition" process. The results imply that substantial information about protein structure and folding is encoded at the level of subdomains, and that chain connectivity has only a minor role in determining the fold.     

Multimeric intermediates in the pathway to the aggregated inclusion body state for P22 tailspike polypeptide chains.

The failure of newly synthesized polypeptide chains to reach the native conformation due to their accumulation as inclusion bodies is a serious problem in biotechnology. The critical intermediate at the junction between the productive folding and the inclusion body pathway has been previously identified for the P22 tailspike endorhamnosidase. We have been able to trap subsequent intermediates in the in vitro pathway to the aggregated inclusion body state. Nondenaturing gel electrophoresis identified a sequential series of multimeric intermediates in the aggregation pathway. These represent discrete species formed from noncovalent association of partially folded intermediates rather than aggregation of native-like trimeric species. Monomer, dimer, trimer, tetramer, pentamer, and hexamer states of the partially folded species were populated in the initial stages of the aggregation reaction. This methodology of isolating early multimers along the aggregation pathway was applicable to other proteins, such as the P22 coat protein and carbonic anhydrase II.     

Modeling the role of disulfide bonds in protein folding: Entropic barriers and pathways

The role of disulfide bonds in directing protein folding is studied using lattice models. We find that the stability and the specificity of the disulfide bond interactions play quite different roles in the folding process: Under some conditions, the stability decreases the overall rate of folding; the specificity, however, by yielding a simpler connectivity of intermediates, always increases the rate of folding. This conclusion is intimately related to the selection mechanism entailed by entropic driving forces, such as the loop formation probability, and entropic barriers separating the native and the many native-like metastable states. The folding time is found to be a minimum for a certain range of the effective disulfide bond interaction. Examination of a model, which allows for the formation of disulfide bonded intermediates, suggests that folding proceeds via a threestage multiple pathways kinetics. We show that there are pathways to the native state involving only native-like intermediates, as well as those that are mediated by nonnative intermediates. These findings are interpreted in terms of the appropriate energy landscape describing the barriers connecting low energy conformations. The consistency of our conclusions with several experimental studies is also discussed. © 1995 Wiley-Liss, Inc.     

The nature of protein folding pathways: The classical versus the new view

Summary Pulsed hydrogen exchange and other studies of the kinetic refolding pathways of several small proteins have established that folding intermediates with native-like secondary structures are well populated, but these studies have also shown that the folding kinetics are not well synchronized. Older studies of the kinetics of formation of the native protein, monitored by optical probes, indicate that the folding kinetics should be synchronized. The model commonly used in these studies is the simple sequential model, which postulates a unique folding pathway with defined and sequential intermediates. Theories of the folding process and Monte Carlo simulations of folding suggest that neither the folding pathway nor the set of folding intermediates is unique, and that folding intermediates accumulate because of kinetic traps caused by partial misfolding. Recent experiments with cytochrome c lend support to this new view of folding pathways. These different views of the folding process are discussed. Misfolding and consequent slowing down of the folding process as a result of cis-trans isomerization about prolyl peptide bonds in the unfolded protein are well known; isomerization occurs before refolding is initiated. The occurrence of equilibrium intermediates on the kinetic folding pathways of some proteins, such as -lactalbumin and apomyoglobin, argues that these intermediates are not caused by kinetic traps but rather are stable intermediates under certain conditions, and this conclusion is consistent with a sequential model of folding. Folding reactions with successive kinetic intermediates, in which late intermediates are more highly folded than early intermediates, indicate that folding is hierarchical. New experiments that test the predictions of the classical and the new views are needed.     

Predictions of protein backbone bond distances and angles from first principles

A procedure is described, based on a spline-function representation of ab initio peptide conformational geometry maps, that allows one to predict backbone bond distances and angles of proteins as functions of the peptide ?(N-C^α)/Ψ(C^α-C′) torsions with an accuracy comparable to that of high-resolution protein crystallography. For example, for the more than 40 residues of crambin, the rms deviation between predicted and crystallographic values of N-C^α-C′ is 1.9° for the 1.5 Å resolution structure and 1.9° for the 0.83 Å resolution structure, compared with angle variations of < 10°. Accurate information on protein backbone geometries is important for establishing dictionaries of flexible geometry functions for use in empirical peptide and protein modeling. © 1995 John Wiley & Sons, Inc.     

Folding of Top7 in unbiased all‐atom Monte Carlo simulations

For computational studies of protein folding, proteins with both helical and β‐sheet secondary structure elements are very challenging, as they expose subtle biases of the physical models. Here, we present reproducible folding of a 92 residue α/β protein (residues 3–94 of Top7, PDB ID: 1QYS) in computer simulations starting from random initial conformations using a transferable physical model which has been previously shown to describe the folding and thermodynamic properties of about 20 other smaller proteins of different folds. Top7 is a de novo designed protein with two α‐helices and a five stranded β‐sheet. Experimentally, it is known to be unusually stable for its size, and its folding transition distinctly deviates from the two‐state behavior commonly seen in natural single domain proteins. In our all‐atom implicit solvent parallel tempering Monte Carlo simulations, Top7 shows a rapid transition to a group of states with high native‐like secondary structure, and a much slower subsequent transition to the native state with a root mean square deviation of about 3.5 Å from the experimentally determined structure. Consistent with experiments, we find Top7 to be thermally extremely stable, although the simulations also find a large number of very stable non‐native states with high native‐like secondary structure. Proteins 2013; 81:1446–1456. © 2013 Wiley Periodicals, Inc.     

Kinetics of protein folding: Nucleation mechanism,time scales,and pathways

The kinetics and thermodynamics of protein folding is investigated using low friction Langevin simulation of minimal continuum mode of proteins. We show that the model protein has two characteristic temperatures: (a) T_θ, at which the chain undergoes a collapse transition from an extended conformation; (b) T_f(< T_θ), at which a finite size first-order transition to the folded state takes place. The kinetics of approach to the native state from initially denatured conformations is probed by several novel correlation functions. We find that the overall kinetics of approach to the native conformation occurs via a three-stage multiple pathway mechanism. The initial stage, characterized by a series of local dihedral angle transitions, eventually results in the compaction of the protein. Subsequently, the molecule acquires native-like structures during the second stage of folding. The final stage of folding involves activated transitions from one of the native-like structures to the native conformation. The first two stages are characterized by a multiplicity of pathways while relatively few paths are involved in the final stage. A detailed analysis of the dynamics of individual trajectories reveals a novel picture of protein folding. We find that afraction of the initial population reaches the native conformation without the formation of any detectable intermediates. This pathway is associated with a nucleation mechanism, i.e., once a critical number of tertiary contacts are established then the native state is reached rapidly. The remaining fraction of molecules become trapped in misfolded structures (stabilized by incorrect tertiary contacts). The slow folding involves transitions over barriers from these structures to the native conformation. The theoretical predictions are compared with recent experiments that probe protein folding kinetics by hydrogen exchange labeling technique. © 1995 John Wiley & Sons, Inc.     

All-atom ab initio folding of a diverse set of proteins

Natural proteins fold to a unique, thermodynamically dominant state. Modeling of the folding process and prediction of the native fold of proteins are two major unsolved problems in biophysics. Here, we show successful all-atom ab initio folding of a representative diverse set of proteins by using a minimalist transferable-energy model that consists of two-body atom-atom interactions, hydrogen bonding, and a local sequence-energy term that models sequence-specific chain stiffness. Starting from a random coil, the native-like structure was observed during replica exchange Monte Carlo (REMC) simulation for most proteins regardless of their structural classes; the lowest energy structure was close to native-in the range of 2-6 A root-mean-square deviation (rmsd). Our results demonstrate that the successful folding of a protein chain to its native state is governed by only a few crucial energetic terms.     

Challenges in structure prediction of oligomeric proteins at the united-residue level: searching the multiple-chain energy landscape with CSA and CFMC

A revised version of the Conformational Space Annealing (CSA) global optimization method is developed, with three separate measures of structural similarity, in order to overcome the inability of a single distance measure to evaluate multiple-chain protein structures adequately. A second search method, Conformational Family Monte Carlo (CFMC), involving genetic-type moves, Monte Carlo-with-minimization perturbations, and explicit clustering of the population into conformational families, is adapted to treat multiple-chain proteins. These two methods are applied to two oligomeric proteins, the retro-GCN4 leucine zipper and the synthetic domain-swapped dimer. CFMC proves superior to CSA in its search for low-energy representatives of its conformational families, but both methods encounter difficulty in finding the native packing arrangements in the absence of native-like symmetry constraints, even when native monomers are present in the population.     

Effect of denaturant and protein concentrations upon protein refolding and aggregation: a simple lattice model.

We present a study of the competition between protein refolding and aggregation for simple lattice model proteins. The effect of solvent conditions (i.e., the denaturant concentration and the protein concentration) on the folding and aggregation behavior of a system of simple, two-dimensional lattice protein molecules has been investigated via (dynamic Monte Carlo simulations. The population profiles and aggregation propensities of the nine most populated intermediate configurations exhibit a complex dependence on the solution conditions that can be understood by considering the competition between intra- and interchain interactions. Some of these configurations are not even seen in isolated chain simulations; they are observed to be highly aggregation prone and are stabilized primarily by the aggregation reaction in multiple-chain systems. Aggregation arises from the association of partially folded intermediates rather than from the association of denatured random-coil states. The aggregation reaction dominates over the folding reaction at high protein concentration and low denaturant concentration, resulting in low refolding yields at those conditions. However, optimum folding conditions exist at which the refolding yield is a maximum, in agreement with some experimental observations.     

Effect of solvent conditions upon refolding pathways and intermediates for a simple lattice protein

Folding pathways and intermediates for a two-dimensional lattice protein have been investigated via computer simulation at various denaturant concentrations. The protein is represented as a chain of 8 hydrophobic (H) and 12 polar (P) beads on a square lattice sequenced in such a way that the native state is a compact hydrophobic core surrounded by a shell of polar beads. Two nonbonded H beads are said to attract each other with a potential of mean force of strength ϵ. Increasing |ϵ/kT| mimics decreasing the denaturant concentration in the solution. Dynamic Monte Carlo simulations have been performed in order to investigate the folding transition and the folding pathways. Sharp folding—unfolding transitions are observed and the folding process proceeds along well-defined pathways that are populated by partially folded intermediates. The folding pathways as well as the populations of the intermediates are strongly dependent upon the denaturant concentration. Generally, intermediates containing long open stretches of H beads are more populated at high denaturant concentration, whereas compact intermediates containing a substantial number of hydrophobic contacts are more populated at low denaturant concentrations. The folding process is also observed to be cooperative in nature in that the chain does not start folding until a key fold in the middle section of the chain is formed correctly. © 1997 John Wiley & Sons, Inc. Biopoly 42: 399–409, 1997     

Folding simulations of small proteins

Understanding how a protein folds is a long-standing challenge in modern science. We have used an optimized atomistic model (united-residue force field) to simulate folding of small proteins of various structures: HP-36 (alpha protein), protein A (beta), 1fsd (alpha+beta), and betanova (beta). Extensive Monte Carlo folding simulations (ten independent runs with 10(9) Monte Carlo steps at a temperature) starting from non-native conformations are carried out for each protein. In all cases, proteins fold into their native-like conformations at appropriate temperatures, and glassy transitions occur at low temperatures. To investigate early folding trajectories, 200 independent runs with 10(6) Monte Carlo steps are also performed at a fixed temperature for a protein. There are a variety of possible pathways during non-equilibrium early processes (fast process, approximately 10(4) Monte Carlo steps). Finally, these pathways converge to the point unique for each protein. The convergence point of the early folding pathways can be determined only by direct folding simulations. The free energy surface, an equilibrium thermodynamic property, dictates the rest of the folding (slow process, approximately 10(8) Monte Carlo steps).     

Non-redox-active small-molecules can accelerate oxidative protein folding by novel mechanisms

Multi-disulfide-bond-containing proteins acquire their native structures through an oxidative folding reaction which involves formation of native disulfide bonds through thiol-disulfide exchange reactions between cysteines and disulfides coupled to a conformational folding event. Oxidative folding rates of the four-disulfide-bond-containing protein bovine pancreatic ribonuclease A (RNase A) in the presence of the synthetic redox-active molecule, (+/-)-trans-1,2-bis(2-mercaptoacetamido)cyclohexane (BMC), and in combination with non-redox-active trimethylamine-N-oxide (TMAO), and trifluorethanol were determined by HPLC analysis. The data indicate that regeneration of RNase A is enhanced 2-fold by BMC (50 microM) and 3-fold upon addition of TMAO (0.2 M) and TFE (3% v/v) relative to control experiments performed in the absence of small-molecules. Examination of the native tendency of the fully-reduced polypeptide and the stability of key folding intermediates suggests that the increased oxidative folding rate can be attributed to native-like elements induced within the fully-reduced polypeptide and the stabilization of native-like species by added non-redox-active molecules.     

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.     

Assembly of protein structure from sparse experimental data: An efficient Monte Carlo model

A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Cαs. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 Å from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 Å are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 Å. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints. Proteins 32:475–494, 1998. © 1998 Wiley-Liss, Inc.     

The oxidative refolding of hen lysozyme and its catalysis by protein disulfide isomerase.

The oxidative refolding of hen lysozyme has been studied by a variety of time-resolved biophysical methods in conjunction with analysis of folding intermediates using reverse-phase HPLC. In order to achieve this, refolding conditions were designed to reduce aggregation during the early stages of the folding reaction. A complex ensemble of relatively unstructured intermediates with on average two disulfide bonds is formed rapidly from the fully reduced protein after initiation of folding. Following structural collapse, the majority of molecules slowly form the four-disulfide-containing fully native protein via rearrangement of a highly native-like, kinetically trapped intermediate, des-[76-94], although a significant population (approximately 30%) appears to fold more quickly via other three-disulfide intermediates. The folding catalyst PDI increases dramatically both yields and rates of lysozyme refolding, largely by facilitating the conversion of des-[76-94] to the native state. This suggests that acceleration of the folding rate may be an important factor in avoiding aggregation in the intracellular environment.     

A coarse-grained protein force field for folding and structure prediction

We have revisited the protein coarse-grained optimized potential for efficient structure prediction (OPEP). The training and validation sets consist of 13 and 16 protein targets. Because optimization depends on details of how the ensemble of decoys is sampled, trial conformations are generated by molecular dynamics, threading, greedy, and Monte Carlo simulations, or taken from publicly available databases. The OPEP parameters are varied by a genetic algorithm using a scoring function which requires that the native structure has the lowest energy, and the native-like structures have energy higher than the native structure but lower than the remote conformations. Overall, we find that OPEP correctly identifies 24 native or native-like states for 29 targets and has very similar capability to the all-atom discrete optimized protein energy model (DOPE), found recently to outperform five currently used energy models.