A unified mechanism for protein folding: predetermined pathways with optional errors

There is a fundamental conflict between two different views of how proteins fold. Kinetic experiments and theoretical calculations are often interpreted in terms of different population fractions folding through different intermediates in independent unrelated pathways (IUP model). However, detailed structural information indicates that all of the protein population folds through a sequence of intermediates predetermined by the foldon substructure of the target protein and a sequential stabilization principle. These contrary views can be resolved by a predetermined pathway--optional error (PPOE) hypothesis. The hypothesis is that any pathway intermediate can incorporate a chance misfolding error that blocks folding and must be reversed for productive folding to continue. Different fractions of the protein population will then block at different steps, populate different intermediates, and fold at different rates, giving the appearance of multiple unrelated pathways. A test of the hypothesis matches the two models against extensive kinetic folding results for hen lysozyme which have been widely cited in support of independent parallel pathways. The PPOE model succeeds with fewer fitting constants. The fitted PPOE reaction scheme leads to known folding behavior, whereas the IUP properties are contradicted by experiment. The appearance of a conflict with multipath theoretical models seems to be due to their different focus, namely on multitrack microscopic behavior versus cooperative macroscopic behavior. The integration of three well-documented principles in the PPOE model (cooperative foldons, sequential stabilization, optional errors) provides a unifying explanation for how proteins fold and why they fold in that way.     

Predicting protein folding pathways

A structured folding pathway, which is a time ordered sequence of folding events, plays an important role in the protein folding process and hence, in the conformational search. Pathway prediction, thus gives more insight into the folding process and is a valuable guiding tool to search the conformation space. In this paper, we propose a novel 'unfolding' approach to predict the folding pathway. We apply graph-based methods on a weighted secondary structure graph of a protein to predict the sequence of unfolding events. When viewed in reverse this yields the folding pathway. We demonstrate the success of our approach on several proteins whose pathway is partially known.     

Prediction of protein folding pathways.

Recent 1H nuclear magnetic resonance (n.m.r.) hydrogen exchange experiments on five different proteins have delineated the secondary structures formed in trapped, partially folded intermediates. The early forming structural elements are identifiable through a technique described in this work to predict folding pathways. The method assumes that the sequential selection of structural fragments such as alpha-helices and beta-strands involved in the folding process is founded upon the maximal burial of solvent accessible surface from both the formation of internal structure and substructure association. The substructural elements were defined objectively by major changes in main-chain direction. The predicted folding pathways are in complete correspondence with the n.m.r. results in that the formed structural fragments found in the folding intermediates are those predicted earliest in the pathways. The technique was also applied to proteins of known tertiary structure and with fold similar to one of the five proteins examined by 1H n.m.r. The pathways for these structures also showed general consistency with the n.m.r. observations, suggesting conservation of a secondary structural framework or molten globule about which folding nucleates and proceeds.     

An analysis of protein folding pathways

We have developed a model of the protein folding process based on three primary assumptions: that burying of hydrophobic area is the dominant contribution to the relative free energy of a conformation, that a record of the folding process is largely preserved in the final structure, and that the denatured state is a random coil. Detailed folding pathways are identified for 19 protein structures. The picture of the folding process that emerges from this analysis is one of nucleation by regions of 8-16 residues. Nucleation sites then lead to larger structures by two mechanisms: propagation and diffusion/collision. A Monte Carlo simulation is used to follow the folding pathway when propagation is the dominant mechanism. Because detailed pathways are derived for each protein, the models are susceptible to experimental verification.     

Hierarchical protein folding pathways: a computational study of protein fragments

We have previously presented a building block folding model. The model postulates that protein folding is a hierarchical top-down process. The basic unit from which a fold is constructed, referred to as a hydrophobic folding unit, is the outcome of combinatorial assembly of a set of "building blocks." Results obtained by the computational cutting procedure yield fragments that are in agreement with those obtained experimentally by limited proteolysis. Here we show that as expected, proteins from the same family give very similar building blocks. However, different proteins can also give building blocks that are similar in structure. In such cases the building blocks differ in sequence, stability, contacts with other building blocks, and in their 3D locations in the protein structure. This result, which we have repeatedly observed in many cases, leads us to conclude that while a building block is influenced by its environment, nevertheless, it can be viewed as a stand-alone unit. For small-sized building blocks existing in multiple conformations, interactions with sister building blocks in the protein will increase the population time of the native conformer. With this conclusion in hand, it is possible to develop an algorithm that predicts the building block assignment of a protein sequence whose structure is unknown. Toward this goal, we have created sequentially nonredundant databases of building block sequences. A protein sequence can be aligned against these, in order to be matched to a set of potential building blocks.     

Morphogenesis of a protein: folding pathways and the energy landscape

Current knowledge on the reaction whereby a protein acquires its native three-dimensional structure was obtained by and large through characterization of the folding mechanism of simple systems. Given the multiplicity of amino acid sequences and unique folds, it is not so easy, however, to draw general rules by comparing folding pathways of different proteins. In fact, quantitative comparison may be jeopardized not only because of the vast repertoire of sequences but also in view of a multiplicity of structures of the native and denatured states. We have tackled the problem of the relationships between the sequence information and the folding pathway of a protein, using a combination of kinetics, protein engineering and computational methods, applied to relatively simple systems. Our strategy has been to investigate the folding mechanism determinants using two complementary approaches, i.e. (i) the study of members of the same family characterized by a common fold, but substantial differences in amino acid sequence, or (ii) heteromorphic pairs characterized by largely identical sequences but with different folds. We discuss some recent data on protein-folding mechanisms by presenting experiments on different members of the PDZ domain family and their circularly permuted variants. Characterization of the energetics and structures of intermediates and TSs (transition states), obtained by Φ-value analysis and restrained MD (molecular dynamics) simulations, provides a glimpse of the malleability of the dynamic states and of the role of the topology of the native states and of the denatured states in dictating folding and misfolding pathways.     

Kinetics and mechanism of the folding of cytochrome c.

The reversible folding of cytochrome c in urea at pH 4.0 was investigated by repetitive pressure perturbation kinetics and by equilibrium spectroscopic methods. Two folding reactions were observed in the 1 ms to 10 s time range. The rates and amplitudes of these reactions depend on urea concentration in a complex manner, which is different for each process. The absorbance spectra of the kinetic amplitudes of the two reactions also differ from each other. A model with a three-state mechanism can quantitatively account for all of the kinetic and equilibrium data, and it enables us to determine the rate constants and volume changes of the two steps. If a rapid protonation step is added to the mechanism, the analysis can be extended to calculate the pH dependence of the rate and amplitude of the faster folding step. This pH dependence is in excellent agreement with previously published data [Tsong, T. Y. (1977) J. Biol. Chem. 252, 8778-8780]. Kinetic experiments in the 695-nm band show clearly that the axial ligand methionine-80 is involved in the slow folding process and the other axial ligand, histidine-18, is involved in the fast process. Additional experiments with a cyanogen bromide fragment of the protein, and fluorescence detection of the folding kinetics of the intact protein, support an interpretation of the model in terms of known structural elements of cytochrome c. This work provides new information about the mechanism of the folding of cytochrome c, resolves conflicts in earlier interpretations, and demonstrates the applicability of the repetitive pressure perturbation kinetics method to protein folding.     

Prediction of protein folding pathways: Bovine pancreatic trypsin inhibitor

A previous theory for the prediction of protein folding pathways [1] is applied to bovine pancreatic trypsin inhibitor and the resulting sequence of folding events shown to corroborate well with available experimental data.     

Optimum folding pathways for growing protein chains

The folding of a protein is studied as it grows residue by residue from the N-terminus and enters an environment that stabilizes the folded state. This mode of folding of a growing chain is different from refolding where the full chain folds from a disordered initial configuration to the native state. We propose a sequential dynamic optimization method that computes the evolution of optimum folding pathways as amino acid residues are added to the peptide chain one by one. The dynamic optimization formulation is deterministic and uses Newton's equations of motion and a Go-type potential that establishes the native contacts and excluded volume effects. The method predicts the optimal energy-minimizing path among all the alternative feasible pathways. As two examples, the folding of the chicken villin headpiece, a 36-residue protein, and chymotrypsin inhibitor 2 (CI2), a 64-residue protein, are studied. Results on the villin headpiece show significant differences from the refolding of the same chain studied previously. Results on CI2 mostly agree with the results of refolding experiments and computational work.     

蛋白质折叠机理的理论研究

简要综述了近年来蛋白质折叠机理的理论研究。首先回顾了蛋白质折叠理论的发展历程,然后对折叠中间体的研究现状作了较详细的介绍。同时,对折叠机理理论研究中的几种理论模型和模拟算法作了细致评述,分析了其现状和存在的问题。最后,总结和讨论了折叠机理理论研究的现存问题及研究热点,并展望了该领域研究的发展趋势。     

Equilibrium folding and unfolding pathways for a model protein

The folding–unfolding process of reduced bovine pancreatic trypsin inhibitor was investigated with an idealized model employing approximate free energies. The protein is regarded to consist of only C^α and C^β atoms. The backbone dihedral angles are the only conformational variables and are permitted to take discrete values at every 10°. Intraresidue energies consist of two terms: an empirical part taken from the observed frequency distributions of (?,ψ) and an additional favorable energy assigned to the native conformation of each residue. Interresidue interactions are simplified by assuming that there is an attractive energy operative only between residue pairs in close contact in the native structure. A total of 230,000 molecular conformations, with no atomic overlaps, ranging from the native state to the denatured state, are randomly generated by changing the sampling bias. Each conformation is classified according to its conformational energy, F; a conformational entropy, S(F) is estimated for each value of F from the number of samples. The dependence of S(F) on energy reveals that the folding–unfolding transition for this idealized model is an “all-or-none” type; this is attributable to the specific long-range interactions. Interresidue contact probabilities, averaged over samples representing various stages of folding, serve to characterize folding intermediates. Most probable equilibrium pathways for the folding–unfolding transition are constructed by connecting conformationally similar intermediates. The specific details obtained for bovine pancreatic trypsin inhibitor are as follows: (1) Folding begins with the appearance of nativelike medium-range contacts at a β-turn and at the α-helix. (2) These grow to include the native pair of interacting β-strands. This state includes intact regular secondary conformations, as well as the interstrand sheet contacts, and corresponds to an activated state with the highest free energy on the pathway. (3) Additional native long-range contacts are completely formed either toward the amino terminus or toward the carboxyl terminus. (4) In a final step, the missing contacts appear. Although these folding pathways for this model are not consistent with experimental reports, it does indicate multiple folding pathways. The method is general and can be applied to any set of calculated conformational energies and furthermore permits investigation of gross folding features.     

Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus

A lattice model with side chains was used to investigate protein folding with computer simulations. In this model, we rigorously demonstrate the existence of a specific folding nucleus. This nucleus contains specific interactions not present in the native state that, when weakened, slow folding but do not change protein stability. Such a decoupling of folding kinetics from thermodynamics has been observed experimentally for real proteins. From our results, we conclude that specific non-native interactions in the transition state would give rise to straight phi-values that are negative or larger than unity. Furthermore, we demonstrate that residue Ile 34 in src SH3, which has been shown to be kinetically, but not thermodynamically, important, is universally conserved in proteins with the SH3 fold. This is a clear example of evolution optimizing the folding rate of a protein independent of its stability and function.     

前导肽介导的蛋白折叠机制及其对脂肪酶影响的研究进展

大多数蛋白质的形成过程主要由合成前体蛋白和合成功能蛋白两个步骤组成.在这个过程中,前导肽能够辅助蛋白质折叠或抑制它的活性.前导肽作为脂肪酶结构中重要的一段多肽链,通常作为分子内分子伴侣来辅助脂肪酶的折叠,同时该序列上包括糖基化位点在内的一些特殊位点,对酶的活性、极端环境稳定性、甲醇耐受性和底物特异性等性质具有重要影响....     

Malleability of the folding mechanism of the outer membrane protein PagP: parallel pathways and the effect of membrane elasticity

Understanding the interactions between membrane proteins and the lipid bilayer is key to increasing our ability to predict and tailor the folding mechanism, structure and stability of membrane proteins. Here, we have investigated the effects of changing the membrane composition and the relative concentrations of protein and lipid on the folding mechanism of the bacterial outer membrane protein PagP. The folding pathway, monitored by tryptophan fluorescence, was found to be characterized by a burst phase, representing PagP adsorption to the liposome surface, followed by a time course that reflects the folding and insertion of the protein into the membrane. In 1,2-dilauroyl-sn-glycero-3-phosphocholine (diC(12:0)PC) liposomes, the post-adsorption time course fits well to a single exponential at high lipid-to-protein ratios (LPRs), but at low LPRs, a second exponential phase with a slower folding rate constant is observed. Interrupted refolding assays demonstrated that the two exponential phases reflect the presence of parallel folding pathways. Partitioning between these pathways was found to be modulated by the elastic properties of the membrane. Folding into mixed 1,2-dilauroyl-sn-glycero-3-phosphoethanolamine:diC(12:0)PC liposomes resulted in a decrease in PagP adsorption to the liposomes and a switch to the slower folding pathway. By contrast, inclusion of 1,2-dilauroyl-sn-glycero-3-phosphoserine into diC(12:0)PC liposomes resulted in a decrease in the folding rate of the fast pathway. The results highlight the effect of lipid composition in tailoring the folding mechanism of a membrane protein, revealing that membrane proteins have access to multiple, competing folding routes to a unique native structure.     

Sequence evolution and the mechanism of protein folding

The impact on protein evolution of the physical laws that govern folding remains obscure. Here, by analyzing in silico-evolved sequences subjected to evolutionary pressure for fast folding, it is shown that: First, a subset of residues in the thermodynamic folding nucleus is mainly responsible for modulating the protein folding rate. Second and most important, the protein topology itself is of paramount importance in determining the location of these residues in the structure. Further stabilization of the interactions in this nucleus leads to fast folding sequences. Third, these nucleation points restrict the sequence space available to the protein during evolution. Correlated mutations between positions around these hot spots arise in a statistically significant manner, and most involve contacting residues. When a similar analysis is carried out on real proteins, qualitatively similar results are obtained.     

Thermal folding and mechanical unfolding pathways of protein secondary structures

Mechanical stretching of secondary structures is studied through molecular dynamics simulations of a Go-like model. Force versus displacement curves are studied as a function of the stiffness and velocity of the pulling device. The succession of stretching events, as measured by the order in which contacts are ruptured, is compared to the sequencing of events during thermal folding and unfolding. Opposite cross-correlations are found for an alpha-helix and a beta-hairpin structure. In a tandem of two alpha-helices, the two constituent helices unravel nearly simultaneously. A simple condition for simultaneous versus sequential unraveling of repeat units is presented.     

The consistency principle in protein structure and pathways of folding

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