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.     

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.     

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。     

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.     

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.     

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.     

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.     

The underlying mechanism for the diversity of disulfide folding pathways

The disulfide folding pathway of bovine pancreatic trypsin inhibitor (BPTI) is characterized by the predominance of folding intermediates with native-like structures. Our laboratory has recently analyzed the folding pathway(s) of four 3-disulfide-containing proteins, including hirudin, potato carboxypeptidase inhibitor, epidermal growth factor, and tick anticoagulant peptide. Their folding mechanism(s) differ from that of BPTI by 1) a higher degree of heterogeneity of 1- and 2-disulfide intermediates and 2) the presence of 3-disulfide scrambled isomers as folding intermediates. To search for the underlying causes of these diversities, we conducted kinetic analyses of the reductive unfolding of these five proteins. The experiment of reductive unfolding was designed to evaluate the relative stability and interdependence of disulfide bonds in the native protein. It is demonstrated here that among these five proteins, there exists a striking correlation between the mechanism(s) of reductive unfolding and that of oxidative folding. Those proteins with their native disulfide bonds reduced in a collective and simultaneous manner exhibit both a high degree of heterogeneity of folding intermediates and the accumulation of scrambled isomers along the folding pathway. A sequential reduction of the native disulfide bonds is associated with the presence of predominant intermediates with native- like structures.     

Malleability of protein folding pathways: a simple reason for complex behaviour

Although the structures of native proteins are generally unique, the pathways by which they form are often free to vary. Some proteins fold by a multitude of different pathways, whereas others seem restricted to only one choice. An explanation for this variation in folding behaviour has recently emerged from studies of transition state changes: the number of accessible pathways is linked to the number of nucleation motifs contained within the native topology. We refer to these nucleation motifs as 'foldons', as they approach the size of an independent cooperative unit. Thus, with respect to pathway malleability and the composition of the folding funnel, proteins can be seen as modular assemblies of competing foldons. For the split beta-alpha-beta fold, these foldons are two-strand-helix motifs coupled by spatial overlap.     

Desolvation shell of hydrogen bonds in folded proteins,protein complexes and folding pathways

A few backbone hydrogen bonds (HBS) in native protein folds are poorly protected from water attack: their desolvation shell contains an inordinately low number of hydrophobic residues. Thus, an approach by solvent-structuring moieties of a binding partner should contribute significantly to enhance their stability. This effect represents an important factor in the site specificity inherent to protein binding, as inferred from a strong correlation between poorly desolvated HBs and binding sites. The desolvation shells were also examined in a dynamic context: except for a few singular under-protected bonds, the size of desolvation shells is preserved along the folding trajectory.     

Amino acid substitutions influencing intracellular protein folding pathways.

Though an increasing variety of chaperonins are emerging as important factors in directing polypeptide chain folding off the ribosome, the primary amino acid sequence remains the major determinant of final conformation. The ability to identify cytoplasmic folding intermediates in the formation of the tailspike endorhamnosidase of phage P22 has made it possible to isolate two classes of mutations influencing folding intermediates-temperature-sensitive folding mutations and global suppressors of tsf mutants. These and related amino acid substitutions in eukaryotic proteins are discussed in the context of inclusion body formation and problems in the recovery of correctly folded proteins.     

Gatekeepers in the ribosomal protein s6: thermodynamics, kinetics, and folding pathways revealed by a minimalist protein model

We investigate the effect of structural gatekeepers on the folding of the ribosomal protein S6. Folding thermodynamics and early refolding kinetics are studied for this system utilizing computer simulations of a minimalist protein model. When gatekeepers are eliminated, the thermodynamic signature of a folding intermediate emerges, and a marked decrease in folding efficiency is observed. We explain the prerequisites that determine the "strength" of a given gatekeeper. The investigated gatekeepers are found to have distinct functions, and to guide the folding and time-dependent packing of non-overlapping secondary structure elements in the protein. Gatekeepers avoid kinetic traps during folding by favoring the formation of "productive topologies" on the way to the native state. The trends in folding rates in the presence/absence of gatekeepers observed for our minimalist model of S6 are in very good agreement with experimental data on this protein.     

Using motion planning to study protein folding pathways.

We present a framework for studying protein folding pathways and potential landscapes which is based on techniques recently developed in the robotics motion planning community. Our focus in this work is to study the protein folding mechanism assuming we know the native fold. That is, instead of performing fold prediction, we aim to study issues related to the folding process, such as the formation of secondary and tertiary structure, and the dependence of the folding pathway on the initial denatured conformation. Our work uses probabilistic roadmap (PRM) motion planning techniques which have proven successful for problems involving high-dimensional configuration spaces. A strength of these methods is their efficiency in rapidly covering the planning space without becoming trapped in local minima. We have applied our PRM technique to several small proteins (~60 residues) and validated the pathways computed by comparing the secondary structure formation order on our paths to known hydrogen exchange experimental results. An advantage of the PRM framework over other simulation methods is that it enables one to easily and efficiently compute folding pathways from any denatured starting state to the (known) native fold. This aspect makes our approach ideal for studying global properties of the protein's potential landscape, most of which are difficult to simulate and study with other methods. For example, in the proteins we study, the folding pathways starting from different denatured states sometimes share common portions when they are close to the native fold, and moreover, the formation order of the secondary structure appears largely independent of the starting denatured conformation. Another feature of our technique is that the distribution of the sampled conformations is correlated with the formation of secondary structure and, in particular, appears to differentiate situations in which secondary structure clearly forms first and those in which the tertiary structure is obtained more directly. Overall, our results applying PRM techniques are very encouraging and indicate the promise of our approach for studying proteins for which experimental results are not available.