Native-state Topology Research Articles

Protein folding thermodynamics and dynamics: where physics, chemistry, and biology meet.

As was noted in our recent review 1 the protein folding field underwent a cyclic development. Initially protein folding was viewed as a strictly experimental field belonging to realm of biochemistry where each protein is viewed as a unique system that requires its own detailed characterization – akin to any mechanism in biology. The theoretical thinking at this stage of development of the field was dominated by the quest to solve so-called “Levinthal paradox” that posits that a protein could not find its native conformation by exhaustive random search. Introduction, in the early nineties, of simplified models to the protein folding field and their success in explaining several key aspects of protein folding, such as two-state folding of many proteins, the nucleation mechanism and its relation to native state topology, have pretty much shifted thinking towards views inspired by physics. The “physics”-centered approach focuses on statistical mechanical aspect of the folding problem by emphasizing universality of folding scenarios over the uniqueness of folding pathways for each protein. Its main achievement is a solution of the protein folding problem in principle, i.e. demonstration how proteins could fold. As a result, a “psychological” solution of the Levinthal paradox was found (i.e. it was generally understood that this is not a paradox. after all). The key success of this stage of the field is discovery of the general requirements for polypeptide sequences to be cooperatively foldable stable proteins and realization that such requirements can be achieved by sequence selection. That put the field strongly into the realm of biology (“Nothing in Biology makes sense except in the light of Evolution” (Theodosius Dobzhansky)) The physics-based fundamental approach to protein folding dominated theoretical thinking in the last decade (reviewed in 1-4) and its successes brought theory and experiment closer together At the present stage we seek better understanding of how protein folding problem is actually solved in Nature. In this sense the protein folding field has made a full circle as attention is again focused on specific proteins and details of their folding mechanism. However these questions are asked at a new level of sophistication of both theory and experiment. Understanding of general principles of folding and vastly improved computer power makes it possible to develop tractable models that sometimes achieve atomic level of accuracy. Further, better general understanding of requirement for polypeptide sequences to fold, lead to establishment of direct links between protein folding and evolution of their sequences This development opened an opportunity to employ powerful methods of bioinformatics to test predictions of various folding models, in addition to more traditional tests of models against experiment After all, evolution presents a giant natural laboratory where sequences are designed to fold and function and availability of vast amounts of data certainly calls for its use to better understand folding of proteins at very high resolution. At the same time in vitro experimental approaches progressed to the point that very accurate time- and structure- resolved data are available. A close interaction with experimentalists helps to keep theorists honest by providing detailed tests of theories and simulation results. In this review, which to a great extent reflects the thinking of the author on the subject, we will first summarize basic questions and present simple, coarse-grained models that provide a basis for a fundamental understanding of protein folding thermodynamics and kinetics. Then we will discuss more recent developments (over last five years) that focus on detailed studies of folding mechanisms of specific proteins, and finally we will briefly discuss some outstanding questions and future directions.

Do Proteins with Similar Folds Have Similar Transition State Structures? A Diffuse Transition State of the 169 Residue Apoflavodoxin

Apoflavodoxin from Anabaena PCC 7119 is a 169 residue globular protein of known structure and energetics. Here, we present a comprehensive Phi-value analysis to characterize the structure of its transition state. A total of 34 non-disruptive mutations are made throughout the structure and a range of Phi-values from zero to one are observed. In addition, a small set of eight aliphatic small-to-large mutations have been introduced in the hydrophobic core of the protein and they have been analyzed to investigate the feasibility of stabilizing the unfolding transition state by creating new non-native interactions. We find that the transition state of apoflavodoxin (so far the largest protein subjected to Phi-analysis) is diffuse and that it can be stabilized by unspecific hydrophobic interactions that can speed up the folding reaction. The data gathered on the apoflavodoxin transition state are compared with results from experimental studies in other proteins to revisit the relationship between the native state topology and transition state structure.

A simple measure of native‐state topology and chain connectivity predicts the folding rates of two‐state proteins with and without crosslinks

The folding rates of two-state proteins have been found to correlate with simple measures of native-state topology. The most prominent among these measures is the relative contact order (CO), which is the average CO, or localness, of all contacts in the native protein structure, divided by the chain length. Here, we test whether such measures can be generalized to capture the effect of chain crosslinks on the folding rate. Crosslinks change the chain connectivity and therefore also the localness of some of the native contacts. These changes in localness can be taken into account by the graph-theoretical concept of effective contact order (ECO). The relative ECO, however, the natural extension of the relative CO for proteins with crosslinks, overestimates the changes in the folding rates caused by crosslinks. We suggest here a novel measure of native-state topology, the relative logCO, and its natural extension, the relative logECO. The relative logCO is the average value for the logarithm of the CO of all contacts, divided by the logarithm of the chain length. The relative log(E)CO reproduces the folding rates of a set of 26 two-state proteins without crosslinks with essentially the same high correlation coefficient as the relative CO. In addition, it also captures the folding rates of eight two-state proteins with crosslinks.

A Statistical Method for Predicting Protein Unfolding Rates from Amino Acid Sequence

The prediction of protein unfolding rates from amino acid sequences is one of the most important challenges in computational biology and chemistry. The analysis on the relationship between protein unfolding rates and physical-chemical, energetic, and conformational properties of amino acid residues provides valuable information to understand and predict the unfolding rates of two- and three-state proteins. We found that the classification of proteins into different structural classes shows an excellent correlation between amino acid properties and unfolding rates of two- and three-state proteins, indicating the importance of native-state topology in determining the protein unfolding rates. We have formulated three independent linear regression equations to different structural classes of proteins for predicting their unfolding rates from amino acid sequences and obtained an excellent agreement between predicted and experimentally observed unfolding rates of proteins; the correlation coefficients are 0.999, 0.990, and 0.992, respectively, for all-alpha, all-beta, and mixed-class proteins. Further, we have derived a general equation applicable to all structural classes of proteins, which can be used for predicting the unfolding rates for proteins of an unknown structural class. We observed a correlation of 0.987 and 0.930, respectively, for back-check and jack-knife tests. These accuracy levels are better than those of other methods in the literature.

Pertactin β-helix folding mechanism suggests common themes for the secretion and folding of autotransporter proteins

Many virulence factors secreted from pathogenic Gram-negative bacteria are autotransporter proteins. The final step of autotransporter secretion is C --> N-terminal threading of the passenger domain through the outer membrane (OM), mediated by a cotranslated C-terminal porin domain. The native structure is formed only after this final secretion step, which requires neither ATP nor a proton gradient. Sequence analysis reveals that, despite size, sequence, and functional diversity among autotransporter passenger domains, >97% are predicted to form parallel beta-helices, indicating this structural topology may be important for secretion. We report the folding behavior of pertactin, an autotransporter passenger domain from Bordetella pertussis. The pertactin beta-helix folds reversibly in isolation, but folding is much slower than expected based on size and native-state topology. Surprisingly, pertactin is not prone to aggregation during folding, even though folding is extremely slow. Interestingly, equilibrium denaturation results in the formation of a partially folded structure, a stable core comprising the C-terminal half of the protein. Examination of the pertactin crystal structure does not reveal any obvious reason for the enhanced stability of the C terminus. In vivo, slow folding would prevent premature folding of the passenger domain in the periplasm, before OM secretion. Moreover, the extra stability of the C-terminal rungs of the beta-helix might serve as a template for the formation of native protein during OM secretion; hence, vectorial folding of the beta-helix could contribute to the energy-independent translocation mechanism. Coupled with the sequence analysis, the results presented here suggest a general mechanism for autotransporter secretion.

An Obligatory Intermediate in the Folding Pathway of Cytochromec552 from Hydrogenobacterthermophilus

The folding mechanism of many proteins involves the population of partially organized structures en route to the native state. Identification and characterization of these intermediates is particularly difficult, as they are often only transiently populated and may play different mechanistic roles, being either on-pathway productive species or off-pathway kinetic traps. Following different spectroscopic probes, and employing state-of-the-art kinetic analysis, we present evidence that the folding mechanism of the thermostable cytochrome c552 from Hydrogenobacter thermophilus does involve the presence of an elusive, yet compact, on-pathway intermediate. Characterization of the folding mechanism of this cytochrome c is particularly interesting for the purpose of comparative folding studies, because H. thermophilus cytochrome c552 shares high sequence identity and structural homology with its homologue from the mesophilic bacterium Pseudomonas aeruginosa cytochrome c551, which refolds through a broad energy barrier without the accumulation of intermediates. Analysis of the folding kinetics and correlation with the three-dimensional structure add new evidence for the validity of a consensus folding mechanism in the cytochrome c family.

The Native Energy Landscape for Interleukin-1β. Modulation of the Population Ensemble through Native-state Topology

A minimalist Go-model, with no energetic frustration in the native conformation, has been shown to describe accurately the folding pathway of the beta-trefoil protein, interleukin-1beta (IL-1beta). While it appears that these models successfully model transition states and intermediates between the unfolded and native ensembles, it is unclear how accurately they capture smaller, yet biologically relevant, structural changes within the native ensemble after energetic perturbation. Here, we address the following questions. Can a simple Go-model of interleukin-1beta, based on native topology, describe changes in structural properties of the native ensemble as the protein stability is changed? Or is it necessary to include a more explicit representation of atoms, electrostatic, hydrogen bonding, and van der Waals forces to describe these changes? The native ensemble of IL-1beta was characterized using a variety of experimental probes under native (0 M NaCl, guanidine hydrochloride (Gdn-HCl)), moderately destabilized (0 M NaCl, 0.8 M Gdn-HCl), and in moderate salt concentration (0.8 M NaCl, 0 M Gdn-HCl). Heteronuclear (1)H-(15)N nuclear Overhauser effect spectroscopy (NOESY) and heteronuclear single quantum correlation (HSQC) NMR spectra confirmed that the beta-trefoil global fold was largely intact under these three conditions. However, 25 of the 153 residues throughout the chain did demonstrate (13)C and (1)H-(15)N chemical shifts when perturbed with 0.8 M NaCl or Gdn-HCl. Despite large differences in protection factors from solvent hydrogen-deuterium exchange for all residues between stable (0 M Gdn-HCl) and destabilized (0.8 M Gdn-HCl) IL-1beta, no difference in steady-state (15)N-(1)H NOE enhancements were measured. Thus, the chemical shifts correlate with a global but limited increase in residue flexibility in the presence of Gdn-HCl. Minimalist simulations highlight the regions of greatest position shift between native and 0.8 M Gdn-HCl, which were determined experimentally. This correlation demonstrates that structural changes within the native ensemble of IL-1beta are, at least partially, governed by the principle of minimal energetic frustration.

A Statistical Model for Predicting Protein Folding Rates from Amino Acid Sequence with Structural Class Information

Prediction of protein folding rates from amino acid sequences is one of the most important challenges in molecular biology. In this work, I have related the protein folding rates with physical-chemical, energetic and conformational properties of amino acid residues. I found that the classification of proteins into different structural classes shows an excellent correlation between amino acid properties and folding rates of two- and three-state proteins, indicating the importance of native state topology in determining the protein folding rates. I have formulated a simple linear regression model for predicting the protein folding rates from amino acid sequences along with structural class information and obtained an excellent agreement between predicted and experimentally observed folding rates of proteins; the correlation coefficients are 0.99, 0.96 and 0.95, respectively, for all-alpha, all-beta and mixed class proteins. This is the first available method, which is capable of predicting the protein folding rates just from the amino acid sequence with the aid of generic amino acid properties and structural class information.

Monomer topology defines folding speed of heptamer.

Small monomeric proteins often fold in apparent two-state processes with folding speeds dictated by their native-state topology. Here we test, for the first time, the influence of monomer topology on the folding speed of an oligomeric protein: the heptameric cochaperonin protein 10 (cpn10), which in the native state has seven beta-barrel subunits noncovalently assembled through beta-strand pairing. Cpn10 is a particularly useful model because equilibrium-unfolding experiments have revealed that the denatured state in urea is that of a nonnative heptamer. Surprisingly, refolding of the nonnative cpn10 heptamer is a simple two-state kinetic process with a folding-rate constant in water (2.1 sec(-1); pH 7.0, 20 degrees C) that is in excellent agreement with the prediction based on the native-state topology of the cpn10 monomer. Thus, the monomers appear to fold as independent units, with a speed that correlates with topology, although the C and N termini are trapped in beta-strand pairing with neighboring subunits. In contrast, refolding of unfolded cpn10 monomers is dominated by a slow association step.

Does Native State Topology Determine the RNA Folding Mechanism?

Recent studies in protein folding suggest that native state topology plays a dominant role in determining the folding mechanism, yet an analogous statement has not been made for RNA, most likely due to the strong coupling between the ionic environment and conformational energetics that make RNA folding more complex than protein folding. Applying a distributed computing architecture to sample nearly 5000 complete tRNA folding events using a minimalist, atomistic model, we have characterized the role of native topology in tRNA folding dynamics: the simulated bulk folding behavior predicts well the experimentally observed folding mechanism. In contrast, single-molecule folding events display multiple discrete folding transitions and compose a largely diverse, heterogeneous dynamic ensemble. This both supports an emerging view of heterogeneous folding dynamics at the microscopic level and highlights the need for single-molecule experiments and both single-molecule and bulk simulations in interpreting bulk experimental measurements.

Unfolding of Globular Proteins: Monte Carlo Dynamics of a Realistic Reduced Model

Reduced lattice models of proteins and Monte Carlo dynamics were used to simulate the initial stages of the unfolding of several proteins of various structural types, and the results were compared to experiment. The models semiquantitatively reproduce the approximate order of events of unfolding as well as subtle mutation effects and effects resulting from differences in sequences of similar folds. The short-time mobility of particular residues, observed in simulations, correlates with the crystallographic temperature factor. The main factor controlling unfolding is the native state topology, with sequence playing a less important role. The correlation with various experiments, especially for sequence-specific effects, strongly suggests that properly designed reduced models of proteins can be used for qualitative studies (or prediction) of protein unfolding pathways.

Class-specific correlations between protein folding rate, structure-derived, and sequence-derived descriptors.

Small single-domain proteins that fold by simple two-state kinetics have been shown to exhibit a wide variation in their folding rates. It has been proposed that folding mechanisms in these proteins are largely determined by the native-state topology, and a significant correlation between folding rate and measures of the average topological complexity, such as relative contact order (RCO), has been reported. We perform a statistical analysis of folding rate and RCO in all three major structural classes (alpha, beta, and alpha/beta) of small two-state proteins and of RCO in groups of analogous and homologous small single-domain proteins with the same topology. We also study correlation between folding rate and the average physicochemical properties of amino acid sequences in two-state proteins. Our results indicate that 1) helical proteins have statistically distinguishable, class-specific folding rates; 2) RCO accounts for essentially all the variation of folding rate in helical proteins, but for only a part of the variation in beta-sheet-containing proteins; and 3) only a small fraction of the protein topologies studied show a topology-specific RCO. We also report a highly significant correlation between the folding rate and average intrinsic structural propensities of protein sequences. These results suggest that intrinsic structural propensities may be an important determinant of the rate of folding in small two-state proteins.

Interplay Among Tertiary Contacts, Secondary Structure Formation and Side-chain Packing in the Protein Folding Mechanism: All-atom Representation Study of Protein L

Experimental and theoretical results suggest that, since proteins are energetically minimally frustrated, the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble and on-pathway intermediate states in protein folding. Although the central role of native state topology in determining the folding mechanism is thought to be a quite general result—at least for small two-state folding proteins—there are remarkable exceptions. Recent experimental findings have shown that topology alone cannot always determine the folding mechanism, and demonstrated that the balance between topology and energetics is very delicate. This balance seems to be particularly critical in proteins with a highly symmetrical native structure, such as proteins L and G, which have similar native structure topology but fold by different mechanisms. Simplified, C α-atom only protein models have shown not be sufficient to differentiate these mechanisms. An all-atom Gō model provides a valuable intermediate model between structurally simplified protein representations and all-atom protein simulations with explicit/implicit solvent descriptions. We present here a detailed study of an all-atom Gō-like representation of protein L, in close comparison with the experimental results and with the results obtained from a simple C α-atom representation of the same protein. We also perform simulations for protein G, where we obtain a folding mechanism in which the protein symmetry is broken exactly in the opposite way to protein L as has been observed experimentally. A detailed analysis for protein L also shows that the role of specific residues is correctly and quantitatively reproduced by the all-atom Gō model over almost the entire protein.

Cooperativity, Smooth Energy Landscapes and the Origins of Topology-dependent Protein Folding Rates

The relative folding rates of simple, single-domain proteins, proteins whose folding energy landscapes are smooth, are highly dispersed and strongly correlated with native-state topology. In contrast, the relative folding rates of small, Gō-potential lattice polymers, which also exhibit smooth energy landscapes, are poorly dispersed and insignificantly correlated with native-state topology. Here, we investigate this discrepancy in light of a recent, quantitative theory of two-state folding kinetics, the topomer search model. This model stipulates that the topology-dependence of two-state folding rates is a direct consequence of the extraordinarily cooperative equilibrium folding of simple proteins. We demonstrate that traditional Gō polymers lack the extreme cooperativity that characterizes the folding of naturally occurring, two-state proteins and confirm that the folding rates of a diverse set of Gō 27-mers are poorly dispersed and effectively uncorrelated with native state topology. Upon modestly increasing the cooperativity of the Gō-potential, however, significantly increased dispersion and strongly topology-dependent kinetics are observed. These results support previous arguments that the cooperative folding of simple, single-domain proteins gives rise to their topology-dependent folding rates. We speculate that this cooperativity, and thus, indirectly, the topology–rate relationship, may have arisen in order to generate the smooth energetic landscapes upon which rapid folding can occur.

Folding Pathways of Prion and Doppel

The relevance of various residue positions for the stability and the folding characteristics of the prion protein in its normal cellular form are investigated by using molecular dynamics simulations of models exploiting the topology of the native state. These models allow for reproducing the experimentally validated two-state behavior of the normal prion isoform. Highly significant correlations are found between the most topologically relevant sites in our analysis and the single point mutations known to be associated with the arousal of the genetic forms of prion disease. Insight into the conformational change is provided by comparing the folding process of cellular prion and doppel that share a similar native state topology: the folding pathways of the former can be grouped in two main classes according to which tertiary structure contacts are formed first enroute to the native state. For the latter a single class of pathways leads to the native state again through a two-state process. Our results are consistent and supportive of the recent experimental findings that doppel lacks the scrapie isoform and that such remarkably different behavior involves residues in the region containing the two β-strands and the intervening helix.

Presence of the cofactor speeds up folding of Desulfovibrio desulfuricans flavodoxin.

Flavodoxin is an alpha/beta protein with a noncovalently bound flavin-mononucleotide (FMN) cofactor. The apo-protein adopts a structure identical to that of the holo-form, although there is more dynamics in the FMN-binding loops. The equilibrium unfolding processes of Azotobacter vinelandii apo-flavodoxin, and Desulfovibrio desulfuricans ATCC strain 27774 apo- and holo-flavodoxins involve rather stable intermediates. In contrast, we here show that both holo- and apo-forms of flavodoxin from D. desulfuricans ATCC strain 29577 (75% sequence similarity with the strain 27774 protein) unfold in two-state equilibrium processes. Moreover, the FMN cofactor remains bound to the unfolded holo-protein. The folding and unfolding kinetics for holo-flavodoxin exhibit two-state behavior, albeit an additional slower phase is present at very low denaturant concentrations. The extrapolated folding time in water for holo-flavodoxin, approximately 280 microsec, is in excellent agreement with that predicted from the protein's native-state topology. Unlike the holo-protein behavior, the folding and unfolding reactions for apo-flavodoxin are best described by two kinetic phases, with rates differing approximately 15-fold, suggesting the presence of a kinetic intermediate. Both folding phases for apo-flavodoxin are orders of magnitude slower (40- and 530-fold, respectively) than that for the holo-protein. We conclude that polypeptide-cofactor interactions in the unfolded state of D. desulfuricans strain 29577 flavodoxin alter the kinetic-folding path towards two-state and speed up the folding reaction.

Studies of Pseudomonas aeruginosa Azurin Mutants: Cavities in β-Barrel Do Not Affect Refolding Speed

Pseudomonas aeruginosa azurin is a blue-copper protein with a Greek-key fold. Removal of copper produces an apoprotein with the same structure as holoazurin. To address the effects on thermodynamic stability and folding dynamics caused by small cavities in a β-barrel, we have studied the behavior of the apo-forms of wild-type and two mutant (His-46-Gly and His-117-Gly) azurins. The equilibrium- and kinetic-folding and unfolding reactions appear as two-state processes for all three proteins. The thermodynamic stability of the two mutants is significantly decreased as compared with the stability of wild-type azurin, in accord with cavities in or near the hydrophobic interior having an overall destabilizing effect. Large differences are also found in the unfolding rates: the mutants unfold much faster than wild-type azurin. In contrast, the folding-rate constants are almost identical for the three proteins and closely match the rate-constant predicted from the native-state topology of azurin. We conclude that the topology is more important than equilibrium stability in determining the folding speed of azurin.

Role of Native-State Topology in the Stabilization of Intracellular Antibodies

The role played by the geometric position of each amino acid in the folding process of the immunoglobulin (Ig) variable domain is identified and measured through molecular dynamics simulations of models based on the topology of its native state. This measure allows identifying the parts of the protein that, for geometrical reasons, when mutated, would result in relevant protein stability changes. Simulations were performed without considering the covalent disulfide bond present in most of the Ig domains. The results are in good agreement with site-directed mutagenesis experiments on the folding of intracellular antibodies in which the disulfide bond does not form. We also found agreement with data on amino acid conservation in the Ig variable domain sequences. This indicates a new way for a rational approach to the design of intracellular antibodies more resistant to the suppression of the disulfide bond that occurs in the cytoplasm.

Prediction of folding mechanism for circular-permuted proteins

Recent theoretical and experimental studies have suggested that real proteins have sequences with sufficiently small energetic frustration that topological effects are central in determining the folding mechanism. A particularly interesting and challenging framework for exploring and testing the viability of these energetically unfrustrated models is the study of circular-permuted proteins. Here we present the results of the application of a topology-based model to the study of circular permuted SH3 and CI2, in comparison with the available experimental results. The folding mechanism of the permuted proteins emerging from our simulations is in very good agreement with the experimental observations. The differences between the folding mechanisms of the permuted and wild-type proteins seem then to be strongly related to the change in the native state topology.

Molecular dynamics studies on HIV-1 protease: Drug resistance and folding pathways

Drug resistance to HIV-1 protease involves the accumulation of multiple mutations in the protein. We investigate the role of these mutations by using molecular dynamics simulations that exploit the influence of the native-state topology in the folding process. Our calculations show that sites contributing to phenotypic resistance of FDA-approved drugs are among the most sensitive positions for the stability of partially folded states and should play a relevant role in the folding process. Furthermore, associations between amino acid sites mutating under drug treatment are shown to be statistically correlated. The striking correlation between clinical data and our calculations suggest a novel approach to the design of drugs tailored to bind regions crucial not only for protein function, but for folding as well. Proteins 2001;43:365–372. © 2001 Wiley-Liss, Inc.