The family feud: do proteins with similar structures fold via the same pathway?

Theoretical and experimental studies of protein folding have suggested that the topology of the native state may be the most important factor determining the folding pathway of a protein, independent of its specific amino acid sequence. To test this concept, many experimental studies have been carried out with the aim of comparing the folding pathways of proteins that possess similar tertiary structures, but divergent sequences. Many of these studies focus on quantitative comparisons of folding transition state structures, as determined by Phi(f) value analysis of folding kinetic data. In some of these studies, folding transition state structures are found to be highly conserved, whereas in others they are not. We conclude that folds displaying more conserved transition state structures may have the most restricted number of possible folding pathways and that folds displaying low transition state structural conservation possess many potential pathways for reaching the native state.     

Effects of the difference in the unfolded-state ensemble on the folding of Escherichia coli dihydrofolate reductase

The unfolded state of a protein is an ensemble of a large number of conformations ranging from fully extended to compact structures. To investigate the effects of the difference in the unfolded-state ensemble on protein folding, we have studied the structure, stability, and folding of "circular" dihydrofolate reductase (DHFR) from Escherichia coli in which the N and C-terminal regions are cross-linked by a disulfide bond, and compared the results with those of disulfide-reduced "linear" DHFR. Equilibrium studies by circular dichroism, difference absorption spectra, solution X-ray scattering, and size-exclusion chromatography show that whereas the native structures of both proteins are essentially the same, the unfolded state of circular DHFR adopts more compact conformations than the unfolded state of the linear form, even with the absence of secondary structure. Circular DHFR is more stable than linear DHFR, which may be due to the decrease in the conformational entropy of the unfolded state as a result of circularization. Kinetic refolding measurements by stopped-flow circular dichroism and fluorescence show that under the native conditions both proteins accumulate a burst-phase intermediate having the same structures and both fold by the same complex folding mechanism with the same folding rates. Thus, the effects of the difference in the unfolded state of circular and linear DHFRs on the refolding reaction are not observed after the formation of the intermediate. This suggests that for the proteins with close termini in the native structure, early compaction of a protein molecule to form a specific folding intermediate with the N and C-terminal regions in close proximity is a crucial event in folding. If there is an enhancement in the folding reflecting the reduction in the breadth of the unfolded-state ensemble for circular DHFR, this acceleration must occur in the sub-millisecond time-range.     

Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins

Recent experimental results suggest that the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble, at least for small, fast-folding proteins. To investigate the extent of the topological control of the folding process, we studied the folding of simplified models of five small globular proteins constructed using a Go-like potential to retain the information about the native structures but drastically reduce the energetic frustration and energetic heterogeneity among residue-residue native interactions. By comparing the structure of the transition state ensemble (experimentally determined by Phi-values) and of the intermediates with those obtained using our models, we show that these energetically unfrustrated models can reproduce the global experimentally known features of the transition state ensembles and "en-route" intermediates, at least for the analyzed proteins. This result clearly indicates that, as long as the protein sequence is sufficiently minimally frustrated, topology plays a central role in determining the folding mechanism.     

Improved Gō-like models demonstrate the robustness of protein folding mechanisms towards non-native interactions

The use of simple theoretical models has provided a considerable contribution to our present understanding of the means by which proteins adopt their native fold from the plethora of available unfolded states. A common assumption in building computationally tractable models has been the neglect of stabilizing non-native interactions in the class of models described as "Gō-like." The focus of this study is the characterization of the folding of a number of proteins via a Gō-like model, which aims to map a maximal amount of information reflecting the protein sequence onto a "minimalist" skeleton. This model is shown to contain sufficient information to reproduce the folding transition states of a number of proteins, including topologically analogous proteins that fold via different transition states. Remarkably, these models also demonstrate consistency with the general features of folding transition states thought to be stabilized by non-native interactions. This suggests that native interactions are the primary determinant of most protein folding transition states, and that non-native interactions lead only to local structural perturbations. A prediction is also included for an asymmetrical folding transition state of bacteriophage lambda protein W, which has yet to be subjected to experimental characterization.     

Protein topology affects the appearance of intermediates during the folding of proteins with a flavodoxin-like fold

The topology of a native protein influences the rate with which it is formed, but does topology affect the appearance of folding intermediates and their specific role in kinetic folding as well? This question is addressed by comparing the folding data recently obtained on apoflavodoxin from Azotobacter vinelandii with those available on all three other alpha-beta parallel proteins the kinetic folding mechanism of which has been studied, i.e. Anabaena apoflavodoxin, Fusarium solani pisi cutinase and CheY. Two kinetic folding intermediates, one on-pathway and the other off-pathway, seem to be present during the folding of proteins with an alpha-beta parallel, also called flavodoxin-like, topology. The on-pathway intermediate lies on a direct route from the unfolded to the native state of the protein involved. The off-pathway intermediate needs to unfold to allow the production of native protein. Available simulation data of the folding of CheY show the involvement of two intermediates with characteristics that resemble those of the two intermediates experimentally observed. Apparently, protein topology governs the appearance and kinetic roles of protein folding intermediates during the folding of proteins that have a flavodoxin-like fold.     

The cooperativity of burst phase reactions explored.

The denaturant-dependence of the major, observable relaxation rates for folding (kobs) of ribonuclease HI from Escherichia coli (RNase H) and phage T4 lysozyme (T4L) reveal that, for both proteins, folding begins with the rapid and transient accumulation of intermediate species in a "burst phase" which precedes the rate-limiting formation of the native state; this is evidenced by a "rollover" in the folding limb of the rate profiles (kobs versus denaturant, or chevron plot). These rate profiles are most simply described by a three-state mechanism (unfolded-to-intermediate-to-native), which implies that the burst phase represents a transition between two distinct thermodynamic states. It is shown here that the equilibrium properties of these burst phase reactions can be equally well modeled by a mechanism involving a continuum of states where the free energy of each state is linearly related to its m-value (the parameter describing the linear relationship between free energy and denaturant). A numerical model is also developed to describe the time evolution of such a system, which exhibits nearly perfect exponential behavior. Both models emphasize how a continuum of states operating under a linear free energy relationship may behave like a two state system. Such a scheme finds experimental justification from an interpretation of recent native state hydrogen exchange data. The analytical model described for a continuum can account for the observed kinetic profiles of several other model proteins. The results, however, appear context specific, suggesting that burst phase reactions are not entirely random and non-specific. The results reported in this study have important implications for the concept of cooperativity in protein folding reactions.     

Commitment and nucleation in the protein G transition state

An accurate characterization of the transition state ensemble (TSE) is central to furthering our understanding of the protein folding reaction. We have extensively tested a recently reported method for studying a protein's TSE, utilizing phi-value data from protein engineering experiments and computational studies as restraints in all-atom Monte Carlo (MC) simulations. The validity of interpreting experimental phi-values as the fraction of native contacts made by a residue in the TSE was explored, revealing that this definition is unable to uniquely specify a TSE. The identification of protein G's second hairpin, in both pre and post-transition conformations demonstrates that high experimental phi-values do not guarantee a residue's importance in the TSE. An analysis of simulations based on structures restrained by experimental phi-values is necessary to yield this result, which is not obvious from a simplistic interpretation of individual phi-values. The TSE that we obtain corresponds to a single, specific nucleation event, characterized by six residues common to all three observed, convergent folding pathways. The same specific nucleus was independently identified from computational and experimental data, and "Conservation of Conservation" analysis in the protein G fold. When associated strictly with complete nucleus formation and concomitant chain collapse, folding is a well-defined two state event. Once the nucleus has formed, the folding reaction enters a slow relaxation process associated with side-chain packing and small, local backbone rearrangements. A detailed analysis of phi-values and their relationship to the transition state ensemble allows us to construct a unified theoretical model of protein G folding.     

The folding mechanics of a knotted protein

An increasing number of proteins are being discovered with a remarkable and somewhat surprising feature, a knot in their native structures. How the polypeptide chain is able to "knot" itself during the folding process to form these highly intricate protein topologies is not known. Here we perform a computational study on the 160-amino-acid homodimeric protein YibK, which, like other proteins in the SpoU family of MTases, contains a deep trefoil knot in its C-terminal region. In this study, we use a coarse-grained C(alpha)-chain representation and Langevin dynamics to study folding kinetics. We find that specific, attractive nonnative interactions are critical for knot formation. In the absence of these interactions, i.e., in an energetics driven entirely by native interactions, knot formation is exceedingly unlikely. Further, we find, in concert with recent experimental data on YibK, two parallel folding pathways that we attribute to an early and a late formation of the trefoil knot, respectively. For both pathways, knot formation occurs before dimerization. A bioinformatics analysis of the SpoU family of proteins reveals further that the critical nonnative interactions may originate from evolutionary conserved hydrophobic segments around the knotted region.     

Protein folding pathways and kinetics: molecular dynamics simulations of beta-strand motifs

The folding pathways and the kinetic properties for three different types of off-lattice four-strand antiparallel beta-strand protein models interacting via a hybrid Go-type potential have been investigated using discontinuous molecular dynamics simulations. The kinetic study of protein folding was conducted by temperature quenching from a denatured or random coil state to a native state. The progress parameters used in the kinetic study include the squared radius of gyration R(2)(g), the fraction of native contacts within the protein as a whole Q, and between specific strands Q(ab). In the time series of folding, the denatured proteins undergo a conformational change toward the native state. The model proteins exhibit a variety of kinetic folding pathways that include a fast-track folding pathway without passing through an intermediate and multiple pathways with trapping into more than one intermediate. The kinetic folding behavior of the beta-strand proteins strongly depends on the native-state geometry of the model proteins and the size of the bias gap g, an artificial measure of a model protein's preference for its native state.     

Predicting protein folding rates from geometric contact and amino acid sequence

Protein folding speeds are known to vary over more than eight orders of magnitude. Plaxco, Simons, and Baker (see References) first showed a correlation of folding speed with the topology of the native protein. That and subsequent studies showed, if the native structure of a protein is known, its folding speed can be predicted reasonably well through a correlation with the "localness" of the contacts in the protein. In the present work, we develop a related measure, the geometric contact number, N (alpha), which is the number of nonlocal contacts that are well-packed, by a Voronoi criterion. We find, first, that in 80 proteins, the largest such database of proteins yet studied, N (alpha) is a consistently excellent predictor of folding speeds of both two-state fast folders and more complex multistate folders. Second, we show that folding rates can also be predicted from amino acid sequences directly, without the need to know the native topology or other structural properties.     

Critical nucleation size in the folding of small apparently two-state proteins

For apparently two-state proteins, we found that the size (number of folded residues) of a transition state is mostly encoded by the topology, defined by total contact distance (TCD) of the native state, and correlates with its folding rate. This is demonstrated by using a simple procedure to reduce the native structures of the 41 two-state proteins with native TCD as a constraint, and is further supported by analyzing the results of eight proteins from protein engineering studies. These results support the hypothesis that the major rate-limiting process in the folding of small apparently two-state proteins is the search for a critical number of residues with the topology close to that of the native state.     

Routes are trees: the parsing perspective on protein folding

An important puzzle in structural biology is the question of how proteins are able to fold so quickly into their unique native structures. There is much evidence that protein folding is hierarchic. In that case, folding routes are not linear, but have a tree structure. Trees are commonly used to represent the grammatical structure of natural language sentences, and chart parsing algorithms efficiently search the space of all possible trees for a given input string. Here we show that one such method, the CKY algorithm, can be useful both for providing novel insight into the physical protein folding process, and for computational protein structure prediction. As proof of concept, we apply this algorithm to the HP lattice model of proteins. Our algorithm identifies all direct folding route trees to the native state and allows us to construct a simple model of the folding process. Despite its simplicity, our model provides an account for the fact that folding rates depend only on the topology of the native state but not on sequence composition.     

Energy barriers, cooperativity, and hidden intermediates in the folding of small proteins

Current theoretical views of the folding process of small proteins (< approximately 100 amino acids) postulate that the landscape of potential mean force (PMF) for the formation of the native state has a funnel shape and that the free energy barrier to folding arises from the chain configurational entropy only. However, recent theoretical studies on the formation of hydrophobic clusters with explicit water suggest that a barrier should exist on the PMF of folding, consistent with the fact that protein folding generally involves a large positive activation enthalpy at room temperature. In addition, high-resolution structural studies of the hidden partially unfolded intermediates have revealed the existence of non-native interactions, suggesting that the correction of the non-native interactions during folding should also lead to barriers on PMF. To explore the effect of a PMF barrier on the folding behavior of proteins, we modified Zwanzig's model for protein folding with an uphill landscape of PMF for the formation of transition states. We found that the modified model for short peptide segments can satisfy the thermodynamic and kinetic criteria for an apparently two-state folding. Since the Levinthal paradox can be solved by a stepwise folding of short peptide segments, a landscape of PMF with a locally uphill search for the transition state and cooperative stabilization of folding intermediates/native state is able to explain the available experimental results for small proteins. We speculate that the existence of cooperative hidden folding intermediates in small proteins could be the consequence of the highly specific structures of the native state, which are selected by evolution to perform specific functions and fold in a biologically meaningful time scale.     

A critical assessment of the topomer search model of protein folding using a continuum explicit-chain model with extensive conformational sampling

Recently, a series of closely related theoretical constructs termed the "topomer search model" (TSM) has been proposed for the folding mechanism of small, single-domain proteins. A basic assumption of the proposed scenarios is that the rate-limiting step in folding is an essentially unbiased, diffusive search for a conformational state called the native topomer defined by an overall native-like topological pattern. Successes in correlating TSM-predicted folding rates with that of real proteins have been interpreted as experimental support for the model. To better delineate the physics entailed, key TSM concepts are examined here using extensive Langevin dynamics simulations of continuum C(alpha) chain models. The theoretical native topomers of four experimentally well-studied two-state proteins are characterized. Consistent with the TSM perspective, we found that the sizes of the native topomers increase with experimental folding rate. However, a careful determination of the corresponding probabilities that the native topomers are populated during a random search fails to reproduce the previously predicted folding rates. Instead, our results indicate that an unbiased TSM search for the native topomer amounts to a Levinthal-like process that would take an impossibly long average time to complete. Furthermore, intraprotein contacts in all four native topomers considered exhibit no apparent correlation with the experimental phi-values determined from the folding kinetics of these proteins. Thus, the present findings suggest that certain basic, generic yet essential energetic features in protein folding are not accounted for by TSM scenarios to date.     

The metastable states of proteins

The intriguing process of protein folding comprises discrete steps that stabilize the protein molecules in different conformations. The metastable state of protein is represented by specific conformational characteristics, which place the protein in a local free energy minimum state of the energy landscape. The native‐to‐metastable structural transitions are governed by transient or long‐lived thermodynamic and kinetic fluctuations of the intrinsic interactions of the protein molecules. Depiction of the structural and functional properties of metastable proteins is not only required to understand the complexity of folding patterns but also to comprehend the mechanisms of anomalous aggregation of different proteins. In this article, we review the properties of metastable proteins in context of their stability and capability of undergoing atypical aggregation in physiological conditions.     

Hydration and protein folding in water and in reverse micelles: compressibility and volume changes

The partial specific volume and adiabatic compressibility of proteins reflect the hydration properties of the solvent-exposed protein surface, as well as changes in conformational states. Reverse micelles, or water-in-oil microemulsions, are protein-sized, optically-clear microassemblies in which hydration can be experimentally controlled. We explore, by densimetry and ultrasound velocimetry, three basic proteins: cytochrome c, lysozyme, and myelin basic protein in reverse micelles made of sodium bis (2-ethylhexyl) sulfosuccinate, water, and isooctane and in aqueous solvents. For comparison, we use beta-lactoglobulin (pI = 5.1) as a reference protein. We examine the partial specific volume and adiabatic compressibility of the proteins at increasing levels of micellar hydration. For the lowest water content compatible with complete solubilization, all proteins display their highest compressibility values, independent of their amino acid sequence and charge. These values lie within the range of empirical intrinsic protein compressibility estimates. In addition, we obtain volumetric data for the transition of myelin basic protein from its initially unfolded state in water free of denaturants, to a folded, compact conformation within the water-controlled microenvironment of reverse micelles. These results disclose yet another aspect of the protein structural properties observed in membrane-mimetic molecular assemblies.     

Identification and characterization of folding inhibitors of hen egg lysozyme: an example of a new paradigm of drug design

Studies of protein folding indicate the presence of native contacts in the denatured state, giving rise to folding elements which contribute to the accomplishment of the native state. The possibility of finding molecules which can interact with specific folding elements of a target protein preventing it from reaching its native state, and hence from becoming biologically active, is particularly attractive. The notion that folding elements not only provide molecular recognition directing the folding process, but also have conserved sequence, implies that targeting such elements will make protein folding inhibitors less susceptible to mutations which, in many cases, abrogate drug effects. The folding-inhibition strategy can lead to a truly novel and rational approach to drug design, aside from providing new insight into folding. This is illustrated in the case of hen egg lysozyme.     

Effect of Substitutions in Surface Amino Acid on Energy Profile of Apomyoglobin

Studies on the process of spontaneous protein folding into a unique native state are an important issue of molecular biology. Apomyoglobin from the sperm whale is a convenient model for these studies in vitro. Here, we present the results of equilibrium and kinetic experiments carried out in a study on the folding and unfolding of eight mutant apomyoglobin forms of with hydrophobic amino acid substitutions on the protein surface. Calculated values of apparent constants of folding/unfolding rates, as well as the data on equilibrium conformational transitions in the urea concentration range of 0–6 M at 11°C are given. Based on the obtained information on the kinetic properties of the studied proteins, a Φ-value analysis of the transition state has been performed and values of urea concentrations corresponding to the midpoint of the transition from the native to intermediate state have been determined for the given forms of mutant apomyoglobin. It has been found that a significant increase in the stability of the native state can be achieved by a small number of amino acid substitutions on the protein surface. It has been shown that the substitution of only one amino acid residue exclusively affects the height of the energy barrier that separates different states of apomyoglobin.     

Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

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.