Folding of circular permutants with decreased contact order: general trend balanced by protein stability

Protein engineering using circular permutation - structure, function, stability, and applications

Protein engineering is important for creating novel variants from natural proteins, enabling a wide range of applications. Approaches such as rational design and directed evolution are routinely used to make new protein variants. Computational tools like de novo design can introduce new protein folds. Expanding the amino acid repertoire to include unnatural amino acids with non-canonical side chains in vitro by native chemical ligation and in vivo via codon expansion methods broadens sequence and structural possibilities. Circular permutation (CP) is an invaluable approach to redesigning a protein by rearranging the amino acid sequence, where the connectivity of the secondary structural elements is altered without changing the overall structure of the protein. Artificial CP proteins (CPs) are employed in various applications such as biocatalysis, sensing of small molecules by fluorescence, genome editing, ligand-binding protein switches, and optogenetic engineering. Many studies have shown that CP can lead to either reduced or enhanced stability or catalytic efficiency. The effects of CP on a protein's energy landscape cannot be predicted a priori. Thus, it is important to understand how CP can affect the thermodynamic and kinetic stability of a protein. In this review, we discuss the discovery and advancement of techniques to create protein CP, and existing reviews on CP. We delve into the plethora of biological applications for designed CP proteins. We subsequently discuss the experimental and computational reports on the effects of CP on the thermodynamic and kinetic stabilities of proteins of various topologies. An understanding of the various aspects of CP will allow the reader to design robust CP proteins for their specific purposes.

Circular permutation at azurin's active site slows down its folding

Circular permutation (CP) is a technique by which the primary sequence of a protein is rearranged to create new termini. The connectivity of the protein is altered but the overall protein structure generally remains unperturbed. Understanding the effect of CP can help design robust proteins for numerous applications such as in genetic engineering, optoelectronics, and improving catalytic activity. Studies on different protein topologies showed that CP usually affects protein stability as well as unfolding rates. Though a significant number of proteins contain metals or other cofactors, reports of metalloprotein CPs are rare. Thus, we chose a bacterial metalloprotein, azurin, and its CP within the metal-binding site (cpF114). We studied the stabilities, folding, and unfolding rates of apo- and Zn2+-bound CP azurin using fluorescence and circular dichroism. The introduced CP had destabilizing effects on the protein. Also, the folding of the Zn2+-CP protein was much slower than that of the Zn2+-WT or apo-protein. We compared this study to our previously reported azurin-cpN42, where we had observed an equilibrium and kinetic intermediate. cpF114 exhibits an apparent two-state equilibrium unfolding but has an off-pathway kinetic intermediate. Our study hinted at CP as a method to modify the energy landscape of proteins to alter their folding pathways. WT azurin, being a faster folder, may have evolved to optimize the folding rate of metal-bound protein compared to its CPs, albeit all of them have the same structure and function. Our study underscores that protein sequence and protein termini positions are crucial for metalloproteins. TOC Figure. (Top) Zn2+-azurin WT structure (PDB code: 1E67) and 2-D topology diagram of Zn2+-cpF114 azurin. (Bottom) Cartoon diagram representing folding (red arrows) and unfolding (blue arrows) of apo- and Zn2+- WT and cpF114 azurins. The width of the arrows represents the rate of the corresponding processes.

Metal-binding and circular permutation-dependent thermodynamic and kinetic stability of azurin

Native topology is known to determine the folding kinetics and the energy landscape of proteins. Furthermore, the circular permutation (CP) of proteins alters the order of the secondary structure connectivity while retaining the three-dimensional structure, making it an elegant and powerful approach to altering native topology. Previous studies elucidated the influence of CP in proteins with different folds such as Greek key β-barrel, β-sandwich, β-α-β, and all α-Greek key. CP mainly affects the protein stability and unfolding kinetics, while folding kinetics remains mostly unaltered. However, the effect of CP on metalloproteins is yet to be elaborately studied. The active site of metalloproteins poses an additional complexity in studying protein folding. Here, we investigate a CP variant (cpN42) of azurin-in both metal-free and metal-bound (holo) forms. As observed earlier in other proteins, apo-forms of wild-type (WT) and cpN42 fold with similar rates. In contrast, zinc-binding accelerates the folding of WT but decelerates the folding of cpN42. On zinc-binding, the spontaneous folding rate of WT increases by >250 times that of cpN42, which is unprecedented and the highest for any CP to date. On the other hand, zinc-binding reduces the spontaneous unfolding rate of cpN42 by ~100 times, making the WT and CP azurins unfold at similar rates. Our study demonstrates metal binding as a novel way to modulate the unfolding and folding rates of CPs compared to their WT counterparts. We hope our study increases the understanding of the effect of CP on the folding mechanism and energy landscape of metalloproteins.

Circuit topology predicts pathogenicity of missense mutations

The contact topology of a protein determines important aspects of the folding process. The topological measure of contact order has been shown to be predictive of the rate of folding. Circuit topology is emerging as another fundamental descriptor of biomolecular structure, with predicted effects on the folding rate. We analyze the residue‐based circuit topological environments of 21 K mutations labeled as pathogenic or benign. Multiple statistical lines of reasoning support the conclusion that the number of contacts in two specific circuit topological arrangements, namely inverse parallel and cross relations, with contacts involving the mutated residue have discriminatory value in determining the pathogenicity of human variants. We investigate how results vary with residue type and according to whether the gene is essential. We further explore the relationship to a number of structural features and find that circuit topology provides nonredundant information on protein structures and pathogenicity of mutations. Results may have implications for the polymer physics of protein folding and suggest that “local” topological information, including residue‐based circuit topology and residue contact order, could be useful in improving state‐of‐the‐art machine learning algorithms for pathogenicity prediction.

Slowest-first protein translation scheme: Structural asymmetry and co-translational folding

Proteins are translated from the N to the C terminus, raising the basic question of how this innate directionality affects their evolution. To explore this question, we analyze 16,200 structures from the Protein Data Bank (PDB). We find remarkable enrichment of α helices at the C terminus and β strands at the N terminus. Furthermore, this α-β asymmetry correlates with sequence length and contact order, both determinants of folding rate, hinting at possible links to co-translational folding (CTF). Hence, we propose the "slowest-first" scheme, whereby protein sequences evolved structural asymmetry to accelerate CTF: the slowest of the cooperatively folding segments are positioned near the N terminus so they have more time to fold during translation. A phenomenological model predicts that CTF can be accelerated by asymmetry in folding rate, up to double the rate, when folding time is commensurate with translation time; analysis of the PDB predicts that structural asymmetry is indeed maximal in this regime. This correspondence is greater in prokaryotes, which generally require faster protein production. Altogether, this indicates that accelerating CTF is a substantial evolutionary force whose interplay with stability and functionality is encoded in secondary structure asymmetry.

Design of a structure-based model for protein folding from flexible conformations

We introduce a coarse-grained, structure-based model for protein folding that considers the flexibility of the native state in the definition of the model interactions.

Contact Order Is a Determinant for the Dependence of GFP Folding on the Chaperonin GroEL

The GroE chaperonin system facilitates protein folding in an ATP-dependent manner. It has remained unclear why some proteins are obligate clients of the GroE system, whereas other closely related proteins are able to fold efficiently in its absence. Factors that cause folding to be slower affect kinetic partitioning between spontaneous folding and chaperone binding in favor of the latter. One such potential factor is contact order (CO), which is the average separation in sequence between residues that are in contact in the native structure. Here, we generated variants of enhanced green fluorescent protein with different COs using circular permutations. We found that GroE dependence in vitro and in vivo increases with increasing CO. Thus, our results show that CO is relevant not only for folding in vitro of relatively simple model systems but also for chaperonin dependence and folding in vivo.

Contribution to the prediction of the fold code: application to immunoglobulin and flavodoxin cases

Background

Folding nucleus of globular proteins formation starts by the mutual interaction of a group of hydrophobic amino acids whose close contacts allow subsequent formation and stability of the 3D structure. These early steps can be predicted by simulation of the folding process through a Monte Carlo (MC) coarse grain model in a discrete space. We previously defined MIRs (Most Interacting Residues), as the set of residues presenting a large number of non-covalent neighbour interactions during such simulation. MIRs are good candidates to define the minimal number of residues giving rise to a given fold instead of another one, although their proportion is rather high, typically [15-20]% of the sequences. Having in mind experiments with two sequences of very high levels of sequence identity (up to 90%) but different folds, we combined the MIR method, which takes sequence as single input, with the “fuzzy oil drop” (FOD) model that requires a 3D structure, in order to estimate the residues coding for the fold. FOD assumes that a globular protein follows an idealised 3D Gaussian distribution of hydrophobicity density, with the maximum in the centre and minima at the surface of the “drop”. If the actual local density of hydrophobicity around a given amino acid is as high as the ideal one, then this amino acid is assigned to the core of the globular protein, and it is assumed to follow the FOD model. Therefore one obtains a distribution of the amino acids of a protein according to their agreement or rejection with the FOD model.

Results

We compared and combined MIR and FOD methods to define the minimal nucleus, or keystone, of two populated folds: immunoglobulin-like (Ig) and flavodoxins (Flav). The combination of these two approaches defines some positions both predicted as a MIR and assigned as accordant with the FOD model. It is shown here that for these two folds, the intersection of the predicted sets of residues significantly differs from random selection. It reduces the number of selected residues by each individual method and allows a reasonable agreement with experimentally determined key residues coding for the particular fold. In addition, the intersection of the two methods significantly increases the specificity of the prediction, providing a robust set of residues that constitute the folding nucleus.

The response of Greek key proteins to changes in connectivity depends on the nature of their secondary structure

What governs the balance between connectivity and topology in regulating the mechanism of protein folding? We use circular permutation to vary the order of the helices in the all-α Greek key protein FADD (Fas-associated death domain) to investigate this question. Unlike all-β Greek key proteins, where changes in the order of secondary structure cause a shift in the folding nucleus, the position of the nucleus in FADD is unchanged, even when permutation reduces the complexity significantly. We suggest that this is because local helical contacts are so dominant that permutation has little effect on the entropic cost of forming the folding nucleus whereas, in all-β Greek key proteins, all interactions in the nucleus are long range. Thus, the type of secondary structure modulates the sensitivity of proteins to changes in connectivity.

Modulation of a protein free-energy landscape by circular permutation

Circular permutations usually retain the native structure and function of a protein while inevitably perturbing its folding dynamics. By using simulations with a structure-based model and a rigorous methodology to determine free-energy surfaces from trajectories, we evaluate the effect of a circular permutation on the free-energy landscape of the protein T4 lysozyme. We observe changes which, although subtle, largely affect the cooperativity between the two subdomains. Such a change in cooperativity has been previously experimentally observed and recently also characterized using single molecule optical tweezers and the Crooks relation. The free-energy landscapes show that both the wild type and circular permutant have an on-pathway intermediate, previously experimentally characterized, in which one of the subdomains is completely formed. The landscapes, however, differ in the position of the rate-limiting step for folding, which occurs before the intermediate in the wild type and after in the circular permutant. This shift of transition state explains the observed change in the cooperativity. The underlying free-energy landscape thus provides a microscopic description of the folding dynamics and the connection between circular permutation and the loss of cooperativity experimentally observed.

Folding circular permutants of IL-1β: route selection driven by functional frustration

Interleukin-1β (IL-1β) is the cytokine crucial to inflammatory and immune response. Two dominant routes are populated in the folding to native structure. These distinct routes are a result of the competition between early packing of the functional loops versus closure of the β-barrel to achieve efficient folding and have been observed both experimentally and computationally. Kinetic experiments on the WT protein established that the dominant route is characterized by early packing of geometrically frustrated functional loops. However, deletion of one of the functional loops, the β-bulge, switches the dominant route to an alternative, yet, as accessible, route, where the termini necessary for barrel closure form first. Here, we explore the effect of circular permutation of the WT sequence on the observed folding landscape with a combination of kinetic and thermodynamic experiments. Our experiments show that while the rate of formation of permutant protein is always slower than that observed for the WT sequence, the region of initial nucleation for all permutants is similar to that observed for the WT protein and occurs within a similar timescale. That is, even permutants with significant sequence rearrangement in which the functional-nucleus is placed at opposing ends of the polypeptide chain, fold by the dominant WT "functional loop-packing route", despite the entropic cost of having to fold the N- and C- termini early. Taken together, our results indicate that the early packing of the functional loops dominates the folding landscape in active proteins, and, despite the entropic penalty of coalescing the termini early, these proteins will populate an entropically unfavorable route in order to conserve function. More generally, circular permutation can elucidate the influence of local energetic stabilization of functional regions within a protein, where topological complexity creates a mismatch between energetics and topology in active proteins.

The HD-exchange motions of ribosomal protein S6 are insensitive to reversal of the protein-folding pathway

An increasing number of protein structures are found to encompass multiple folding nuclei, allowing their structures to be formed by several competing pathways. A typical example is the ribosomal protein S6, which comprises two folding nuclei (sigma1 and sigma2) defining two competing pathways in the folding energy landscape: sigma1 --> sigma2 and sigma2 --> sigma1. The balance between the two pathways, and thus the order of folding events, is easily controlled by circular permutation. In this study, we make use of this ability to manipulate the folding pathway to demonstrate that the dynamic motions of the S6 structure are independent of how the protein folds. The HD-exchange protection factors remain the same upon complete reversal of the folding order. The phenomenon arises because the HD-exchange motions and the high-energy excitations controlling the folding pathway occur at separated free-energy levels: the Boltzmann distribution of unproductive unfolding attempts samples all unfolding channels in parallel, even those that end up in excessively high barriers. Accordingly, the findings provide a simple rationale for how to interpret native-state dynamics without the need to invoke fluctuations off the normal unfolding reaction coordinate.

Prediction of the protein folding core: application to the immunoglobulin fold

We propose an algorithm that allows predicting residues important for the formation of the structure of globular proteins. It relies on a simulation that detects the amino acids presenting a maximum number of neighbours during the early steps of the folding process. They have been called MIR (Most Interacting Residues). Independently, description of the protein structures in fragments with closed ends shows the correlation between these extremities and the core of the globules. These fragments are of rather constant length, typically between 20 and 25 amino acids, and we have previously shown that their extremities are preferentially occupied by MIR. Introduction of rules derived from this fragment analysis of tertiary structures allows to smooth the distribution of MIR, for a better match between TEF ends and MIR. In order to assess this prediction of the folding core, a large family of structures has been used, with sequences as different as possible. A dataset of 56 immunoglobulin structures of various functions but common fold has been used in this study. This fold was chosen because it is one of the most populated with a large amount of data available on its nucleus. In the immunoglobulin domain, "functional and structural load is clearly separated: loops are responsible for binding and recognition while interactions between several residues of the buried core provide stability and fast folding"[1]. We then determined the positions susceptible of high importance for the folding process to occur and compared them to published data, either to High Throw Out Order (HTOO), Conservatism of Conservatism (CoC) or Phi value experiments. It results a reasonable agreement between the positions that we predict and experimental data. Besides, our prediction goes beyond the simple use of a null solvent accessibility of amino acids as a criterion to predict the core. We find the same quality of our prediction on the flavodoxin like superfamily.

Folding and misfolding in a naturally occurring circularly permuted PDZ domain

One of the most extreme and fascinating examples of naturally occurring mutagenesis is represented by circular permutation. Circular permutations involve the linking of two chain ends and cleavage at another site. Here we report the first description of the folding mechanism of a naturally occurring circularly permuted protein, a PDZ domain from the green alga Scenedesmus obliquus. Data reveal that the folding of the permuted protein is characterized by the presence of a low energy off-pathway kinetic trap. This finding contrasts with what was previously observed for canonical PDZ domains that, although displaying a similar primary structure when structurally re-aligned, fold via an on-pathway productive intermediate. Although circular permutation of PDZ domains may be necessary for a correct orientation of their functional sites in multi-domain protein scaffolds, such structural rearrangement may compromise their folding pathway. This study provides a straightforward example of the divergent demands of folding and function.

Loop-closure principles in protein folding

Simple theoretical concepts and models have been helpful to understand the folding rates and routes of single-domain proteins. As reviewed in this article, a physical principle that appears to underly these models is loop closure.

Folding behavior of ribosomal protein S6 studied by modified Gō-like model

Recent experimental and theoretical studies suggest that, although topology is the determinant factor in protein folding, especially for small single-domain proteins, energetic factors also play an important role in the folding process. The ribosomal protein S6 has been subjected to intensive studies. A radical change of the transition state in its circular permutants has been observed, which is believed to be caused by a biased distribution of contact energies. Since the simplistic topology-only Gō-like model is not able to reproduce such an observation, we modify the model by introducing variable contact energies between residues based on their physicochemical properties. The modified Gō-like model can successfully reproduce the Phi-value distributions, folding nucleus, and folding pathways of both the wild-type and circular permutants of S6. Furthermore, by comparing the results of the modified and the simplistic models, we find that the hydrophobic effect constructs the major force that balances the loop entropies. This may indicate that nature maintains the folding cooperativity of this protein by carefully arranging the location of hydrophobic residues in the sequence. Our study reveals a strategy or mechanism used by nature to get out of the dilemma when the native structure, possibly required by biological function, conflicts with folding cooperativity. Finally, the possible relationship between such a design of nature and amyloidosis is also discussed.

Folding of S6 structures with divergent amino acid composition: pathway flexibility within partly overlapping foldons

Studies of circular permutants have demonstrated that the folding reaction of S6 from Thermus thermophilus (S6(T)) is malleable and responds in an ordered manner to changes of the sequence separation between interacting residues: the S6(T) permutants retain a common nucleation pattern in the form of a two-strand-helix motif that can be recruited from different parts of the structure. To further test the robustness of the two-strand-helix nucleus we have here determined the crystal structure and folding reaction of an evolutionary divergent S6 protein from the hyperthermophilic bacterium Aquifex aeolicus (S6(A)). Although the overall topology of S6(A) is very similar to that of S6(T) the architecture of the hydrophobic core is radically different by containing a large proportion of stacked Phe side-chains. Despite this disparate core composition, the folding rate constant and the kinetic m values of S6(A) are identical to those of S6(T). The folding nucleus of S6(A) is also found to retain the characteristic two-strand-helix motif of the S6(T) permutants, but with a new structural emphasis. The results suggest that the protein folding reaction is linked to topology only in the sense that the native-state topology determines the repertoire of accessible nucleation motifs. If the native structure allows several equivalent ways of recruiting a productive nucleus the folding reaction is free to redistribute within these topological constraints.

Minimalist protein model as a diagnostic tool for misfolding and aggregation

We propose a realistic coarse-grained protein model and a technique to "anchor" the model to available experimental data. We apply this procedure to characterize the effect of multiple mutations on the folding mechanism of protein S6. We show that the mutation of a few "gatekeeper" residues triggers significant changes on the folding landscape of S6. These results suggest that gatekeeper residues control the flexibility of critical regions of S6, that in turn regulates the delicate balance between folding and aggregation. Although obtained with a minimalist protein model, these results are fully consistent with experimental evidence and offer a clue to understand the interplay between folding and aggregation in protein S6.

Common Motifs and Topological Effects in the Protein Folding Transition State

Through extensive experiment, simulation, and analysis of protein S6 (1RIS), we find that variations in nucleation and folding pathway between circular permutations are determined principally by the restraints of topology and specific nucleation, and affected by changes in chain entropy. Simulations also relate topological features to experimentally measured stabilities. Despite many sizable changes in phi values and the structure of the transition state ensemble that result from permutation, we observe a common theme: the critical nucleus in each of the mutants share a subset of residues that can be mapped to the critical nucleus residues of the wild-type. Circular permutations create new N and C termini, which are the location of the largest disruption of the folding nucleus, leading to a decrease in both phi values and the role in nucleation. Mutant nuclei are built around the wild-type nucleus but are biased towards different parts of the S6 structure depending on the topological and entropic changes induced by the location of the new N and C termini.

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.

Identification of the minimal protein-folding nucleus through loop-entropy perturbations

To explore the plasticity and structural constraints of the protein-folding nucleus we have constructed through circular permutation four topological variants of the ribosomal protein S6. In effect, these topological variants represent entropy mutants with maintained spatial contacts. The proteins were characterized at two complementary levels of detail: by phi-value analysis estimating the extent of contact formation in the transition-state ensemble and by Hammond analysis measuring the site-specific growth of the folding nucleus. The results show that, although the loop-entropy alterations markedly influence the appearance and structural location of the folding nucleus, it retains a common motif of one helix docking against two strands. This nucleation motif is built around a shared subset of side chains in the center of the hydrophobic core but extends in different directions of the S6 structure following the permutant-specific differences in local loop entropies. The adjustment of the critical folding nucleus to alterations in loop entropies is reflected by a direct correlation between the phi-value change and the accompanying change in local sequence separation.

Experimental characterization of the folding kinetics of the notch ankyrin domain

Proteins constructed from linear arrays of tandem repeats provide a simplified architecture for understanding protein folding. Here, we examine the folding kinetics of the ankyrin repeat domain from the Drosophila Notch receptor, which consists of six folded ankyrin modules and a seventh partly disordered N-terminal ankyrin repeat sequence. Both the refolding and unfolding kinetics are best described as a sum of two exponential phases. The slow, minor refolding phase is limited by prolyl isomerization in the denatured state (D). The minor unfolding phase, which appears as a lag during fluorescence-detected unfolding, is consistent with an on-pathway intermediate (I). This intermediate, although not directly detected during refolding, is shown to be populated by interrupted refolding experiments. When plotted against urea, the rate constants for the major unfolding and refolding phases define a single non-linear v-shaped chevron, as does the minor unfolding phase. These two chevrons, along with unfolding amplitudes, are well-fitted by a sequential three-state model, which yields rate constants for the individual steps in folding and unfolding. Based on these fitted parameters, the D to I step is rate-limiting, and closely matches the major observed refolding phase at low denaturant concentrations. I appears to be midway between N and D in folding free energy and denaturant sensitivity, but has Trp fluorescence properties close to N. Although the Notch ankyrin domain has a simple architecture, folding is slow, with the limiting refolding rate constant as much as seven orders of magnitude smaller than expected from topological predictions.

Symmetric connectivity of secondary structure elements enhances the diversity of folding pathways

The influence of native connectivity of secondary structure elements (SSE) on folding is studied using coarse-grained models of proteins with mixed alpha and beta structure and the analysis of the structural database of wild-type proteins. We found that the distribution of SSE along a sequence determines the diversity of folding pathways. If alpha and beta SSE are localized in different parts of a sequence, the diversity of folding pathways is restricted. An even (symmetric) distribution of alpha and beta SSE with respect to sequence midpoint favors multiple folding routes. Simulations are supplemented by the database analysis of the distribution of SSE in wild-type protein sequences. On an average, two-thirds of wild-type proteins with mixed alpha and beta structure have symmetric distribution of alpha and beta SSE. The propensity for symmetric distribution of SSE is especially evident for large proteins with the number of SSE > or = 10. We suggest that symmetric SSE distribution in protein sequences may arise due to nearly random allocation of alpha and beta structure along wild-type sequences. The tendency of long sequences to misfold is perhaps compensated by the enhanced pathway diversity. In addition, folding pathways are shown to progress via hierarchic assembly of SSE in accordance with their proximity along a sequence. We demonstrate that under mild denaturation conditions folding and unfolding pathways are similar. However, the reversibility of folding/unfolding pathways is shown to depend on the distribution of SSE. If alpha and beta SSE are localized in different parts of a sequence, folding and unfolding pathways are likely to coincide.

Transition State Contact Orders Correlate with Protein Folding Rates

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.

Alteration of the disulfide-coupled folding pathway of BPTI by circular permutation

The kinetics of disulfide-coupled folding and unfolding of four circularly permuted forms of bovine pancreatic trypsin inhibitor (BPTI) were studied and compared with previously published results for both wild-type BPTI and a cyclized form. Each of the permuted proteins was found to be less stable than either the wild-type or circular proteins, by 3-8 kcal/mole. These stability differences were used to estimate effective concentrations of the chain termini in the native proteins, which were 1 mM for the wild-type protein and 2.5 to 4000 M for the permuted forms. The circular permutations increased the rates of unfolding and caused a variety of effects on the kinetics of refolding. For two of the proteins, the rates of a direct disulfide-formation pathway were dramatically increased, making this process as fast or faster than the competing disulfide rearrangement mechanism that predominates in the folding of the wild-type protein. These two permutations break the covalent connectivity among the beta-strands of the native protein, and removal of these constraints appears to facilitate direct formation and reduction of nearby disulfides that are buried in the folded structure. The effects on folding kinetics and mechanism do not appear to be correlated with relative contact order, a measure of overall topological complexity. These observations are consistent with the results of other recent experimental and computational studies suggesting that circular permutation may generally influence folding mechanisms by favoring or disfavoring specific interactions that promote alternative pathways, rather than through effects on the overall topology of the native protein.

Optimal combination of theory and experiment for the characterization of the protein folding landscape of S6: how far can a minimalist model go?

The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques provide accurate thermodynamic and kinetic measurements on restricted regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are oftentimes built on assumptions and approximations that affect the accuracy of the results. We present a new methodology that allows to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape. We prove that this new procedure allows a simplified protein model to reproduce remarkably well (correlation coefficient > 0.9) all experimental data available on free energies differences upon single mutations for S6 ribosomal protein and two circular permutants. Our results confirm and quantify the hypothesis, recently formulated on the basis of experimental data, that the folding landscape of protein S6 is strongly affected by an atypical distribution of contact energies.

Quantifying the roughness on the free energy landscape: entropic bottlenecks and protein folding rates

The prediction of protein folding rates and mechanisms is currently of great interest in the protein folding community. A close comparison between theory and experiment in this area is promising to advance our understanding of the physical-chemical principles governing the folding process. The delicate interplay of entropic and energetic/enthalpic factors in the protein free energy regulates the details of this complex reaction. In this article, we propose the use of topological descriptors to quantify the amount of heterogeneity in the configurational entropy contribution to the free energy. We apply the procedure to a set of 16 two-state folding proteins. The results offer a clean and simple theoretical explanation for the experimentally measured folding rates and mechanisms, in terms of the intrinsic entropic roughness along the populated folding routes on the protein free energy landscape.

Using protein folding rates to test protein folding theories

The fastest simple, kinetically two-state protein folds a million times more rapidly than the slowest. Here we review many recent theories of protein folding kinetics in terms of their ability to qualitatively rationalize, if not quantitatively predict, this fundamental experimental observation.

The "two-state folder" MerP forms partially unfolded structures that show temperature dependent hydrogen exchange

We have analysed the folding energy landscape of the 72 amino acid protein MerP by monitoring native state hydrogen exchange as a function of temperature in the range of 7-55 degrees C. The temperature dependence of the hydrogen exchange has allowed us to determine DeltaG, DeltaH and DeltaC(p) values for the conformational processes that permit hydrogen exchange. When studied with the traditional probes, fluorescence and CD, MerP appears to behave as a typical two-state protein, but the results from the hydrogen exchange analysis reveal a much more complex energy landscape. Analysis at the individual amino acid level show that exchange is allowed from an ensemble of partially unfolded structures (i.e. intermediates) in which the stabilities at the amino acid level form a broad distribution throughout the protein. The formation of partially unfolded structures might contribute to the unusually slow folding of MerP.

Transition states for folding of circular-permuted proteins

To explore the role of entropy and chain connectivity in protein folding, a particularly interesting scheme, namely, the circular permutation, has been used. Recently, experimental observations showed that there are large differences in the folding mechanisms between the wild-type proteins and their circular permutants. These differences are strongly related to the change in the intrachain connectivity. Some results obtained by molecular dynamics simulations also showed a good agreement with the experimental findings. Here, we use a topology-based free-energy functional method to study the role of the chain connectivity in folding by comparing features of transition states of the wild-type proteins with those of their circular permutants. We concentrate our study on 3 small globular proteins, namely, the alpha-spectrin SH3 domain (SH3), the chymotrypsin inhibitor 2 (CI2), and the ribosomal protein S6, and obtain exciting results that are consistent with the available experimental and simulation results. A heterogeneity of the interaction energies between contacts for protein CI2 and for protein S6 is also introduced, which characterizes the strong interactions between contacts with long loops, as speculated from experiments for protein S6. The comparison between the folding nucleus of the wild-type proteins and those of their circular permutants indicates that chain connectivity affects remarkably the shapes of the energy profiles and thus the folding mechanism. Further comparisons between our theoretical calculated phi(th) values and the experimental observed phi(exp) values for the 3 proteins and their permutants show that our results are in good agreement with experimental ones and that correlations between them are high. These indicate that the free-energy functional method really provides a way to analyze the folding behavior of the circular-permuted proteins and therefore the folding mechanism of the wild-type proteins.

Scattered Hammond plots reveal second level of site-specific information in protein folding: phi' (beta++)

Site-specific information about structural heterogeneities of the protein-folding transition-state ensemble is commonly derived from the scatter of the Brønsted plot through the individual values of = Delta logk(f)/Delta logK(D-N). Here, we provide a second level of site-specific detail in the transition-state analysis by demonstrating that the scatter of the Hammond plot is related to heterogeneities in the -value growth. That is, the extent of transition-state movement (Delta beta(++)) is proportional to the free-energy gradient of the mutational perturbation across the top of the activation barrier, '(beta(++)) proportional, variant Delta logK(D-N). The analysis is applied to the two-state protein L23 where the site-specific free-energy gradients are used to identify the interactions that show the highest degree of consolidation after crossing the barrier top. These interactions are distributed as a shell around the high- initiation point and denote the side-chain contacts that add criticality to the folding nucleus.

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.

Folding kinetics of two-state proteins: effect of circularization, permutation, and crosslinks

Protein folding kinetics has recently been probed by clever experiments using circular permutants and other topological mutations. A circular permutant is created from a wild-type protein by covalently linking together the chain ends and cleaving elsewhere in the chain. An interesting puzzle is why circular permutation causes no apparent change in the folding mechanism of CI2, but dramatic changes in the folding mechanisms of S6 and of an SH3 domain, as determined by Phi-value experiments. Here, we use a computational model to predict the folding routes of topological variants, based on a measure (effective contact order) of the chain entropy loss at each folding step. The predictions are consistent with the experiments, leading to insights into the folding routes and into the meaning of Phi-values in general. We find that Phi-values do not always describe time sequences of folding events, or positions along a single reaction coordinate; rather, Phi reflects only the degree of rate control. For example, the circular permutant P(40-41) of CI2 is predicted to reverse the time sequence of the formation of beta(1)beta(4) relative to beta(2)beta(3), without changing the diffuse Phi-value distribution, while the circular permutant P(13-14) of S6 switches the rate-limiting step from the formation of beta(1)beta(4) to beta(1)beta(3), changing the Phi-value distribution from diffuse to strongly polarized. As a test of the model, we propose mutations that should reverse these outcomes.

Comparison of the folding processes of distantly related proteins. Importance of hydrophobic content in folding

The N-terminal domain of HypF from Escherichia coli (HypF-N) is a 91 residue protein module sharing the same folding topology and a significant sequence identity with two extensively studied human proteins, muscle and common-type acylphosphatases (mAcP and ctAcP). With the aim of learning fundamental aspects of protein folding from the close comparison of so similar proteins, the folding process of HypF-N has been studied using stopped-flow fluorescence. While mAcP and ctAcP fold in a two-state fashion, HypF-N was found to collapse into a partially folded intermediate before reaching the fully folded conformation. Formation of a burst-phase intermediate is indicated by the roll over in the Chevron plot at low urea concentrations and by the large jump of intrinsic and 8-anilino-1-naphtalenesulphonic acid-derived fluorescence immediately after removal of denaturant. Furthermore, HypF-N was found to fold rapidly with a rate constant that is approximately two and three orders of magnitudes faster than ctAcP and mAcP, respectively. Differences between the bacterial protein and the two human counterparts were also found as to the involvement of proline isomerism in their respective folding processes. The results clearly indicate that features that are often thought to be relevant in protein folding are not highly conserved in the evolution of the acylphosphatase superfamily. The large difference in folding rate between mAcP and HypF-N cannot be entirely accounted for by the difference in relative contact order or related topological metrics. The analysis shows that the higher folding rate of HypF-N is in part due to the relatively high hydrophobic content of this protein. This conclusion, which is also supported by the highly significant correlation found between folding rate and hydrophobic content within a group of proteins displaying the topology of HypF-N and AcPs, suggests that the average hydrophobicity of a protein sequence is an important determinant of its folding rate.

Perturbed folding kinetics of circularly permuted RNAs with altered topology

The folding pathway of the Tetrahymena ribozyme correlates inversely with the sequence distance between native interactions, or contact order. The rapidly folding P4-P6 domain has a low contact order, while the slowly folding P3-P7 region has a high contact order. To examine the role of topology and contact order in RNA folding, we screened for circular permutants of the ribozyme that retain catalytic activity. Permutants beginning in the P4-P6 domain fold 5 to 20 times more slowly than the wild-type ribozyme. By contrast, 50% of a permuted RNA that disjoins a non-native interaction in P3 folds tenfold faster than the wild-type ribozyme. Hence, the probability of rapidly folding to the native state depends on the topology of tertiary domains.

A thermodynamic and kinetic analysis of the folding pathway of an SH3 domain entropically stabilised by a redesigned hydrophobic core

The folding thermodynamics and kinetics of the alpha-spectrin SH3 domain with a redesigned hydrophobic core have been studied. The introduction of five replacements, A11V, V23L, M25V, V44I and V58L, resulted in an increase of 16% in the overall volume of the side-chains forming the hydrophobic core but caused no remarkable changes to the positions of the backbone atoms. Judging by the scanning calorimetry data, the increased stability of the folded structure of the new SH3-variant is caused by entropic factors, since the changes in heat capacity and enthalpy upon the unfolding of the wild-type and mutant proteins were identical at 298 K. It appears that the design process resulted in an increase in burying both the hydrophobic and hydrophilic surfaces, which resulted in a compensatory effect upon the changes in heat capacity and enthalpy. Kinetic analysis shows that both the folding and unfolding rate constants are higher for the new variant, suggesting that its transition state becomes more stable compared to the folded and unfolded states. The phi(double dagger-U) values found for a number of side-chains are slightly lower than those of the wild-type protein, indicating that although the transition state ensemble (TSE) did not change overall, it has moved towards a more denatured conformation, in accordance with Hammond's postulate. Thus, the acceleration of the folding-unfolding reactions is caused mainly by an improvement in the specific and/or non-specific hydrophobic interactions within the TSE rather than by changes in the contact order. Experimental evidence showing that the TSE changes globally according to its hydrophobic content suggests that hydrophobicity may modulate the kinetic behaviour and also the folding pathway of a protein.

Weak cooperativity in the core causes a switch in folding mechanism between two proteins of the cks family

The human protein ckshs1 (cks1) is a 79 residue alpha/beta protein with low thermodynamic and kinetic stability. Its folding mechanism was probed by mutation at sites throughout the structure. Many of the mutations caused changes in the slope of the unfolding arm of the chevron plot. The effects can be rationalised in terms of either transition-state movement or native-state "breathing", and in either case, the magnitude of the effect enables the sequence of events in the folding reaction to be determined. Those sites that fold early exhibit a small perturbation, whilst those sites that fold late exhibit a large perturbation. The results show that cks1 folds sequential pairs of beta-strands first; beta1/beta2 and beta3/beta4. Subsequently, these pairs pack against each other and onto the alpha-helical region to form the core. The folding process of cks1 contrasts with that of the homologue, suc1. The 113 residue suc1 has the same beta-sheet core structure but, additionally, two large insertions that confer much greater thermodynamic and kinetic stability. The more extensive network of tertiary interactions in suc1 provides sufficient enthalpic gain to overcome the entropic cost of forming the core and thus tips the balance in favour of non-local interactions: the non-local, central beta-strand pair, beta2/beta4, forms first and the periphery strands pack on later. Moreover, the greater cooperativity of the core of suc1 protects its folding from perturbation and consequently the slope of the unfolding arm of the chevron plot is much less sensitive to mutation.

The topomer search model: A simple, quantitative theory of two-state protein folding kinetics

Most small, single-domain proteins fold with the uncomplicated, single-exponential kinetics expected for diffusion on a smooth energy landscape. Despite this energetic smoothness, the folding rates of these two-state proteins span a remarkable million-fold range. Here, we review the evidence in favor of a simple, mechanistic description, the topomer search model, which quantitatively accounts for the broad scope of observed two-state folding rates. The model, which stipulates that the search for those unfolded conformations with a grossly correct topology is the rate-limiting step in folding, fits observed rates with a correlation coefficient of approximately 0.9 using just two free parameters. The fitted values of these parameters, the pre-exponential attempt frequency and a measure of the difficulty of ordering an unfolded chain, are consistent with previously reported experimental constraints. These results suggest that the topomer search process may dominate the relative barrier heights of two-state protein-folding reactions.

Experimental evaluation of topological parameters determining protein-folding rates

Recent work suggests that structural topology plays a key role in determining protein-folding rates and pathways. The refolding rates of small proteins that fold without intermediates are found to correlate with simple structural parameters such as relative contact order, long-range order, or the fraction of short-range contacts. To test and evaluate the role of structural topology experimentally, a set of circular permutants of the ribosomal protein S6 from Thermus thermophilus was analyzed. Despite a wide range of relative contact order, the permuted proteins all fold with similar rates. These results suggest that alternative topological parameters may better describe the role of topology in protein-folding rates.

Conformational plasticity in folding of the split beta-alpha-beta protein S6: evidence for burst-phase disruption of the native state

An increasing number of folding studies of two-state proteins shows that point mutations sometimes change the kinetic m-values, leading to kinks and curves in the chevron plots. The molecular origin of these changes is yet unclear although it is speculated that they are linked to structural rearrangement of the transition state or to accumulation of meta-stable intermediates. To shed more light on this issue, we present here a combined m and phi-value analysis of the split beta-alpha-beta protein S6. Wild-type S6 displays classical two-state kinetics with v-shaped chevron plot, but a majority of its mutants display distinct m-value changes or curved chevrons. We observe that this kinetic aberration of S6 is linked to mutations that are clustered in distinct regions of the native structure. The most pronounced changes, i.e. decrease in the m-value for the unfolding rate constant, are seen upon truncation of interactions between the N and C termini, whereas mutations in the centre of the hydrophobic core show smaller or even opposed effects. As a consequence, the calculated phi-values display a systematic increase upon addition of denaturant. In the case of S6, the phenomenon seems to arise from a general plasticity of the different species on the folding pathway. That is, the structure of the denatured ensemble, the transition state, and the native ground-state for unfolding seem to change upon mutation. From these changes, it is concluded that interactions spanning the centre of the hydrophobic core form early in folding, whereas the entropically disfavoured interactions linking the N and C termini consolidate very late, mainly on the down-hill-side of the folding barrier.