Protein unfolding rates correlate as strongly as folding rates with native structure

Although the folding rates of proteins have been studied extensively, both experimentally and theoretically, and many native state topological parameters have been proposed to correlate with or predict these rates, unfolding rates have received much less attention. Moreover, unfolding rates have generally been thought either to not relate to native topology in the same manner as folding rates, perhaps depending on different topological parameters, or to be more difficult to predict. Using a dataset of 108 proteins including two-state and multistate folders, we find that both unfolding and folding rates correlate strongly, and comparably well, with well-established measures of native topology, the absolute contact order and the long range order, with correlation coefficient values of 0.75 or higher. In addition, compared to folding rates, the absolute values of unfolding rates vary more strongly with native topology, have a larger range of values, and correlate better with thermodynamic stability. Similar trends are observed for subsets of different protein structural classes. Taken together, these results suggest that choosing a scaffold for protein engineering may require a compromise between a simple topology that will fold sufficiently quickly but also unfold quickly, and a complex topology that will unfold slowly and hence have kinetic stability, but fold slowly. These observations, together with the established role of kinetic stability in determining resistance to thermal and chemical denaturation as well as proteases, have important implications for understanding fundamental aspects of protein unfolding and folding and for protein engineering and design.     

Direct observation of microscopic reversibility in single-molecule protein folding

Both folded and unfolded conformations should be observed for a protein at its melting temperature (T(m)), where DeltaG between these states is zero. In an all-atom molecular dynamics simulation of chymotrypsin inhibitor 2 (CI2) at its experimental T(m), the protein rapidly loses its low-temperature native structure; it then unfolds before refolding to a stable, native-like conformation. The initial unfolding follows the unfolding pathway described previously for higher-temperature simulations: the hydrophobic core is disrupted, the beta-sheet pulls apart and the alpha-helix unravels. The unfolded state reached under these conditions maintains a kernel of structure in the form of a non-native hydrophobic cluster. Refolding simply reverses this path, the side-chain interactions shift, the helix refolds, and the native packing and hydrogen bonds are recovered. The end result of this refolding is not the initial crystal structure; it contains the proper topology and the majority of the native contacts, but the structure is expanded and the contacts are long. We believe this to be the native state at elevated temperature, and the change in volume and contact lengths is consistent with experimental studies of other native proteins at elevated temperature and the chemical denaturant equivalent of T(m).     

Stability and folding of a mutant ribose-binding protein ofEscherichia coli

A mature mutant ribose-binding protein (RBP) ofEscherichia coli was obtained by site-directed mutagenesis, replacing Thr-3 in the N-domain of wild-type mature RBP (WT-mRBP) with a Trp residue (N-Trp-mRBP). The equilibrium unfolding properties and the refolding kinetics of this protein were monitored by fluorescence and circular dichroism (CD). The stability of N-Trp-mRBP appears to be the same as that of C-Trp-mRBP, another mutant obtained by replacing Phe-187 with a Trp, and lower than that of WT-mRBP. The overall refolding rate of N-Trp-mRBP is much smaller than that of C-Trp-mRBP, which, in turn, is similar to that of WT-mRBP. For the case of WT-mRBP, the rate constant obtained by Tyr fluorescence is identical to the value obtained by CD. But with C-Trp-mRBP, the rate constant from CD is smaller than the value from the Trp fluorescence and this difference in the rate constants is much greater with the N-TrpmRBP.     

Structure of stable protein folding intermediates by equilibrium phi-analysis: the apoflavodoxin thermal intermediate

Protein intermediates in equilibrium with native states may play important roles in protein dynamics but, in cases, can initiate harmful aggregation events. Investigating equilibrium protein intermediates is thus important for understanding protein behaviour (useful or pernicious) but it is hampered by difficulties in gathering structural information. We show here that the phi-analysis techniques developed to investigate transition states of protein folding can be extended to determine low-resolution three-dimensional structures of protein equilibrium intermediates. The analysis proposed is based solely on equilibrium data and is illustrated by determination of the structure of the apoflavodoxin thermal unfolding intermediate. In this conformation, a large part of the protein remains close to natively folded, but a 40 residue region is clearly unfolded. This structure is fully consistent with the NMR data gathered on an apoflavodoxin mutant designed specifically to stabilise the intermediate. The structure shows that the folded region of the intermediate is much larger than the proton slow-exchange core at 25 degrees C. It also reveals that the unfolded region is made of elements whose packing surface is more polar than average. In addition, it constitutes a useful guide to rationally stabilise the native state relative to the intermediate state, a far from trivial task.     

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.     

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.     

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.     

Clustering tendency in the protein fold space

Several non-redundant ensembles of protein three-dimensional structures were analyzed in order to estimate their natural clustering tendency by means of the Cox-Lewis coefficient. It was observed that, despite proteins tend to aggregate into different and well separated groups, some overlap between different clusters occurs. This suggests that classifications bases only on structural data cannot allow a systematic classification of proteins. Additional information are in particular needed in order to monitor completely the complex evolutionary relationships between proteins.     

Allosteric switching by mutually exclusive folding of protein domains

Many proteins are built from structurally and functionally distinct domains. A major goal is to understand how conformational change transmits information between domains in order to achieve biological activity. A two-domain, bi-functional fusion protein has been designed so that the mechanical stress imposed by the folded structure of one subunit causes the other subunit to unfold, and vice versa. The construct consists of ubiquitin inserted into a surface loop of barnase. The distance between the amino and carboxyl ends of ubiquitin is much greater than the distance between the termini of the barnase loop. This topological constraint causes the two domains to engage in a thermodynamic tug-of-war in which only one can exist in its folded state at any given time. This conformational equilibrium, which is cooperative, reversible, and controllable by ligand binding, serves as a model for the coupled binding and folding mechanism widely used to mediate protein-protein interactions and cellular signaling processes. The position of the equilibrium can be adjusted by temperature or ligand binding and is monitored in vivo by cell death. This design forms the basis for a new class of cytotoxic proteins that can be activated by cell-specific effector molecules, and can thus target particular cell types for destruction.     

Diffusing and colliding: the atomic level folding/unfolding pathway of a small helical protein

Proteins with ultra-fast folding/unfolding kinetics are excellent candidates for study by molecular dynamics. Here, we describe such simulations of a three helix bundle protein, the engrailed homeodomain (En-HD), which folds via the diffusion-collision model. The unfolding pathway of En-HD was characterized by seven simulations of the protein and 12 simulations of its helical fragments yielding over 1.1 micros of simulation time in water. Various conformational states along the unfolding pathway were identified. There is the compact native-like transition state, a U-shaped helical intermediate and an unfolded state with dynamic helical segments. Each of these states is in good agreement with experimental data. Examining these states as well as the transitions between them, we find the role of long-range tertiary contacts, specifically salt-bridges, important in the folding/unfolding pathway. In the folding direction, charged residues form long-range tertiary contacts before the hydrophobic core is formed. The formation of HII is assisted by a specific salt-bridge and by non-specific (fluctuating) tertiary contacts, which we call contact-assisted helix formation. Salt-bridges persist as the protein approaches the transition state, stabilizing HII until the hydrophobic core is formed. To complement this information, simulations of fragments of En-HD illustrate the helical propensities of the individual segments. By thermal denaturation, HII proved to be the least stable helix, unfolding in less than 450 ps at high temperature. We observed the low helical propensity of C-terminal residues from HIII in fragment simulations which, when compared to En-HD unfolding simulations, link the unraveling of HIII to the initial event that drives the unfolding of En-HD.     

Using linear algebra for protein structural comparison and classification

In this article, we describe a novel methodology to extract semantic characteristics from protein structures using linear algebra in order to compose structural signature vectors which may be used efficiently to compare and classify protein structures into fold families. These signatures are built from the pattern of hydrophobic intrachain interactions using Singular Value Decomposition (SVD) and Latent Semantic Indexing (LSI) techniques. Considering proteins as documents and contacts as terms, we have built a retrieval system which is able to find conserved contacts in samples of myoglobin fold family and to retrieve these proteins among proteins of varied folds with precision of up to 80%. The classifier is a web tool available at our laboratory website. Users can search for similar chains from a specific PDB, view and compare their contact maps and browse their structures using a JMol plug-in.     

Calculation of the free energy of association for protein complexes.

We have developed a method for calculating the association energy of quaternary complexes starting from their atomic coordinates. The association energy is described as the sum of two solvation terms and an energy term to account for the loss of translational and rotational entropy. The calculated solvation energy, using atomic solvation parameters and the solvent accessible surface areas, has a correlation of 96% with experimentally determined values. We have applied this methodology to examine intermediates in viral assembly and to assess the contribution isomerization makes to the association energy of molecular complexes. In addition, we have shown that the calculated association can be used as a predictive tool for analyzing modeled molecular complexes.     

A database of protein structure families with common folding motifs.

The availability of fast and robust algorithms for protein structure comparison provides an opportunity to produce a database of three-dimensional comparisons, called families of structurally similar proteins (FSSP). The database currently contains an extended structural family for each of 154 representative (below 30% sequence identity) protein chains. Each data set contains: the search structure; all its relatives with 70-30% sequence identity, aligned structurally; and all other proteins from the representative set that contain substructures significantly similar to the search structure. Very close relatives (above 70% sequence identity) rarely have significant structural differences and are excluded. The alignments of remote relatives are the result of pairwise all-against-all structural comparisons in the set of 154 representative protein chains. The comparisons were carried out with each of three novel automatic algorithms that cover different aspects of protein structure similarity. The user of the database has the choice between strict rigid-body comparisons and comparisons that take into account interdomain motion or geometrical distortions; and, between comparisons that require strictly sequential ordering of segments and comparisons, which allow altered topology of loop connections or chain reversals. The data sets report the structurally equivalent residues in the form of a multiple alignment and as a list of matching fragments to facilitate inspection by three-dimensional graphics. If substructures are ignored, the result is a database of structure alignments of full-length proteins, including those in the twilight zone of sequence similarity.(ABSTRACT TRUNCATED AT 250 WORDS)     

Optimal ratio between the average conformational entropy and the average energy of interaction between residues for fast protein folding

Based on available experimental data and using a theoretical model of protein folding, we demonstrate that there is an optimal ratio between the average conformational entropy and the average contact energy per residue for fast protein folding. A statistical analysis of the conformational entropy and the number of contacts per residue for 5829 protein domains from four main classes (α, β, α/β, α+β) shows that each class has its own characteristic average number of contacts per residue and average conformational entropy per residue. These class-specific characteristics determine the protein folding rates: α-proteins are the fastest to fold, β-proteins are the second fastest, α+β-proteins are the third, and α/β-proteins are the last to fold.     

Structural basis for GroEL-assisted protein folding from the crystal structure of (GroEL-KMgATP)14 at 2.0A resolution

Nucleotide regulates the affinity of the bacterial chaperonin GroEL for protein substrates. GroEL binds protein substrates with high affinity in the absence of ATP and with low affinity in its presence. We report the crystal structure of (GroEL-KMgATP)(14) refined to 2.0 A resolution in which the ATP triphosphate moiety is directly coordinated by both K(+) and Mg(2+). Upon the binding of KMgATP, we observe previously unnoticed domain rotations and a 102 degrees rotation of the apical domain surface helix I. Two major consequences are a large lateral displacement of, and a dramatic reduction of hydrophobicity in, the apical domain surface. These results provide a basis for the nucleotide-dependent regulation of protein substrate binding and suggest a mechanism for GroEL-assisted protein folding by forced unfolding.     

Cooperativity in two-state protein folding kinetics

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.     

Determination of ultrafast protein folding rates from loop formation dynamics

Quenching of the triplet state of tryptophan by contact with cysteine can be used to measure the kinetics of loop formation in unfolded proteins. Here we show that cysteine quenching dynamics also provide a novel method for measuring folding rates when the exchange between folded and unfolded states is faster than the unquenched triplet lifetime (approximately 100 micros). We use this technique to investigate folding/unfolding kinetics of the 35 residue headpiece subdomain of the protein villin, which contains a single tryptophan residue and was engineered to contain a cysteine residue at the N terminus. At intermediate concentrations of denaturant the time-course of the triplet decay consists of two relaxations, the rates and amplitudes of which reveal the fast kinetics for folding and unfolding of this protein. The folding rates extracted using a simple kinetic model are close to those reported previously from laser-induced temperature-jump experiments that employ the change in tryptophan fluorescence as a probe. However, the results differ significantly from those reported from dynamic NMR line shape analysis on a variant with methionine at the N terminus, an issue that remains to be resolved. The analysis of the triplet quenching kinetics also shows that the quenching rates in the unfolded state increase with decreasing denaturant concentration, indicating a compaction of the unfolded protein.