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.     

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.     

Topological determinants of protein unfolding rates

For proteins that fold by two-state kinetics, the folding and unfolding processes are believed to be closely related to their native structures. In particular, folding and unfolding rates are influenced by the native structures of proteins. Thus, we focus on finding important topological quantities from a protein structure that determine its unfolding rate. After constructing graphs from protein native structures, we investigate the relationships between unfolding rates and various topological quantities of the graphs. First, we find that the correlation between the unfolding rate and the contact order is not as prominent as in the case of the folding rate and the contact order. Next, we investigate the correlation between the unfolding rate and the clustering coefficient of the graph of a protein native structure, and observe no correlation between them. Finally, we find that a newly introduced quantity, the impact of edge removal per residue, has a good overall correlation with protein unfolding rates. The impact of edge removal is defined as the ratio of the change of the average path length to the edge removal probability. From these facts, we conclude that the protein unfolding process is closely related to the protein native structure.     

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.     

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.     

Direct correlation between proteins' folding rates and their amino acid compositions: an ab initio folding rate prediction

Discovering the mechanism of protein folding, in molecular biology, is a great challenge. A key step to this end is to find factors that correlate with protein folding rates. Over the past few years, many empirical parameters, such as contact order, long-range order, total contact distance, secondary structure contents, have been developed to reflect the correlation between folding rates and protein tertiary or secondary structures. However, the correlation between proteins' folding rates and their amino acid compositions has not been explored. In the present work, we examined systematically the correlation between proteins' folding rates and their amino acid compositions for two-state and multistate folders and found that different amino acids contributed differently to the folding progress. The relation between the amino acids' molecular weight and degeneracy and the folding rates was examined, and the role of hydrophobicity in the protein folding process was also inspected. As a consequence, a new indicator called composition index was derived, which takes no structure factors into account and is merely determined by the amino acid composition of a protein. Such an indicator is found to be highly correlated with the protein's folding rate (r > 0.7). From the results of this work, three points of concluding remarks are evident. (1) Two-state folders and multistate folders have different rate-determining amino acids. (2) The main determining information of a protein's folding rate is largely reflected in its amino acid composition. (3) Composition index may be the best predictor for an ab initio protein folding rate prediction directly from protein sequence from the standpoint of practical application.     

Contact order revisited: influence of protein size on the folding rate

Guided by the recent success of empirical model predicting the folding rates of small two-state folding proteins from the relative contact order (CO) of their native structures, by a theoretical model of protein folding that predicts that logarithm of the folding rate decreases with the protein chain length L as L(2/3), and by the finding that the folding rates of multistate folding proteins strongly correlate with their sizes and have very bad correlation with CO, we reexamined the dependence of folding rate on CO and L in attempt to find a structural parameter that determines folding rates for the totality of proteins. We show that the Abs_CO = CO x L, is able to predict rather accurately folding rates for both two-state and multistate folding proteins, as well as short peptides, and that this Abs_CO scales with the protein chain length as L(0.70 +/- 0.07) for the totality of studied single-domain proteins and peptides.     

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.     

Sequence optimization for native state stability determines the evolution and folding kinetics of a small protein

Investigating the relative importance of protein stability, function, and folding kinetics in driving protein evolution has long been hindered by the fact that we can only compare modern natural proteins, the products of the very process we seek to understand, to each other, with no external references or baselines. Through a large-scale all-atom simulation of protein evolution, we have created a large diverse alignment of SH3 domain sequences which have been selected only for native state stability, with no other influencing factors. Although the average pairwise identity between computationally evolved and natural sequences is only 17%, the residue frequency distributions of the computationally evolved sequences are similar to natural SH3 sequences at 86% of the positions in the domain, suggesting that optimization for the native state structure has dominated the evolution of natural SH3 domains. Additionally, the positions which play a consistent role in the transition state of three well-characterized SH3 domains (by phi-value analysis) are structurally optimized for the native state, and vice versa. Indeed, we see a specific and significant correlation between sequence optimization for native state stability and conservation of transition state structure.     

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.     

Cooperativity,smooth energy landscapes and the origins of topology-dependent protein folding rates

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

Folding rates and low-entropy-loss routes of two-state proteins

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.     

The effects of nonnative interactions on protein folding rates: theory and simulation

Proteins are minimally frustrated polymers. However, for realistic protein models, nonnative interactions must be taken into account. In this paper, we analyze the effect of nonnative interactions on the folding rate and on the folding free energy barrier. We present an analytic theory to account for the modification on the free energy landscape upon introduction of nonnative contacts, added as a perturbation to the strong native interactions driving folding. Our theory predicts a rate-enhancement regime at fixed temperature, under the introduction of weak, nonnative interactions. We have thoroughly tested this theoretical prediction with simulations of a coarse-grained protein model, by using an off-lattice C(alpha)model of the src-SH3 domain. The strong agreement between results from simulations and theory confirm the nontrivial result that a relatively small amount of nonnative interaction energy can actually assist the folding to the native structure.     

Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics

We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.     

Relationship between stability of folding intermediates and amyloid formation for the yeast prion Ure2p: a quantitative analysis of the effects of pH and buffer system

The dimeric yeast protein Ure2 shows prion-like behaviour in vivo and forms amyloid fibrils in vitro. A dimeric intermediate is populated transiently during refolding and is apparently stabilized at lower pH, conditions suggested to favour Ure2 fibril formation. Here we present a quantitative analysis of the effect of pH on the thermodynamic stability of Ure2 in Tris and phosphate buffers over a 100-fold protein concentration range. We find that equilibrium denaturation is best described by a three-state model via a dimeric intermediate, even under conditions where the transition appears two-state by multiple structural probes. The free energy for complete unfolding and dissociation of Ure2 is up to 50 kcal mol(-1). Of this, at least 20 kcal mol(-1) is contributed by inter-subunit interactions. Hence the native dimer and dimeric intermediate are significantly more stable than either of their monomeric counterparts. The previously observed kinetic unfolding intermediate is suggested to represent the dissociated native-like monomer. The native state is stabilized with respect to the dimeric intermediate at higher pH and in Tris buffer, without significantly affecting the dissociation equilibrium. The effects of pH, buffer, protein concentration and temperature on the kinetics of amyloid formation were quantified by monitoring thioflavin T fluorescence. The lag time decreases with increasing protein concentration and fibril formation shows pseudo-first order kinetics, consistent with a nucleated assembly mechanism. In Tris buffer the lag time is increased, suggesting that stabilization of the native state disfavours amyloid nucleation.     

Rapid cooperative two-state folding of a miniature alpha-beta protein and design of a thermostable variant

There is a great deal of interest in developing small stably folded miniature proteins. A limited number of these molecules have been described, however they typically have not been characterized in depth. In particular, almost no detailed studies of the thermodynamics and folding kinetics of these proteins have been reported. Here we describe detailed studies of the thermodynamics and kinetics of folding of a 39 residue mixed alpha-beta protein (NTL9(1-39)) derived from the N-terminal domain of the ribosomal protein L9. The protein folds cooperatively and rapidly in a two-state fashion to a native state typical of those found for normal globular proteins. At pH 5.4 in 20mM sodium acetate, 100mM NaCl the temperature of maximum stability is 6 degrees C, the t(m) is 65.3 degrees C, deltaH degrees (t(m)) is between 24.6 kcalmol(-1) and 26.3 kcalmol(-1), and deltaC(p) degrees is 0.38 kcalmol(-1)deg(-1). The thermodynamic parameters are in the range expected on the basis of per residue values determined from databases of globular proteins. H/2H exchange measurements reveal a set of amides that exchange via global unfolding, exactly as expected for a normal cooperatively folded globular protein. Kinetic measurements show that folding is two-state folding. The folding rate is 640 s(-1) and the value of deltaG degrees calculated from the folding and unfolding rates is in excellent agreement with the equilibrium value. A designed thermostable variant, generated by mutating K12 to M, was characterized and found to have a t(m) of 82 degrees C. Equilibrium and kinetic measurements demonstrate that its folding is cooperative and two-state.     

New insights into structural determinants of prion protein folding and stability

Prions are the etiological agent of fatal neurodegenerative diseases called prion diseases or transmissible spongiform encephalopathies. These maladies can be sporadic, genetic or infectious disorders. Prions are due to post-translational modifications of the cellular prion protein leading to the formation of a β-sheet enriched conformer with altered biochemical properties. The molecular events causing prion formation in sporadic prion diseases are still elusive. Recently, we published a research elucidating the contribution of major structural determinants and environmental factors in prion protein folding and stability. Our study highlighted the crucial role of octarepeats in stabilizing prion protein; the presence of a highly enthalpically stable intermediate state in prion-susceptible species; and the role of disulfide bridge in preserving native fold thus avoiding the misfolding to a β-sheet enriched isoform. Taking advantage from these findings, in this work we present new insights into structural determinants of prion protein folding and stability.     

New insights into structural determinants of prion protein folding and stability

Abstract

Prions are the etiological agent of fatal neurodegenerative diseases called prion diseases or transmissible spongiform encephalopathies. These maladies can be sporadic, genetic or infectious disorders. Prions are due to post-translational modifications of the cellular prion protein leading to the formation of a β-sheet enriched conformer with altered biochemical properties. The molecular events causing prion formation in sporadic prion diseases are still elusive. Recently, we published a research elucidating the contribution of major structural determinants and environmental factors in prion protein folding and stability. Our study highlighted the crucial role of octarepeats in stabilizing prion protein; the presence of a highly enthalpically stable intermediate state in prion-susceptible species; and the role of disulfide bridge in preserving native fold thus avoiding the misfolding to a β-sheet enriched isoform. Taking advantage from these findings, in this work we present new insights into structural determinants of prion protein folding and stability.