Predicting repeat protein folding kinetics from an experimentally determined folding energy landscape

The Notch ankyrin domain is a repeat protein whose folding has been characterized through equilibrium and kinetic measurements. In previous work, equilibrium folding free energies of truncated constructs were used to generate an experimentally determined folding energy landscape (Mello and Barrick, Proc Natl Acad Sci USA 2004;101:14102–14107). Here, this folding energy landscape is used to parameterize a kinetic model in which local transition probabilities between partly folded states are based on energy values from the landscape. The landscape‐based model correctly predicts highly diverse experimentally determined folding kinetics of the Notch ankyrin domain and sequence variants. These predictions include monophasic folding and biphasic unfolding, curvature in the unfolding limb of the chevron plot, population of a transient unfolding intermediate, relative folding rates of 19 variants spanning three orders of magnitude, and a change in the folding pathway that results from C‐terminal stabilization. These findings indicate that the folding pathway(s) of the Notch ankyrin domain are thermodynamically selected: the primary determinants of kinetic behavior can be simply deduced from the local stability of individual repeats.     

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)     

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.     

The folding mechanism of a two-domain protein: folding kinetics and domain docking of the gene-3 protein of phage fd

The gene-3 protein (G3P) of filamentous phages is essential for the infection of Escherichia coli. The carboxy-terminal domain anchors this protein in the phage coat, whereas the two amino-terminal domains N1 and N2 protrude from the phage surface. We analyzed the folding mechanism of the two-domain fragment N1-N2 of G3P (G3P(*)) and the interplay between folding and domain assembly. For this analysis, a variant of G3P(*) was used that contained four stabilizing mutations (IIHY-G3P(*)). The observed refolding kinetics extend from 10 ms to several hours. Domain N1 refolds very rapidly (with a time constant of 9.4 ms at 0.5 M guanidinium chloride, 25 degrees C) both as a part of IIHY-G3P(*) and as an isolated protein fragment. The refolding of domain N2 is slower and involves two reactions with time constants of seven seconds and 42 seconds. These folding reactions of the individual domains are followed by a very slow, spectroscopically silent docking process, which shows a time constant of 6200 seconds. This reaction was detected by a kinetic unfolding assay for native molecules. Before docking, N1 and N2 unfold fast and independently, after docking they unfold slowly in a correlated fashion. A high energy barrier is thus created by domain docking, which protects G3P kinetically against unfolding. The slow domain docking is possibly important for the infection of E.coli by the phage. Upon binding to the F pilus, the N2 domain separates from N1 and the binding site for TolA on domain N1 is exposed. Since domain reassembly is so slow, this binding site remains accessible until pilus retraction has brought N1 close to TolA on the bacterial surface.     

Equilibrium amide hydrogen exchange and protein folding kinetics

The classical Linderstrøm-Lang hydrogen exchange (HX) model is extended to describe the relationship between the HX behaviors (EX1 and EX2) and protein folding kinetics for the amide protons that can only exchange by global unfolding in a three-state system including native (N), intermediate (I), and unfolded (U) states. For these slowly exchanging amide protons, it is shown that the existence of an intermediate (I) has no effect on the HX behavior in an off-pathway three-state system (IUN). On the other hand, in an on-pathway three-state system (UIN), the existence of a stable folding intermediate has profound effect on the HX behavior. It is shown that fast refolding from the unfolded state to the stable intermediate state alone does not guarantee EX2 behavior. The rate of refolding from the intermediate state to the native state also plays a crucial role in determining whether EX1 or EX2 behavior should occur. This is mainly due to the fact that only amide protons in the native state are observed in the hydrogen exchange experiment. These new concepts suggest that caution needs to be taken if one tries to derive the kinetic events of protein folding from equilibrium hydrogen exchange experiments.     

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.     

Revisiting the folding kinetics of bacteriorhodopsin

The elucidation of the physical principles that govern the folding and stability of membrane proteins is one of the greatest challenges in protein science. Several insights into the folding of α-helical membrane proteins have come from the investigation of the conformational equilibrium of H. halobium bacteriorhodopsin (bR) in mixed micelles using SDS as a denaturant. In an effort to confirm that folded bR and SDS-denatured bR reach the same conformational equilibrium, we found that bR folding is significantly slower than has been previously known. Interrogation of the effect of the experimental variables on folding kinetics reveals that the rate of folding is dependent not only on the mole fraction of SDS but also on the molar concentrations of mixed micelle components, a variable that was not controlled in the previous study of bR folding kinetics. Moreover, when the molar concentrations of mixed micelle components are fixed at the concentrations commonly employed for bR equilibrium studies, conformational relaxation in the transition zone is slower than hydrolysis of the retinal Schiff base. As a result, the conformational equilibrium between folded bR and SDS-denatured bR cannot be achieved under the conventional condition. Our finding suggests that the molar concentrations of mixed micelle components are important experimental variables in the investigation of the kinetics and thermodynamics of bR folding and should be accounted for to ensure the accurate assessment of the conformational equilibrium of bR without the interference of retinal hydrolysis.     

Role of unfolded state heterogeneity and en-route ruggedness in protein folding kinetics

In order to improve our understanding of the physical bases of protein folding, there is a compelling need for better connections between experimental and computational approaches. This work addresses the role of unfolded state conformational heterogeneity and en-route intermediates, as an aid for planning and interpreting protein folding experiments. The expected kinetics were modeled for different types of energy landscapes, including multiple parallel folding routes, preferential paths dominated by one primary folding route, and distributed paths with a wide spectrum of microscopic folding rate constants. In the presence of one or more preferential routes, conformational exchange among unfolded state populations slows down the observed rates for native protein formation. We find this to be a general phenomenon, taking place even when unfolded conformations interconvert much faster than the "escape" rate constants to folding. Dramatic kinetic deceleration is expected in the presence of an increasing number of folding-incompetent unfolded conformations. This argues for the existence of parallel folding paths involving several folding-competent unfolded conformations, during the early stages of protein folding. Deviations from single-exponential behavior are observed for unfolded conformations exchanging at comparable rates or more slowly than folding events. Analysis of the effect of en-route (on-path) intermediate formation and landscape ruggedness on folding kinetics leads to the following unexpected conclusions: (1) intermediates, which often retard native state formation, may in some cases accelerate folding, and (2) rugged landscapes, usually associated with stretched exponentials, display single-exponential behavior in the presence of late high-friction paths.     

Simple physical models connect theory and experiment in protein folding kinetics

Our understanding of the principles underlying the protein-folding problem can be tested by developing and characterizing simple models that make predictions which can be compared to experimental data. Here we extend our earlier model of folding free energy landscapes, in which each residue is considered to be either folded as in the native state or completely disordered, by investigating the role of additional factors representing hydrogen bonding and backbone torsion strain, and by using a hybrid between the master equation approach and the simple transition state theory to evaluate kinetics near the free energy barrier in greater detail. Model calculations of folding phi-values are compared to experimental data for 19 proteins, and for more than half of these, experimental data are reproduced with correlation coefficients between r=0.41 and 0.88; calculations of transition state free energy barriers correlate with rates measured for 37 single domain proteins (r=0.69). The model provides insight into the contribution of alternative-folding pathways, the validity of quasi-equilibrium treatments of the folding landscape, and the magnitude of the Arrhenius prefactor for protein folding. Finally, we discuss the limitations of simple native-state-based models, and as a more general test of such models, provide predictions of folding rates and mechanisms for a comprehensive set of over 400 small protein domains of known 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.     

Water as a conformational editor in protein folding

As molecules approach one another in aqueous solution, desolvation free energy barriers to association are encountered. Experiments suggest these (de)solvation effects contribute to the free energy barriers separating the folded and unfolded states of protein molecules. To explore their influence on the energy landscapes of protein folding reactions, we have incorporated desolvation barriers into a semi-realistic, off-lattice protein model that uses a simplified physico-chemical force-field determined solely by the sequence of amino acids. Monte Carlo sampling techniques were used to study the effects on the thermodynamics and kinetics of folding of a number of systems, diverse in structure and sequence. In each case, desolvation barriers increase the stability of the native conformation and the cooperativity of the major folding/unfolding transition. The folding times of these systems are reduced significantly upon inclusion of desolvation barriers, demonstrating that the particulate nature of the solvent engenders a more defined route to the native fold.     

Local interactions and the optimization of protein folding

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig's simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of energy functions in which the energy of the native structure is fixed, but the relative contributions of local and nonlocal interactions to this energy are varied over a broad range. For funnel shaped energy landscapes, we find that 1) the rate of folding increases, but the stability of the folded state decreases, as the contribution of local interactions to the energy of the native structure increases, and 2) the amount of native structure in the unfolded state and the transition state vary considerably with the local interaction strength. Simple exponential kinetics and a well-defined free energy barrier separating folded and unfolded states are observed when nonlocal interactions make an appreciable contribution to the energy of the native structure; in such cases a transition state theory type approximation yields reasonably accurate estimates of the folding rate. Bumps in the folding funnel near the native state, which could result from desolvation effects, side chain freezing, or the breaking of nonnative contacts, significantly alter the dependence of the folding rate on the local interaction strength: the rate of folding decreases when the local interaction strength is increased beyond a certain point. A survey of the distribution of strong contacts in the protein structure database suggests that evolutionary optimization has involved both kinetics and thermodynamics: strong contacts are enriched at both very short and very long sequence separations. Proteins 29:282–291, 1997. © 1997 Wiley-Liss, Inc.     

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.     

Surprisingly high correlation between early and late stages in non-two-state protein folding

We collected quantitative kinetic data on early and late stages of folding in non-two-state proteins from the literature, and studied the relationship between the kinetics of the two stages. There was a surprisingly high correlation between the rate constants of these stages. The correlation coefficient of the logarithmic rate constants was as high as 0.97, which could not be caused by chance. We also studied relationships of the logarithmic rate constants of the two stages with native three-dimensional structures represented by the residue-residue contact map. There were again surprisingly high correlations between the logarithmic rate constants and the number of non-local contact clusters obtained from the contact maps. Because the number of non-local contact clusters represents overall arrangement of substructures in a native protein, the results strongly suggested the importance of the arrangement of the substructures for the kinetics of both early and late stages of protein folding.     

SCOP数据库蛋白质折叠类型的自动分类分析

蛋白质折叠规律研究是生命科学领域重要的前沿课题之一,蛋白质折叠类型分类是折叠规律研究的基础。本研究以SCOP数据库的蛋白质折叠类型分类为基础、以Astral SCOPe 2.05数据库中相似性小于40%的α、β、α+β及α/β类所属的折叠类型为研究对象,完成了989种蛋白质折叠类型的模板构建并形成模板数据库;基于折叠类型设计模板建立了蛋白质折叠类型分类方法,实现了SCOP数据库蛋白质折叠类型的自动化分类。家族模板自洽性检验与独立性检验所得的敏感性、特异性以及MCC的平均值分别为:95.00%、99.99%、0.94与90.00%、99.97%、0.92,折叠类型模板自洽性检验与独立性检验所得的敏感性、特异性以及MCC的平均值分别为:93.71%、99.97%、0.91与86.00%、99.93%、0.87。结果表明:模板设计合理,可有效用于对已知结构的蛋白质进行分类。     

Further experimental studies of the disulfide folding transition of ribonuclease A

Two very different mechanisms of folding have been proposed from experimental studies of disulfide formation in reduced ribonuclease A. (1) A pathway in which the rate-limiting step separates fully folded protein from all other disulfide intermediates and occurs solely in three-disulfide intermediates. (2) A multiple pathway mechanism with different rate-limiting steps for each pathway. The various rate-limiting steps involve disulfide breakage, formation, and rearrangement in intermediates with one, two, three, and four protein disulfides. To distinguish between these two mechanisms, we have carried out further studies of both unfolding and refolding. Refolding of reduced ribonuclease A requires three-disulfide intermediates to accumulate; negligible refolding occurs when only the nearly random one- and two-disulfide intermediate species are populated. Therefore, no rate-limiting steps of the type postulated in mechanism (2) occur in intermediates with one and two protein disulfides. Unfolding and disulfide reduction is an all-or-none process; no disulfide intermediates accumulate to detectable levels or precede the rate-limiting step. Mechanism (2) requires that such intermediates precede the rate-limiting step and accumulate to substantial levels. The different proposals were shown not to result from the use of different solution conditions or disulfide reagents; the two sets of data are not inconsistent. Instead, the inappropriate mechanism (2) resulted from an incorrect kinetic analysis and misinterpretation of the kinetics of disulfide formation and breakage.     

Entropic barriers, transition states, funnels, and exponential protein folding kinetics: a simple model

This paper presents an analytically tractable model that captures the most elementary aspect of the protein folding problem, namely that both the energy and the entropy decrease as a protein folds. In this model, the system diffuses within a sphere in the presence of an attractive spherically symmetric potential. The native state is represented by a small sphere in the center, and the remaining space is identified with unfolded states. The folding temperature, the time-dependence of the populations, and the relaxation rate are calculated, and the folding dynamics is analyzed for both golf-course and funnel-like energy landscapes. This simple model allows us to illustrate a surprising number of concepts including entropic barriers, transition states, funnels, and the origin of single exponential relaxation kinetics.     

The folding mechanics of a knotted protein

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