Redesigning the hydrophobic core of a model beta-sheet protein: destabilizing traps through a threading approach

An off-lattice 46-bead model of a small all-beta protein has been recently criticized for possessing too many traps and long-lived intermediates compared with the folding energy landscape predicted for real proteins and models using the principle of minimal frustration. Using a novel sequence design approach based on threading for finding beneficial mutations for destabilizing traps, we proposed three new sequences for folding in the beta-sheet model. Simulated annealing on these sequences found the global minimum more reliably, indicative of a smoother energy landscape, and simulated thermodynamic variables found evidence for a more cooperative collapse transition, lowering of the collapse temperature, and higher folding temperatures. Folding and unfolding kinetics were acquired by calculating first-passage times, and the new sequences were found to fold significantly faster than the original sequence, with a concomitant lowering of the glass temperature, although none of the sequences have highly stable native structures. The new sequences found here are more representative of real proteins and are good folders in the T(f) > T(g) sense, and they should prove useful in future studies of the details of transition states and the nature of folding intermediates in the context of simplified folding models. These results show that our sequence design approach using threading can improve models possessing glasslike folding dynamics.     

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

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

The nature of protein folding pathways: The classical versus the new view

Summary Pulsed hydrogen exchange and other studies of the kinetic refolding pathways of several small proteins have established that folding intermediates with native-like secondary structures are well populated, but these studies have also shown that the folding kinetics are not well synchronized. Older studies of the kinetics of formation of the native protein, monitored by optical probes, indicate that the folding kinetics should be synchronized. The model commonly used in these studies is the simple sequential model, which postulates a unique folding pathway with defined and sequential intermediates. Theories of the folding process and Monte Carlo simulations of folding suggest that neither the folding pathway nor the set of folding intermediates is unique, and that folding intermediates accumulate because of kinetic traps caused by partial misfolding. Recent experiments with cytochrome c lend support to this new view of folding pathways. These different views of the folding process are discussed. Misfolding and consequent slowing down of the folding process as a result of cis-trans isomerization about prolyl peptide bonds in the unfolded protein are well known; isomerization occurs before refolding is initiated. The occurrence of equilibrium intermediates on the kinetic folding pathways of some proteins, such as -lactalbumin and apomyoglobin, argues that these intermediates are not caused by kinetic traps but rather are stable intermediates under certain conditions, and this conclusion is consistent with a sequential model of folding. Folding reactions with successive kinetic intermediates, in which late intermediates are more highly folded than early intermediates, indicate that folding is hierarchical. New experiments that test the predictions of the classical and the new views are needed.     

Exploring the folding pathway of green fluorescent protein through disulfide engineering

We have introduced two disulfide crosslinks into the loop regions on opposite ends of the beta barrel in superfolder green fluorescent protein (GFP) in order to better understand the nature of its folding pathway. When the disulfide on the side opposite the N/C‐termini is formed, folding is 2× faster, unfolding is 2000× slower, and the protein is stabilized by 16 kJ/mol. But when the disulfide bond on the side of the termini is formed we see little change in the kinetics and stability. The stabilization upon combining the two crosslinks is approximately additive. When the kinetic effects are broken down into multiple phases, we observe Hammond behavior in the upward shift of the kinetic m‐value of unfolding. We use these results in conjunction with structural analysis to assign folding intermediates to two parallel folding pathways. The data are consistent with a view that the two fastest transition states of folding are "barrel closing" steps. The slower of the two phases passes through an intermediate with the barrel opening occurring between strands 7 and 8, while the faster phase opens between 9 and 4. We conclude that disulfide crosslink‐induced perturbations in kinetics are useful for mapping the protein folding pathway.     

Toward minimalist models of larger proteins: a ubiquitin-like protein

Our recently developed off-lattice bead model capable of simulating protein structures with mixed alpha/beta content has been extended to model the folding of a ubiquitin-like protein and provides a means for examining the more complex kinetics involved in the folding of larger proteins. Using trajectories generated from constant-temperature Langevin dynamics simulations and sampling with the multiple multi-histogram method over five-order parameters, we are able to characterize the free energy landscape for folding and find evidence for folding through compact intermediates. Our model reproduces the observation that the C-terminus loop structure in ubiquitin is the last to fold in the folding process and most likely plays a spectator role in the folding kinetics. The possibility of a productive metastable intermediate along the folding pathway consisting of collapsed states with no secondary structure, and of intermediates or transition structures involving secondary structural elements occurring early in the sequence, is also supported by our model. The kinetics of folding remain multi-exponential below the folding temperature, with glass-like kinetics appearing at T/T(f) approximately 0.86. This new physicochemical model, designed to be predictive, helps validate the value of modeling protein folding at this level of detail for genomic-scale studies, and motivates further studies of other protein topologies and the impact of more complex energy functions, such as the addition of solvation forces.     

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an alpha/beta protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multihistogram method combined with constant-temperature Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--similar to experiments on protein G, and one pathway contains no intermediates-similar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus nonlocal interactions in various fold classes, addressing the effect of sequence mutations affecting secondary structure propensities, and providing a computationally feasible model for studying the role of solvation forces in protein folding.     

Recombination of S-peptide with S-protein during folding of ribonuclease S. I. Folding pathways of the slow-folding and fast-folding classes of unfolded S-protein.

The refolding kinetics of ribonuclease S have been measured by tyrosine absorbance, by tyrosine fluorescence emission, and by rapid binding of the specific inhibitor 2′CMP ² to folded RNAase S. The S-protein is first unfolded at pH 1.7 and then either mixed with S-peptide as refolding is initiated by a stopped-flow pH jump to pH 6.8, or the same results are obtained if S-protein and S-peptide are present together before refolding is initiated. The refolding kinetics of RNAase S have been measured as a function of temperature (10 to 40 °C) and of protein concentration (10 to 120 μm). The results are compared to the folding kinetics of S-protein alone and to earlier studies of RNAase A. A thermal folding transition of S-protein has been found below 30 °C at pH 1.7; its effects on the refolding kinetics are described in the following paper (Labhardt &; Baldwin, 1979).In this paper we characterize the refolding kinetics of unfolded S-protein, as it is found above 30 °C at pH 1.7, together with the kinetics of combination between S-peptide and S-protein during folding at pH 6.8. Two classes of unfolded S-protein molecules are found, fast-folding and slow-folding molecules, in a 20: 80 ratio. This is the same result as that found earlier for RNAase A; it is expected if the slow-folding molecules are produced by the slow cis-trans isomerization of proline residues after unfolding, since S-protein contains all four proline residues of RNAase A.The refolding kinetics of the fast-folding molecules show clearly that combination between S-peptide and S-protein occurs before folding of S-protein is complete. If combination occurred only after complete folding, then the kinetics of formation of RNAase S should be rather slow (5 s and 100 s at 30 °C) and nearly independent of protein concentration, as shown by separate measurements of the folding kinetics of S-protein, and of the combination between S-peptide and folded S-protein. The observed folding kinetics are faster than predicted by this model and also the folding rate increases strongly with protein concentration (apparent 1.6 order kinetics). The fact that RNAase S is formed more rapidly than S-protein alone is sufficient by itself to show that combination with S-peptide precedes complete folding of S-protein. Computer simulation of a simple, parallel-pathway scheme is able to reproduce the folding kinetics of the fast-folding molecules. All three probes give the same folding kinetics.These results exclude the model for protein folding in which the rate-limiting step is an initial diffusion of the polypeptide chain into a restricted range of three-dimensional configurations (“nueleation”) followed by rapid folding (“propagation”). If this model were valid, one would expect comparable rates of folding for RNAase A and for S-protein and one would also expect to find no populated folding intermediates, so that combination between S-peptide and S-protein should occur after folding is complete. Instead, RNAase A folds 60 times more rapidly than S-protein and also combination with S-peptide occurs before folding of S-protein is complete. The results demonstrate that the folding rate of S-protein increases after the formation, or stabilization, of an intermediate which results from combination with S-peptide. They support a sequential model for protein folding in which the rates of successive steps in folding depend on the stabilities of preceding intermediates.The refolding kinetics of the slow-folding molecules are complex. Two results demonstrate the presence of folding intermediates: (1) the three probes show different kinetic progress curves, and (2) the folding kinetics are concentration-dependent, in contrast to the results expected if complete folding of S-protein precedes combination with S-peptide. A faster phase of the slow-refolding reaction is detected both by tyrosine absorbance and fluorescence emission but not by 2′CMP binding, indicating that native RNAase S is not formed in this phase. Comparison of the kinetic progress curves measured by different probes is made with the use of the kinetic ratio test, which is defined here.     

Proline can have opposite effects on fast and slow protein folding phases

Proline isomerization is well known to cause additional slow phases during protein refolding. We address a new question: does the presence of prolines significantly affect the very fast kinetics that lead to the formation of folding intermediates? We examined both the very slow (10-100 min) and very fast (4 micro s-2.5 ms) folding kinetics of the two-domain enzyme yeast phosphoglycerate kinase by temperature-jump relaxation. Phosphoglycerate kinase contains a conserved cis-proline in position 204, in addition to several trans-prolines. Native cis-prolines have the largest effect on folding kinetics because the unfolded state favors trans isomerization, so we compared the kinetics of a P204H mutant with the wild-type as a proof of principle. The presence of Pro-204 causes an additional slow phase upon refolding from the cold denatured state, as reported in the literature. Contrary to this, the fast folding events are sped up in the presence of the cis-proline, probably by restriction of the conformational space accessible to the molecule. The wild-type and Pro204His mutant would be excellent models for off-lattice simulations probing the effects of conformational restriction on short timescales.     

Conversion of two-state to multi-state folding kinetics on fusion of two protein foldons

Chymotrypsin inhibitor 2 (CI2) is the archetypal single-foldon protein that folds in simple two-state kinetics without the accumulation of a folding intermediate. To model the effects of fusion of single foldons to give a multi-foldon protein, we engineered a "double-CI2" protein, in which another CI2 polypeptide was inserted into the loop region of the parent CI2. CD and HSQC spectra demonstrated that while the double-CI2 protein adopted two kinds of native conformations, CI2-like structure was almost preserved in both the domains of double-CI2. In the folding kinetic studies, double-CI2 exhibited a remarkable rollover of the observed folding rates at low denaturant concentrations, indicating that double-CI2 accumulated a kinetic folding intermediate. The different folding mechanisms between WT-CI2 and double-CI2 support the present view that protein size or number of domains is an important determinant for formation of folding intermediates.     

Folding thermodynamics of model four-strand antiparallel beta-sheet proteins.

The thermodynamic properties for three different types of off-lattice four-strand antiparallel beta-strand protein models interacting via a hybrid Go-type potential have been investigated. Discontinuous molecular dynamic simulations have been performed for different sizes of the bias gap g, an artificial measure of a model protein's preference for its native state. The thermodynamic transition temperatures are obtained by calculating the squared radius of gyration R(g)(2), the root-mean-squared pair separation fluctuation Delta(B), the specific heat C(v), the internal energy of the system E, and the Lindemann disorder parameter Delta(L). Despite these models' simplicity, they exhibit a complex set of protein transitions, consistent with those observed in experimental studies on real proteins. Starting from high temperature, these transitions include a collapse transition, a disordered-to-ordered globule transition, a folding transition, and a liquid-to-solid transition. The high temperature transitions, i.e., the collapse transition and the disordered-to-ordered globule transition, exist for all three beta-strand proteins, although the native-state geometry of the three model proteins is different. However the low temperature transitions, i.e., the folding transition and the liquid-to-solid transition, strongly depend on the native-state geometry of the model proteins and the size of the bias gap.     

Mg2+-dependent folding of a large ribozyme without kinetic traps

The folding kinetics of the catalytic domain of Bacillus subtilis ribonuclease P is analyzed here by fluorescence and catalytic activity. The folding pathway is apparently free of kinetic traps, as indicated by a decrease in folding rates upon the addition of urea. We apply Mg2+ and urea chevron analysis to fully describe the folding and unfolding kinetics of this ribozyme. A folding scheme containing two kinetic intermediates completely accounts for the free energy, the Mg2+ Hill coefficient and the surface buried in the equilibrium transition. At saturating Mg 2+concentrations, folding is limited by a barrier that is independent of Mg2+ and urea. These results describe the first trap-free folding pathway of a large ribozyme and indicate that kinetic traps are not an obligate feature of RNA folding.     

Kinetic coupling between protein folding and prolyl isomerization. I. Theoretical models.

Kinetic models were developed to describe the influence of prolyl peptide bond isomerization on the kinetics of reversible protein folding for cases in which structural intermediates do not occur. In the simulations, the number of prolyl residues and the relative rates of folding and isomerization were varied. The experimentally observed rate constants were found to be identical with the intrinsic rate constants of folding and isomerization only when folding remains much faster than prolyl isomerization throughout the transition region. When the rate of folding becomes similar to or lower than the rate of isomerization, the observed kinetic parameters are complex functions of all microscopic rate constants. In particular, the observed folding rates in the transition region decrease with the number of prolyl residues. Pseudo two-state kinetics with single folding and unfolding reactions are observed in several cases, although the apparent folding rates depend strongly on prolyl isomerization reactions in the unfolded chain. This virtual simplicity can easily lead to misinterpretation of kinetic data. Additional phases can be resolved when refolding is started from the fast-folding species (UF). The coupling between folding and prolyl peptide bond isomerization also modifies the dependence on denaturant concentration of the apparent rate constants of folding. We suggest several tests to detect and characterize the contributions of folding and isomerization steps to the observed folding kinetics.     

Kinetic coupling between protein folding and prolyl isomerization. II. Folding of ribonuclease A and ribonuclease T1.

The folding and unfolding kinetics within the transition region were measured for RNase A and for RNase T1. The data were used to evaluate the theoretical models for the influence of prolyl isomerization on the observed folding kinetics. These two proteins were selected, since the folding reaction of RNase A is faster than prolyl isomerization, whereas in RNase T1, folding is slower than isomerization in the transition region. Folding of RNase T1 was investigated for three variants with different numbers of cis prolyl residues. The results indicate that in the transition region the folding rates are indeed strongly dependent on the number of prolyl residues. The variant of RNase T1 that contains only one cis prolyl residue folds about ten times faster than two variants that contain two cis prolyl residues. For both RNase A and RNase T1, the apparent rates of folding and unfolding as well as the corresponding amplitudes depend on the concentration of denaturant in a manner that was predicted by the model calculations. When refolding was started from the fast-folding species, additional kinetic phases could be observed in the transition region for both proteins. The obtained values could be used to calculate the microscopic rate constants of folding and isomerization on the basis of theoretical models.     

Evidence for identity between the equilibrium unfolding intermediate and a transient folding intermediate: a comparative study of the folding reactions of alpha-lactalbumin and lysozyme

The refolding kinetics of alpha-lactalbumin at different concentrations of guanidine hydrochloride have been investigated by means of kinetic circular dichroism and stopped-flow absorption measurements. The refolding reaction consists of at least two stages, the instantaneous accumulation of the transient intermediate that has peptide secondary structure and the subsequent slow process associated with formation of tertiary structure. The transient intermediate is compared with the well-characterized equilibrium intermediate observed during the denaturant-induced unfolding. Stabilities of the secondary structures against the denaturant, affinities for Ca2+, and tryptophan absorption properties of the transient and equilibrium intermediates were investigated. In all of these respects, the transient intermediate is identical with the equilibrium one, demonstrating the validity of the use of the equilibrium intermediate as a model of the folding intermediate. Essentially the same transient intermediate was also detected in the folding of lysozyme, the protein known to be homologous to alpha-lactalbumin but whose equilibrium unfolding is represented as a two-state reaction. The stability and cooperativity of the secondary structure of the intermediate of lysozyme are compared with those of alpha-lactalbumin. The results show that the protein folding occurring via the intermediate is not limited to the proteins that show equilibrium intermediates. Although the unfolding equilibria of most proteins are well approximated as a two-state reaction, the two-state hypothesis may not be applicable to the folding reaction under the native condition. Two models of protein folding, intermediate-controlled folding model and multiple-pathway folding model, which are different in view of the role of the intermediate in determining the pathway of folding, are also discussed.     

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.     

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.     

The GAAA tetraloop-receptor interaction contributes differentially to folding thermodynamics and kinetics for the P4-P6 RNA domain

Tetraloops with the generic sequence GNRA are commonly found in RNA secondary structure, and interactions of such tetraloops with "receptors" elsewhere in RNA play important roles in RNA structure and folding. However, the contributions of tetraloop-receptor interactions specifically to the kinetics of RNA tertiary folding, rather than the thermodynamics of maintaining tertiary structure once folded, have not been reported. Here we investigate the role of the key GAAA tetraloop-receptor motif in folding of the P4-P6 domain of the Tetrahymena group I intron RNA. Insertions of one or more nucleotides into the tetraloop significantly disrupt the thermodynamics of tertiary folding; single-nucleotide insertions shift the folding free energy by 2-4 kcal/mol (DeltaDeltaG(o)'). The folding kinetics of several modified P4-P6 domains were determined by stopped-flow fluorescence spectroscopy, using an internally incorporated pyrene residue as the chromophore. In contrast to the thermodynamic results, the kinetics of Mg(2+)-induced folding were barely affected by the tetraloop modifications, with a DeltaDeltaG(++) of 0.2-0.4 kcal/mol and a Phi value (ratio of the kinetic and thermodynamic contributions) of <0.1. These data indicate an early transition state for folding of P4-P6 with respect to forming the tetraloop-receptor contact, consistent with previous results for modifications elsewhere in P4-P6. We conclude that the GAAA tetraloop-receptor motif contributes little to the stabilization of the transition state for Mg(2+)-induced P4-P6 folding. Rather, the tetraloop-receptor motif acts to clamp the RNA once folding has occurred. This is the first report to correlate the kinetic and thermodynamic contributions of an important RNA tertiary motif, the GNRA tetraloop-receptor. The results are related to possible models for the Mg(2+)-induced folding of the P4-P6 RNA, including a model invoking rapid nonspecific electrostatic collapse.     

Gatekeepers in the ribosomal protein s6: thermodynamics, kinetics, and folding pathways revealed by a minimalist protein model

We investigate the effect of structural gatekeepers on the folding of the ribosomal protein S6. Folding thermodynamics and early refolding kinetics are studied for this system utilizing computer simulations of a minimalist protein model. When gatekeepers are eliminated, the thermodynamic signature of a folding intermediate emerges, and a marked decrease in folding efficiency is observed. We explain the prerequisites that determine the "strength" of a given gatekeeper. The investigated gatekeepers are found to have distinct functions, and to guide the folding and time-dependent packing of non-overlapping secondary structure elements in the protein. Gatekeepers avoid kinetic traps during folding by favoring the formation of "productive topologies" on the way to the native state. The trends in folding rates in the presence/absence of gatekeepers observed for our minimalist model of S6 are in very good agreement with experimental data on this protein.