The early folding kinetics of apomyoglobin.

The folding pathway of apomyoglobin has been experimentally shown to have early kinetic intermediates involving the A, B, G, and H helices. The earliest detected kinetic events occur on a ns to micros time scale. We show that the early folding kinetics of apomyoglobin may be understood as the association of nascent helices through a network of diffusion-collision-coalescence steps G + H <--> GH + A <--> AGH + B <--> ABGH obtained by solving the diffusion-collision model in a chemical kinetics approximation. Our reproduction of the experimental results indicates that the model is a useful way to analyze folding data. One prediction from our fit is that the nascent A and H helices should be relatively more helix-like before coalescence than the other apomyoglobin helices.     

Redesigning the folding energetics of a model three-helix bundle protein by site-directed mutagenesis

Because of their limited size and complexity, de novo designed proteins are particularly useful for the detailed investigation of folding thermodynamics and mechanisms. Here, we describe how subtle changes in the hydrophobic core of a model three-helix bundle protein (GM-0) alter its folding energetics. To explore the folding tolerance of GM-0 toward amino acid sequence variability, two mutant proteins (GM-1 and GM-2) were generated. In the mutants, cavities were created in the hydrophobic core of the protein by either singly (GM-1; L35A variant) or doubly (GM-2; L35A/I39A variant) replacing large hydrophobic side chains by smaller Ala residues. The folding of GM-0 is characterized by two partially folded intermediate states exhibiting characteristics of molten globules, as evidenced by pressure-unfolding and pressure-assisted cold denaturation experiments. In contrast, the folding energetics of both mutants, GM-1 and GM-2, exhibit only one folding intermediate. Our results support the view that simple but biologically important folding motifs such as the three-helix bundle can reveal complex folding plasticity, and they point to the role of hydrophobic packing as a determinant of the overall stability and folding thermodynamic of the helix bundle.     

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.     

Folding kinetics of designer proteins. Application of the diffusion-collision model to a de novo designed four-helix bundle.

A folding algorithm is described, based on the diffusion-collision model, combining static and dynamic calculational methods. The algorithm is applied to predict the basic structure and schematic folding pathways of an artificial four-helix bundle.     

Characterization of the folding kinetics of a three-helix bundle protein via a minimalist Langevin model.

We use a simple off-lattice Langevin model of protein folding to characterize the folding and unfolding of a fast-folding, 46 residue three-helix bundle. Under conditions at which the C-terminal helix is 30 % stable, we observe a clear three-state folding mechanism. In the on-pathway intermediate state, the middle and C-terminal helices are folded and in contact with each other, while the N-terminal region remains disordered. Nevertheless, under these conditions this intermediate is thermodynamically unstable relative to its unfolded state. The first and highest folding barrier corresponds to the organization of the hinge between the middle and C-terminal helices. A subsequent major barrier corresponds to the organization of the hinge between the middle and N-terminal helices. Hyperstabilizing the hinge regions leads to twice the folding rate that is obtained from hyperstabilizing the helices, even though much fewer contacts are involved in hinge hyperstabilization than in helix hyperstabilization. Unfolding follows single-exponential kinetics, even at temperatures only slightly above the folding transition temperature.     

Local secondary structure content predicts folding rates for simple,two-state proteins

Many single-domain proteins exhibit two-state folding kinetics, with folding rates that span more than six orders of magnitude. A quantity of much recent interest for such proteins is their contact order, the average separation in sequence between contacting residue pairs. Numerous studies have reached the surprising conclusion that contact order is well-correlated with the logarithm of the folding rate for these small, well-characterized molecules. Here, we investigate the physico-chemical basis for this finding by asking whether contact order is actually a composite number that measures the fraction of local secondary structure in the protein; viz. turns, helices, and hairpins. To pursue this question, we calculated the secondary structure content for 24 two-state proteins and obtained coefficients that predict their folding rates. The predicted rates correlate strongly with experimentally determined rates, comparable to the correlation with contact order. Further, these predicted folding rates are correlated strongly with contact order. Our results suggest that the folding rate of two-state proteins is a function of their local secondary structure content, consistent with the hierarchic model of protein folding. Accordingly, it should be possible to utilize secondary structure prediction methods to predict folding rates from sequence alone.     

Sequence-based study of two related proteins with different folding behaviors

Z(SPA-1) is an engineered protein that binds to its parent, the three-helix-bundle Z domain of staphylococcal protein A. Uncomplexed Z(SPA-1) shows a reduced helix content and a melting behavior that is less cooperative, compared with the wild-type Z domain. Here we show that the difference in folding behavior between these two sequences can be partly understood in terms of an off-lattice model with 5-6 atoms per amino acid and a minimalistic potential, in which folding is driven by backbone hydrogen bonding and effective hydrophobic attraction.     

Domains in folding of model proteins.

By means of Monte Carlo simulation, we investigated the equilibrium between folded and unfolded states of lattice model proteins. The amino acid sequences were designed to have pronounced energy minimum target conformations of different length and shape. For short fully compact (36-mer) proteins, the all-or-none transition from the unfolded state to the native state was observed. This was not always the case for longer proteins. Among 12 designed sequences with the native structure of a fully compact 48-mer, a simple all-or-none transition was observed in only three cases. For the other nine sequences, three states of behavior-the native, denatured, and intermediate states-were found. The contiguous part of the native structure (domain) was conserved in the intermediate state, whereas the remaining part was completely unfolded and structureless. These parts melted separately from each other.     

The role of sequence and structure in protein folding kinetics; the diffusion-collision model applied to proteins L and G

The diffusion-collision model (DCM) is applied to the folding kinetics of protein L and protein G. In the DCM, the two proteins are treated as consisting of two beta-hairpins and one alpha-helix, so that they are isomorphous with the three-helix bundle DCM model. In the absence of sequence dependent factors, both proteins would fold in the same way in the DCM, with the coalescence of the N-terminal hairpin and the helix slightly favored over the C-terminal hairpin and the helix because the former are closer together than the latter. However, sequence dependent factors make the N-terminal hairpin of protein L and the C-terminal hairpin of protein G more stable in the ensemble of unfolded conformations. This difference in the stabilities gives rise to the difference in the calculated folding behavior, in agreement with experiment.     

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.     

Use of quantitative structure-property relationships to predict the folding ability of model proteins

We investigate the folding of a 125-bead heteropolymer model for proteins subject to Monte Carlo dynamics on a simple cubic lattice. Detailed study of a few sequences revealed a folding mechanism consisting of a rapid collapse followed by a slow search for a stable core that served as the transition state for folding to a near-native intermediate. Rearrangement from the intermediate to the native state slowed folding further because it required breaking native-like local structure between surface monomers so that those residues could condense onto the core. We demonstrate here the generality of this mechanism by a statistical analysis of a 200 sequence database using a method that employs a genetic algorithm to pick the sequence attributes that are most important for folding and an artificial neural network to derive the corresponding functional dependence of folding ability on the chosen sequence attributes [quantitative structure-property relationships (QSPRs)]. QSPRs that use three sequence attributes yielded substantially more accurate predictions than those that use only one. The results suggest that efficient search for the core is dependent on both the native state's overall stability and its amount of kinetically accessible, cooperative structure, whereas rearrangement from the intermediate is facilitated by destabilization of contacts between surface monomers. Implications for folding and design are discussed. Proteins 33:177–203, 1998. © 1998 Wiley-Liss, Inc.     

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.     

Retinal proteins as model systems for membrane protein folding

Experimental folding studies of membrane proteins are more challenging than water-soluble proteins because of the higher hydrophobicity content of membrane embedded sequences and the need to provide a hydrophobic milieu for the transmembrane regions. The first challenge is their denaturation: due to the thermodynamic instability of polar groups in the membrane, secondary structures in membrane proteins are more difficult to disrupt than in soluble proteins. The second challenge is to refold from the denatured states. Successful refolding of membrane proteins has almost always been from very subtly denatured states. Therefore, it can be useful to analyze membrane protein folding using computational methods, and we will provide results obtained with simulated unfolding of membrane protein structures using the Floppy Inclusions and Rigid Substructure Topography (FIRST) method. Computational methods have the advantage that they allow a direct comparison between diverse membrane proteins. We will review here both, experimental and FIRST studies of the retinal binding proteins bacteriorhodopsin and mammalian rhodopsin, and discuss the extension of the findings to deriving hypotheses on the mechanisms of folding of membrane proteins in general. This article is part of a Special Issue entitled: Retinal Proteins—You can teach an old dog new tricks.     

All-atom folding of the three-helix HIV accessory protein with an adaptive parallel tempering method

All-atom protein structure prediction from the amino acid sequence alone remains an important goal of biophysical chemistry. Recent progress in force field development and validation suggests that the PFF01 free-energy force field correctly predicts the native conformation of various helical proteins as the global optimum of its free-energy surface. Reproducible protein structure prediction requires the availability of efficient optimization methods to locate the global minima of such complex potentials. Here we investigate an adapted version of the parallel tempering method as an efficient parallel stochastic optimization method for protein structure prediction. Using this approach we report the reproducible all-atom folding of the three-helix 40 amino acid HIV accessory protein from random conformations to within 2.4 A backbone RMS deviation from the experimental structure with modest computational resources.     

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.     

Probing the folding and unfolding dynamics of secondary and tertiary structures in a three-helix bundle protein

Fast relaxation kinetics studies of the B-domain of staphylococcal protein A were performed to characterize the folding and unfolding of this small three-helix bundle protein. The relaxation kinetics were initiated using a laser-induced temperature jump and probed using time-resolved infrared spectroscopy. The kinetics monitored within the amide I' absorbance of the polypeptide backbone exhibit two distinct kinetics phases with nanosecond and microsecond relaxation times. The fast kinetics relaxation time is close to the diffusion limits placed on protein folding reactions. The fast kinetics phase is dominated by the relaxation of the solvated helix (nu = 1632 cm(-1)), which reports on the fast relaxation of the individual helices. The slow kinetics phase follows the cooperative relaxation of the native helical bundle core that is monitored by both solvated (nu = 1632 cm(-1)) and buried helical IR bands (nu = 1652 cm(-1)). The folding rates of the slow kinetics phase calculated over an extended temperature range indicate that the core formation of this protein follows a pathway that is energetically downhill. The unfolding rates are much more strongly temperature-dependent indicating an activated process with a large energy barrier. These results provide significant insight into the primary process of protein folding and suggest that fast formation of helices can drive the folding of helical proteins.     

Bicelle size modulates the rate of bacteriorhodopsin folding

The conformational equilibria of integral membrane proteins have proven extremely difficult to characterize within native lipid bilayers. To circumvent technical issues, investigations of the structure and stability of α‐helical membrane proteins are often carried out in mixed micelle or bicelle solvents that mimic the membrane and facilitate measurements of reversible folding. Under these conditions, the energetics of membrane protein folding are typically proportional to the mole fraction of an anionic detergent in the micelle. However, investigations of the folding and unfolding of bacteriorhodopsin (bR) surprisingly revealed that the folding rate is also highly sensitive to the bulk molar concentration of lipids and detergents. We show here that this rate enhancement coincides with changes in bicelle size and suggest this effect arises through restriction of the conformational search space during folding. In conjunction with previous mutagenic studies, these results provide additional evidence that a topological search limits the rate of bR folding. Furthermore, this finding provides insights into the manner by which micellar and bicellar environments influence the conformational stability of polytopic membrane proteins.