Study of the compact denatured state of a protein by molecular dynamics simulation]

The native state can be considered as a unique conformation of the protein molecule with the lowest free energy of residue contacts. In this case, all other conformations correspond to the denatured state. The degree of their compactness varies significantly. Under folding conditions, the compact denatured state rather than the random coil is in equilibrium with native protein. The balance between the main forces of protein folding, the solvophobic interactions and conformational entropy, suggests that some properties of the compact denatured state are close to those of native protein, whereas other properties are close to those of the random coil. To investigate the molecular structure of the compact denatured state, the method of molecular dynamics simulation seems to be very useful.     

Statistical mechanics of protein folding by cluster distance geometry

This is our second type of model for protein folding where the configurational parameters and the effective potential energy function are chosen in such a way that all conformations are described and the canonical partition function can be evaluated analytically. Structure is described in terms of distances between pairs of sequentially contiguous blocks of eight residues, and all possible conformations are grouped into 71 subsets in terms of bounds on these distances. The energy is taken to be a sum of pairwise interactions between such blocks. The 210 energy parameters were adjusted so that the native folds of 32 small proteins are favored in free energy over the denatured state. We then found 146 proteins having negligible sequence similarity to any of the training proteins, yet the free energy of the respective correct native states were favored over the denatured state.     

Electrostatic interactions in the denatured state and in the transition state for protein folding: effects of denatured state interactions on the analysis of transition state structure

The development of electrostatic interactions during the folding of the N-terminal domain of the ribosomal protein L9 (NTL9) is investigated by pH-dependent rate equilibrium free energy relationships. We show that Asp8, among six acidic residues, is involved in non-native, electrostatic interactions with K12 in the transition state for folding as well as in the denatured state. The perturbed native state pK(a) of D8 (pK(a) = 3.0) appears to be maintained through non-native interactions in both the transition state and the denatured state. Mutational effects on the stability of the transition state for protein (un)folding are often analyzed in respect to change in ground states. Thus, the interpretation of transition state analysis critically depends on an understanding of mutational effects on both the native and denatured state. Increasing evidence for structurally biased denatured states under physiological conditions raises concerns about possible denatured state effects on folding studies. We show that the structural interpretation of transition state analysis can be altered dramatically by denatured state effects.     

Mechanisms of the multiphasic kinetics in the folding and unfolding of globular proteins

The multiphasic kinetics of the protein folding and unfolding processes are examined for a “cluster model” with only two thermodynamically stable macroscopic states, native (N) and denatured (D), which are essentially distributions of microscopic states. The simplest kinetic schemes consistent with the model are: N-(fast) → I-(slow) → D for unfolding and N ← (fast)-D₂ ← (slow)-D₁ for refolding. The fast phase during the unfolding process can be visualized as the redistribution of the native population N to I within its free energy valley. Then, this population crosses over the free energy barrier to the denatured state D in the slow phase. Therefore, the macrostate I is a kinetic intermediate which is not stable at equilibrium. For the refolding process, the initial equilibrium distribution of the denatured state D appears to be separated into D₁ and D₂ in the final condition because of the change in position of the free energy barrier. The fast refolding species D₂ is due to the “leak” from the broadly distributed D state, while the rest is the slow refolding species D₁, which must overpass the free energy barrier to reach N. At an early stage of the folding process the amino acid chain is considered to be composed of several locally ordered regions, which we call clusters, connected by random coil chain parts. Thus, the denatured state contains different sizes and distributions of clusters depending on the external condition. A later stage of the folding process is the association of smaller clusters. The native state is expressed by a maximum-size cluster with possible fluctuation sites reflecting this association. A general discussion is given of the correlation between the kinetics and thermodynamics of proteins from the overall shape of the free energy function. The cluster model provides a conceptual link between the folding kinetics and the structural patterns of globular proteins derived from the X-ray crystallographic data.     

An expanded view of the protein folding landscape of PDZ domains

Most protein domains fold in an apparently co-operative and two-state manner with only the native and denatured states significantly populated at any experimental condition. However, the protein folding energy landscape is often rugged and different transition states may be rate limiting for the folding reaction under different conditions, as seen for the PDZ protein domain family. We have here analyzed the folding kinetics of two PDZ domains and found that a previously undetected third transition state is rate limiting under conditions that stabilize the native state relative to the denatured state. In light of these results, we have re-analyzed previous folding data on PDZ domains and present a unified folding mechanism with three distinct transition states separated by two high-energy intermediates. Our data show that sequence composition tunes the relative stabilities of folding transition states within the PDZ family, while the overall mechanism is determined by topology. This model captures the kinetic folding mechanism of all PDZ domains studied to date.     

Dimensions,energetics, and denaturant effects of the protein unstructured state

Determining the energetics of the unfolded state of a protein is essential for understanding the folding mechanics of ordered proteins and the structure–function relation of intrinsically disordered proteins. Here, we adopt a coil‐globule transition theory to develop a general scheme to extract interaction and free energy information from single‐molecule fluorescence resonance energy transfer spectroscopy. By combining protein stability data, we have determined the free energy difference between the native state and the maximally collapsed denatured state in a number of systems, providing insight on the specific/nonspecific interactions in protein folding. Both the transfer and binding models of the denaturant effects are demonstrated to account for the revealed linear dependence of inter‐residue interactions on the denaturant concentration, and are thus compatible under the coil‐globule transition theory to further determine the dimension and free energy of the conformational ensemble of the unfolded state. The scaling behaviors and the effective θ‐state are also discussed.     

Denatured-state energy landscapes of a protein structural database reveal the energetic determinants of a framework model for folding

Position-specific denatured-state thermodynamics were determined for a database of human proteins by use of an ensemble-based model of protein structure. The results of modeling denatured protein in this manner reveal important sequence-dependent thermodynamic properties in the denatured ensembles as well as fundamental differences between the denatured and native ensembles in overall thermodynamic character. The generality and robustness of these results were validated by performing fold-recognition experiments, whereby sequences were matched with their respective folds based on amino acid propensities for the different energetic environments in the protein, as determined through cluster analysis. Correlation analysis between structure and energetic information revealed that sequence segments destined for β-sheet in the final native fold are energetically more predisposed to a broader repertoire of states than are sequence segments destined for α-helix. These results suggest that within the subensemble of mostly unstructured states, the energy landscapes are dominated by states in which parts of helices adopt structure, whereas structure formation for sequences destined for β-strand is far less probable. These results support a framework model of folding, which suggests that, in general, the denatured state has evolutionarily evolved to avoid low-energy conformations in sequences that ultimately adopt β-strand. Instead, the denatured state evolved so that sequence segments that ultimately adopt α-helix and coil will have a high intrinsic structure formation capability, thus serving as potential nucleation sites.     

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.     

The osmophobic effect: natural selection of a thermodynamic force in protein folding

Intracellular organic osmolytes are present in certain organisms adapted to harsh environments and these osmolytes protect intracellular macromolecules against the denaturing environmental stress. In natural selection of organic osmolytes as protein stabilizers, it appears that the osmolyte property selected for is the unfavorable interaction between the osmolyte and the peptide backbone, a solvophobic thermodynamic force that we call the osmophobic effect. Because the peptide backbone is highly exposed to osmolyte in the denatured state, the osmophobic effect preferentially raises the free energy of the denatured state, shifting the equilibrium in favor of the native state. By focusing the solvophobic force on the denatured state, the native state is left free to function relatively unfettered by the presence of osmolyte. The osmophobic effect is a newly uncovered thermodynamic force in nature that complements the well-recognized hydrophobic interactions, hydrogen bonding, electrostatic and dispersion forces that drive protein folding. In organisms whose survival depends on the intracellular presence of osmolytes that can counteract denaturing stresses, the osmophobic effect is as fundamental to protein folding as these well-recognized forces.     

The stability and folding process of amyloidogenic mutant human lysozymes.

Amyloid deposits are frequently formed by mutant proteins that have a lower stability than the wild-type proteins. Some reports, however, have shown that mutant-induced thermodynamic destabilization is not always a general mechanism of amyloid formation. To obtain a better understanding of the mechanism of amyloid fibril formation, we show in this study that equilibrium and kinetic refolding-unfolding reaction experiments with two amyloidogenic mutant human lysozymes (I56T and D67H) yield folding pathways that can be drawn as Gibbs energy diagrams. The equilibrium stabilities between the native and denatured states of both mutant proteins were decreased, but the degrees of instability were different. The Gibbs energy diagrams of the folding process reveal that the Gibbs energy change between the native and folding intermediate states was similar for both proteins, and also that the activation Gibbs energy change from the native state to the transition state decreased. Our results confirm that the tendency to favor the intermediate of denaturation facilitates amyloid formation by the mutant human lysozymes more than equilibrium destabilization between the native and completely denatured states does.     

Compact dimension of denatured states of staphylococcal nuclease

Fluorescence and circular dichroism stopped-flow have been widely used to determine the kinetics of protein folding including folding rates and possible folding pathways. Yet, these measurements are not able to provide spatial information of protein folding/unfolding. Especially, conformations of denatured states cannot be elaborated in detail. In this study, we apply the method of fluorescence energy transfer with a stopped-flow technique to study global structural changes of the staphylococcal nuclease (SNase) mutant K45C, where lysine 45 is replaced by cysteine, during folding and unfolding. By labeling the thiol group of cysteine with TNB (5,5'-dithiobis-2-nitrobenzoic acid) as an energy acceptor and the tryptophan at position 140 as a donor, distance changes between the acceptor and the donor during folding and unfolding are measured from the efficiency of energy transfer. Results indicate that the denatured states of SNase are highly compact regardless of how the denatured states (pH-induced or GdmCl-induced) are induced. The range of distance changes between two probes is between 25.6 and 25.4 A while it is 20.4 A for the native state. Furthermore, the folding process consists of three kinetic phases while the unfolding process is a single phase. These observations agree with our previous sequential model: N(0) left arrow over right arrow D(1) left arrow over right arrow D(2) left arrow over right arrow D(3) (Chen et al., J Mol Biol 1991;220:771-778). The efficiency of protein folding may be attributed to initiating the folding process from these compact denatured structures.     

Kinetic analysis of local structure formations in protein folding

The protein folding process is described by a cluster model based on the assumption that local structures or clusters are formed at an early stage in different regions of the polypeptide chain. Possible local structural elements in a globular protein are helices, bends, and hydrophobic cores whose formation is presumably determined by the interaction with the environment. Thus the tendency of local structure formation is expressed by a surface free energy of the cluster, which is assigned to the interface between the cluster and its environment. The probability of finding the chain of N residues with k clusters and m residues in the cluster is represented by a cluster distribution map. The cluster model exhibits a distinct two-state-like equilibrium transition, which can be seen on this map as well-separated native and denatured populations at the midpoint of the transition. The native population is localized at k ≈ 1 and m ≈ N, while the position of the denatured population can vary significantly depending on the surface free energy of the cluster. If the surface free energy is strong, the denatured population is localized near k = 0 and m = 0. On the other hand, if the surface free energy is weak, the denatured population is localized at high k and m values. The dynamics of the cluster model are treated as a stochastic process involving the transition from a state (k,m) to one of its six neighbors. The transition probability for each transition is determined by the free energy difference between two states; thus no activation process is assumed. However, the conversion of the two macrostates, native and denatured populations, involves the free energy activation due to the cooperative interaction of the macrosystem. The dynamics are analyzed by following the time evolution of the population profile on the cluster distribution map. Kinetic schemes are proposed to describe the multistep mechanism of protein folding and unfolding.     

How random is a highly denatured protein?

There has been renewed interest in determining the physicochemical properties of denatured states of proteins. In many denatured states there is evidence for the existence of nonrandom configurational distributions. Here we examine the small-angle neutron scattering profile of yeast phosphoglycerate kinase in the native state and in highly denaturing conditions. We show that the denatured protein scattering profile can be interpreted using a model developed for synthetic polymers in which the chain behaves as a random coil in a good solvent, i.e. with excluded volume interactions. The implications of this result for our appreciation of the protein folding process are discussed.     

RNA and protein folding: common themes and variations

Visualizing the navigation of an ensemble of unfolded molecules through the bumpy energy landscape in search of the native state gives a pictorial view of biomolecular folding. This picture, when combined with concepts in polymer theory, provides a unified theory of RNA and protein folding. Just as for proteins, the major folding free energy barrier for RNA scales sublinearly with the number of nucleotides, which allows us to extract the elusive prefactor for RNA folding. Several folding scenarios can be anticipated by considering variations in the energy landscape that depend on sequence, native topology, and external conditions. RNA and protein folding mechanism can be described by the kinetic partitioning mechanism (KPM) according to which a fraction (Phi) of molecules reaches the native state directly, whereas the remaining fraction gets kinetically trapped in metastable conformations. For two-state folders Phi approximately 1. Molecular chaperones are recruited to assist protein folding whenever Phi is small. We show that the iterative annealing mechanism, introduced to describe chaperonin-mediated folding, can be generalized to understand protein-assisted RNA folding. The major differences between the folding of proteins and RNA arise in the early stages of folding. For RNA, folding can only begin after the polyelectrolyte problem is solved, whereas protein collapse requires burial of hydrophobic residues. Cross-fertilization of ideas between the two fields should lead to an understanding of how RNA and proteins solve their folding problems.     

Structural Characteristic of the Initial Unfolded State on Refolding Determines Catalytic Efficiency of the Folded Protein in Presence of Osmolytes

Osmolytes are low molecular weight organic molecules accumulated by organisms to assist proper protein folding, and to provide protection to the structural integrity of proteins under denaturing stress conditions. It is known that osmolyte-induced protein folding is brought by unfavorable interaction of osmolytes with the denatured/unfolded states. The interaction of osmolyte with the native state does not significantly contribute to the osmolyte-induced protein folding. We have therefore investigated if different denatured states of a protein (generated by different denaturing agents) interact differently with the osmolytes to induce protein folding. We observed that osmolyte-assisted refolding of protein obtained from heat-induced denatured state produces native molecules with higher enzyme activity than those initiated from GdmCl- or urea-induced denatured state indicating that the structural property of the initial denatured state during refolding by osmolytes determines the catalytic efficiency of the folded protein molecule. These conclusions have been reached from the systematic measurements of enzymatic kinetic parameters (K _m and k _cat), thermodynamic stability (T _m and ΔH _m) and secondary and tertiary structures of the folded native proteins obtained from refolding of various denatured states (due to heat-, urea- and GdmCl-induced denaturation) of RNase-A in the presence of various osmolytes.     

Protein folding cooperativity: basic insights from minimalist models

Basic concepts about two-state, cooperative protein folding and its relation to first-order phase transitions are reviewed. Minimalist models capable of reproducing the required free energy barrier between folded and unfolded macroscopic states are described. A significantly more restrictive "calorimetric" criterion is also discussed, which is based on direct comparison between model and experimental heat capacities with additional assumptions about conformational enthalpy variation in the unfolded state.     

Denatured states of yeast cytochrome c induced by heat and guanidinium chloride are structurally and thermodynamically different

A sequence alignment of mammalian cytochromes c with yeast iso-1-cytochrome c (y-cyt-c) shows that the yeast protein contains five extra N-terminal residues. We have been interested in understanding the question: What is the role of these five extra N-terminal residues in folding and stability of the protein? To answer this question we have prepared five deletants of y-cyt-c by sequentially removing these extra residues. During our studies on the wild type (WT) protein and its deletants, we observed that the amount of secondary structure in the guanidinium chloride (GdmCl)-induced denatured (D) state of each protein is different from that of the heat-induced denatured (H) state. This finding is confirmed by the observation of an additional cooperative transition curve of optical properties between H and D states on the addition of different concentrations of GdmCl to the already heat denatured WT y-cyt-c and its deletants at pH 6.0 and 68°C. For each protein, analysis of transition curves representing processes, native (N) state ? D state, N state ? H state, and H state ? D state, was done to obtain Gibbs free energy changes associated with all the three processes. This analysis showed that, for each protein, thermodynamic cycle accommodates Gibbs free energies associated with transitions between N and D states, N and H states, and H and D states, the characteristics required for a thermodynamic function. All these experimental observations have been supported by our molecular dynamics simulation studies.     

Titration Properties and Thermodynamics of the Transition State for Folding: Comparison of Two-state and Multi-state Folding Pathways

CI2 folds and unfolds as a single cooperative unit by simple two-state kinetics, which enables the properties of the transition state to be measured from both the forward and backward rate constants. We have examined how the free energy of the transition state for the folding of chymotrypsin inhibitor 2 (CI2) changes with pH and temperature. In addition to the standard thermodynamic quantities, we have measured the overall acid-titration properties of the transition state and its heat capacity relative to both the denatured and native states. We were able to determine the latter by a method analogous to a well-established procedure for measuring the change in heat capacity for equilibrium unfolding: the enthalpy of activation of unfolding at different values of acid pH were plotted against the average temperature of each determination. Our results show that the transition state of CI2 has lost most of the electrostatic and van der Waals' interactions that are found in the native state, but it remains compact and this prevents water molecules from entering some parts of the hydrophobic core. The properties of the transition state of CI2 are then compared with the major folding transition state of the larger protein barnase, which folds by a multi-state mechanism, with the accumulation of a partly structured intermediate (D^physor I). CI2 folds from a largely unstructured denatured state under physiological conditionsviaa transition state which is compact but relatively uniformly unstructured, with tertiary and secondary structure being formed in parallel. We term this an expanded pathway. Conversely, barnase folds from a largely structured denatured state in which elements of structure are well formed through a transition state that has islands of folded elements of structure. We term this a compact pathway. These two pathways may correspond to the two extreme ends of a continuous spectrum of protein folding mechanisms. Although the properties of the two transition states are very different, the activation barrier for folding (D^phys→3 ) is very similar for both proteins.     

Is protein unfolding the reverse of protein folding? A lattice simulation analysis.

Simulations and experiments that monitor protein unfolding under denaturing conditions are commonly employed to study the mechanism by which a protein folds to its native state in a physiological environment. Due to the differences in conditions and the complexity of the reaction, unfolding is not necessarily the reverse of folding. To assess the relevance of temperature initiated unfolding studies to the folding problem, we compare the folding and unfolding of a 125-residue protein model by Monte Carlo dynamics at two temperatures; the lower one corresponds to the range used in T -jump experiments and the higher one to the range used in unfolding simulations of all-atom models. The trajectories that lead from the native state to the denatured state at these elevated temperatures are less diverse than those observed in the folding simulations. At the lower temperature, the system unfolds through a mandatory intermediate that corresponds to a local free energy minimum. At the higher temperature, no such intermediate is observed, but a similar pathway is followed. The structures contributing to the unfolding pathways resemble most closely those that make up the "fast track" of folding. The transition state for unfolding at the lower temperature (above Tm) is determined and is found to be more structured than the transition state for folding below the melting temperature. This shift towards the native state is consistent with the Hammond postulate. The implications for unfolding simulations of higher resolution models and for unfolding experiments of proteins are discussed.     

Understanding the Mechanism of Prosegment-catalyzed Folding by Solution NMR Spectroscopy

Multidomain protein folding is often more complex than a two-state process, which leads to the spontaneous folding of the native state. Pepsin, a zymogen-derived enzyme, without its prosegment (PS), is irreversibly denatured and folds to a thermodynamically stable, non-native conformation, termed refolded pepsin, which is separated from native pepsin by a large activation barrier. While it is known that PS binds refolded pepsin and catalyzes its conversion to the native form, little structural details are known regarding this conversion. In this study, solution NMR was used to elucidate the PS-catalyzed folding mechanism by examining the key equilibrium states, e.g. native and refolded pepsin, both in the free and PS-bound states, and pepsinogen, the zymogen form of pepsin. Refolded pepsin was found to be partially structured and lacked the correct domain-domain structure and active-site cleft formed in the native state. Analysis of chemical shift data revealed that upon PS binding refolded pepsin folds into a state more similar to that of pepsinogen than to native pepsin. Comparison of pepsin folding by wild-type and mutant PSs, including a double mutant PS, indicated that hydrophobic interactions between residues of prosegment and refolded pepsin lower the folding activation barrier. A mechanism is proposed for the binding of PS to refolded pepsin and how the formation of the native structure is mediated.