Thermal folding and mechanical unfolding pathways of protein secondary structures

Mechanical stretching of secondary structures is studied through molecular dynamics simulations of a Go-like model. Force versus displacement curves are studied as a function of the stiffness and velocity of the pulling device. The succession of stretching events, as measured by the order in which contacts are ruptured, is compared to the sequencing of events during thermal folding and unfolding. Opposite cross-correlations are found for an alpha-helix and a beta-hairpin structure. In a tandem of two alpha-helices, the two constituent helices unravel nearly simultaneously. A simple condition for simultaneous versus sequential unraveling of repeat units is presented.     

pH-jump-induced folding and unfolding studies of barstar: evidence for multiple folding and unfolding pathways.

Equilibrium and kinetic characterization of the high pH-induced unfolding transition of the small protein barstar have been carried out in the pH range 7-12. A mutant form of barstar, containing a single tryptophan, Trp 53, completely buried in the core of the native protein, has been used. It is shown that the protein undergoes reversible unfolding above pH 10. The pH 12 form (the D form) appears to be as unfolded as the form unfolded by 6 M guanidine hydrochloride (GdnHCl) at pH 7 (the U form): both forms have similar fluorescence and far-UV circular dichroism (CD) signals and have similar sizes, as determined by dynamic light scattering and size-exclusion chromatography. No residual structure is detected in the D form: addition of GdnHCl does not alter its fluorescence and far-UV CD properties. The fluorescence signal of Trp 53 has been used to monitor folding and unfolding kinetics. The kinetics of folding of the D form in the pH range 7-11 are complex and are described by four exponential processes, as are the kinetics of unfolding of the native state (N state) in the pH range 10.5-12. Each kinetic phase of folding decreases in rate with increase in pH from 7 to 10.85, and each kinetic phase of unfolding decreases in rate with decrease in pH from 12 to 10.85. At pH 10.85, the folding and unfolding rates for any particular kinetic phase are identical and minimal. The two slowest phases of folding and unfolding have identical kinetics whether measured by Trp 53 fluorescence or by mean residue ellipticity at 222 nm. Direct determination of the increase in the N state with time of folding at pH 7 and of the D form with time of unfolding at pH 12, by means of double-jump assays, show that between 85 and 95% of protein molecules fold or unfold via fast pathways between the two forms. The remaining 5-15% of protein molecules appear to fold or unfold via slower pathways, on which at least two intermediates accumulate. The mechanism of folding from the high pH-denatured D form is remarkably similar to the mechanism of folding from the urea or GdnHCl-denatured U form.     

Equilibrium and kinetic studies of protein cooperativity using urea-induced folding/unfolding of a Ubq-UIM fusion protein

Understanding the origins of cooperativity in proteins remains an important topic in protein folding. This study describes experimental folding/unfolding equilibrium and kinetic studies of the engineered protein Ubq-UIM, consisting of ubiquitin (Ubq) fused to the sequence of the ubiquitin interacting motif (UIM) via a short linker. Urea-induced folding/unfolding profiles of Ubq-UIM were monitored by far-UV circular dichroism and fluorescence spectroscopies and compared to those of the isolated Ubq domain. It was found that the equilibrium data for Ubq-UIM is inconsistent with a two-state model. Analysis of the kinetics of folding shows similarity in the folding transition state ensemble between Ubq and Ubq-UIM, suggesting that formation of Ubq domain is independent of UIM. The major contribution to the stabilization of Ubq-UIM, relative to Ubq, was found to be in the rates of unfolding. Moreover, it was found that the kinetic m-values for Ubq-UIM unfolding, monitored by different probes (far-UV circular dichroism and fluorescence spectroscopies), are different; thereby, further supporting deviations from a two-state behavior. A thermodynamic linkage model that involves four states was found to be applicable to the urea-induced unfolding of Ubq-UIM, which is in agreement with the previous temperature-induced unfolding study. The applicability of the model was further supported by site-directed variants of Ubq-UIM that have altered stabilities of Ubq/UIM interface and/or stabilities of individual Ubq- and UIM-domains. All variants show increased cooperativity and one variant, E43N_Ubq-UIM, appears to behave very close to an equilibrium two-state.     

Machinery of protein folding and unfolding

During the past two years, a large amount of biochemical, biophysical and low- to high-resolution structural data have provided mechanistic insights into the machinery of protein folding and unfolding. It has emerged that dual functionality in terms of folding and unfolding might exist for some systems. The majority of folding/unfolding machines adopt oligomeric ring structures in a cooperative fashion and utilise the conformational changes induced by ATP binding/hydrolysis for their specific functions.     

Equilibrium folding and stability of myotrophin: a model ankyrin repeat protein

Proteins containing stretches of repeating amino acid sequences are prevalent throughout nature, yet little is known about the general folding and assembly mechanisms of these systems. Here we propose myotrophin as a model system to study the folding of ankyrin repeat proteins. Myotrophin is folded over a large pH range and is soluble at high concentrations. Thermal and urea denaturation studies show that the protein displays cooperative two-state folding properties despite its modular nature. Taken together with previous studies on other ankyrin repeat proteins, our data suggest that the two-state folding pathway may be characteristic of ankyrin repeat proteins and other integrated alpha-helical repeat proteins in general.     

Predicting protein folding pathways

A structured folding pathway, which is a time ordered sequence of folding events, plays an important role in the protein folding process and hence, in the conformational search. Pathway prediction, thus gives more insight into the folding process and is a valuable guiding tool to search the conformation space. In this paper, we propose a novel 'unfolding' approach to predict the folding pathway. We apply graph-based methods on a weighted secondary structure graph of a protein to predict the sequence of unfolding events. When viewed in reverse this yields the folding pathway. We demonstrate the success of our approach on several proteins whose pathway is partially known.     

Equilibrium and kinetics of the folding and unfolding of canine milk lysozyme

The equilibrium and kinetics of canine milk lysozyme folding/unfolding were studied by peptide and aromatic circular dichroism and tryptophan fluorescence spectroscopy. The Ca2+-free apo form of the protein exhibited a three-state equilibrium unfolding, in which the molten globule state is well populated as an unfolding intermediate. A rigorous analysis of holo protein unfolding, including the data from the kinetic refolding experiments, revealed that the holo protein also underwent three-state unfolding with the same molten globule intermediate. Although the observed kinetic refolding curves of both forms were single-exponential, a burst-phase change in the peptide ellipticity was observed in both forms, and the burst-phase intermediates of both forms were identical to each other with respect to their stability, indicating that the intermediate does not bind Ca2+. This intermediate was also shown to be identical to the molten globule state observed at equilibrium. The phi-value analysis, based on the effect of Ca2+ on the folding and unfolding rate constants, showed that the Ca2+-binding site was not yet organized in the transition state of folding. A comparison of the result with that previously reported for alpha-lactalbumin indicated that the folding initiation site is different between canine milk lysozyme and alpha-lactalbumin, and hence, the folding pathways must be different between the two proteins. These results thus provide an example of the phenomenon wherein proteins that are very homologous to each other take different folding pathways. It is also shown that the native state of the apo form is composed of at least two species that interconvert.     

Multiple-probe analysis of folding and unfolding pathways of human serum albumin. Evidence for a framework mechanism of folding.

The changes in the far-UV CD signal, intrinsic tryptophan fluorescence and bilirubin absorbance showed that the guanidine hydrochloride (GdnHCl)-induced unfolding of a multidomain protein, human serum albumin (HSA), followed a two-state process. However, using environment sensitive Nile red fluorescence, the unfolding and folding pathways of HSA were found to follow a three-state process and an intermediate was detected in the range 0.25-1.5 m GdnHCl. The intermediate state displayed 45% higher fluorescence intensity than that of the native state. The increase in the Nile red fluorescence was found to be due to an increase in the quantum yield of the HSA-bound Nile red. Low concentrations of GdnHCl neither altered the binding affinity of Nile red to HSA nor induced the aggregation of HSA. In addition, the secondary structure of HSA was not perturbed during the first unfolding transition (<1.5 m GdnHCl); however, the secondary structure was completely lost during the second transition. The data together showed that the half maximal loss of the tertiary structure occurred at a lower GdnHCl concentration than the loss of the secondary structure. Further kinetic studies of the refolding process of HSA using multiple spectroscopic techniques showed that the folding occurred in two phases, a burst phase followed by a slow phase. An intermediate with native-like secondary structure but only a partial tertiary structure was found to form in the burst phase of refolding. Then, the intermediate slowly folded into the native state. An analysis of the refolding data suggested that the folding of HSA could be best explained by the framework model.     

Optimum folding pathways for growing protein chains

The folding of a protein is studied as it grows residue by residue from the N-terminus and enters an environment that stabilizes the folded state. This mode of folding of a growing chain is different from refolding where the full chain folds from a disordered initial configuration to the native state. We propose a sequential dynamic optimization method that computes the evolution of optimum folding pathways as amino acid residues are added to the peptide chain one by one. The dynamic optimization formulation is deterministic and uses Newton's equations of motion and a Go-type potential that establishes the native contacts and excluded volume effects. The method predicts the optimal energy-minimizing path among all the alternative feasible pathways. As two examples, the folding of the chicken villin headpiece, a 36-residue protein, and chymotrypsin inhibitor 2 (CI2), a 64-residue protein, are studied. Results on the villin headpiece show significant differences from the refolding of the same chain studied previously. Results on CI2 mostly agree with the results of refolding experiments and computational work.     

Minimal model for studying prion-like folding pathways

The Monte Carlo technique is used to simulate the energy landscape and the folding kinetics of a minimal prion-like protein model. We show that the competition between hydrogen-bonding and hydrophobic interactions yields two energetically favored secondary structures, an alpha-helix and a beta-hairpin. Folding simulations indicate that the probability of reaching the alpha-helix form from a denatured random conformation is much higher than the probability of reaching the beta-sheet form, even though the beta-sheet has a lower energy. The existence of a lower energy beta-sheet state gives the possibility for the normal alpha-helix structure to take a structural transformation into the beta-sheet structure under external influences.     

Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways. II. Alpha-helical motifs

Dynamic Monte Carlo simulations of the folding pathways of alpha-helical protein motifs have been undertaken in the context of a diamond lattice model of globular proteins. The first question addressed in the nature of the assembly process of an alpha-helical hairpin. While the hairpin could, in principle, be formed via the diffusion-collision-adhesion of isolated performed helices, this is not the dominant mechanism of assembly found in the simulations. Rather, the helices that form native hairpins are constructed on-site, with folding initiating at or near the turn in almost all cases. Next, the folding/unfolding pathways of four-helix bundles having tight bends and one and two long loops in the native state are explored. Once again, an on-site construction mechanism of folding obtains, with a hairpin forming first, followed by the formation of a three-helix bundle, and finally the fourth helix of the native bundle assembles. Unfolding is essentially the reverse of folding. A simplified analytic theory is developed that reproduces the equilibrium folding transitions obtained from the simulations remarkably well and, for the dominant folding pathway, correctly identifies the intermediates seen in the simulations. The analytic theory provides the free energy along the reaction co-ordinate and identifies the transition state for all three motifs as being quite close to the native state, with three of the four helices assembled, and approximately one turn of the fourth helix in place. The transition state is separated from the native conformation by a free-energy barrier of mainly energetic origin and from the denatured state by a barrier of mainly entropic origin. The general features of the folding pathway seen in all variants of the model four-helix bundles are similar to those observed in the folding of beta-barrel, Greek key proteins; this suggests that many of the qualitative aspects of folding are invariant to the particular native state topology and secondary structure.     

RNA folding and unfolding

Single-molecule studies of RNA folding and unfolding are providing impressive details of the intermediates that occur and their rates of interconversion. The folding and unfolding of RNA are controlled by varying the concentration of magnesium ions and measuring fluorescence energy transfer, or by applying force to the RNA and measuring the end-to-end distance. The hierarchical nature of RNA folding - first secondary structure, then tertiary structure - makes the process susceptible to analysis and prediction.     

Equilibrium and kinetic folding pathways of a TIM barrel with a funneled energy landscape

The role of native contact topology in the folding of a TIM barrel model based on the alpha-subunit of tryptophan synthase (alphaTS) from Salmonella typhimurium (Protein Data Bank structure 1BKS) was studied using both equilibrium and kinetic simulations. Equilibrium simulations of alphaTS reveal the population of two intermediate ensembles, I1 and I2, during unfolding/refolding at the folding temperature, Tf = 335 K. Equilibrium intermediate I1 demonstrates discrete structure in regions alpha0-beta6 whereas intermediate I2 is a loose ensemble of states with N-terminal structure varying from at least beta1-beta3 (denoted I2A) to alpha0-beta4 at most (denoted I2B). The structures of I1 and I2 match well with the two intermediate states detected in equilibrium folding experiments of Escherichia coli alphaTS. Kinetic folding simulations of alphaTS reveal the sequential population of four intermediate ensembles, I120Q, I200Q, I300Q, and I360Q, during refolding. Kinetic intermediates I120Q, I200Q, and I300Q are highly similar to equilibrium alphaTS intermediates I2A, I2B, and I1, respectively, consistent with kinetic experiments on alphaTS from E. coli. A small population (approximately 10%) of kinetic trajectories are trapped in the I120Q intermediate ensemble and require a slow and complete unfolding step to properly refold. Both the on-pathway and off-pathway I120Q intermediates show structure in beta1-beta3, which is also strikingly consistent with kinetic folding experiments of alphaTS. In the off-pathway intermediate I(120Q), helix alpha2 is wrapped in a nonnative chiral arrangement around strand beta3, sterically preventing the subsequent folding step between beta3 and beta4. These results demonstrate the success of combining kinetic and equilibrium simulations of minimalist protein models to explore TIM barrel folding and the folding of other large proteins.     

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.     

An analysis of protein folding pathways

We have developed a model of the protein folding process based on three primary assumptions: that burying of hydrophobic area is the dominant contribution to the relative free energy of a conformation, that a record of the folding process is largely preserved in the final structure, and that the denatured state is a random coil. Detailed folding pathways are identified for 19 protein structures. The picture of the folding process that emerges from this analysis is one of nucleation by regions of 8-16 residues. Nucleation sites then lead to larger structures by two mechanisms: propagation and diffusion/collision. A Monte Carlo simulation is used to follow the folding pathway when propagation is the dominant mechanism. Because detailed pathways are derived for each protein, the models are susceptible to experimental verification.     

Prediction of protein folding pathways.

Recent 1H nuclear magnetic resonance (n.m.r.) hydrogen exchange experiments on five different proteins have delineated the secondary structures formed in trapped, partially folded intermediates. The early forming structural elements are identifiable through a technique described in this work to predict folding pathways. The method assumes that the sequential selection of structural fragments such as alpha-helices and beta-strands involved in the folding process is founded upon the maximal burial of solvent accessible surface from both the formation of internal structure and substructure association. The substructural elements were defined objectively by major changes in main-chain direction. The predicted folding pathways are in complete correspondence with the n.m.r. results in that the formed structural fragments found in the folding intermediates are those predicted earliest in the pathways. The technique was also applied to proteins of known tertiary structure and with fold similar to one of the five proteins examined by 1H n.m.r. The pathways for these structures also showed general consistency with the n.m.r. observations, suggesting conservation of a secondary structural framework or molten globule about which folding nucleates and proceeds.     

Hierarchical protein folding pathways: a computational study of protein fragments

We have previously presented a building block folding model. The model postulates that protein folding is a hierarchical top-down process. The basic unit from which a fold is constructed, referred to as a hydrophobic folding unit, is the outcome of combinatorial assembly of a set of "building blocks." Results obtained by the computational cutting procedure yield fragments that are in agreement with those obtained experimentally by limited proteolysis. Here we show that as expected, proteins from the same family give very similar building blocks. However, different proteins can also give building blocks that are similar in structure. In such cases the building blocks differ in sequence, stability, contacts with other building blocks, and in their 3D locations in the protein structure. This result, which we have repeatedly observed in many cases, leads us to conclude that while a building block is influenced by its environment, nevertheless, it can be viewed as a stand-alone unit. For small-sized building blocks existing in multiple conformations, interactions with sister building blocks in the protein will increase the population time of the native conformer. With this conclusion in hand, it is possible to develop an algorithm that predicts the building block assignment of a protein sequence whose structure is unknown. Toward this goal, we have created sequentially nonredundant databases of building block sequences. A protein sequence can be aligned against these, in order to be matched to a set of potential building blocks.