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.     

Identification of rare partially unfolded states in equilibrium with the native conformation in an all beta-barrel protein

Human acidic fibroblast growth factor 1 (hFGF-1) is an all beta-barrel protein, and the secondary structural elements in the protein include 12 antiparallel beta-strands arranged into a beta-trefoil fold. In the present study, we investigate the stability of hFGF-1 by hydrogen-deuterium exchange as a function of urea concentration. Urea-induced equilibrium unfolding of hFGF-1 monitored by fluorescence and CD spectroscopy suggests that the protein unfolds by a two-state (native to denatured) mechanism. Hydrogen exchange in hFGF-1, under the experimental conditions used, occurs by the EX2 mechanism. In contrast to the equilibrium unfolding events monitored by optical probes, native state hydrogen exchange data show that the beta-trefoil architecture of hFGF-1 does not behave as a single cooperative unit. There are at least two structurally independent units with differing stabilities in hFGF-1. Beta-strands I, II, III, VI, VII, X, XI, and XII fit into the global unfolding isotherm. By contrast, residues in beta-strands IV, V, VIII, and IX exchange by the subfolding isotherm and could be responsible for the occurrence of high-energy partially unfolded state(s) in hFGF-1. There appears to be a broad continuum of stabilities among the four beta-strands (beta-strands IV, V, VIII, and IX) constituting the subglobal folding unit. The slow exchanging residues in hFGF-1 do not represent the folding nucleus of the protein.     

Comparison of the hemocyanin beta-barrel with other Greek key beta-barrels: possible importance of the "beta-zipper" in protein structure and folding.

The Greek key beta-barrel topology is a folding motif observed in many proteins of widespread evolutionary origin. The arthropodan hemocyanins also have such a Greek key beta-barrel, which forms the core of the third domain of this protein. The hemocyanin beta-barrel was found to be structurally very similar to the beta-barrels of the immunoglobulin domains, Cu,Zn-superoxide dismutase and the chromophore carrying antitumor proteins. The structural similarity within this group of protein families is not accompanied by an evolutionary or functional relationship. It is therefore possible to study structure-sequence relations without bias from nonstructural constraints. The present study reports a conserved pattern of features in these Greek key beta-barrels that is strongly suggestive of a folding nucleation site. This proposed nucleation site, which we call a "beta-zipper," shows a pattern of well-conserved, large hydrophobic residues on two sequential beta-strands joined by a short loop. Each beta-zipper strand is near the center of one of the beta-sheets, so that the two strands face each other from opposite sides of the barrel and interact through their hydrophobic side chains, rather than forming a hydrogen-bonded beta-hairpin. Other protein families with Greek key beta-barrels that do not as strongly resemble the immunoglobulin fold--such as the azurins, plastocyanins, crystallins, and prealbumins--also contain the beta-zipper pattern, which might therefore be a universal feature of Greek key beta-barrel proteins.     

Unfolding of the cold shock protein studied with biased molecular dynamics

The cold shock protein from Bacillus caldolyticus is a small beta-barrel protein that folds in a two-state mechanism. For the native protein and for several mutants, a wealth of experimental data are available on stability and folding, so that it is an optimal system to study this process. We compare data from unfolding simulations (trajectories of 5 and up to 12 ns) obtained with a bias potential at room temperature and from unbiased thermal unfolding simulations with experimental data. The unfolding patterns derived from the trajectories starting from different native-like conformations and subject to different unfolding conditions agree. The transition state found in the simulations of unfolding is close to the native structure in agreement with experiment. Moreover, a lower value of the free energy barrier of unfolding was found for the mutant R3E than for the mutant E46A and the native protein, as indicated by experimental data. The first unfolding event involves the three-stranded beta-sheet whose decomposition corresponds to the transition state. In contrast to conclusions drawn from experiments, we found that the two-stranded beta-strand forms the most stable substructure, which decomposes very late in the unfolding process. However, assuming that this structure forms very early in the folding process, our findings would not contradict the experiments but require a different interpretation of them.     

Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

The nature of folded states of globular proteins.

We suggest, using dynamical simulations of a simple heteropolymer modelling the alpha-carbon sequence in a protein, that generically the folded states of globular proteins correspond to statistically well-defined metastable states. This hypothesis, called the metastability hypothesis, states that there are several free energy minima separated by barriers of various heights such that the folded conformations of a polypeptide chain in each of the minima have similar structural characteristics but have different energies from one another. The calculated structural characteristics, such as bond angle and dihedral angle distribution functions, are assumed to arise from only those configurations belonging to a given minimum. The validity of this hypothesis is illustrated by simulations of a continuum model of a heteropolymer whose low temperature state is a well-defined beta-barrel structure. The simulations were done using a molecular dynamics algorithm (referred to as the "noisy" molecular dynamics method) containing both friction and noise terms. It is shown that for this model there are several distinct metastable minima in which the structural features are similar. Several new methods of analyzing fluctuations in structures belonging to two distinct minima are introduced. The most notable one is a dynamic measure of compactness that can in principle provide the time required for maximal compactness to be achieved. The analysis shows that for a given metastable state in which the protein has a well-defined folded structure the transition to a state of higher compactness occurs very slowly, lending credence to the notion that the system encounters a late barrier in the process of folding to the most compact structure. The examination of the fluctuations in the structures near the unfolding----folding transition temperature indicates that the transition state for the unfolding to folding process occurs closer to the folded state.     

Some recommendations for the practitioner to improve the precision of experimentally determined protein folding rates and phi values

The mechanism by which proteins fold from an initially random conformation into a functional, native structure remains a major unsolved question in molecular biology. Of particular interest to the protein folding community is the structure that the protein adopts in the folding transition state (the highest free energy state on the pathway from unfolded to folded), as that state forms the barrier that defines the folding pathway. Unfortunately, however, unlike those of the initial, unfolded state and the final, folded state of the protein, the structure in the transition state cannot be directly assessed via experiment. Instead, experimentalists infer the structure of the transition state, often by estimating changes in its free energy by measuring the effects of amino acid substitutions on folding and unfolding rates (Phi-value analysis). In this article we show how to obtain more efficient estimates of these important quantities via improved experimental designs, and how to avoid common pitfalls in the analysis of kinetic data during the extraction of these parameters.     

The major outer membrane protein of Fusobacterium nucleatum (FomA) folds and inserts into lipid bilayers via parallel folding pathways

Membrane protein insertion and folding was studied for the major outer membrane protein of Fusobacterium nucleatum (FomA), which is a voltage-dependent general diffusion porin. The transmembrane domain of FomA forms a beta-barrel that is predicted to consist of 14 beta-strands. Here, unfolded FomA is shown to insert and fold spontaneously and quantitatively into phospholipid bilayers upon dilution of the denaturant urea, which was shown previously only for outer membrane protein A (OmpA) of Escherichia coli. Folding of FomA is demonstrated by circular dichroism and fluorescence spectroscopy, by SDS-polyacrylamide gel electrophoresis, and by single-channel recordings. Refolded FomA had a single-channel conductance of 1.1 nS at 1 M KCl, in agreement with the conductance of FomA isolated from membranes in native form. In contrast to OmpA, which forms a smaller eight-stranded beta-barrel domain, folding kinetics of the larger FomA were slower and provided evidence for parallel folding pathways of FomA into lipid bilayers. Two pathways were observed independent of membrane thickness with two different lipid bilayers, which were either composed of dicapryl phosphatidylcholine or dioleoyl phosphatidylcholine. This is the first observation of parallel membrane insertion and folding pathways of a beta-barrel membrane protein from an unfolded state in urea into lipid bilayers. The kinetics of both folding pathways depended on the chain length of the lipid and on temperature with estimated activation energies of 19 kJ/mol (dicapryl phosphatidylcholine) and 70 kJ/mol (dioleoyl phosphatidylcholine) for the faster pathways.     

Characterization of the folding and unfolding reactions of a small beta-barrel protein of novel topology, the MTCP1 oncogene product P13.

The equilibrium and kinetic folding properties of a small oncogene product, P13(MTCP1), of novel topology have been investigated using perturbation by guanidine hydrochloride and observation by fluorescence, circular dichroism and two-dimensional heteronuclear NMR spectroscopy. The structure of P13(MTCP1) is comprised of a canonical filled beta-barrel, although the topology of the structure is absolutely unique, rendering the folding properties of this protein of great interest. Equilibrium measurements of the intrinsic fluorescence emission spectrum, the fluorescence decay, the circular dichroism spectrum and the (15)N-(1)H heteronuclear single quantum coherence (HSQC) correlation spectrum as a function of increasing concentrations of denaturant showed no evidence for the population of any equilibrium intermediates, although negative amplitudes on the blue edge of the tryptophan emission and loss of intensity of the native HSQC correlation peaks were indicative of increased conformational dynamics at low denaturant concentrations. The free energy and cooperativity of unfolding as observed by fluorescence and circular dichroism were in relatively good agreement, also consistent with a two-state transition. Kinetics measurements of the fluorescence emission as a function of denaturant concentration revealed that P13(MTCP1) is the slowest folding beta-structure protein reported to date. Comparison of the activation cooperativity values (m(f) and m(u)) indicates that the structure of the transition state is quite close to the folded state in terms of exposed surface area. The calculated contact order of P13(MTCP1) is relatively low and does not appear to explain its slow rate of folding. We suggest that the complex topology of this protein, which would require the ordering of the beta-barrel through a long loop joining the two L-shaped components of the barrel, could provide an explanation for this slow folding. Copyright.     

Folding stability and cooperativity of the three forms of 1-110 residues fragment of staphylococcal nuclease

Folding stability and cooperativity of the three forms of 1-110 residues fragment of staphylococcal nuclease (SNase110) have been studied by various biophysical and NMR methods. Samples of G-88W- and V-66W-mutant SNase110, namely G-88W110 and V-66W110, in aqueous solution and SNase110 in 2.0 M TMAO are adopted in this study. The unfolding transitions and folded conformations of the three SNase fragments were detected by far- and near-ultraviolet circular dichroism and intrinsic tryptophan fluorescence measurements. The tertiary structures and internal motions of the fragments were determined by NMR spectroscopy. Both G-88W and V-66W single mutations as well as a small organic osmolyte (Trimethylamine N-oxide, TMAO) can fold the fragment into a native-like conformation. However, the tertiary structures of the three fragments exhibit different degrees of folding stability and compactness. G-88W110 adopts a relatively rigid structure representing a most stable native-like beta-subdomain conformation of the three fragments. V-66W110- and TMAO-stabilized SNase110 produce less compact structures having a less stable "beta-barrel" structural region. The different folding status accounts for the different backbone dynamic and urea-unfolding transition features of the three fragments. The G-20I/G-29I-mutant variants of the three fragments have provided the evidence that the folding status is correlated closely to the packing of the beta-strands in the beta-barrel of the fragments. The native-like beta-barrel structural region acts as a nonlocal nucleus for folding the fragment. The tertiary folding of the three fragments is initiated by formation of the local nucleation sites at two beta-turn regions, I-18-D-21 and Y-27-Q-30, and developed by the formation of a nonlocal nucleation site at the beta-barrel region. The formation of beta-barrel and overall structure is concerted, but the level of cooperativity is different for the three 1-110 residues SNase fragments.     

Hopping around an entropic barrier created by force

We use Langevin dynamics to investigate the role played by the recently discovered force-induced entropic energy barrier on the two-state hopping phenomena that has been observed in single RNA, DNA and protein molecules placed under a stretching force. Simple considerations about the free energy of a molecule readily show that the application of force introduces an entropic barrier separating the collapsed state of the molecule, from a force-driven extended conformation. A notable characteristic of the force induced barrier is its long distances to transition state, up to tens of nanometers, which renders the kinetics of crossing this barrier highly sensitive to an applied force. Langevin dynamics across such force induced barriers readily demonstrates the hopping behavior observed for a variety of single molecules placed under force. Such hopping is frequently interpreted as a manifestation of two-state folding/unfolding reactions observed in bulk experiments. However, given that such barriers do not exist at zero force these reactions do not take place at all in bulk.     

Temperature-dependent downhill unfolding of ubiquitin. I. Nanosecond-to-millisecond resolved nonlinear infrared spectroscopy

Transient thermal unfolding of ubiquitin is investigated using nonlinear infrared spectroscopy after a nanosecond laser temperature jump (T-jump). The abrupt change in the unfolding free energy surface and the ns time resolution allow us to observe a fast response on ns to micros time-scales, which we attribute to downhill unfolding, before a cross-over to ms kinetics. The downhill unfolding by a sub-population of folded proteins is induced through a shift of the barrier toward the native state. By adjusting the T-jump width, the effect of the initial (T(i)) and final (T(f)) temperature on the unfolding dynamics can be separated. From the amplitude of the fast downhill unfolding, the fractional population prepared at the unfolding transition state is obtained. This population increases with both T(i) and with T(f). A two-state kinetic analysis of the ms refolding provides thermodynamic information about the barrier height. By a combination of the fast and slow unfolding and folding parameters, a quasi-two-state kinetic analysis is performed to calculate the time-dependent population changes of the folded state. This calculation coincides with the experimentally obtained population changes at low temperature but deviations are found in the T-jump from 67 to 78 degrees C. Using temperature-dependent barrier height changes, a temperature Phi value analysis is performed. The result shows a decreasing trend of Phi(T) with temperature, which indicates an increase of the heterogeneity of the transition state. We conclude that ubiquitin unfolds along a well-defined pathway at low temperature which expands with increasing temperature to include multiple routes.     

Burst-phase expansion of native protein prior to global unfolding in SDS

Although numerous studies have been directed at understanding early folding events through the characterization of folding intermediates, there are few reports on the very late folding events, i.e. on the events taking place on the native side of the folding barrier and on alternative conformations of the folded state. To shed further light on these issues, we have characterized by protein engineering the structure of an expanded but native-like intermediate that accumulates transiently in the unfolding reaction of the small protein S6 in the presence of SDS. The results show that the SDS micelles attack the native protein in the dead-time of the denaturation experiment, causing an expansion of the hydrophobic core prior to the major unfolding transition. We distinguish two forms of the unfolding intermediate that are correlated with the micellar structure. With spherical micelles, the expansion is seen mainly as a weakening of the interactions which anchor the two alpha-helices to the core of the S6 structure. With cylindrical micelles, prevalent at higher SDS concentrations, the expansion is more global and produces a species which closely resembles the transition-state structure for unfolding in GdmCl. Despite the highly weakened core, the micelle-associated intermediate displays cooperative unfolding, indicating a significant structural plasticity of the species on the native side of the folding barrier in the presence of SDS.     

Folding of a designed simple ankyrin repeat protein

Ankyrin repeats (AR) are 33-residue motifs containing a beta-turn, followed by two alpha-helices connected by a loop. AR occur in tandem arrangements and stack side-by-side to form elongated domains involved in very different cellular tasks. Recently, consensus libraries of AR repeats were constructed. Protein E1_5 represents a member of the shortest library, and consists of only a single consensus repeat flanked by designed N- and C-terminal capping repeats. Here we present a biophysical characterization of this AR domain. The protein is compactly folded, as judged from the heat capacity of the native state and from the specific unfolding enthalpy and entropy. From spectroscopic data, thermal and urea-induced unfolding can be modeled by a two-state transition. However, scanning calorimetry experiments reveal a deviation from the two-state behavior at elevated temperatures. Folding and unfolding at 5 degrees C both follow monoexponential kinetics with k(folding) = 28 sec(-1) and k(unfolding) = 0.9 sec(-1). Kinetic and equilibrium unfolding parameters at 5 degrees C agree very well. We conclude that E1_5 folds in a simple two-state manner at low temperatures while equilibrium intermediates become populated at higher temperatures. A chevron-plot analysis indicates that the protein traverses a very compact transition state along the folding/unfolding pathway. This work demonstrates that a designed minimal ankyrin repeat protein has the thermodynamic and kinetic properties of a compactly folded protein, and explains the favorable properties of the consensus framework.     

Ruggedness in the Free Energy Landscape Dictates Misfolding of the Prion Protein

Experimental determination of the key features of the free energy landscapes of proteins, which dictate their adeptness to fold correctly, or propensity to misfold and aggregate and which are modulated upon a change from physiological to aggregation-prone conditions, is a difficult challenge. In this study, sub-millisecond kinetic measurements of the folding and unfolding of the mouse prion protein reveal how the free energy landscape becomes more complex upon a shift from physiological (pH 7) to aggregation-prone (pH 4) conditions. Folding and unfolding utilize the same single pathway at pH 7, but at pH 4, folding occurs on a pathway distinct from the unfolding pathway. Moreover, the kinetics of both folding and unfolding at pH 4 depend not only on the final conditions but also on the conditions under which the processes are initiated. Unfolding can be made to switch to occur on the folding pathway by varying the initial conditions. Folding and unfolding pathways appear to occupy different regions of the free energy landscape, which are separated by large free energy barriers that change with a change in the initial conditions. These barriers direct unfolding of the native protein to proceed via an aggregation-prone intermediate previously identified to initiate the misfolding of the mouse prion protein at low pH, thus identifying a plausible mechanism by which the ruggedness of the free energy landscape of a protein may modulate its aggregation propensity.     

Cytochrome c folds through a smooth funnel

A dominant feature of folding of cytochrome c is the presence of nonnative His-heme kinetic traps, which either pre-exist in the unfolded protein or are formed soon after initiation of folding. The kinetically trapped species can constitute the majority of folding species, and their breakdown limits the rate of folding to the native state. A temperature jump (T-jump) relaxation technique has been used to compare the unfolding/folding kinetics of yeast iso-2 cytochrome c and a genetically engineered double mutant that lacks His-heme kinetic traps, H33N,H39K iso-2. The results show that the thermodynamic properties of the transition states are very similar. A single relaxation time tau(obs) is observed for both proteins by absorbance changes at 287 nm, a measure of solvent exclusion from aromatic residues. At temperatures near Tm, the midpoint of the thermal unfolding transitions, tau(obs) is four to eight times faster for H33N,H39K iso-2 (tau(obs) approximately 4-10 ms) than for iso-2 (tau(obs) approximately 20-30 ms). T-jumps show that there are no kinetically unresolved (tau < 1-3 micros T-jump dead time) "burst" phases for either protein. Using a two-state model, the folding (k(f)) and unfolding (k(u)) rate constants and the thermodynamic activation parameters standard deltaGf, standard deltaGu, standard deltaHf, standard deltaHu, standard deltaSf, standard deltaSu are evaluated by fitting the data to a function describing the temperature dependence of the apparent rate constant k(obs) (= tau(obs)(-1)) = k(f) + k(u). The results show that there is a small activation enthalpy for folding, suggesting that the barrier to folding is largely entropic. In the "new view," a purely entropic kinetic barrier to folding is consistent with a smooth funnel folding landscape.     

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.