Evidence of discrete substates and unfolding pathways in green fluorescent protein

We present evidence of conformational substates of a green fluorescent protein mutant, GFPmut2, and of their relationship with the protein behavior during chemical unfolding. The fluorescence of single molecules, excited by two infrared photons from a pulsed laser, was detected in two separate channels that simultaneously collected the blue or the green emission from the protein chromophore chemical states (anionic or neutral, respectively). Time recording of the fluorescence signals from molecules in the native state shows that the chromophore, an intrinsic probe sensitive to conformational changes, switches between the two states with average rates that are found to assume distinct values, thereby suggesting a multiplicity of protein substates. Furthermore, under denaturing conditions, the chromophore switching rate displays different and reproducible time evolutions that are characterized by discrete unfolding times. The correlation that is found between native molecules' switching rate values and unfolding times appears as direct evidence that GFPmut2 can unfold only along distinct paths that are determined by the initial folded substate of the protein.     

Characterization of the pressure-induced intermediate and unfolded state of red-shifted green fluorescent protein--a static and kinetic FTIR,UV/VIS and fluorescence spectroscopy study

The green fluorescence proteins (GFP) are widely used as reporters in molecular and cell biology. For their use it in high-pressure microbiology and biotechnology studies, their structural properties, thermodynamic parameters and stability diagrams have to be known. We investigated the pressure stability of the red-shifted green fluorescent protein (rsGFP) using Fourier-transform infrared spectroscopy, fluorescence and UV/Vis spectroscopy. We found that rsGFP does not unfold up to approximately 9kbar at room temperature. Its unique three-dimensional structure is held responsible for the high-pressure stability. At higher temperatures, its secondary structure collapses below 9kbar (e.g. the denaturation pressure at 58 degrees C is 7.8kbar). The analysis of the IR data shows that the pressure-denatured state contains more disordered structures at the expense of a decrease of intramolecular beta-sheets. As indicated by the large volume change of DeltaV degrees (u) approximately -250(+/-50)mlmol(-1) at 58 degrees C, this highly cooperative transition can be interpreted as a collapse of the beta-can structure of rsGFP. For comparison, the temperature-induced unfolding of rsGFP has also been studied. At high temperature (T(m)=78 degrees C), the unfolding resulted in the formation of an aggregated state. Contrary to the pressure-induced unfolding, the temperature-induced unfolding and aggregation of GFP is irreversible. From the FT-IR data, a tentative p,T-stability diagram for the secondary structure collapse of GFP has been obtained. Furthermore, changes in fluorescence and absorptivity were found which are not correlated to the secondary structural changes. The fluorescence and UV/Vis data indicate smaller conformational changes in the chromophore region at much lower pressures ( approximately 4kbar) which are probably accompanied by the penetration of water into the beta-can structure. In order to investigate also the kinetics of this initial step, pressure-jump relaxation experiments were carried out. The partial activation volumes observed indicate that the conformational changes in the chromophore region when passing the transition state are indeed rather small, thus leading to a comparably small volume change of -20 ml mol(-1) only. The use of the chromophore absorption and fluorescence band of rsGFP in using GFP as reporter for gene expression and other microbiological studies under high pressure conditions is thus limited to pressures of about 4kbar, which still exceeds the pressure range relevant for studies in vivo in micro-organisms, including piezophilic bacteria from deep-sea environments.     

Mutants of Discosoma red fluorescent protein with a GFP-like chromophore

The green fluorescent protein (GFP)-homologous red fluorescent protein (RFP) from Discosoma (drFP583) which emits bright red fluorescence peaking at 583 nm is an interesting novel genetic marker. We show here that RFP maturation involves a GFP-like fluorophore which can be stabilized by point mutations selected from a randomly mutated expression library. By homology modeling, these point mutations cluster near the imidazolidinone ring of the chromophore. Exciting the GFP-like absorption band in the mutant proteins produces both green and red fluorescence. Upon unfolding and heating, the absorption spectrum of the RFP chromophore slowly becomes similar to that of the GFP chromophore. This can be interpreted as a covalent modification of the GFP chromophore in RFP that appears to occur in the final maturation step.     

Can the fluorescence of green fluorescent protein chromophore be related directly to the nativity of protein structure?

In studies of green fluorescence protein (GFP) or other proteins with the use of GFP as a marker, the fluorescence of GFP is for the most part related directly to the nativity of its structure. Naturally, such a relation does exist since the chromophore of this protein is formed autocatalytically only just after GFP acquires its native structure. However, the fluorescence method may not yield reliable information on protein structure when studying renaturation and denaturation of this protein (with the formed chromophore). Using proteolysis, denaturant gradient gel electrophoresis and circular dichroism, we demonstrate herein that at major disturbances of the native structure of protein GFP-cycle3 the intensity of fluorescence of its chromophore can change insignificantly. In other words, the chromophore fluorescence does not reliably mirror alterations in protein structure. Since the main conclusions of this study are especially qualitative, it can be suggested that during renaturation/denaturation of wild-type GFP and its “multicolored” mutants their fluorescence is also not always associated with the changes in the structure of these proteins.     

The rough energy landscape of superfolder GFP is linked to the chromophore

Many green fluorescent protein (GFP) variants have been developed for use as fluorescent tags, and recently a superfolder GFP (sfGFP) has been developed as a robust folding reporter. This new variant shows increased stability and improved folding kinetics, as well as 100% recovery of native protein after denaturation. Here, we characterize sfGFP, and find that this variant exhibits hysteresis as unfolding and refolding equilibrium titration curves are non-coincident even after equilibration for more than eight half-lives as estimated from kinetic unfolding and refolding studies. This hysteresis is attributed to trapping in a native-like intermediate state. Mutational studies directed towards inhibiting chromophore formation indicate that the novel backbone cyclization is responsible for the hysteresis observed in equilibrium titrations of sfGFP. Slow equilibration and the presence of intermediates imply a rough landscape. However, de novo folding in the absence of the chromophore is dominated by a smoother energy landscape than that sampled during unfolding and refolding of the post-translationally modified polypeptide.     

Role of histidine 148 in stability and dynamics of a highly fluorescent GFP variant

The armory of GFP mutants available to biochemists and molecular biologists is huge. Design and selection of mutants are usually driven by tailored spectroscopic properties, but some key aspects of stability, folding and dynamics of selected GFP variants still need to be elucidated. We have prepared, expressed and characterized three H148 mutants of the highly fluorescent variant GFPmut2. H148 is known to be involved in the H-bonding network surrounding the chromophore, and all the three mutants, H148G, H148R and H148K, show increased pK_a values of the chromophore. Only H148G GFPmut2 (Mut2G) gave good expression and purification yields, indicating that position 148 is critical for efficient folding in vivo. The chemical denaturation of Mut2G was monitored by fluorescence emission, absorbance and far-UV circular dichroism spectroscopy. The mutation has little effect on the spectroscopic properties of the protein and on its stability in solution. However, the unfolding kinetics of the protein encapsulated in wet nanoporous silica gels, a system that allows to stabilize conformations that are poorly or only transiently populated in solution, indicate that the unfolding pathway of Mut2G is markedly different from the parent molecule. In particular, encapsulation allowed to identify an unfolding intermediate that retains a native-like secondary structure despite a destructured chromophore environment. Thus, H148 is a critical residue not only for the chromophoric and photodynamic properties, but also for the correct folding of GFP, and its substitution has great impact on expression yields and stability of the mature protein.     

Effect of the point mutation H148G on GFPmut2 unfolding kinetics by fluorescence spectroscopy

We have used fluorescence spectroscopy techniques such as fluorescence correlation spectroscopy and fluorescence anisotropy decay on a wide time range, from nanoseconds to seconds, to investigate the unfolding kinetics induced by guanidinium chloride of GFPMut2 and its point mutation H148G, which has proved to be relevant for GFP photochemistry and photophysics. The mutation affects the unfolding kinetics of GFP leading to a much faster process at alkaline pH values, where protonation dynamics is negligible, that can be ascribed to a twofold role of His148, either as a proton shutter towards the chromophore and as a conformation stabiliser. For both mutants a soft region located near beta-strand 3 is found that starts to gain flexibility in the ns range at denaturant concentrations far lower than those required to turn off the chromophore fluorescence, as derived from the anisotropy decay of an extrinsic probe covalently bound to the proteins.     

Understanding the role of Arg96 in structure and stability of green fluorescent protein

Arg96 is a highly conservative residue known to catalyze spontaneous green fluorescent protein (GFP) chromophore biosynthesis. To understand a role of Arg96 in conformational stability and structural behavior of EGFP, the properties of a series of the EGFP mutants bearing substitutions at this position were studied using circular dichroism, steady state fluorescence spectroscopy, fluorescence lifetime, kinetics and equilibrium unfolding analysis, and acrylamide-induced fluorescence quenching. During the protein production and purification, high yield was achieved for EGFP/Arg96Cys variant, whereas EGFP/Arg96Ser and EGFP/Arg96Ala were characterized by essentially lower yields and no protein was produced when Arg96 was substituted by Gly. We have also shown that only EGFP/Arg96Cys possessed relatively fast chromophore maturation, whereas it took EGFP/Arg96Ser and EGFP/Arg96Ala about a year to develop a noticeable green fluorescence. The intensity of the characteristic green fluorescence measured for the EGFP/Arg96Cys and EGFP/Arg96Ser (or EGFP/Arg96Ala) was 5- and 50-times lower than that of the nonmodified EGFP. Intriguingly, EGFP/Arg96Cys was shown to be more stable than EGFP toward the GdmCl-induced unfolding both in kinetics and in the quasi-equilibrium experiments. In comparison with EGFP, tryptophan residues of EGFP/Arg96Cys were more accessible to the solvent. These data taken together suggest that besides established earlier crucial catalytic role, Arg96 is important for the overall folding and conformational stability of GFP.     

Temperature-pressure stability of green fluorescent protein: a Fourier transform infrared spectroscopy study

Green fluorescent protein (GFP) is widely used as a marker in molecular and cell biology. For its use in high-pressure microbiology experiments, its fluorescence under pressure was recently investigated. Changes in fluorescence with pressure were found. To find out whether these are related to structural changes, we investigated the pressure stability of wild-type GFP (wtGFP) and three of its red shift mutants (AFP, GFP(mut1), and GFP(mut2)) using Fourier transform infrared spectroscopy. For the wt GFP, GFP(mut1), and GFP(mut2) we found that up to 13-14 kbar the secondary structure remains intact, whereas AFP starts unfolding around 10 kbar. The 3-D structure is held responsible for this high-pressure stability. Previously observed changes in fluorescence at low pressure are rationalized in terms of the pressure-induced elastic effect. Above 6 kbar, loss of fluorescence is due to aggregation. Revisiting the temperature stability of GFP, we found that an intermediate state is populated along the unfolding pathway of wtGFP. At higher temperatures, the unfolding resulted in the formation of aggregates of wtGFP and its mutants.     

Stable intermediate states and high energy barriers in the unfolding of GFP

We present a study of the denaturation of a truncated, cycle3 variant of green fluorescent protein (GFP). Chemical denaturation is used to unfold the protein, with changes in structure being monitored by the green fluorescence, tyrosine fluorescence and far-UV circular dichroism. The results show that the denaturation behaviour of GFP is complex compared to many small proteins: equilibrium is established only very slowly, over the time course of weeks, suggesting that there are high folding/unfolding energy barriers. Unfolding kinetics confirm that the rates of unfolding at low concentrations of denaturant are very low, consistent with the slow establishment of the equilibrium. In addition, we find that GFP significantly populates an intermediate state under equilibrium conditions, which is compact and stable with respect to the unfolded state (m(IU)=4.6 kcal mol(-1) M(-1) and Delta G(IU)=12.5 kcal mol(-1)). The global and local stability of GFP was probed further by measuring the hydrogen/deuterium (H/D) NMR exchange rates of more than 157 assigned amide protons. Analysis at two different values of pH showed that amide protons within the beta-barrel structure exchange at the EX2 limit, consequently, free energies of exchange could be calculated and compared to those obtained from the denaturation-curve studies providing further support for the three-state model and the existence of a stable intermediate state. Analysis reveals that amide protons in beta-strands 7, 8, 9 and 10 have, on average, higher exchange rates than others in the beta-barrel, suggesting that there is greater flexibility in this region of the protein. Forty or so amide protons were found which do not undergo significant exchange even after several months and these are clustered into a core region encompassing most of the beta-strands, at least at one end of the barrel structure. It is likely that these residues play an important role in stabilizing the structure of the intermediate state. The intermediate state observed in the chemical denaturation studies described here, is similar to that observed at pH 4 in other studies.     

Quantitative measurement of green fluorescent protein expression

Summary Data presented here shows a time course analysis of E. coli shake flask cultures expressing the reporter gene green fluorescent protein (GFP) with simultaneous comparison of microbial fluorescence intensity measurements and GFP concentration measured by Western blot. There is an apparent lag between the presence of GFP and its fluorescence due to the time required for formation of the chromophore. We demonstrate that GFP fluorescence can be used as a quantifiable reporter gene, provided the cyclization time for chromophore formation is considered.     

Effects of chaotropic and kosmotropic cosolvents on the pressure-induced unfolding and denaturation of proteins: an FT-IR study on staphylococcal nuclease

FT-IR spectroscopy was used to study the effects of various chaotropic and kosmotropic cosolvents (glycerol, sucrose, sorbitol, K(2)SO(4), CaCl(2), and urea) on the secondary structure and thermodynamic properties upon unfolding and denaturation of staphylococcal nuclease (Snase). The data show that the different cosolvents have a profound effect on the denaturation pressure and the Gibbs free energy (DeltaG(o)) and volume (DeltaV(o) change of unfolding. Moreover, by analysis of the amide I' infrared bands, conformational changes of the protein upon unfolding in the different cosolvents have been determined. An increase, a reduction, or an independence of the volume change of unfolding is observed, depending on the type of cosolvent, which can at least in part be attributed to the formation of a different unfolded state structure of the protein. The data are compared with the corresponding thermodynamic values of DeltaV(o) for the temperature-induced unfolding process of Snase as obtained by pressure perturbation calorimetry, and significant differences are observed and discussed.     

Kinetic study of de novo chromophore maturation of fluorescent proteins

Green fluorescent protein (GFP) has a chromophore that forms autocatalytically within the folded protein. Although many studies have focused on the precise mechanism of chromophore maturation, little is known about the kinetics of de novo chromophore maturation. Here we present a simple and efficient method for examining the de novo kinetics. GFP with an immature chromophore was synthesized in a reconstituted cell-free protein synthesis system under anaerobic conditions. Chromophore maturation was initiated by rapid dilution in an air-saturated maturation buffer, and the time course of fluorescence development was monitored. Comparison of the de novo maturation rates in various GFP variants revealed that some folding mutations near the chromophore promoted rapid chromophore maturation and that the accumulation of mutations could reduce the maturation rate. Our method will contribute to the design of rapidly maturing fluorescent proteins with improved characteristics for real-time monitoring of cellular events.     

Folding of green fluorescent protein and the cycle3 mutant

Although the correct folding of green fluorescent protein (GFP) is required for formation of the chromophore, it is known that wild-type GFP cannot mature efficiently in vivo in Escherichia coli at 37 degrees C or higher temperatures that the jellyfish in the Pacific Northwest have never experienced. Recently, by random mutagenesis by the polymerase chain reaction (PCR) method, a mutant called Cycle3 was constructed. This mutant had three mutations, F99S, M153T, and V163A, on or near the surface of the GFP molecule and was able to mature correctly even at 37 degrees C [Crameri et al. (1996) Nat. Biotechnol. 143, 315-319]. In the present study, we investigated the differences in their folding behavior in vitro. We observed the folding and unfolding reactions of both wild-type GFP and the Cycle3 mutant by using green fluorescence as an indicator of the formation of the native structure and examining hydrogen-exchange reactions by Fourier transform infrared spectroscopy. Both proteins showed unusually slow refolding and unfolding rates, and their refolding rates were almost identical under the native state at 25 and at 35 degrees C. On the other hand, aggregation studies in vitro showed that wild-type GFP had a strong tendency to aggregate, while the Cycle3 mutant did not. These results indicated that the ability to mature efficiently in vivo at 37 degrees C was not due to the improved folding and that reduced hydrophobicity on the surface of the Cycle3 mutant was a more critical factor for efficient maturation in vivo.     

Investigations of combinations of mutations in the jellyfish green fluorescent protein (GFP) that afford brighter fluorescence, and use of a version (VisGreen) in plant, bacterial, and animal cells

Among the GFPs used for imaging green fluorescence, the Emerald version has been considered the best GFP to use but there is no formal report on its construction or the relevance of the amino acid (aa) substitutions in it relative to the commonly used GFPs. Here, we have shown that a version of Emerald makes Escherichia coli host cells visibly green even under dim room light conditions. Exploiting this feature, we have determined for the first time whether the changes in the structure of Emerald protein brought about by the aa substitutions are all indeed essential for brightness. F64L and S72A accompanying the classical S65T substitution on the chromophore-bearing helix are essential. Two amino acid changes, one on the surface (N149K) of the beta barrel that encases the helix and the other (I167T) near the chromophore enhance the visible green colour individually and additively when present together. The other two substitutions, M153T (on the surface) and H231L (on the surface), do not contribute to the visible green phenotype, even though in earlier studies M153T has been reported to enhance GFP fluorescence. The GFP version with F64L-S65T-S72A-N149K-I167T is referred to as VisGreen. We found VisGreen and Emerald to be indistinguishable in their quantum yield, molar extinction coefficient, folding efficiency, or photosensitivity. VisGreen rendered bacterial, plant, and animal cells highly fluorescent. Interestingly, N149K in the above combination was not essential to render bacterial cells highly fluorescent.     

Distinct Effects of Guanidine Thiocyanate on the Structure of Superfolder GFP

Having a high folding efficiency and a low tendency to aggregate, the superfolder GFP (sfGFP) offers a unique opportunity to study the folding of proteins that have a β-barrel topology. Here, we studied the unfolding–refolding of sfGFP that was induced by guanidine thiocyanate (GTC), which is a stronger denaturing agent than GdnHCl or urea. Structural perturbations of sfGFP were studied by spectroscopic methods (absorbance, fluorescence, and circular dichroism), by acrylamide quenching of tryptophan and green chromophore fluorescence, and by size-exclusion chromatography. Low concentrations of GTC (up to 0.1 M) induce subtle changes in the sfGFP structure. The pronounced changes in the visible absorption spectrum of sfGFP which are accompanied by a dramatic decrease in tryptophan and green chromophore fluorescence was recorded in the range 0–0.7 M GNC. These alterations of sfGFP characteristics that erroneously can be mixed up with appearance of intermediate state in fact have pure spectroscopic but not structural nature. Higher concentrations of GTC (from 0.7 to 1.7 M), induce a disruption of the sfGFP structure, that is manifested in simultaneous changes of all of the detected parameters. Full recovery of native properties of denaturated sfGFP was observed after denaturant removal. The refolding of sfGFP passes through the accumulation of the off-pathway intermediate state, in which inner alpha-helix and hence green chromophore and Trp57 are still not tuned up to (properly integrated into) the already formed β-barrel scaffold of protein. Incorporation of the chromophore in the β-barrel in the pathway of refolding and restoration of its ability to fluoresce occur in a narrow range of GTC concentrations from 1.0 to 0.7 M, and a correct insertion of Trp 57 occurs at concentrations ranging from 0.7 to 0 M GTC. These two processes determine the hysteresis of protein unfolding and refolding.     

Using high-performance liquid chromatography to measure the effects of protein-stabilizing cosolvents on a model protein and fluorescent probes

The effect of cosolvents on the fluorescence of solutes was measured manually and in an automated high-performance liquid chromatography (HPLC) system that eliminates fluorescent contaminants on-line. The HPLC system was used to show that the effect of cosolvents on the fluorescence spectrum of heated chymotrypsin (a measure of unfolding) correlates with the effect of the solutes on the heat stabilization of catalytic activity; r2=0.73 with 12 example cosolvents. Changes in the fluorescence of model probes showed that known counteracting solutes slightly decrease the polarity of the solvent. Different cosolvents affect the proton transfer indicator, 2-naphthol (a model for tyrosinyl residues) differently, polyhydric alcohols enhance the protonated naphthol emission whereas zwitterionic solutes enhance naphthoxide fluorescence. The results with the automated system are consistent with the known stabilizing effects of the cosolvents and validate it as a tool to explore the development of novel cosolvents and their effects on multiple biological systems.     

Deletion mapping of the Aequorea victoria green fluorescent protein

Aequorea victoria green fluorescent protein (GFP) is a promising fluorescent marker which is active in a diverse array of prokaryotic and eukaryotic organisms. A key feature underlying the versatility of GFP is its capacity to undergo heterocyclic chromophore formation by cyclization of a tripeptide present in its primary sequence and thereby acquiring fluorescent activity in a variety of intracellular environments. In order to define further the primary structure requirements for chromophore formation and fluorescence in GFP, a series of N- and C-terminal GFP deletion variant expression vectors were created using the polymerase chain reaction. Scanning spectrofluorometric analyses of crude soluble protein extracts derived from eleven GFP expression constructs revealed that amino acid (aa) residues 2–232, of a total of 238 aa in the native protein, were required for the characteristic emission and absorption spectra of native GFP. Heterocyclic chromophore formation was assayed by comparing the absorption spectrum of GFP deletion variants over the 300–500-nm range to the absorption spectra of full-length GFP and GFP deletion variants missing the chromophore substrate domain from the primary sequence. GFP deletion variants lacking fluorescent activity showed no evidence of heterocyclic ring structure formation when the soluble extracts of their bacterial expression hosts were studied at pH 7.9. These observations suggest that the primary structure requirements for the fluorescent activity of GFP are relatively extensive and are compatible with the view that much of the primary structure serves an autocatalytic function.     

One- and two-photon excited fluorescence lifetimes and anisotropy decays of green fluorescent proteins

We have used one- (OPE) and two-photon (TPE) excitation with time-correlated single-photon counting techniques to determine time-resolved fluorescence intensity and anisotropy decays of the wild-type Green Fluorescent Protein (GFP) and two red-shifted mutants, S65T-GFP and RSGFP. WT-GFP and S65T-GFP exhibited a predominant approximately 3 ns monoexponential fluorescence decay, whereas for RSGFP the main lifetimes were approximately 1.1 ns (main component) and approximately 3.3 ns. The anisotropy decay of WT-GFP and S65T-GFP was also monoexponential (global rotational correlation time of 16 +/- 1 ns). The approximately 1.1 ns lifetime of RSGFP was associated with a faster rotational depolarization, evaluated as an additional approximately 13 ns component. This feature we attribute tentatively to a greater rotational freedom of the anionic chromophore. With OPE, the initial anisotropy was close to the theoretical limit of 0.4; with TPE it was higher, approaching the TPE theoretical limit of 0.57 for the colinear case. The measured power dependence of the fluorescence signals provided direct evidence for TPE. The general independence of fluorescence decay times, rotation correlation times, and steady-state emission spectra on the excitation mode indicates that the fluorescence originated from the same distinct excited singlet states (A*, I*, B*). However, we observed a relative enhancement of blue fluorescence peaked at approximately 440 nm for TPE compared to OPE, indicating different relative excitation efficiencies. We infer that the two lifetimes of RSGFP represent the deactivation of two substates of the deprotonated intermediate (I*), distinguished by their origin (i.e., from A* or B*) and by nonradiative decay rates reflecting different internal environments of the excited-state chromophore.     

The equilibrium unfolding intermediate observed at pH 4 and its relationship with the kinetic folding intermediates in green fluorescent protein

Folding mechanisms of a variant of green fluorescent protein (F99S/M153T/V163A) were investigated by a wide variety of spectroscopic techniques. Equilibrium measurements on acid-induced denaturation of the protein monitored by chromophore and tryptophan fluorescence and small-angle X-ray scattering revealed that this protein accumulates at least two equilibrium intermediates, a native-like intermediate and an unfolding intermediate, the latter of which exhibits the characteristics of the molten globule state under moderately denaturing conditions at pH 4. To elucidate the role of the equilibrium unfolding intermediate in folding, a series of kinetic refolding experiments with various combinations of initial and final pH values, including pH 7.5 (the native condition), pH 4.0 (the moderately denaturing condition where the unfolding intermediate is accumulated), and pH 2.0 (the acid-denaturing condition) were carried out by monitoring chromophore and tryptophan fluorescence. Kinetic on-pathway intermediates were accumulated during the folding on the refolding reaction from pH 2.0 to 7.5. However, the signal change corresponding to the conversion from the acid-denatured to the kinetic intermediate states was significantly reduced on the refolding reaction from pH 4.0 to pH 7.5, whereas only the signal change corresponding to the above conversion was observed on the refolding reaction from pH 2.0 to pH 4.0. These results indicate that the equilibrium unfolding intermediate is composed of an ensemble of the folding intermediate species accumulated during the folding reaction, and thus support a hierarchical model of protein folding.