Domains in folding of model proteins.

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

Mechanical unfolding of RNA: from hairpins to structures with internal multiloops

Mechanical unfolding of RNA structures, ranging from hairpins to ribozymes, using laser optical tweezer experiments have begun to reveal the features of the energy landscape that cannot be easily explored using conventional experiments. Upon application of constant force (f), RNA hairpins undergo cooperative transitions from folded to unfolded states whereas subdomains of ribozymes unravel one at a time. Here, we use a self-organized polymer model and Brownian dynamics simulations to probe mechanical unfolding at constant force and constant-loading rate of four RNA structures of varying complexity. For simple hairpins, such as P5GA, application of constant force or constant loading rate results in bistable cooperative transitions between folded and unfolded states without populating any intermediates. The transition state location (DeltaxFTS) changes dramatically as the loading rate is varied. At loading rates comparable to those used in laser optical tweezer experiments, the hairpin is plastic, with DeltaxFTS being midway between folded and unfolded states; whereas at high loading rates, DeltaxFTS moves close to the folded state, i.e., RNA is brittle. For the 29-nucleotide TAR RNA with the three-nucleotide bulge, unfolding occurs in a nearly two-state manner with an occasional pause in a high free energy metastable state. Forced unfolding of the 55 nucleotides of the Hepatitis IRES domain IIa, which has a distorted L-shaped structure, results in well-populated stable intermediates. The most stable force-stabilized intermediate represents straightening of the L-shaped structure. For these structures, the unfolding pathways can be predicted using the contact map of the native structures. Unfolding of a RNA motif with internal multiloop, namely, the 109-nucleotide prohead RNA that is part of the 29 DNA packaging motor, at constant value of rf occurs with three distinct rips that represent unraveling of the paired helices. The rips represent kinetic barriers to unfolding. Our work shows 1), the response of RNA to force is largely determined by the native structure; and 2), only by probing mechanical unfolding over a wide range of forces can the underlying energy landscape be fully explored.     

Ligand binding to a high‐energy partially unfolded protein

The conformational energy landscape of a protein determines populations of all possible conformations of the protein and also determines the kinetics of the conversion between the conformations. Interaction with ligands influences the conformational energy landscapes of proteins and shifts populations of proteins in different conformational states. To investigate the effect of ligand binding on partial unfolding of a protein, we use Escherichia coli dihydrofolate reductase (DHFR) and its functional ligand NADP⁺ as a model system. We previously identified a partially unfolded form of DHFR that is populated under native conditions. In this report, we determined the free energy for partial unfolding of DHFR at varying concentrations of NADP⁺ and found that NADP⁺ binds to the partially unfolded form as well as the native form. DHFR unfolds partially without releasing the ligand, though the binding affinity for NADP⁺ is diminished upon partial unfolding. Based on known crystallographic structures of NADP⁺‐bound DHFR and the model of the partially unfolded protein we previously determined, we propose that the adenosine‐binding domain of DHFR remains folded in the partially unfolded form and interacts with the adenosine moiety of NADP⁺. Our result demonstrates that ligand binding may affect the conformational free energy of not only native forms but also high‐energy non‐native forms.     

Compaction of ribosomal protein S6 by sucrose occurs only under native conditions

The effect of osmolyte sucrose on the stability and compaction of the folded and unfolded states of ribosomal protein S6 from Thermus thermophilus was analyzed. Confirming previous results obtained with sodium sulfate and trehalose, refolding stopped-flow measurements of S6 show that sucrose favors the conversion of the unfolded state ensemble to a highly compact structure (75% as compact as the folded state). This conversion occurs when the unfolded state is suddenly placed under native conditions and the compact state accumulates in a transient off-folding pathway. This effect of sucrose on the compaction of the unfolded state ensemble is counteracted by guanidinium hydrochloride. The compact state does not accumulate at higher guanidinium concentrations and the unfolded state ensemble does not display increased compaction in the presence of 6 M guanidinium as evaluated by collisional quenching of tryptophan fluorescence. In contrast, accessibility of the tryptophan residue of folded S6 above 1 M sucrose concentration decreased as a result of an increased compaction of the folded state. Unfolding stopped-flow measurements of S6 reflect this increased compaction of the folded state, but the unfolding pathway is not affected by sucrose. Compaction of folded and unfolded S6 induced by sucrose occurs under native conditions indicating that decreased protein conformational entropy significantly contributes to the mechanism of protein stabilization by osmolytes.     

Characterizing a partially folded intermediate of the villin headpiece domain under non-denaturing conditions: contribution of His41 to the pH-dependent stability of the N-terminal subdomain

The contribution of interactions involving the imidazole ring of His41 to the pH-dependent stability of the villin headpiece (HP67) N-terminal subdomain has been investigated by nuclear magnetic resonance (NMR) spin relaxation. NMR-derived backbone N-H order parameters (S2) for wild-type (WT) HP67 and H41Y HP67 indicate that reduced conformational flexibility of the N-terminal subdomain in WT HP67 is due to intramolecular interactions with the His41 imidazole ring. These interactions, together with desolvation effects, contribute to significantly depress the pKa of the buried imidazole ring in the native state. 15N R1rho relaxation dispersion data indicate that WT HP67 populates a partially folded intermediate state that is 10.9 kJ mol(-1) higher in free energy than the native state under non-denaturing conditions at neutral pH. The partially folded intermediate is characterized as having an unfolded N-terminal subdomain while the C-terminal subdomain retains a native-like fold. Although the majority of the residues in the N-terminal subdomain sample a random-coil distribution of conformations, deviations of backbone amide 1H and 15N chemical shifts from canonical random-coil values for residues within 5A of the His41 imidazole ring indicate that a significant degree of residual structure is maintained in the partially folded ensemble. The pH-dependence of exchange broadening is consistent with a linear three-state exchange model whereby unfolding of the N-terminal subdomain is coupled to titration of His41 in the partially folded intermediate with a pKa,I=5.69+/-0.07. Although maintenance of residual interactions with the imidazole ring in the unfolded N-terminal subdomain appears to reduce pKa,I compared to model histidine compounds, protonation of His41 disrupts these interactions and reduces the difference in free energy between the native state and partially folded intermediate under acidic conditions. In addition, chemical shift changes for residues Lys70-Phe76 in the C-terminal subdomain suggest that the HP67 actin binding site is disrupted upon unfolding of the N-terminal subdomain, providing a potential mechanism for regulating the villin-dependent bundling of actin filaments.     

Energetic coupling between native-state prolyl isomerization and conformational protein folding

In folded proteins, prolyl peptide bonds are usually thought to be either trans or cis because only one of the isomers can be accommodated in the native folded protein. For the N-terminal domain of the gene-3 protein of the filamentous phage fd (N2 domain), Pro161 resides at the tip of a beta hairpin and was found to be cis in the crystal structure of this protein. Here we show that Pro161 exists in both the cis and the trans conformations in the folded form of the N2 domain. We investigated how conformational folding and prolyl isomerization are coupled in the unfolding and refolding of N2 domain. A combination of single-mixing and double-mixing unfolding and refolding experiments showed that, in unfolded N2 domain, 7% of the molecules contain a cis-Pro161 and 93% of the molecules contain a trans-Pro161. During refolding, the fraction of molecules with a cis-Pro161 increases to 85%. This implies that 10.3 kJ mol(-1) of the folding free energy was used to drive this 75-fold change in the Pro161 cis/trans equilibrium constant during folding. The stabilities of the forms with the cis and the trans isomers of Pro161 and their folding kinetics could be determined separately because their conformational folding is much faster than the prolyl isomerization reactions in the native and the unfolded proteins. The energetic coupling between conformational folding and Pro161 isomerization is already fully established in the transition state of folding, and the two isomeric forms are thus truly native forms. The folding kinetics are well described by a four-species box model, in which the N2 molecules with either isomer of Pro161 can fold to the native state and in which cis/trans isomerization occurs in both the unfolded and the folded proteins.     

The sequence TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase displays structural ambivalence and interconverts between alpha-helical and beta-hairpin conformations mediated by collapsed conformational states.

The peptide TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase adopts a helical conformation in the crystal structure and is a site for two hydrated helical segments, which are thought to be helical folding intermediates. Overlapping sequences of four to five residues from the peptide, sample both helical and strand conformations in known protein structures, which are dissimilar to glyceraldehyde-3-phosphate dehydrogenase suggesting that the peptide may have a structural ambivalence. Molecular dynamics simulations of the peptide sequence performed for a total simulation time of 1.2 micros, starting from the various initial conformations using GROMOS96 force field under NVT conditions, show that the peptide samples a large number of conformational forms with transitions from alpha-helix to beta-hairpin and vice versa. The peptide, therefore, displays a structural ambivalence. The mechanism from alpha-helix to beta-hairpin transition and vice versa reveals that the compact bends and turns conformational forms mediate such conformational transitions. These compact structures including helices and hairpins have similar hydrophobic radius of gyration (Rgh) values suggesting that similar hydrophobic interactions govern these conformational forms. The distribution of conformational energies is Gaussian with helix sampling lowest energy followed by the hairpins and coil. The lowest potential energy of the full helix may enable the peptide to take up helical conformation in the crystal structure of the glyceraldehyde-3-phosphate dehydrogenase, even though the peptide has a preference for hairpin too. The relevance of folding and unfolding events observed in our simulations to hydrophobic collapse model of protein folding are discussed.     

A semiflexible polymer model applied to loop formation in DNA hairpins

A statistical mechanical "zipper" model is applied to describe the equilibrium melting of short DNA hairpins with poly(dT) loops ranging from 4 to 12 bases in the loop. The free energy of loop formation is expressed in terms of the persistence length of the chain. This method provides a new measurement of the persistence length of single-stranded DNA, which is found to be approximately 1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of the hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of > or = 7, much larger than the exponent of approximately 1.5-1.8 expected from considerations of loop entropy alone. This result indicates a strong dependence of the excess stability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arising from favorable hydrophobic interactions among the bases in tight loops and which diminish as the loops get larger. Free energy profiles along a generalized reaction coordinate are calculated from the equilibrium zipper model. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a lower enthalpy than the random coil state. The equilibrium model predicts apparent activation energy of approximately -11 kcal/mol for the hairpin closing step, in remarkable agreement with the value obtained from kinetics measurements.     

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.     

Kinetic analysis of molecular dynamics simulations reveals changes in the denatured state and switch of folding pathways upon single-point mutation of a beta-sheet miniprotein

The effects of a single-point mutation on folding thermodynamics and kinetics are usually interpreted by focusing on the native structure and the transition state. Here, the entire conformational spaces of a 20-residue three-stranded antiparallel beta-sheet peptide (double hairpin) and of its single-point mutant W10V are sampled close to the melting temperature by equilibrium folding-unfolding molecular dynamics simulations for a total of 40 micros. The folded state as well as the most populated free energy basins in the denatured state are isolated by grouping conformations according to fast relaxation at equilibrium. Such kinetic analysis provides more detailed and useful information than a simple projection of the free energy. The W10V mutant has the same native structure as the wild type peptide, and similar folding rate and stability. In the denatured state, the N-terminal hairpin is about 20% more structured in W10V than the wild type mainly because of van der Waals interactions. Notably, the W10V mutation influences also the van der Waals energy at the transition state ensemble causing a shift in the ratio of fluxes between two different transition state regions on parallel folding pathways corresponding to nucleation at either of the two beta-hairpins. Previous experimental studies have focused on the effects of denaturant-dependent or temperature-dependent changes in the structure of the denatured state. The atomistic simulations show that a single-point mutation in the central strand of a beta-sheet peptide results in remarkable changes in the topography of the denatured state ensemble. These changes modulate the relative accessibility of parallel folding pathways because of kinetic partitioning of the denatured state. Therefore, the observed dependence of the folding process on the starting ensemble raises questions on the biological significance of in vitro folding studies under strongly denaturing conditions.     

Autonomous folding of a peptide corresponding to the N-terminal beta-hairpin from ubiquitin.

The N-terminal 17 residues of ubiquitin have been shown by 1H NMR to fold autonomously into a beta-hairpin structure in aqueous solution. This structure has a specific, native-like register, though side-chain contacts differ in detail from those observed in the intact protein. An autonomously folding hairpin has previously been identified in the case of streptococcal protein G, which is structurally homologous with ubiquitin, but remarkably, the two are not in topologically equivalent positions in the fold. This suggests that the organization of folding may be quite different for proteins sharing similar tertiary structures. Two smaller peptides have also been studied, corresponding to the isolated arms of the N-terminal hairpin of ubiquitin, and significant differences from simple random coil predictions observed in the spectra of these subfragments, suggestive of significant limitation of the backbone conformational space sampled, presumably as a consequence of the strongly beta-structure favoring composition of the sequences. This illustrates the ability of local sequence elements to express a propensity for beta-structure even in the absence of actual sheet formation. Attempts were made to estimate the population of the folded state of the hairpin, in terms of a simple two-state folding model. Using published "random coil" values to model the unfolded state, and values derived from native ubiquitin for the putative unique, folded state, it was found that the apparent population varied widely for different residues and with different NMR parameters. Use of the spectra of the subfragment peptides to provide a more realistic model of the unfolded state led to better agreement in the estimates that could be obtained from chemical shift and coupling constant measurements, while making it clear that some other approaches to population estimation could not give meaningful results, because of the tendency to populate the beta-region of conformational space even in the absence of the hairpin structure.     

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.     

Structural transitions of carboxymethylated cytochrome c: calorimetric and circular dichroic studies

Circular dichroism and differential scanning calorimetry studies on the unfolding-refolding process of native and carboxymethylated cytochrome c, induced either by temperature or chemical agents, have been performed. The results have shown that the modified protein has a decreased conformational stability with respect to the native state, in agreement with a structure less compact, but still highly folded, which behaves as a thermodynamically stable "intermediate" between native and fully unfolded cytochrome c.     

Structure of a partially unfolded form of Escherichia coli dihydrofolate reductase provides insight into its folding pathway

Proteins frequently fold via folding intermediates that correspond to local minima on the conformational energy landscape. Probing the structure of the partially unfolded forms in equilibrium under native conditions can provide insight into the properties of folding intermediates. To elucidate the structures of folding intermediates of Escherichia coli dihydrofolate reductase (DHFR), we investigated transient partial unfolding of DHFR under native conditions. We probed the structure of a high‐energy conformation susceptible to proteolysis (cleavable form) using native‐state proteolysis. The free energy for unfolding to the cleavable form is clearly less than that for global unfolding. The dependence of the free energy on urea concentration (m‐value) also confirmed that the cleavable form is a partially unfolded form. By assessing the effect of mutations on the stability of the partially unfolded form, we found that native contacts in a hydrophobic cluster formed by the F‐G and Met‐20 loops on one face of the central β‐sheet are mostly lost in the partially unfolded form. Also, the folded region of the partially unfolded form is likely to have some degree of structural heterogeneity. The structure of the partially unfolded form is fully consistent with spectroscopic properties of the near‐native kinetic intermediate observed in previous folding studies of DHFR. The findings suggest that the last step of the folding of DHFR involves organization in the structure of two large loops, the F‐G and Met‐20 loops, which is coupled with compaction of the rest of the protein.     

Unfolding of rabbit muscle creatine kinase induced by acid. A study using electrospray ionization mass spectrometry,isothermal titration calorimetry,and fluorescence spectroscopy

Electrospray ionization mass spectrometry, isothermal titration calorimetry (ITC), fluorescence spectroscopy, and glutaraldehyde cross-linking SDS-PAGE have been used to study the unfolding of rabbit muscle creatine kinase (MM-CK) induced by acid. The mass spectrometric experiments show that MM-CK is unfolded gradually when titrated with acid. MM-CK is a dimer (the native state) at pH 7.0 and becomes an equilibrium mixture of the dimer and a partially folded monomer (the intermediate) between pH 6.7 and 5.0. The dimeric protein becomes an equilibrium mixture of the intermediate and an unfolded monomer (the unfolded state) between pH 5.0 and 3.0 and is almost fully unfolded at pH 3.0 reached. The results from a "phase diagram" method of fluorescence show that the conformational transition between the native state and the intermediate of MM-CK occurs in the pH range of 7.0-5.2, and the transition between the intermediate and the unfolded state of the protein occurs between pH 5.2 and 3.0. The intrinsic molar enthalpy changes for formation of the unfolded state of MM-CK induced by acid at 15.0, 25.0, 30.0, and 37.0 degrees C have been determined by ITC. A large positive molar heat capacity change of the unfolding, 8.78 kcal mol-1 K-1, at all temperatures examined indicates that hydrophobic interaction is the dominant driving force stabilizing the native structure of MM-CK. Combining the results from these four methods, we conclude that the acid-induced unfolding of MM-CK follows a "three-state" model and that the intermediate state of the protein is a partially folded monomer.     

Single-Molecule Studies of the Im7 Folding Landscape

Under appropriate conditions, the four-helical Im7 (immunity protein 7) folds from an ensemble of unfolded conformers to a highly compact native state via an on-pathway intermediate. Here, we investigate the unfolded, intermediate, and native states populated during folding using diffusion single-pair fluorescence resonance energy transfer by measuring the efficiency of energy transfer (or proximity or P ratio) between pairs of fluorophores introduced into the side chains of cysteine residues placed in the center of helices 1 and 4, 1 and 3, or 2 and 4. We show that while the native states of each variant give rise to a single narrow distribution with high P values, the distributions of the intermediates trapped at equilibrium (denoted I^eqm) are fitted by two Gaussian distributions. Modulation of the folding conditions from those that stabilize the intermediate to those that destabilize the intermediate enabled the distribution of lower P value to be assigned to the population of the unfolded ensemble in equilibrium with the intermediate state. The reduced stability of the I^eqm variants allowed analysis of the effect of denaturant concentration on the compaction and breadth of the unfolded state ensemble to be quantified from 0 to 6 M urea. Significant compaction is observed as the concentration of urea is decreased in both the presence and absence of sodium sulfate, as previously reported for a variety of proteins. In the presence of Na₂SO₄ in 0 M urea, the P value of the unfolded state ensemble approaches that of the native state. Concurrent with compaction, the ensemble displays increased peak width of P values, possibly reflecting a reduction in the rate of conformational exchange among iso-energetic unfolded, but compact conformations. The results provide new insights into the initial stages of folding of Im7 and suggest that the unfolded state is highly conformationally constrained at the outset of folding.     

Computational studies of colicin insertion into membranes: the closed state

Colicins are water-soluble toxins that, upon interaction with membranes, undergo a conformational change, insert, and form pores in them. Pore formation activity is localized in a bundle of 10 α-helices named the pore-forming domain (PFD). There is evidence that colicins attach to the membrane via a hydrophobic hairpin embedded in the core of the PFD. Two main models have been suggested for the membrane-bound state: penknife and umbrella, differing in regard to the orientation of the hydrophobic hairpin with respect to the membrane. The arrangement of the amphipathic helices has been described as either a compact three-dimensional structure or a two-dimensional array of loosely interacting helices on the membrane surface. Using molecular dynamics simulations with an implicit membrane model, we studied the structure and stability of the conformations proposed earlier for four colicins. We find that colicins are initially driven towards the membrane by electrostatic interactions between basic residues and the negatively charged membrane surface. They do not have a unique binding orientation, but in the predominant orientations the central hydrophobic hairpin is parallel to the membrane. In the inserted state, the estimated free energy tends to be lower for the compact arrangements of the amphipathic helix, but the more expanded ones are in better agreement with experimental distance distributions. The difference in energy between penknife and umbrella conformations is small enough for equilibrium to exist between them. Elongation of the hydrophobic hairpin helices and membrane thinning were found unable to produce stabilization of the transmembrane configuration of the hydrophobic hairpin.