Conformation and aggregation of M13 coat protein studied by molecular dynamics.

Molecular dynamics (MD) simulations are performed on M13 coat protein, a small membrane protein for which both alpha- and beta-structures have been suggested. The simulations are started from initial conformations that are either monomers or dimers of alpha-helices or U-shaped beta-sheets. The lipid bilayer is represented by a hydrophobic potential. The results are analyzed in terms of stability, energy and secondary structure. The U-shaped beta-structure changes from a planar to a twisted form with larger twist for the monomer than the dimer. The beta-sheet is much more flexible than the alpha-helix as monitored by the root mean square (rms) fluctuations of the C alpha atoms. A comparison of the energies after 100 ps MD simulation shows that of the monomers, the alpha-helix has the lowest energy. The energy difference between alpha- and beta-structures decreases from 266 kJ/mol to 148 kJ/mol, when going from monomers to dimers. It is expected that this difference will decrease with higher aggregation numbers.     

Reversible unfolding of beta-sheets in membranes: a calorimetric study

The hexapeptide acetyl-Trp-Leu(5) (AcWL(5)) has the remarkable ability to assemble reversibly and spontaneously into beta-sheets on lipid membranes as a result of monomer partitioning followed by cooperative assembly. This system provides a unique opportunity to study the thermodynamics of protein folding in membranes, which we have done using isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC). The results, which may represent the first example of reversible thermal unfolding of peptides in membranes, help to define the contribution of hydrogen bonding to the extreme thermal stability of membrane proteins. ITC revealed that the enthalpy change for partitioning of monomeric, unstructured AcWL(5) from water into membranes was zero within experimental error over the temperature range of 5 degrees C to 75 degrees C. DSC showed that the beta-sheet aggregates underwent a reversible, endothermic, and very asymmetric thermal transition with a concentration-dependent transition temperature (T(m)) in the range of 60 degrees C to 80 degrees C. A numerical model of nucleation and growth-dependent assembly of oligomeric beta-sheets, proposed earlier to describe beta-sheet formation in membranes, recreated remarkably well the unusual shape and concentration-dependence of the transition peaks. The enthalpy for thermal unfolding of AcWL(5) beta-sheets in the membrane was found to be about 8(+/-1)kcal mol(-1), or about 1.3(+/-0.2)kcal mol(-1) per residue.     

Reconstruction of the src-SH3 protein domain transition state ensemble using multiscale molecular dynamics simulations

We use an integrated computational approach to reconstruct accurately the transition state ensemble (TSE) for folding of the src-SH3 protein domain. We first identify putative TSE conformations from free energy surfaces generated by importance sampling molecular dynamics for a fully atomic, solvated model of the src-SH3 protein domain. These putative TSE conformations are then subjected to a folding analysis using a coarse-grained representation of the protein and rapid discrete molecular dynamics simulations. Those conformations that fold to the native conformation with a probability (P(fold)) of approximately 0.5, constitute the true transition state. Approximately 20% of the putative TSE structures were found to have a P(fold) near 0.5, indicating that, although correct TSE conformations are populated at the free energy barrier, there is a critical need to refine this ensemble. Our simulations indicate that the true TSE conformations are compact, with a well-defined central beta sheet, in good agreement with previous experimental and theoretical studies. A structured central beta sheet was found to be present in a number of pre-TSE conformations, however, indicating that this element, although required in the transition state, does not define it uniquely. An additional tight cluster of contacts between highly conserved residues belonging to the diverging turn and second beta-sheet of the protein emerged as being critical elements of the folding nucleus. A number of commonly used order parameters to identify the transition state for folding were investigated, with the number of native Cbeta contacts displaying the most satisfactory correlation with P(fold) values.     

Probing the kinetic cooperativity of beta-sheet folding perpendicular to the strand direction

In an attempt to determine how the folding dynamics of multistranded beta-sheets vary with the strand number, we have studied the temperature-induced relaxation kinetics of a four-stranded beta-sheet, DPDPDP. Our results show that the thermally induced relaxation of DPDPDP occurs on the nanosecond time scale; however, a comparison of the current results with those obtained on a sequence-related, three-stranded beta-sheet suggests that increasing the strand number from three to four increases the folding free energy barrier by a minimum of 0.8 kcal/mol, depending on the folding mechanism. Therefore, these results together suggest that the relaxation kinetics of DPDPDP can be analyzed according to a two-state model even though its folding may actually involve parallel (but degenerate or nearly degenerate) kinetic pathways. The apparent, two-state folding time of DPDPDP is determined to be approximately 0.44 micros at the thermal melting temperature, which makes it one of the fastest folders known to date.     

Secondary structure length as a determinant of folding rate of proteins with two- and three-state kinetics

We present a simple method for determining the folding rates of two- and three-state proteins from the number of residues in their secondary structures (secondary structure length). The method is based on the hypothesis that two- and three-state foldings share a common pattern. Three-state proteins first condense into metastable intermediates, subsequent forming of alpha-helices, turns, and beta-sheets at slow rate-limiting step. The folding rate of such proteins anticorrelate with the length of these beta-secondary structures. It is also assumed that in two-state folding, rapidly folded alpha-helices and turns may facilitate formation of fleeting unobservable intermediates and thus show two-state behavior. There is an inverse relationship between the folding rate and the length of beta-sheets and loops. Our study achieves 94.0 and 88.1% correlations with folding rates determined experimentally for 21 three- and 38 two-state proteins, respectively, suggesting that protein-folding rates are determined by the secondary structure length. The kinetic kinds are selected on the basis of a competitive formation of hydrophobic collapse and alpha-structure in early intermediates.     

A general model of the P2 protein of peripheral nervous system myelin based on secondary structure predictions, tertiary folding principles, and experimental observations

The amino acid sequence of the P2 protein of peripheral myelin was analyzed with regard to regions of probable alpha-helix, beta-structure, beta-turn, and unordered conformation by means of several algorithms commonly used to predict secondary structure in proteins. Because of the high beta-sheet content and virtual absence of alpha-helix shown by the circular dichroic spectra of the protein, a bias was introduced into the algorithms to favor the beta-structure over the alpha-helical conformation. In order to define those beta-sheet residues that could lie on the external hydrophilic surface of the protein and those that could lie in its hydrophobic interior, the predicted beta-strands were examined for charged and uncharged amino acids located at alternating positions in the sequence. The sequential beta-strands in the predicted secondary structure were then ordered into beta-sheets and aligned according to generally accepted tertiary folding principles and certain chemical properties peculiar to the P2 protein. The general model of the P2 protein that emerged was a "Greek key" beta-barrel, consisting of eight antiparallel beta-strands with a two-stranded ribbon of antiparallel beta-structure emerging from one end. The model has an uncharged, hydrophobic core and a highly hydrophilic surface. The two Cys residues, which form a disulfide, occur in a loop connecting two adjacent antiparallel strands. Two hydrophilic loops, each containing a cluster of acidic residues and a single Phe, protrude from one end of the molecule. The general model is consistent with many of the properties of the actual protein, including the relatively weak nature of its association with myelin lipids and the positions of amino acid substitutions. Alternative beta-strand orderings yield three specific models having different interstrand connections across the barrel ends.     

Beta-sheet capping: signals that initiate and terminate beta-sheet formation

In the present work, we address the question of whether different amino acids have different beta-sheet initiating and terminating characteristics. Using a large scale analysis of parallel and antiparallel beta-sheets in a non-redundant dataset of proteins, we observed that most of the amino acids show significant under- or over-representation in at least one of the positions at the two ends of beta-sheets, which are denoted as N-cap and C-cap. In addition, based on statistical data and structural comparison, we found that certain amino acids, especially Asp, Asn, Gly and Pro have strong tendencies to block beta-sheet continuation. Hence, we can consider these residues as beta-sheet terminators. It was also proposed that the dipole moments in parallel beta-sheets, whose direction is from C-terminal (partially negative) to N-terminal (partially positive), are much stronger than has previously been suggested. In fact, enhancement of dipole moments in parallel beta-sheets is a result of the positioning of positively charged residues at N-cap and negatively charged residues at C-cap. This enhancement in dipole moment magnitude leads to strengthened dipolar interactions between parallel beta-sheets dipoles and other partners especially alpha-helices dipoles. The results provide an explanation for the antiparallel alignment of parallel beta-sheets with alpha-helices.     

Discovery of a significant,nontopological preference for antiparallel alignment of helices with parallel regions in sheets

To help elucidate the role of secondary structure packing preferences in protein folding, here we present an analysis of the packing geometry observed between alpha-helices and between alpha-helices and beta-sheets in 1316 diverse, nonredundant protein structures. Finite-length vectors were fit to the alpha-carbon atoms in each of the helices and strands, and the packing angle between the vectors, Omega, was determined at the closest point of approach within each helix-helix or helix-sheet pair. Helix-sheet interactions were found in 391 of the proteins, and the distributions of Omega values were calculated for all the helix-sheet and helix-helix interactions. The packing angle preferences for helix-helix interactions are similar to those previously observed. However, analysis of helix-strand packing preferences uncovered a remarkable tendency for helices to align antiparallel to parallel regions of beta-sheets, independent of the topological constraints or prevalence of beta-alpha-beta motifs in the proteins. This packing angle preference is significantly diminished in helix interactions involving mixed and antiparallel beta-sheets, suggesting a role for helix-sheet dipole alignment in guiding supersecondary structure formation in protein folding. This knowledge of preferred packing angles can be used to guide the engineering of stable protein modules.     

Pathway and stability of protein folding.

We describe an experimental approach to the problem of protein folding and stability which measures interaction energies and maps structures of intermediates and transition states during the folding pathway. The strategy is based on two steps. First, protein engineering is used to remove interactions that stabilize defined positions in barnase, the RNAse from Bacillus amyloliquefaciens. The consequent changes in stability are measured from the changes in free energy of unfolding of the protein. Second, each mutation is used as a probe of the structure around the wild-type side chain during the folding process. Kinetic measurements are made on the folding and unfolding of wild-type and mutant proteins. The kinetic and thermodynamic data are combined and analysed to show the role of individual side chains in the stabilization of the folded, transition and intermediate states of the protein. The protein engineering experiments are corroborated by nuclear magnetic resonance studies of hydrogen exchange during the folding process. Folding is a multiphasic process in which alpha-helices and beta-sheet are formed relatively early. Formation of the hydrophobic core by docking helix and sheet is (partly) rate determining. The final steps involve the forming of loops and the capping of the N-termini of helices.     

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.     

Determining beta-sheet stability by Fourier transform infrared difference spectra

We describe here a new method for determining the conformational stability of antiparallel beta-sheets. Due to coupling between the transition dipoles, beta-sheet conformations typically exhibit a characteristic high-frequency amide I component centered at approximately 1680 cm(-1). Using one beta-sheet protein and two small beta-hairpins, we demonstrate that this high-frequency component, which is fairly narrow (approximately 8-10 cm(-1)), can be quantitatively resolved and used in thermal stability determination. Compared with the commonly used CD and fluorescence techniques, this ir method offers advantages. Since the area of this high-frequency component is only proportional to the folded population, it eliminates the need for a priori information of the folded and unfolded baselines encountered in other methods. Thus, it is applicable to a variety of beta-sheet systems.     

Early intermediates in the folding of dihydrofolate reductase from Escherichia coli detected by hydrogen exchange and NMR.

The kinetic folding mechanism for Escherichia coli dihydrofolate reductase postulates two distinct types of transient intermediates. The first forms within 5 ms and has substantial secondary structure but little stability. The second is a set of four species that appear over the course of several hundred milliseconds and have secondary structure, specific tertiary structure, and significant stability (Jennings PA, Finn BE, Jones BE, Matthews CR, 1993, Biochemistry 32:3783-3789). Pulse labeling hydrogen exchange experiments were performed to determine the specific amide hydrogens in alpha-helices and beta-strands that become protected from exchange through the formation of stable hydrogen bonds during this time period. A significant degree of protection was observed for two subsets of the amide hydrogens within the dead time of this experiment (6 ms). The side chains of one subset form a continuous nonpolar strip linking six of the eight strands in the beta-sheet. The other subset corresponds to a nonpolar cluster on the opposite face of the sheet and links three of the strands and two alpha-helices. Taken together, these data demonstrate that the complex strand topology of this eight-stranded sheet can be formed correctly within 6 ms. Measurement of the protection factors at three different folding times (13 ms, 141 ms, and 500 ms) indicates that, of the 13 amide hydrogens displaying significant protection within 6 ms, 8 exhibit an increase in their protection factors from approximately 5 to approximately 50 over this time range; the remaining five exhibit protection factors > 100 at 13 ms. Only approximately half of the population of molecules form this set of stable hydrogen bonds. Thirteen additional hydrogens in the beta-sheet become protected from exchange as the set of native conformers appear, suggesting that the stabilization of this network reflects the global cooperativity of the folding reaction.     

Stability and folding properties of a model beta-sheet protein, Escherichia coli CspA.

Although beta-sheets represent a sizable fraction of the secondary structure found in proteins, the forces guiding the formation of beta-sheets are still not well understood. Here we examine the folding of a small, all beta-sheet protein, the E. coli major cold shock protein CspA, using both equilibrium and kinetic methods. The equilibrium denaturation of CspA is reversible and displays a single transition between folded and unfolded states. The kinetic traces of the unfolding and refolding of CspA studied by stopped-flow fluorescence spectroscopy are monoexponential and thus also consistent with a two-state model. In the absence of denaturant, CspA refolds very fast with a time constant of 5 ms. The unfolding of CspA is also rapid, and at urea concentrations above the denaturation midpoint, the rate of unfolding is largely independent of urea concentration. This suggests that the transition state ensemble more closely resembles the native state in terms of solvent accessibility than the denatured state. Based on the model of a compact transition state and on an unusual structural feature of CspA, a solvent-exposed cluster of aromatic side chains, we propose a novel folding mechanism for CspA. We have also investigated the possible complications that may arise from attaching polyhistidine affinity tags to the carboxy and amino termini of CspA.     

Folding thermodynamics and kinetics of the leucine-rich repeat domain of the virulence factor Internalin B

Although the folding of alpha-helical repeat proteins has been well characterized, much less is known about the folding of repeat proteins containing beta-sheets. Here we investigate the folding thermodynamics and kinetics of the leucine-rich repeat (LRR) domain of Internalin B (InlB), an extracellular virulence factor from the bacterium Lysteria monocytogenes. This domain contains seven tandem leucine-rich repeats, of which each contribute a single beta-strand that forms a continuous beta-sheet with neighboring repeats, and an N-terminal alpha-helical capping motif. Despite its modular structure, InlB folds in an equilibrium two-state manner, as reflected by the identical thermodynamic parameters obtained by monitoring its sigmoidal urea-induced unfolding transition by different spectroscopic probes. Although equilibrium two-state folding is common in alpha-helical repeat proteins, to date, InlB is the only beta-sheet-containing repeat protein for which this behavior is observed. Surprisingly, unlike other repeat proteins exhibiting equilibrium two-state folding, InlB also folds by a simple two-state kinetic mechanism lacking intermediates, aside from the effects of prolyl isomerization on the denatured state. However, like other repeat proteins, InlB also folds significantly more slowly than expected from contact order. When plotted against urea, the rate constants for the fast refolding and single unfolding phases constitute a linear chevron that, when fitted with a kinetic two-state model, yields thermodynamic parameters matching those observed for equilibrium folding. Based on these kinetic parameters, the transition state is estimated to comprise 40% of the total surface area buried upon folding, indicating that a large fraction of the native contacts are formed in the rate-limiting step to folding.     

Ranking the factors that contribute to protein beta-sheet folding

The formation of beta-sheet domains in proteins involves five energetically important factors: the formation of networks of hydrogen bonds and hydrophobic faces, and the residue propensities, or preferences, to be found at the edges of the beta-sheet, to adopt the extended conformation, and to make contact with other residues. These relative energy contributions define a potential energy function. Here, we show how optimizing this potential energy function reveals the formation of hydrophobic faces as the utmost factor. The potential energy function was optimized to minimize the Z-scores of the native topologies among the exhaustive sets of over 400 different beta-sheets. These results corroborate with experimental data that showed the environment of a protein is an important modulator of beta-sheet folding. The contact propensities were found to be the least important, which could explain the poor predictive power of beta-strand alignment methods based on pair-wise contact matrices.     

Effects of alanine substitutions in alpha-helices of sperm whale myoglobin on protein stability.

The peptide backbones in folded native proteins contain distinctive secondary structures, alpha-helices, beta-sheets, and turns, with significant frequency. One question that arises in folding is how the stability of this secondary structure relates to that of the protein as a whole. To address this question, we substituted the alpha-helix-stabilizing alanine side chain at 16 selected sites in the sequence of sperm whale myoglobin, 12 at helical sites on the surface of the protein, and 4 at obviously internal sites. Substitution of alanine for bulky side chains at internal sites destabilizes the protein, as expected if packing interactions are disrupted. Alanine substitutions do not uniformly stabilize the protein, either in capping positions near the ends of helices or at mid-helical sites near the surface of myoglobin. When corrected for the extent of exposure of each side chain replaced by alanine at a mid-helix position, alanine replacement still has no clear effect in stabilizing the native structure. Thus linkage between the stabilization of secondary structure and tertiary structure in myoglobin cannot be demonstrated, probably because of the relatively small free energy differences between side chains in stabilizing isolated helix. By contrast, about 80% of the variance in free energy observed can be accounted for by the loss in buried surface area of the native residue substituted by alanine. The differential free energy of helix stabilization does not account for any additional variation.     

Beta-sheet folding mechanisms from perturbation energetics

Amide backbone and sidechain mutagenesis data can be used in combination with kinetic and thermodynamic measurements to understand the energetic contributions of backbone hydrogen bonding and the hydrophobic effect to the acquisition of beta-sheet structure. For example, it has been revealed that loop 1 of the WW domain forms in the transition state, consistent with the emerging theme that reverse turn formation is rate limiting in beta-sheet folding. A distinct subset of WW domain residues principally influences thermodynamic stability by forming hydrogen bonds and hydrophobic interactions that stabilize the native state. Energetic data and sequence mining reveal that only a small subset of the molecular information contained in sequences or observed in high-resolution structures is required to generate folded functional beta-sheets, consistent with evolutionary robustness.