De novo design of a monomeric three-stranded antiparallel beta-sheet

Natural polypeptide scaffolds: beta-sheets, beta-turns, and beta-hairpins

This paper provides an introduction to fundamental conformational states of polypeptides in the beta-region of phi,psi space, in which the backbone is extended near to its maximal length, and to more complex architectures in which extended segments are linked by turns and loops. There are several variants on these conformations, and they comprise versatile scaffolds for presentation of side chains and backbone amides for molecular recognition and designed catalysts. In addition, the geometry of these fundamental folds can be readily mimicked in peptidomimetics.

Conversion of type I 4:6 to 3:5 beta-turn types in human acidic fibroblast growth factor: effects upon structure, stability, folding, and mitogenic function

Human acidic fibroblast growth factor (FGF-1) is a member of the beta-trefoil superfold, a protein architecture that exhibits a characteristic threefold axis of structural symmetry. FGF-1 contains 11 beta-turns, the majority being type I 3:5; however, a type I 4:6 turn is also found at three symmetry-related locations. The relative uniqueness of the type I 4:6 turn in the FGF-1 structure suggests it may play a key role in the stability, folding, or function of the protein. To test this hypothesis a series of deletion mutations were constructed, the aim of which was to convert existing type I 4:6 turns at two locations into type I 3:5 turns. The results show it is possible to successfully substitute the type I 4:6 turn by a type I 3:5 turn with minimal impact upon protein stability or folding. Thus, these different turn structures, even though they differ in length, exhibit similar energetic properties. Additional sequence swapping mutations within the introduced type I 3:5 turns suggests that the turn sequence primarily affects stability but not turn structure (which appears dictated primarily by the local environment). Although the results suggest that a stable, foldable beta-trefoil protein may be designed utilizing a single turn type (type I 3:5), a type I 4:6 turn at turn 1 of FGF-1 appears essential for efficient mitogenic function.

Exploring peptide energy landscapes: a test of force fields and implicit solvent models

A biased Monte Carlo-minimization/annealing conformational search was used to characterize five descriptions of the energy landscape for each of three model systems: the 20-residue "trp-cage" miniprotein, the 20-residue "BS1" peptide, and the 17-residue "U(1-17)T9D" peptide. The EEF1 and SASA energy landscapes were studied as well as those defined by using the GB/ACE implicit water model with one of three protein force fields: CHARMM19, CHARMM22, and CHARMM22/CMAP. The lowest-energy structures of the trp-cage and BS1 peptides found for the EEF1 landscape have main-chain root-mean-square deviations (rmsds) from the respective NMR structures of less than 2 A; for U(1-17)T9D, the deviation is less than 3 A using EEF1. The main-chain rmsd of the minimum-energy trp-cage conformation obtained for the GB/ACE/CHARMM22/CMAP landscape is less than 1 A. However, this energy function strongly favored helical structures for the two peptides shown by NMR to form beta-sheet structures. Brief annealing of the system following main-chain conformational changes was found to enhance the exploration of low-energy states. The thousands of simulations reported here suggest that the prediction of protein structure might be improved by the simultaneous use of a CMAP-like description of the main chain and an EEF1-like description of the solvent.

A multibody, whole-residue potential for protein structures, with testing by Monte Carlo simulated annealing

A new multibody, whole-residue potential for protein tertiary structure is described. The potential is based on the local environment surrounding each main-chain alpha carbon (CA), defined as the set of all residues whose CA coordinates lie within a spherical volume of set radius in 3-dimensional (3D) space surrounding that position. It is shown that the relative positions of the CAs in these local environments belong to a set of preferred templates. The templates are derived by cluster analysis of the presently available database of over 3000 protein chains (750,000 residues) having not more than 30% sequence similarity. For each template is derived also a set of residue propensities for each topological position in the template. Using lookup tables of these derived templates, it is then possible to calculate an energy for any conformation of a given protein sequence. The application of the potential to ab initio protein tertiary structure prediction is evaluated by performing Monte Carlo simulated annealing on test protein sequences.

NMR structural analysis of a peptide mimic of the bridging sheet of HIV-1 gp120 in methanol and water

gp120 is a subunit of the Env (viral envelope protein) of HIV-1. The protein consists of inner and outer domains linked by a bridging sheet. Several gp120 residues that bind the neutralizing antibody 17b as well as the cellular co-receptor CCR5 (CC chemokine receptor 5), are located in the bridging sheet. Peptides that mimic the 17b-binding regions of gp120 would be useful potential immunogens for the generation of neutralizing antibodies against HIV-1. Towards this end, a 26-residue, four-stranded beta-sheet peptide was designed on the basis of the structure of the bridging sheet, and its structure was characterized in methanol by NMR. In methanol, amide and alpha-proton resonances were well resolved and dispersed. A number of interstrand NOEs (nuclear Overhauser effects) were observed, providing good evidence for multiple turn beta-hairpin structure. NOEs also provided good evidence for all Xxx-D-Pro bonds in the trans configuration and all three turns formed by a two residue D-Pro-Gly segment to be of type II' turn. The structure conforms well to the designed four-stranded beta-sheet structure. Approx. 20% of the peptide was estimated to adopt a folded conformation in water, as evidenced by CD spectroscopy. This was consistent with smaller, but still significant, downfield shifts of C(alpha)H protons relative to random-coil values. A second peptide was designed with two disulphide bonds to further constrain the peptide backbone. While structured in methanol, this peptide, like the previous one, also exhibits only partial structure formation in water, as evidenced by CD spectroscopy.

Folding cooperativity in a three-stranded beta-sheet model

The thermodynamic behavior of a previously designed three-stranded beta-sheet was studied via several microseconds of standard and replica exchange molecular dynamics simulations. The system is shown to populate at least four thermodynamic minima, including two partially folded states in which only a single hairpin is formed. Simulated melting curves show different profiles for the C and N-terminal hairpins, consistent with differences in secondary structure content in published NMR and CD/FTIR measurements, which probed different regions of the chain. Individual beta-hairpins that comprise the three-stranded beta-sheet are observed to form cooperatively. Partial folding cooperativity between the component hairpins is observed, and good agreement between calculated and experimental values quantifying this cooperativity is obtained when similar analysis techniques are used. However, the structural detail in the ensemble of conformations sampled in the simulations permits a more direct analysis of this cooperativity than has been performed on the basis of experimental data. The results indicate the actual folding cooperativity perpendicular to strand direction is significantly larger than the lower bound obtained previously.

How well can simulation predict protein folding kinetics and thermodynamics?

Simulation of protein folding has come a long way in five years. Notably, new quantitative comparisons with experiments for small, rapidly folding proteins have become possible. As the only way to validate simulation methodology, this achievement marks a significant advance. Here, we detail these recent achievements and ask whether simulations have indeed rendered quantitative predictions in several areas, including protein folding kinetics, thermodynamics, and physics-based methods for structure prediction. We conclude by looking to the future of such comparisons between simulations and experiments.

The βαβαβ elementary supersecondary structure of the Rossmann fold from porcine lactate dehydrogenase exhibits characteristics of a molten globule

Protein classifications show that the Rossmann fold, which consists of two betaalphabetaalphabeta motifs (BABAB) related by a rough twofold axis, is the most populated alphabeta fold, and that the betaalphabeta submotif (BAB) is a widespread elementary structural arrangement. Herein, we report MD simulations, circular dichroism and NMR analyses on BAB and BABAB from porcine lactate dehydrogenase to evaluate their intrinsic stability. Our results demonstrate that BAB is not stable in solution and is not a folding nucleus. We also find that BABAB, despite its appearance of a functional and structural unit, is not an independent and thermodynamically stable folding unit. Rather, we show that BABAB retains most native secondary structure but very little tertiary structure, thus displaying characteristics of a molten globule.

beta-Sheet mediated self-assembly of dipeptides of omega-amino acids and remarkable fibrillation in the solid state

Single crystal X-ray diffraction studies show that the extended structure of dipeptide Boc-beta-Ala-m-ABA-OMe (m-ABA: meta-aminobenzoic acid) self-assembles in the solid state by intermolecular hydrogen bonding to create an infinite parallel beta-sheet structure. In dipeptide Boc-gamma-Abu-m-ABA-OMe (gamma-Abu: gamma-aminobutyric acid), two such parallel beta-sheets are further cross-linked by intermolecular hydrogen bonding through m-aminobenzoic acid moieties. SEM (scanning electron microscopy) studies reveal that both the peptides and form amyloid-like fibrils in the solid state. The fibrils are also found to be stained readily by Congo red, a characteristic feature of the amyloid fiber whose accumulation causes several fatal diseases such as Alzheimer's, prion-protein etc.

Estimation of protein folding probability from equilibrium simulations

The assumption that similar structures have similar folding probabilities (p(fold)) leads naturally to a procedure to evaluate p(fold) for every snapshot saved along an equilibrium folding-unfolding trajectory of a structured peptide or protein. The procedure utilizes a structurally homogeneous clustering and does not require any additional simulation. It can be used to detect multiple folding pathways as shown for a three-stranded antiparallel beta-sheet peptide investigated by implicit solvent molecular dynamics simulations.

Comparison of sequence-based and structure-based energy functions for the reversible folding of a peptide

We used computer simulations to compare the reversible folding of a 20-residue peptide, as described by sequence-based and structure-based energy functions. Sequence-based energy functions are transferable and can be used to describe the behavior of different proteins, since interactions are defined between atomic species. Conversely, structure-based energy functions are not transferable, since the interactions are defined relative to the native conformation, which is assumed to correspond to the global minimum of the energy. Our results indicate that the sequence-based and the structure-based descriptions are in qualitative agreement in characterizing the two-state behavior of the peptide that we studied. We also found, however, that several equilibrium properties, including the free-energy landscape, can be significantly different in the various models. These results suggest that the fact that a model describes the native state of a polypeptide chain does not necessarily imply that the thermodynamic and kinetic properties will also be reproduced correctly.

Phi-value analysis by molecular dynamics simulations of reversible folding

In Phi-value analysis, the effects of mutations on the folding kinetics are compared with the corresponding effects on thermodynamic stability to investigate the structure of the protein-folding transition state (TS). Here, molecular dynamics (MD) simulations (totaling 0.65 ms) have been performed for a large set of single-point mutants of a 20-residue three-stranded antiparallel beta-sheet peptide. Between 57 and 120 folding events were sampled at near equilibrium for each mutant, allowing for accurate estimates of folding/unfolding rates and stability changes. The Phi values calculated from folding and unfolding rates extracted from the MD trajectories are reliable if the stability loss upon mutation is larger than approximately 0.6 kcal/mol, which is observed for 8 of the 32 single-point mutants. The same heterogeneity of the TS of the wild type was found in the mutated peptides, showing two possible pathways for folding. Single-point mutations can induce significant TS shifts not always detected by Phi-value analysis. Specific nonnative interactions at the TS were observed in most of the peptides studied here. The interpretation of Phi values based on the ratio of atomic contacts at the TS over the native state, which has been used in the past in MD and Monte Carlo simulations, is in agreement with the TS structures of wild-type peptide. However, Phi values tend to overestimate the nativeness of the TS ensemble, when interpreted neglecting the nonnative interactions.

Sequence swapping does not result in conformation swapping for the beta4/beta5 and beta8/beta9 beta-hairpin turns in human acidic fibroblast growth factor

The beta-turn is the most common type of nonrepetitive structure in globular proteins, comprising ~25% of all residues; however, a detailed understanding of effects of specific residues upon beta-turn stability and conformation is lacking. Human acidic fibroblast growth factor (FGF-1) is a member of the beta-trefoil superfold and contains a total of five beta-hairpin structures (antiparallel beta-sheets connected by a reverse turn). beta-Turns related by the characteristic threefold structural symmetry of this superfold exhibit different primary structures, and in some cases, different secondary structures. As such, they represent a useful system with which to study the role that turn sequences play in determining structure, stability, and folding of the protein. Two turns related by the threefold structural symmetry, the beta4/beta5 and beta8/beta9 turns, were subjected to both sequence-swapping and poly-glycine substitution mutations, and the effects upon stability, folding, and structure were investigated. In the wild-type protein these turns are of identical length, but exhibit different conformations. These conformations were observed to be retained during sequence-swapping and glycine substitution mutagenesis. The results indicate that the beta-turn structure at these positions is not determined by the turn sequence. Structural analysis suggests that residues flanking the turn are a primary structural determinant of the conformation within the turn.

Folding thermodynamics of three beta-sheet peptides: a model study

We study the folding thermodynamics of a beta-hairpin and two three-stranded beta-sheet peptides using a simplified sequence-based all-atom model, in which folding is driven mainly by backbone hydrogen bonding and effective hydrophobic attraction. The native populations obtained for these three sequences are in good agreement with experimental data. We also show that the apparent native population depends on which observable is studied; the hydrophobicity energy and the number of native hydrogen bonds give different results. The magnitude of this dependence matches well with the results obtained in two different experiments on the beta-hairpin.

Applications of model β‐hairpin peptides

In recent years, beta-hairpin peptides have been studied in great detail. Much of the focus has been on the thermodynamic stability of beta-hairpin structure. Structural measurements have been conducted with nuclear magnetic resonance, with additional information obtained from circular dichroism, Fourier transform infrared, and molecular dynamic simulation studies. Point mutations, both in the beta-strands and in the turn region, have systematically explored the role of turn sequence, side-chain-side-chain interactions, intramolecular hydrogen bonding, and beta-strand length on beta-hairpin peptide conformational stability. In addition to studying the elements of structural stability independently, the cooperative nature of the individual components to combine to form the overall structure has also been investigated. Because the beta-hairpin peptides often spontaneously form their conformation, they have begun to serve as models for studying peptide binding and therapeutic agents.

Formation of the folding nucleus of an SH3 domain investigated by loosely coupled molecular dynamics simulations

The experimentally well-established folding mechanism of the src-SH3 domain, and in particular the phi-value analysis of its transition state, represents a sort of testing table for computational investigations of protein folding. Here, parallel molecular dynamics simulations of the src-SH3 domain have been performed starting from denatured conformations. By rescuing and restarting only trajectories approaching the folding transition state, an ensemble of conformations was obtained with a completely structured central beta-sheet and a native-like packing of residues Ile-110, Ala-121, and Ile-132. An analysis of the trajectories shows that there are several pathways leading to the formation of the central beta-sheet whereas its two hairpins form in a different but consistent way.

The protein folding network

The conformation space of a 20 residue antiparallel beta-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Snapshots saved along the trajectory are grouped according to secondary structure into nodes of the network and the transitions between them are links. The conformation space network describes the significant free energy minima and their dynamic connectivity without requiring arbitrarily chosen reaction coordinates. As previously found for the Internet and the World-Wide Web as well as for social and biological networks, the conformation space network is scale-free and contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the native basin exhibits a hierarchical organization, which is not found for a random heteropolymer lacking a predominant free-energy minimum. The network topology is used to identify conformations in the folding transition state (TS) ensemble, and provides a basis for understanding the heterogeneity of the TS and denatured state ensemble as well as the existence of multiple pathways.

X-ray structure analysis of a designed oligomeric miniprotein reveals a discrete quaternary architecture

The x-ray crystal structure of an oligomeric miniprotein has been determined to a 1.2-A resolution by means of multiwavelength anomalous diffraction phasing with selenomethionine analogs that retain the biophysical characteristics of the native peptide. Peptide 1, comprising alpha and beta secondary structure elements with only 21 aa per monomer, associates as a discrete tetramer. The peptide adopts a previously uncharacterized quaternary structure in which alpha and beta components interact to form a tightly packed and well defined hydrophobic core. The structure provides insight into the origins of the unusual thermal stability of the oligomer. The miniprotein shares many characteristics of larger proteins, including cooperative folding, lack of 1-anilino-8-naphthalene sulfonate binding, and limited deuterium exchange, and possesses a buried surface area typical of native proteins.

Measuring the refolding of beta-sheets with different turn sequences on a nanosecond time scale

Whether turns play an active or passive role in protein folding remains a controversial issue at this juncture. Here we use a photolabile cage strategy in combination with laser-flash photolysis and photoacoustic calorimetry to study the effects of different turns on the kinetics of beta-hairpin refolding on a nanosecond time scale. This strategy opens up a temporal window to allow the observation of early kinetic events in the protein refolding process at ambient temperature and pH without interference from any denaturants. Our results provide direct evidence demonstrating that even a one-residue difference in the turn region can change the refolding kinetics of a peptide. This observation suggests an active role for turn formation in directing protein folding.

Factors involved in the stability of isolated beta-sheets: Turn sequence, beta-sheet twisting, and hydrophobic surface burial

We have recently reported on the design of a 20-residue peptide able to form a significant population of a three-stranded up-and-down antiparallel beta-sheet in aqueous solution. To improve our beta-sheet model in terms of the folded population, we have modified the sequences of the two 2-residue turns by introducing the segment DPro-Gly, a sequence shown to lead to more rigid type II' beta-turns. The analysis of several NMR parameters, NOE data, as well as Deltadelta(CalphaH), DeltadeltaC(beta), and Deltadelta(Cbeta) values, demonstrates that the new peptide forms a beta-sheet structure in aqueous solution more stable than the original one, whereas the substitution of the DPro residues by LPro leads to a random coil peptide. This agrees with previous results on beta-hairpin-forming peptides showing the essential role of the turn sequence for beta-hairpin folding. The well-defined beta-sheet motif calculated for the new designed peptide (pair-wise RMSD for backbone atoms is 0.5 +/- 0.1 A) displays a high degree of twist. This twist likely contributes to stability, as a more hydrophobic surface is buried in the twisted beta-sheet than in a flatter one. The twist observed in the up-and-down antiparallel beta-sheet motifs of most proteins is less pronounced than in our designed peptide, except for the WW domains. The additional hydrophobic surface burial provided by beta-sheet twisting relative to a "flat" beta-sheet is probably more important for structure stability in peptides and small proteins like the WW domains than in larger proteins for which there exists a significant contribution to stability arising from their extensive hydrophobic cores.

Efficient evaluation of the effective dielectric function of a macromolecule in aqueous solution

We propose an analytical approach to calculate the effective dielectric function of proteins in aqueous solution. The screening effect if quantified by a measure of enclosure which is based on the distribution of solute atomic volumes around a pair of charges in a macromolecule. For protein conformations that vary significantly in size and shape, a comparison with finite difference Poisson calculations shows that pair interaction energies, their sums and solvation energies are well reproduced. The approach rivals the speed of simple distance dependent dielectric functions and the accuracy of the generalized Born model.

Fast protein folding on downhill energy landscape

Proteins fold in a time range of microseconds to minutes despite the large amount of possible conformers. Molecular dynamics simulations of a three-stranded antiparallel beta-sheet peptide (for a total of 12.6 microsec and 72 folding events) show that at the melting temperature the unfolded state ensemble contains many more conformers than those sampled during a folding event.

Analysis of the distributed computing approach applied to the folding of a small beta peptide

In the recently proposed distributed computing approach to protein folding a very large number of short independent simulations is performed. Using this method, folding events on a time scale orders of magnitude shorter than the experimental one have been reported. However, it has also been observed that the folding process is not an elementary kinetic step and that the presence of initial lag phases can bias short simulations toward atypical pathways. We study here a 20-residue three-stranded antiparallel beta-sheet peptide whose equilibrium properties can be characterized by atomistic molecular dynamics simulations. We found that the folding rate of this peptide is estimated correctly by the distributed computing approach when trajectories > approximately 1/100 of the equilibrium folding time are considered. We also found that the fastest folding events occur through high-energy pathways, which are unlikely under equilibrium conditions. These very fast folding pathways do not relax within the equilibrium denatured state that is stabilized by the transient presence of both native and non-native interactions, and they are characterized by the nearly simultaneous formation of the two beta-hairpins and a very small number of non-native contacts.

Optical spectroscopic investigations of model beta-sheet hairpins in aqueous solution

In this contribution we report optical spectroscopic data on a series of designed beta hairpins previously shown by NMR to contain a substantial population of beta-sheet structure. These models contain a designed hydrophobic cluster and a (D)Pro-Gly sequence to promote formation of a turn geometry. FTIR, electronic and vibrational CD (ECD and VCD) spectra for these small peptides are comparable to expected bandshapes for peptides of high beta-sheet content. The (D)Pro-Gly sequence provides a better turn motif than Asn-Gly as measured by its beta-sheet spectral characteristics. IR and VCD spectra are in qualitative agreement with theoretical simulations based on transfer of parameters from ab initio quantum mechanical force field and intensity computations for the turn and strands. These calculations provide assignments for some distinguishing modes in both IR and VCD spectra. Increased sheet structure can be induced in these hairpins by use of mixed solvent conditions. Thermal denaturation studies reveal that these hairpins undergo very broad unfolding transitions. Guanidine hydrochloride unfolding transitions for the selected hairpin models are similarly broad. However, the "end-states" of temperature and chaotropic denaturation are spectroscopically differentiable.

The role of side-chain interactions in the early steps of aggregation: Molecular dynamics simulations of an amyloid-forming peptide from the yeast prion Sup35

Understanding the early steps of aggregation at atomic detail might be crucial for the rational design of therapeutics preventing diseases associated with amyloid deposits. In this paper, aggregation of the heptapeptide GNNQQNY, from the N-terminal prion-determining domain of the yeast protein Sup35, was studied by 20 molecular dynamics runs for a total simulation time of 20 micros. The simulations generate in-register parallel packing of GNNQQNY beta-strands that is consistent with x-ray diffraction and Fourier transform infrared data. The statistically preferred aggregation pathway does not correspond to a purely downhill profile of the energy surface because of the presence of enthalpic barriers that originate from out-of-register interactions. The parallel beta-sheet arrangement is favored over the antiparallel because of side-chain contacts; in particular, stacking interactions of the tyrosine rings and hydrogen bonds between amide groups. No ordered aggregation was found in control simulations with the mutant sequence SQNGNQQRG in accord with experimental data and the strong sequence dependence of aggregation.

Insights into the determinants of beta-sheet stability: 1H and 13C NMR conformational investigation of three-stranded antiparallel beta-sheet-forming peptides

In a previous study we designed a 20-residue peptide able to adopt a significant population of a three-stranded antiparallel beta-sheet in aqueous solution (de Alba et al. [1999]Protein Sci.8, 854-865). In order to better understand the factors contributing to beta-sheet folding and stability we designed and prepared nine variants of the parent peptide by substituting residues at selected positions in its strands. The ability of these peptides to form the target motif was assessed on the basis of NMR parameters, in particular NOE data and 13Calpha conformational shifts. The populations of the target beta-sheet motif were lower in the variants than in the parent peptide. Comparative analysis of the conformational behavior of the peptides showed that, as expected, strand residues with low intrinsic beta-sheet propensities greatly disfavor beta-sheet folding and that, as already found in other beta-sheet models, specific cross-strand side chain-side chain interactions contribute to beta-sheet stability. More interestingly, the performed analysis indicated that the destabilization effect of the unfavorable strand residues depends on their location at inner or edge strands, being larger at the latter. Moreover, in all the cases examined, favorable cross-strand side chain-side chain interactions were not strong enough to counterbalance the disfavoring effect of a poor beta-sheet-forming residue, such as Gly.

Interplay between hydrophobic cluster and loop propensity in beta-hairpin formation: a mechanistic study

We investigated the structural determinants of the stability of a designed beta-hairpin containing a natural hydrophobic cluster from the protein GB1 and a D-Pro-Gly turn forming sequence. The results of our simulations shed light on the factors leading to an ordered secondary structure in a model peptide: in particular, the importance of the so-called diagonal interactions in forming a stable hydrophobic nucleus in the beta-hairpin, together with the more obvious lateral interactions, is examined. With the use of long timescale MD simulations in explicit water, we show the role of diagonal interactions in driving the peptide to the correct folded structure (formation of the hydrophobic core with Trp 2, Tyr 4, and Phe 9 in the first stages of refolding) and in keeping it in the ensemble of folded conformations. The combination of the stabilizing effects of the D-Pro-Gly turn sequence and of the hydrophobic nucleus formation thus favors the attainment of an ordered secondary structure compatible with the one determined experimentally. Moreover, our data underline the importance of the juxtapositions of the side chains of amino acids not directly facing each other in the three-dimensional structure. The combination of these interactions forces the peptide to sample a nonrandom portion of the conformational space, as can be seen in the rapid collapse to an ordered structure in the refolding simulation, and shows that the unfolded state can be closely correlated to the folded ensemble of structures, at least in the case of small model peptides.

Influence of strand number on antiparallel beta-sheet stability in designed three- and four-stranded beta-sheets

We describe experiments that probe whether antiparallel beta-sheet secondary structure becomes more stable as the number of strands increases. Several groups, including ours, have explored this issue with peptides designed to adopt three-stranded beta-sheet conformations, but the conclusions have not been consistent. In this study, we examine the effect on conformational stability of beta-sheet lengthening perpendicular to the strand direction via analysis of designed peptides that adopt three-stranded or four-stranded antiparallel beta-sheet conformations in aqueous solution. The findings reported here, along with the context provided by earlier studies, suggest that antiparallel beta-sheet does, in general, become more stable when the number of strands is increased from two to three. We show that this conclusion is not influenced by the rigidity of the loop segment used to link adjacent beta-strands (D-Pro-Gly versus Asn-Gly). We show that further extension, from three strands to four, leads to a further increase in antiparallel beta-sheet stability.

Protein folding pathways and kinetics: molecular dynamics simulations of beta-strand motifs

The folding pathways and the kinetic properties for three different types of off-lattice four-strand antiparallel beta-strand protein models interacting via a hybrid Go-type potential have been investigated using discontinuous molecular dynamics simulations. The kinetic study of protein folding was conducted by temperature quenching from a denatured or random coil state to a native state. The progress parameters used in the kinetic study include the squared radius of gyration R(2)(g), the fraction of native contacts within the protein as a whole Q, and between specific strands Q(ab). In the time series of folding, the denatured proteins undergo a conformational change toward the native state. The model proteins exhibit a variety of kinetic folding pathways that include a fast-track folding pathway without passing through an intermediate and multiple pathways with trapping into more than one intermediate. The kinetic folding behavior of the beta-strand proteins strongly depends on the native-state geometry of the model proteins and the size of the bias gap g, an artificial measure of a model protein's preference for its native state.

BetaCore, a designed water soluble four-stranded antiparallel beta-sheet protein

BetaCore is a designed approximately 50-residue protein in which two BPTI-derived core modules, CM I and CM II, are connected by a 22-atom cross-link. At low temperature and pH 3, homo- and heteronuclear NMR data report a dominant folded ('f') conformation with well-dispersed chemical shifts, i, i+1 periodicity, numerous long-range NOEs, and slowed amide hydrogen isotope exchange patterns that is a four-stranded antiparallel beta-sheet with nonsymmetrical and specific association of CM I and CM II. BetaCore 'f' conformations undergo reversible, global, moderately cooperative, non-two-state thermal transitions to an equilibrium ensemble of unfolded 'u' conformations. There is a significant energy barrier between 'f' and 'u' conformations. This is the first designed four-stranded antiparallel beta-sheet that folds in water.

Analysis of the factors that stabilize a designed two-stranded antiparallel beta-sheet

Autonomously folding beta-hairpins (two-strand antiparallel beta-sheets) have become increasingly valuable tools for probing the forces that control peptide and protein conformational preferences. We examine the effects of variations in sequence and solvent on the stability of a previously designed 12-residue peptide (1). This peptide adopts a beta-hairpin conformation containing a two-residue loop (D-Pro-Gly) and a four-residue interstrand sidechain cluster that is observed in the natural protein GB1. We show that the conformational propensity of the loop segment plays an important role in beta-hairpin stability by comparing 1 with (D)P--> N mutant 2. In addition, we show that the sidechain cluster contributes both to conformational stability and to folding cooperativity by comparing 1 with mutant 3, in which two of the four cluster residues have been changed to serine. Thermodynamic analysis suggests that the high loop-forming propensity of the (D)PG segment decreases the entropic cost of beta-hairpin formation relative to the more flexible NG segment, but that the conformational rigidity of (D)PG may prevent optimal contacts between the sidechains of the GB1-derived cluster. The enthalpic favorability of folding in these designed beta-hairpins suggests that they are excellent scaffolds for studying the fundamental mechanisms by which amino acid sidechains interact with one another in folded proteins.

Weak temperature dependence of the free energy surface and folding pathways of structured peptides

The thermodynamics and energetics of a 20-residue synthetic peptide with a stable three-stranded antiparallel beta-sheet fold are investigated by implicit solvent molecular dynamics (MD) at 330 K (slightly above the melting temperature in the model) and compared with previous simulation results at 360 K. At both temperature values, the peptide folds reversibly to the NMR solution conformation, irrespective of the starting conformation. The sampling of the conformational space (2.3 micros and 25 folding events at 330 K, and 3 micros and 50 folding events at 360 K) is sufficient to obtain a thermodynamic description of minima and transition states on the free energy surface, which is determined near equilibrium by counting populations. The free energy surface, plotted as a function of two-order parameters that monitor formation of either of the beta-hairpins, is similar at both temperature values. The statistically predominant folding pathway and its frequency (about two-thirds of the folding events) are the same at 330 K and 360 K. Furthermore, the main unfolding route is the reverse of the predominant folding pathway. The effective energy and its electrostatic and van der Waals contributions show a downhill profile at both temperatures, implying that the free energy barrier is of entropic origin and corresponds to the freezing of about two-thirds of the chain into a beta-hairpin conformation. The average folding rate is nearly the same at 330 K and 360 K, while the unfolding rate is about four times slower at 330 K than at 360 K. Taken together with previous MD analysis of alpha-helices and beta-hairpins, the present simulation results indicate that the free energy surface and folding mechanism of structured peptides have a weak temperature dependence.

Molecular dynamics study of peptides in implicit water: ab initio folding of beta-hairpin, beta-sheet, and beta beta alpha-motif

In this communication, we have demonstrated that molecular dynamics simulations using a GB implicit solvation model with the all-atom based force field (CHARMM19) can describe the spontaneous folding of small peptides in aqueous solution. The native structures of peptides with various structural motifs (beta-hairpin, beta-sheet, and betabetaalpha-moiety) were successfully predicted within reasonable time scales by MD simulations at moderately elevated temperatures. It is expected that the present simulations provide further insight into mechanism/pathways of the peptide folding.

A noncovalent approach to antiparallel beta-sheet formation

Four tripeptide chains, when attached to the same end of a hydrogen-bonded duplex (1.2) with the unsymmetrical, complementary sequences of ADAA/DADD, have been brought into proximity, leading to the formation of four hybrid duplexes, 1a.2a, 1a.2b, 1b.2a, and 1b.2b, each of which contains a two-stranded beta-sheet segment. The extended conformations of the peptide chains were confirmed by 1D and 2D NMR. The peptide strands stay registered through hydrogen bonding and the beta-sheets are stabilized by side chain interactions. Two-dimensional NMR data also indicate that the duplex template prevents further aggregation in the peptide segment. When the peptide chains are attached to the two different termini of the duplex template, NMR studies show the presence of a mixture with no clearly defined conformations. In the absence of the duplex template, the tripeptides are found to associate randomly. Finally, isothermal titration calorimetry studies revealed that the hybrid duplex 1a.2a was more stable than either the duplex template or the peptides alone.

Rationally designed mutations convert de novo amyloid-like fibrils into monomeric beta-sheet proteins

Amyloid fibrils are associated with a variety of neurodegenerative maladies including Alzheimer's disease and the prion diseases. The structures of amyloid fibrils are composed of beta-strands oriented orthogonal to the fibril axis ("cross beta" structure). We previously reported the design and characterization of a combinatorial library of de novo beta-sheet proteins that self-assemble into fibrillar structures resembling amyloid. The libraries were designed by using a "binary code" strategy, in which the locations of polar and nonpolar residues are specified explicitly, but the identities of these residues are not specified and are varied combinatorially. The initial libraries were designed to encode proteins containing amphiphilic beta-strands separated by reverse turns. Each beta-strand was designed to be seven residues long, with polar (open circle) and nonpolar (shaded circle) amino acids arranged with an alternating periodicity ([see text]). The initial design specified the identical polar/nonpolar pattern for all of the beta-strands; no strand was explicitly designated to form the edges of the resulting beta-sheets. With all beta-strands preferring to occupy interior (as opposed to edge) locations, intermolecular oligomerization was favored, and the proteins assembled into amyloid-like fibrils. To assess whether explicit design of edge-favoring strands might tip the balance in favor of monomeric beta-sheet proteins, we have now redesigned the first and/or last beta-strands of several sequences from the original library. In the redesigned beta-strands, the binary pattern is changed from [see text] (K denotes lysine). The presence of a lysine on the nonpolar face of a beta-strand should disfavor fibrillar structures because such structures would bury an uncompensated charge. The nonpolar right arrow lysine mutations, therefore, would be expected to favor monomeric structures in which the [see text] sequences form edge strands with the charged lysine side chain accessible to solvent. To test this hypothesis, we constructed several second generation sequences in which the central nonpolar residue of either the N-terminal beta-strand or the C-terminal beta-strand (or both) is changed to lysine. Characterization of the redesigned proteins shows that they form monomeric beta-sheet proteins.

Evaluation of a fast implicit solvent model for molecular dynamics simulations

A solvation term based on the solvent accessible surface area (SASA) is combined with the CHARMM polar hydrogen force field for the efficient simulation of peptides and small proteins in aqueous solution. Only two atomic solvation parameters are used: one is negative for favoring the direct solvation of polar groups and the other positive for taking into account the hydrophobic effect on apolar groups. To approximate the water screening effects on the intrasolute electrostatic interactions, a distance-dependent dielectric function is used and ionic side chains are neutralized. The use of an analytical approximation of the SASA renders the model extremely efficient (i.e., only about 50% slower than in vacuo simulations). The limitations and range of applicability of the SASA model are assessed by simulations of proteins and structured peptides. For the latter, the present study and results reported elsewhere show that with the SASA model it is possible to sample a significant amount of folding/unfolding transitions, which permit the study of the thermodynamics and kinetics of folding at an atomic level of detail.

Computer simulations aimed at structure prediction of supersecondary motifs in proteins

It is well established that protein structures are more conserved than protein sequences. One-third of all known protein structures can be classified into ten protein folds, which themselves are composed mainly of alpha-helical hairpin, beta hairpin, and betaalphabeta supersecondary structural elements. In this study, we explore the ability of a recent Monte Carlo-based procedure to generate the 3D structures of eight polypeptides that correspond to units of supersecondary structure and three-stranded antiparallel beta sheet. Starting from extended or misfolded compact conformations, all Monte Carlo simulations show significant success in predicting the native topology using a simplified chain representation and an energy model optimized on other structures. Preliminary results on model peptides from nucleotide binding proteins suggest that this simple protein folding model can help clarify the relation between sequence and topology.

Length-dependent stability and strand length limits in antiparallel beta -sheet secondary structure

Designed peptides that fold autonomously to specific conformations in aqueous solution are useful for elucidating protein secondary structural preferences. For example, autonomously folding model systems have been essential for establishing the relationship between alpha-helix length and alpha-helix stability, which would be impossible to probe with alpha-helices embedded in folded proteins. Here, we use designed peptides to examine the effect of strand length on antiparallel beta-sheet stability. alpha-Helices become more stable as they grow longer. Our data show that a two-stranded beta-sheet ("beta-hairpin") becomes more stable when the strands are lengthened from five to seven residues, but that further strand lengthening to nine residues does not lead to further beta-hairpin stabilization for several extension sequences examined. (In one case, all-threonine extension, there may be an additional stabilization on strand lengthening from seven to nine residues.) These results suggest that there may be an intrinsic limit to strand length for most sequences in antiparallel beta-sheet secondary structure.

Computer-aided design of beta-sheet peptides

The design of beta-sheet proteins is still a challenge in the field of de novo protein design. Here, we have tested the validity of automatic design methods to create and/or improve beta-sheet peptides and proteins. We chose Betanova, a three-stranded beta-sheet peptide, as target system, and, as an automatic design tool, a protein design algorithm called PERLA (protein engineering rotamer library algorithm). PERLA was used to define both stabilising and destabilising single- and multiple-residue mutations of Betanova. Conformational analysis by NMR spectroscopy and far-UV circular dichroism (CD) allowed us to evaluate population differences among the set of designed peptides. Some of the new mutants are approximately 1 kcal/mol more stable than the wild-type peptide. Comparison of the scale of predicted and observed stabilities demonstrates that they are in good agreement for most peptides studied. Our results show that automatic design algorithms can be successfully applied to the design of beta-sheet peptides.

Effects of turn residues in directing the formation of the beta-sheet and in the stability of the beta-sheet

The designed peptide (denoted 20-mer, sequence VFITS(D)PGKTYTEV(D)PGOKILQ) has been shown to form a three-strand antiparallel beta-sheet. It is generally believed that the (D)Pro-Gly segment has the propensity to adopt a type II' beta-turn, thereby promoting the formation of this beta-sheet. Here, we replaced (D)Pro-Gly with Asp-Gly, which should favor a type I' turn, to examine the influence of different type of turns on the stability of the beta-sheet. Contrary to our expectation, the mutant peptide, denoted P6D, forms a five-residue type I turn plus a beta-bulge between the first two strands due to a one amino-acid frameshift in the hydrogen bonding network and side-chain inversion of the first beta-strand. In contrast, the same kind of substitution at (D)Pro-14 in the double mutant, denoted P6DP14D, does not yield the same effect. These observations suggest that the SDGK sequence disfavors the type I' conformation while the VDGO sequence favors a type I' turn, and that the frameshift in the first strand provides a way for the peptide to accommodate a disfavored turn sequence by protruding a bulge in the formation of the beta-hairpin. Thus, different types of turns can affect the stability of a beta-structure.

Knowledge-based potential defined for a rotamer library to design protein sequences

A knowledge-based potential for a rotamer library was developed to design protein sequences. Protein side-chain conformations are represented by 56 templates. Each of their fitness to a given structural site-environment is evaluated by a combined function of the three knowledge-based terms, i.e. two-body side-chain packing, one-body hydration and local conformation. The number of matches between the native sequence and the structural site-environment in the database and that of the virtually settled mismatches, counted in advance, were transformed into the energy scores. In the best-14 test (assessment for the reproduction ability of the native rotamer on its structural site within a quarter of 56 fitness rank positions), the structural stability analysis on mutants of human and T4 lysozymes and the inverse-folding search by a structure profile against the sequence database, this function performs better than the function deduced with the conventional normalization and our previously developed function. Targeting various structural motifs, de novo sequence design was conducted with the function. The sequences thus obtained exhibit reasonable molecular masses and hydrophobic/hydrophilic patterns similar to the native sequences of the target and act as if they were the homologs to the target proteins in BLASTP search. This significant improvement is discussed in terms of the reference state for normalization and the crucial role of short-range repulsion to prohibit residue bumps.

Formation of the single-layer beta-sheet of Borrelia burgdorferi OspA in the absence of the C-terminal capping globular domain

Borrelia outer surface protein A (OspA) contains a unique single-layer beta-sheet that connects N and C-terminal globular domains. This single-layer beta-sheet segment (beta-strands 8-10) is highly stable in solution, although it is exposed to the solvent on both faces of the sheet and thus it does not contain a hydrophobic core. Here, we tested whether interactions with the C-terminal domain are essential for the formation of the single-layer beta-sheet. We characterized the solution structure, dynamics and stability of an OspA fragment corresponding to beta-strands 1-12 (termed OspA[27-163]), which lacks a majority of the C-terminal globular domain. Analyses of NMR chemical shifts and backbone nuclear Overhauser effect (NOE) connectivities showed that OspA[27-163] is folded except the 12th and final beta-strand. (1)H-(15)N heteronuclear NOE measurements and amide H-(2)H exchange revealed that the single-layer beta-sheet in this fragment is more flexible than the corresponding region in full-length OspA. Thermal-denaturation experiments using differential scanning calorimetry and NMR spectroscopy revealed that the N-terminal globular domain in the fragment has a conformational stability similar to that of the same region in the full-length protein, and that the single-layer beta-sheet region also has a modest thermal stability. These results demonstrate that the unique single-layer beta-sheet retains its conformation in the absence of its interactions with the C-terminal domain. This fragment is significantly smaller than the full-length OspA, and thus it is expected to facilitate studies of the folding mechanism of this unusual beta-sheet structure.

13C(alpha) and 13C(beta) chemical shifts as a tool to delineate beta-hairpin structures in peptides

Unravelling the factors that contribute to the formation and the stability of beta-sheet structure in peptides is a subject of great current interest. A beta-hairpin, the smallest beta-sheet motif, consists of two antiparallel hydrogen-bonded beta-strands linked by a loop region. We have performed a statistical analysis on protein beta-hairpins showing that the most abundant types of beta-hairpins, 2:2, 3:5 and 4:4, have characteristic patterns of 13C(alpha) and 13C(beta) conformational shifts, as expected on the basis of their phi and psi angles. This fact strongly supports the potential value of 13C(alpha) and 13C(beta) conformational shifts as a means to identify beta-hairpin motifs in peptides. Their usefulness was confirmed by analysing the patterns of 13C(alpha) and 13C(beta) conformational shifts in 13 short peptides, 10-15 residues long, that adopt beta-hairpin structures in aqueous solution. Furthermore, we have investigated their potential as a method to quantify beta-hairpin populations in peptides.

Native topology or specific interactions: what is more important for protein folding?

Fifty-five molecular dynamics runs of two three-stranded antiparallel beta-sheet peptides were performed to investigate the relative importance of amino acid sequence and native topology. The two peptides consist of 20 residues each and have a sequence identity of 15 %. One peptide has Gly-Ser (GS) at both turns, while the other has d-Pro-Gly ((D)PG). The simulations successfully reproduce the NMR solution conformations, irrespective of the starting structure. The large number of folding events sampled along the trajectories at 360 K (total simulation time of about 5 micros) yield a projection of the free-energy landscape onto two significant progress variables. The two peptides have compact denatured states, similar free-energy surfaces, and folding pathways that involve the formation of a beta-hairpin followed by consolidation of the unstructured strand. For the GS peptide, there are 33 folding events that start by the formation of the 2-3 beta-hairpin and 17 with first the 1-2 beta-hairpin. For the (D)PG peptide, the statistical predominance is opposite, 16 and 47 folding events start from the 2-3 beta-hairpin and the 1-2 beta-hairpin, respectively. These simulation results indicate that the overall shape of the free-energy surface is defined primarily by the native-state topology, in agreement with an ever-increasing amount of experimental and theoretical evidence, while the amino acid sequence determines the statistically predominant order of the events.