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 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.     

Folding thermodynamics of model four-strand antiparallel beta-sheet proteins.

The thermodynamic 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. Discontinuous molecular dynamic simulations have been performed for different sizes of the bias gap g, an artificial measure of a model protein's preference for its native state. The thermodynamic transition temperatures are obtained by calculating the squared radius of gyration R(g)(2), the root-mean-squared pair separation fluctuation Delta(B), the specific heat C(v), the internal energy of the system E, and the Lindemann disorder parameter Delta(L). Despite these models' simplicity, they exhibit a complex set of protein transitions, consistent with those observed in experimental studies on real proteins. Starting from high temperature, these transitions include a collapse transition, a disordered-to-ordered globule transition, a folding transition, and a liquid-to-solid transition. The high temperature transitions, i.e., the collapse transition and the disordered-to-ordered globule transition, exist for all three beta-strand proteins, although the native-state geometry of the three model proteins is different. However the low temperature transitions, i.e., the folding transition and the liquid-to-solid transition, strongly depend on the native-state geometry of the model proteins and the size of the bias gap.     

HRMAS NMR observation of beta-sheet secondary structure on a water swollen solid support.

In this paper HRMAS NMR was used to investigate whether peptides on a peptidyl resin swollen in aqueous solution can adopt an intramolecular beta-sheet structure. A model peptide YQNPDGSQA, that was previously shown to adopt such a secondary structure in solution, (Blanco et al, J. Am. Chem. Soc., 1993) was grafted onto three different solid supports that swell in aqueous solution to examine the influence of the resin on the structure. Both parameters of resin loading and pH inside the swollen peptidyl resin proved to be important for the physicochemical behaviour of the peptide on the support.     

Tachyplesin I as a model peptide for antiparallel beta-sheet DNA binding motif.

In this study, we present a model compound for antiparallel beta-sheet-DNA interaction. Tachyplesin I, cationic antimicrobial peptide, interacts through contacts with the minor groove. Secondary structure of tachyplesin I, antiparallel beta-sheet constrained by two disulfide bridges and connected by beta-turn, contributes significantly to its DNA binding. The present results give valuable information for design of sequence-specific DNA binding peptide based on antiparallel beta-sheet.     

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.     

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.     

Induction of beta-sheet structure in amyloidogenic peptides by neutralization of aspartate: a model for amyloid nucleation.

Amyloid fibril formation is widely accepted as a critical step in all types of amyloidosis. Amyloid fibrils derived from different amyloidogenic proteins share structural elements including beta-sheet secondary structure and similar tertiary structure. While some amyloidogenic proteins are rich in beta-sheet in their soluble form, others, like Alzheimer beta-amyloid peptide (Abeta) or serum amyloid A, must undergo significant structural transition to acquire a high beta-sheet content. We postulate that Abeta and other amyloidogenic proteins undergo a transition to beta-sheet as a result of aging-related chemical modifications of aspartyl residues to the form of succinimide or isoaspartyl methyl ester. We hypothesize that spontaneous cyclization of aspartate residues in amyloidogenic proteins can serve as a nucleation event in amyloidogenesis. To test this hypothesis, we synthesized a series of designed peptides having the sequence VTVKVXAVKVTV, where X represents aspartic acid or its derivatives. Studies using circular dichroism showed that neutralization of the aspartate residue through the formation of a methyl ester or an amide, or replacement of aspartate with glutamate led to an increased beta-sheet content at neutral and basic pH. A higher content of beta-sheet structure correlated with increased propensity for fibril formation and decreased solubility at neutral pH.     

Stability of the beta-sheet of the WW domain: A molecular dynamics simulation study.

The WW domain consists of approximately 40 residues, has no disulfide bridges, and forms a three-stranded antiparallel beta-sheet that is monomeric in solution. It thus provides a model system for studying beta-sheet stability in native proteins. We performed molecular dynamics simulations of two WW domains, YAP65 and FBP28, with very different stability characteristics, in order to explore the initial unfolding of the beta-sheet. The less stable YAP domain is much more sensitive to simulation conditions than the FBP domain. Under standard simulation conditions in water (with or without charge-balancing counterions) at 300 K, the beta-sheet of the YAP WW domain disintegrated at early stages of the simulations. Disintegration commenced with the breakage of a hydrogen bond between the second and third strands of the beta-sheet due to an anticorrelated transition of the Tyr-28 psi and Phe-29 phi angles. Electrostatic interactions play a role in this event, and the YAP WW domain structure is more stable when simulated with a complete explicit model of the surrounding ionic strength. Other factors affecting stability of the beta-sheet are side-chain packing, the conformational entropy of the flexible chain termini, and the binding of cognate peptide.     

An atomic model for the pleated beta-sheet structure of Abeta amyloid protofilaments.

Synchrotron x-ray studies on amyloid fibrils have suggested that the stacked pleated beta-sheets are twisted so that a repeating unit of 24 beta-strands forms a helical turn around the fibril axis (. J. Mol. Biol. 273:729-739). Based on this morphological study, we have constructed an atomic model for the twisted pleated beta-sheet of human Abeta amyloid protofilament. In the model, 48 monomers of Abeta 12-42 stack (four per layer) to form a helical turn of beta-sheet. Each monomer is in an antiparallel beta-sheet conformation with a turn located at residues 25-28. Residues 17-21 and 31-36 form a hydrophobic core along the fibril axis. The hydrophobic core should play a critical role in initializing Abeta aggregation and in stabilizing the aggregates. The model was tested using molecular dynamics simulations in explicit aqueous solution, with the particle mesh Ewald (PME) method employed to accommodate long-range electrostatic forces. Based on the molecular dynamics simulations, we hypothesize that an isolated protofilament, if it exists, may not be twisted, as it appears to be when in the fibril environment. The twisted nature of the protofilaments in amyloid fibrils is likely the result of stabilizing packing interactions of the protofilaments. The model also provides a binding mode for Congo red on Abeta amyloid fibrils. The model may be useful for the design of Abeta aggregation inhibitors.     

An adaptive bin framework search method for a beta-sheet protein homopolymer model

Background  

The problem of protein structure prediction consists of predicting the functional or native structure of a protein given its linear sequence of amino acids. This problem has played a prominent role in the fields of biomolecular physics and algorithm design for over 50 years. Additionally, its importance increases continually as a result of an exponential growth over time in the number of known protein sequences in contrast to a linear increase in the number of determined structures. Our work focuses on the problem of searching an exponentially large space of possible conformations as efficiently as possible, with the goal of finding a global optimum with respect to a given energy function. This problem plays an important role in the analysis of systems with complex search landscapes, and particularly in the context of ab initio protein structure prediction.     

Calorimetric dissection of thermal unfolding of OspA,a predominantly beta-sheet protein containing a single-layer beta-sheet

Outer surface protein A (OspA) from Borrelia burgdorferi is a predominantly beta-sheet protein comprised of beta-strands beta1-beta21 and a short C-terminal alpha-helix. It contains two globular domains (N and C-terminal domains) and a unique single-layer beta-sheet (central beta-sheet) that connects the two domains. OspA contains an unusually large number of charged amino acid residues. To understand the mechanism of stabilization of this unique beta-sheet protein, thorough thermodynamic investigations of OspA and its truncated mutant lacking a part of the C-terminal domain were conducted using calorimetry and circular dichroism. The stability of OspA was found to be sensitive to pH and salt concentration. The heat capacity curve clearly consisted of two components, and all the thermodynamic parameters were obtained for each step. The thermodynamic parameters associated with the two transitions are consistent with a previously proposed model, in which the first transition corresponds to the unfolding of the C-terminal domain and the last two beta-strands of the central beta-sheet, and the second transition corresponds to that of the N-terminal domain and the first beta-strand of the central beta-sheet in the second peak. The ratio of calorimetric and van't Hoff enthalpies indicates that the first peak includes another thermodynamic intermediate state. Large heat capacity changes were observed for both transitions, indicative of large changes in the exposure of hydrophobic surfaces associated with the transitions. This observation demonstrates that hydrophobic parts are buried efficiently in the native structure in spite of the low content of hydrophobic residues in OspA. By decomposing the enthalpy, entropy, and Gibbs free energy into contributions from different interactions, we found that the enthalpy changes for hydrogen bonding and polar interactions are exceptionally large, indicating that OspA maintains its stability by making full use of its unique beta-sheet and high content of polar residues. These thermodynamic analyses demonstrated that it is possible to maintain protein tertiary structure by making effective use of an unusual amino acid composition.     

Redesigning the hydrophobic core of a model beta-sheet protein: destabilizing traps through a threading approach

An off-lattice 46-bead model of a small all-beta protein has been recently criticized for possessing too many traps and long-lived intermediates compared with the folding energy landscape predicted for real proteins and models using the principle of minimal frustration. Using a novel sequence design approach based on threading for finding beneficial mutations for destabilizing traps, we proposed three new sequences for folding in the beta-sheet model. Simulated annealing on these sequences found the global minimum more reliably, indicative of a smoother energy landscape, and simulated thermodynamic variables found evidence for a more cooperative collapse transition, lowering of the collapse temperature, and higher folding temperatures. Folding and unfolding kinetics were acquired by calculating first-passage times, and the new sequences were found to fold significantly faster than the original sequence, with a concomitant lowering of the glass temperature, although none of the sequences have highly stable native structures. The new sequences found here are more representative of real proteins and are good folders in the T(f) > T(g) sense, and they should prove useful in future studies of the details of transition states and the nature of folding intermediates in the context of simplified folding models. These results show that our sequence design approach using threading can improve models possessing glasslike folding dynamics.     

Stability in a two host epidemic model

An epidemic model is derived for a two host infectious disease. It is shown that if a non-trivial equilibrium solution exists, it is globally stable. This result is also proved for a similar one host model.     

Engineering of betabellin 14D: disulfide-induced folding of a beta-sheet protein.

The betabellin target structure consists of 2 32-residue beta sheets packed against each other by hydrophobic interactions. We have designed, chemically synthesized, and biophysically characterized betabellin 14S, a single chain, and betabellin 14D, the disulfide-bridged double chain. The 32-residue nongenetic betabellin-14 chain (HSLTASIkaLTIHVQakTATCQVkaYTVHISE, a = D-Ala, k = D-Lys) has a palindromic pattern of polar (p), nonpolar (n), end (e), and beta-turn (t,r) residues (epnpnpnttnpnpnprrpnpnpnttnpnpnpe). Each half contains the same 14-residue palindromic pattern (underlined). Pairs of D-amino acid residues are used to favor formation of inverse-common (type-I') beta turns. In water at pH 6.5, the single chain of betabellin 14S is not folded, but the disulfide-linked betabellin 14D is folded into a stable beta-sheet structure. Thus, folding of the covalent dimer beta-bellin 14D is induced by formation of the single interchain disulfide bond. The binary pattern of alternating polar and nonpolar residues of its beta-sheets is not sufficient to induce folding. Betabellin 14D is a very water-soluble (10 mg/mL), small (64 residues), nongenetic (12 D residues) beta-sheet protein with properties (well-dispersed proton NMR resonances; Tm = 58 degrees C and delta Hm = 106 kcal/mol at pH 5.5) like those of a native protein structure.     

Crystal structure of tert.-butyloxycarbonyl-L-prolyl-D-alanyl-D-alanyl-N-methylamide. Dimeric beta-sheet formation.

The crystal structure of the tripeptide t-Boc-L-Pro-D-Ala-D-Ala-NHCH3, monohydrate, (C17H30N4O5.H2O, molecular weight = 404.44) has been determined by single crystal X-ray diffraction. The crystals are monoclinic, space group P2(1), a = 9.2585(4), b = 9.3541(5), c = 12.4529(4)A, beta = 96.449(3) degrees, Z = 2. The peptide units are in the trans and the tBoc-Pro bond in the cis orientation. The first and third peptide units show significant deviations from planarity (delta omega = 5.2 degrees and delta omega = 3.7 degrees, respectively). The backbone torsion angles are: phi 1 = -60 degrees, psi 1 = 143.3 degrees, omega 1 = -174.8 degrees, phi 2 = 148.4 degrees, psi 2 = -143.1 degrees, omega 2 = -179.7 degrees, phi 3 = 151.4 degrees, psi 3 = -151.9 degrees, omega 3 = -176.3 degrees. The pyrrolidine ring of the proline residue adopts the C2-C gamma conformation. The molecular packing gives rise to an antiparallel beta-sheet structure formed of dimeric repeating units of the peptide. The surface of the dimeric beta-sheet is hydrophobic. Water molecules are found systematically at the edges of the sheets interacting with the urethane oxygen and terminal amino groups. Surface catalysis of an L-Ala to D-Ala epimerization process by water molecules adsorbed on to an incipient beta-sheet is suggested as a mechanism whereby crystals of the title peptide were obtained from a solution of tBoc-Pro-D-Ala-Ala-NHCH3.     

Stability of simian rotavirus in fresh and estuarine water.

The rates of inactivation of poliovirus 1, echovirus 7, coxsackievirus B3, and simian rotavirus SA11 were compared in polluted and nonpolluted fresh and estaurine water samples. The study was done in two parts, comparing virus survival in samples taken 1 year apart from the same sites. The survival studies were performed at 20 degrees C and at the natural pH of the water samples. In the first part of the study, the time required for a 3-log10 reduction in the initial virus titers was 2 to 3 days in the estaurine water samples and varied from 3 to greater than 14 days in the freshwater samples. In the second part of the study, no clear distinction was found between survival of viruses in freshwater samples and survival in estaurine water samples. The time required for a 3-log10 reduction in the initial virus titers in the second part of the study varied from 12 to greater than 14 days. This indicates that there is a nonseasonal change in factors in the water which affect virus survival. In this study SA11 survival time (used as a model for human virus) was well within the range exhibited by the enteroviruses, indicating that it also is environmentally stable in natural waters.     

Stability in a metapopulation model with density-dependent dispersal

A spatially explicit metapopulation model with positive density-dependent migration is analysed. We obtained conditions under which a previously stable system can be driven to instability caused by a density-dependent migration mechanism. The stability boundary depends on the rate of increase of the number of migrants on each site at local equilibrium, on the intrinsic rate of increase at local level, on the number of patches, and on topological aspects regarding the connectivity between patches. A concrete example is presented illustrating the dynamics on the dispersal-induced unstable regime.     

Stability analysis of a mathematical neuron model

The “second method” of Liapunov is used to perform a stability analysis of a mathematical model of the neuron. This analysis is based on the hypothesis that the firing of the neuron coincides with a temporary state of instability of the system, and that the initiation of all-or-none process depends on the magnitude of membrane depolarization and its first time derivative. It is found that the stability (and hence the possibility of a second firing) is restored approximately when the rate of membrane repolarization is at a maximum. This result predicts that the duration of the period of absolute refractoriness in neurons would be about 75 per cent of the spike duration, and thus shorter than the value usually obtained from experimental measurements.     

Unfolding of beta-sheet proteins in SDS

Beta-sheet proteins are particularly resistant to denaturation by sodium dodecyl sulfate (SDS). Here we compare unfolding of two beta-sandwich proteins TNfn3 and TII27 in SDS. The two proteins show different surface electrostatic potential. Correspondingly, TII27 unfolds below the critical micelle concentration via the formation of hemimicelles on the protein surface, whereas TNfn3 only unfolds around the critical micelle concentration. Isothermal titration calorimetry confirms that unfolding of TII27 sets in at lower SDS concentrations, although the total number of bound SDS molecules is similar at the end of unfolding. In mixed micelles with the nonionic detergent dodecyl maltoside, where the concentration of monomeric SDS is insignificant, the behavior of the two proteins converges. TII27 unfolds more slowly than TNfn3 in SDS and follows a two-mode behavior. Additionally TNfn3 shows inhibition of SDS unfolding at intermediate SDS concentrations. Mutagenic analysis suggests that the overall unfolding mechanism is similar to that observed in denaturant for both proteins. Our data confirm the kinetic robustness of beta-sheet proteins toward SDS. We suggest this is related to the inability of SDS to induce significant amounts of alpha-helix structure in these proteins as part of the denaturation process, forcing the protein to denature by global rather than local unfolding.