Role of foldability and stability in designing real protein sequences

This work explores the effects of two different fitness criteria, the free energy of folding (ΔG(folding)) and foldability (Φ) of mutated sequences, by measuring the designed protein's robustness via cumulative random point mutations. The results of a self-consistent mean-field based theory are used to design 'wild type' protein sequences corresponding to a specified target structure for a given foldability criteria Φ. The theory is applied on three 36-mer real protein conformations and the 'wild type' sequences are identified in terms of site specific monomer probabilities corresponding to a given foldability. Unlike the stability criteria, ΔG(folding) < 0, the foldability criteria Φ(mutated) < -1 effectively identifies sequences of different site-specific monomer identities by specifying the mean and variance of the energy of the unfolded state ensemble. The results depict a distinct difference in the pattern of mutational robustness of the neutral sequence space, Φ(mutated) < -1 scans more number of neutral sequences compared to ΔG(folding) < 0 to find the evolutionary fit sequences. Φ(mutated) < -1 also accounts for marginally stable sequences which are not effectively scanned by ΔG(folding) < 0 to determine evolutionary fitness. The results clearly point out that viable mutated sequences that are foldable, may not always conform to ΔG(fold) < 0, hence assessing the role of foldability in addition to stability for determining protein's robustness towards cumulative random point mutations. These observations may be used in engineering and designing de novo protein sequences which are more robust towards random point mutations.     

A minimal proteinlike lattice model: an alpha-helix motif

A simple protein model of a four-helix bundle motif on a face-centered cubic lattice has been studied. Total energy of a conformation includes attractive interactions between hydrophobic residues, repulsive interactions between hydrophobic and polar residues, and a potential that favors helical turns. Using replica exchange Monte Carlo simulations we have estimated a set of parameters for which the native structure is a global minimum of conformational energy. Then we have shown that all the above types of interactions are necessary to guarantee the cooperativity of folding transition and to satisfy the thermodynamic hypothesis.     

Expected and unexpected results from combined beta-hairpin design elements

A model beta-hairpin dodecapeptide [EFGWVpGKWTIK] was designed by including a favorable D-ProGly Type II' beta-turn sequence and a Trp-zip interaction, while also incorporating a beta-strand unfavorable glycine residue in the N-terminal strand. This peptide is highly folded and monomeric in aqueous solution as determined by combined analysis with circular dichroism and 1H NMR spectroscopy. A peptide representing the folded conformation of the model beta-hairpin [cyclic(EFGWVpGKWTIKpG)] and a linear peptide representing the unfolded conformation [EFGWVPGKWTIK] yield unexpected relative deviations between the CD and 1H NMR spectroscopic results that are attributed to variations in the packing interactions of the aromatic side chains. Mutational analysis of the model beta-hairpin indicates that the Trp-zip interaction favors folding and stability relative to an alternate hydrophobic cluster between Trp and Tyr residues [EFGYVpGKWTIK]. The significance of select diagonal interactions in the model beta-hairpin was tested by rearranging the cross-strand hydrophobic interactions to provide a folded peptide [EWFGIpGKTYWK] displaying evidence of an unusual backbone conformation at the hydrophobic cluster. This unusual conformation does not appear to be a result of the glycine residue in the beta-strand, as replacement with a serine results in a peptide [EWFSIpGKTYWK] with a similar and seemingly characteristic CD spectrum. However, an alternate arrangement of hydrophobic residues with a Trp-zip interaction in a similar position to the parent beta-hairpin [EGFWVpGKWITK] results in a folded beta-hairpin conformation. The differences between side chain packing of these peptides precludes meaningful thermodynamic analysis and illustrates the caution necessary when interpreting beta-hairpin folding thermodynamics that are driven, at least in part, by aromatic cross strand interactions.     

Prediction of stability changes upon single-site mutations using database-derived potentials

One of the purposes of studying protein stability changes upon mutations is to get information about the dominating interactions that drive folding and stabilise the native structure. With this in mind, we present a method that predicts folding free-energy variations caused by point mutations using combinations of two types of database-derived potentials, i.e. backbone torsion-angle potentials and distance potentials, describing local and non-local interactions along the chain, respectively. The method is applied to evaluate the folding free-energy changes of 344 single-site mutations introduced in six different proteins and a synthetic peptide. We found that the relative importance of local versus non-local interactions along the chain is essentially a function of the solvent accessibility of the mutated residues. For the subset of totally buried residues, the optimal potential is the sum of a distance potential and a torsion potential weighted by a factor of 0.4. This combination yields a correlation coefficient between measured and computed changes in folding free energy of 0.80. For mutations of partially buried residues, the best potential is the sum of a torsion potential and a distance potential weighted by 0.7. For fully accessible residues, the torsion potentials taken alone perform best, reaching correlation coefficients of 0.87 on all but 10 mutations; the excluded mutations seem to modify the backbone structure or to involve interactions that are atypical for the surface. These results show that the relative weight of non-local interactions along the sequence decreases as the solvent accessibility of the mutated residue increases, and vanishes at the protein surface. On the contrary, the weight of local interactions increases with solvent accessibility. The latter interactions are nevertheless never negligible, even for the most buried residues. Received: 20 May 1998 / Accepted: 3 September 1998 / Published online: 7 December 1998     

Statistical theory for protein ensembles with designed energy landscapes

Combinatorial protein libraries provide a promising route to investigate the determinants and features of protein folding and to identify novel folding amino acid sequences. A library of sequences based on a pool of different monomer types are screened for folding molecules, consistent with a particular foldability criterion. The number of sequences grows exponentially with the length of the polymer, making both experimental and computational tabulations of sequences infeasible. Herein a statistical theory is extended to specify the properties of sequences having particular values of global energetic quantities that specify their energy landscape. The theory yields the site-specific monomer probabilities. A foldability criterion is derived that characterizes the properties of sequences by quantifying the energetic separation of the target state from low-energy states in the unfolded ensemble and the fluctuations of the energies in the unfolded state ensemble. For a simple lattice model of proteins, excellent agreement is observed between the theory and the results of exact enumeration. The theory may be used to provide a quantitative framework for the design and interpretation of combinatorial experiments.     

Dynamic redox environment-intensified disulfide bond shuffling for protein refolding in vitro: molecular simulation and experimental validation

One challenge in protein refolding is to dissociate the non-native disulfide bonds and promote the formation of native ones. In this study, we present a coarse-grained off-lattice model protein containing disulfide bonds and simulate disulfide bond shuffling during the folding of this model protein. Introduction of disulfide bonds in the model protein led to enhanced conformational stability but reduced foldability in comparison to counterpart protein without disulfide bonds. The folding trajectory suggested that the model protein retained the two-step folding mechanism in terms of hydrophobic collapse and structural rearrangement. The disulfide bonds located in the hydrophobic core were formed before the collapsing step, while the bonds located on the protein surface were formed during the rearrangement step. While a reductive environment at the initial stage of folding favored the formation of native disulfide bonds in the hydrophobic core, an oxidative environment at a later stage of folding was required for the formation of disulfide bonds at protein surface. Appling a dynamic redox environment, that is, one that changes from reductive to oxidative, intensified disulfide bond shuffling and thus resulted in improved recovery of the native conformation. The above-mentioned simulation was experimentally validated by refolding hen-egg lysozyme at different urea concentrations and oxidized glutathione/reduced glutathione (GSSG/GSH) ratios, and an optimal redox environment, in terms of the GSSG to GSH ratio, was identified. The implementation of a dynamic redox environment by tuning the GSSG/GSH ratio further improved the refolding yield of lysozyme, as predicted by molecular simulation.     

Contributions of a Surface Hydrophobic Cluster to the Folding and Structural Stability of Ubiquitin

The role of the small exterior hydrophobic cluster (SEHC) in the strand region of the N‐terminal β‐hairpin of ubiquitin on the structural stability and the folding/unfolding kinetics of the protein have been examined. We introduce a Phe→Ala substitution at residue 4 in the strand region of the N‐terminal β‐hairpin of the ubiquitin. A peptide with the same amino acid sequence as the first 21 residues of the mutated ubiquitin has also been synthesized. The F4A mutation unfolds the hairpin structure of the peptide segment without disruption of the turn. The same mutation does not seem to affect the overall structure, but the stability of the mutated full‐length protein decreases by approx. 2 kcal/mol. Kinetically, the entire hairpin structure is implicated in the transition state during folding of the wild type protein. The rate of refolding is retarded by the F4A mutation in ～80% of the protein molecules. The F4A substitution also increases the unfolding rate of the protein by 10 fold. Thus the hydrophobic side‐chain of Phe‐4 not only contributes to the stability of the hairpin, but also to the stability of the entire protein by forming a cluster together with the hydrophobic residues on the C‐terminal strand.     

蛋白质分子的HNP格点模型

从 6 0种球形蛋白质的结构出发 ,采用Miyazawa Jernigan相互作用矩阵 ,计算了蛋白质分子中氨基酸之间的相互作用能 .发现构成蛋白质分子的 2 0种氨基酸可分成疏水 (Hydrophobic ,H)、中性 (Neutral,N)、亲水(Hydrophilic ,P)基团 .在计算它们之间相互作用能的基础上 ,建立了蛋白质分子的HNP格点模型 .用这个模型计算了二维蛋白质分子在自然态 (Nativestate)时的构象性质 .同时研究了氨基酸序列为HHNHNPNHPP HPNPPHPHPPHHPHNH的折叠过程 ,得到其基态能量为 - 6 4 89RT .这能为研究球形蛋白质的构象性质及折叠过程提供一种更合理的格点模型     

Interstrand side chain--side chain interactions in a designed beta-hairpin: significance of both lateral and diagonal pairings

The contributions of interstrand side chain-side chain contacts to beta-sheet stability have been examined with an autonomously folding beta-hairpin model system. RYVEV(D)PGOKILQ-NH2 ((D)P = D-proline, O = ornithine) has previously been shown to adopt a beta-hairpin conformation in aqueous solution, with a two-residue loop at D-Pro-Gly. In the present study, side chains that display interstrand NOEs (Tyr-2, Lys-9, and Leu-11) are mutated to alanine or serine, and the conformational impact of the mutations is assessed. In the beta-hairpin conformation Tyr-2 and Leu-11 are directly across from one another (non-hydrogen bonded pair). This "lateral" juxtaposition of two hydrophobic side chains appears to contribute to beta-hairpin conformational stability, which is consistent with results from other beta-sheet model studies and with statistical analyses of interstrand residue contacts in protein crystal structures. Interaction between the side chains of Tyr-2 and Lys-9 also stabilizes the beta-hairpin conformation. Tyr-2/Lys-9 is a "diagonal" interstrand juxtaposition because these residues are not directly across from one another in terms of the hydrogen bonding registry between the strands. This diagonal interaction arises from the right-handed twist that is commonly observed among beta-sheets. Evidence of diagonal side chain-side chain contacts has been observed in other autonomously folding beta-sheet model systems, but we are not aware of other efforts to determine whether a diagonal interaction contributes to beta-sheet stability.     

Influence of the chain stiffness on the thermodynamics of a Gō-type model for protein folding

The relative importance of local and long range interactions in the characteristics of the protein folding process has long been a matter of controversy. Computer simulations based on Gō-type models have been widely used to study this topic, but without much agreement on which type of interactions is more relevant for the foldability of a protein. In this work, the authors also employ a topology-based potential and simulation model to analyze the influence of local and long range interactions on the thermodynamics of the folding transition. The former are mainly used to control the degree of flexibility (or stiffness) of the chain, mostly appreciable in the unfolded (noncompact) state. Our results show the different effects that local and nonlocal interactions have on the entropy and the energy of the system. This implies that a balance between both types of interactions is required, so that a free energy barrier exists between the native and the denatured states. The variations in the contribution of both types of interactions have also a direct effect on the stability of the chain conformations, including the possible appearance of thermodynamic folding intermediates.     

A Thermodynamic Perspective on Potential G-Quadruplex Structures as Silencer Elements in the MYC Promoter

Multiple G-tracts within the promoter region of the c-myc oncogene may fold into various G-quadruplexes with the recruitment of different tracts and guanosine residues for the G-core assembly. Thermodynamic profiles for the folding of wild-type and representative truncated as well as mutated sequences were extracted by comprehensive DSC experiments. The unique G-quadruplex involving consecutive G-tracts II–V with formation of two one-nucleotide and one central two-nucleotide propeller loop, previously proposed to be the biologically most relevant species, was found to be the most stable fold in terms of its Gibbs free energy of formation at ambient temperatures. Its stability derives from its short propeller loops but also from the favorable type of loop residues. Whereas quadruplex folds with long propeller loops are significantly disfavored, a snap-back loop structure formed by incorporating a 3’-terminal guanosine into the empty position of a tetrad seems highly competitive based on its thermodynamic stability. However, its destabilization by extending the 3’-terminus questions the significance of such a species under in vivo conditions.     

Effects of turn stability on the kinetics of refolding of a hairpin in a beta-sheet

As part of our continuing study of the effects of the turn sequence on the conformational stability as well as the mechanism of folding of a beta-sheet structure, we have undertaken a parallel investigation of the solution structure, conformational stability, and kinetics of refolding of the beta-sheet VFIVDGOTYTEV(D)PGOKILQ. The latter peptide is an analogue of the original Gellman beta-sheet VFITS(D)PGKTYTEV(D)PGOKILQ, wherein the TS(D)PGK turn sequence in the first hairpin has been replaced by VDGO. Thermodynamics studies revealed comparable conformational stability of the two peptides. However, unlike the Gellman peptide, which showed extremely rapid refolding of the first hairpin, early kinetic events associated with the refolding of the corresponding hairpin in the VDGO mutant were found to be significantly slower. A detailed study of the conformation of the modified peptide suggested that hydrophobic interactions might be contributing to its stability. Accordingly, we surmise that the early kinetic events are sensitive to whether the formation of the hairpin is nucleated at the turn or by sequestering of the hydrophobic residues across the strand, before structural rearrangements to produce the nativelike topology. Nucleation of the hairpin at the turn is expected to be intrinsically rapid for a strong turn. However, if the process must involve collapse of hydrophobic side chains, the nucleation should be slower as solvent molecules must be displaced to sequester the hydrophobic residues. These findings reflect the contribution of different forces toward nucleation of hairpins in the mechanism of folding of beta-sheets.     

二维紧密蛋白质链折叠序列的特性研究

采用完全计数法,研究了二维紧密蛋白质链在不同HP序列时的构象性质,特别是具有唯一基态能量的折叠序列的性质.对于具有N个单体的紧密蛋白质链,发现有一定比例的序列为折叠序列.在这些折叠序列中,疏水基团(H)的数目比亲水基团(P)多20%,并同200种真实蛋白质分子的疏水基团和亲水基团的结果进行了比较.对于不同的折叠序列,根据序列中其疏水基团的数目,把具有相同疏水基团数目的序列归在同一类,发现这样的序列在总的序列中的相对含量满足高斯分布.同时还对序列中H(或者P)团族大小及其分别进行了研究,发现折叠序列与无规随机序列不同.还研究了不同折叠序列在不同链长时的比热情况,发现其相转变温度TC主要与链长有关,与折叠序列无关.     

Examination of the folding of a short alanine-based helical peptide with salt bridges using molecular dynamics simulation

A molecular dynamics simulation of the folding of a short alanine-based helical peptide of 17 residues with three Glu...Lys (i, i + 4) salt bridge pairs, referred to as the AEK17 peptide, was carried out. The simulation gave an estimated simulation folding time of 2.5 ns, shorter than 12 ns for an alanine-based peptide of 16 residues with three Lys residues only, referred to as the AK16 peptide, simulated previously. After folded, the AEK17 peptide had a helical content of 77%, in excellent agreement with the experimentally determined value of 80%. An examination of the folding pathways of AEK17 indicated that the peptide proceeded via three-turn helix conformations more than the helix-turn-helix conformation in the folding pathways. An analysis of interactions indicated that the formation of hydrogen bonds between Lys residue side chains and backbone carbonyls is a major factor in the abundant conformation of the three-turn helix intermediate. The substitution of three Ala with Glu residues reduces the extent of hydrophobic interaction in alanine-based AK peptides with the result that the breaking of the interactions of Lys epsilon-NH3+(side chain)...C=O(backbone) is a major activation action for the AEK17 to achieve a complete fold, in contrast to the AK16 peptide, in which breaking non-native hydrophobic interaction is the rate-determining step.     

Denatured-state ensemble and the early-stage folding of the G29A mutant of the B-domain of protein A

The folding mechanism of the G29A mutant of the B-domain of protein A (BdpA) has been studied by all-atom molecular dynamics simulation using AMBER force field (ff03) and generalized Born continuum solvent model. Started from the extended chain conformation, a total of 16 simulations (400 ns each) at 300 K captured some early folding events of the G29A mutant of BdpA. In one of the 16 trajectories, the G29A mutant folded within 2.8 A (root mean square) of the wild-type NMR structure. We observed that the fast burial of hydrophobic residues was the driving force to bring the distant residues into close proximity. The initiation of the helix I and III occurred during the stage of hydrophobic collapse. The initiation and growth of the helix II was slow. Both the secondary structure formation and the development of the native tertiary contacts suggested a multistage folding process. Clustering analysis indicated that two helix species (helices I and III) could be intermediates. Further analysis revealed that the hydrophobic residues of partially folded helix II formed nativelike hydrophobic contacts with helices I and III that stabilized a nativelike state and delayed the completion of folding of the entire protein. The details of the early folding process were compared with other theoretical and experimental studies. It was found that a nativelike hydrophobic cluster was formed by residues including F(30), I(31), L(34), L(44), L(45), and A(48) that prevented further development of the native structures, and breaking the hydrophobic cluster like this one contributed to the rate-limiting step. This was in complete agreement with the recent kinetic measurements in which mutations of these residues to Gly and Ala substantially increased the folding rates by as much as 60 times. Apparently, destabilization of nonnative states dramatically enhanced the folding rates.     

Conformations of hydrophobic polyelectrolytes

Recent studies on the (hypercoiled) compact conformation and the pH-induced conformational transition to the extended coil of the hydrophobic poly(acids or bases), which have been well used in industrial and medical circles, are summarized, especially on the basis of our studies on poly(alpha-alkyl acrylic acids) and maleic acid copolymers with hydrophobic aromatic monomers. The stability of the compact conformation and values of various thermodynamic parameters of the transition of the hydrophobic polyelectrolytes suggest the importance of hydrophobic interaction among the side chains to form the compact conformation. Characterization of various physicochemical methods, including 1H-NMR measurements, gives a model of the compact conformation with a more expanded structure than in globular proteins, a free-draining property of the solvent, the conformation fluctuation, etc. Also, the apparent two-state character of each segment in the transition region, a life-time in each state and the cooperative parameter for the compact form formation are discussed. A review of our conformational studies on the hydrophobic-hydrophilic polypeptides is also given. For the anion-induced conformation transition in basic homopoly(alpha-amino acids), hydrophobic characters of the anion and the side chain in the polypeptide are shown to be important, especially in terms of solvation. The difference in the induced conformation by the anion between random and alternating basic copolypeptides is explained by introducing a model which shows the importance of the sequence of hydrophobic and hydrophilic residues in the polypeptide to induce the ordered conformation of the anions. Also, we attempt to explain the difference between the induction of ordered conformation in the basic homo- or copolypeptide in reversed micelles with a large sulfonate (AOT) vs. that in aqueous AOT in terms of the hydrophobic character of the side chains in the polypeptides, AOT and the medium.     

Conformations of hydrophobic polyelectrolytes

Recent studies on the (hypercoiled) compact conformation and the pH-induced conformational transition to the extended coil of the hydrophobic poly(acids or bases), which have been well used in industrial and medical circles, are summarized, especially on the basis of our studies on poly(α-alkyl acrylic acids) and maleic acid copolymers with hydrophobic aromatic monomers. The stability of the compact conformation and values of various thermodynamic parameters of the transition of the hydrophobic polyelectrolytes suggest the importance of hydrophobic interaction among the side chains to form the compact conformation. Characterization of various physicochemical methods, including ¹H-NMR measurements, gives a model of the compact conformation with a more expanded structure than in globular proteins, a free-draining property of the solvent, the conformation fluctuation, etc. Also, the apparent two-state character of each segment in the transition region, a life-time in each state and the cooperative parameter for the compact form formation are discussed.A review of our conformational studies on the hydrophobic-hydrophilic polypeptides is also given. For the anion-induced conformation transition in basic homopoly(α-amino acids), hydrophobic characters of the anion and the side chain in the polypeptide are shown to be important, especially in terms of solvation. The difference in the induced conformation by the anion between random and alternating basic copolypeptides is explained by introducing a model which shows the importance of the sequence of hydrophobic and hydrophilic residues in the polypeptide to induce the ordered conformation of the anions. Also, we attempt to explain the difference between the induction of ordered conformation in the basic homo- or copolypeptide in reversed micelles with a large sulfonate (AOT) vs. that in aqueous AOT in terms of the hydrophobic character of the side chains in the polypeptides, AOT and the medium.     

Identification of characteristic protein folding channels in a coarse-grained hydrophobic-polar peptide model

Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a heteropolymer sequence lead to completely different folding behaviors. Studying three exemplified sequences with the same content of hydrophobic and polar residues, we can reproduce within this simple model two-state folding, folding through intermediates, as well as metastability.     

Thermodynamical properties of reaction intermediates during apoplastocyanin folding in time domain

Two intermediates observed for the folding process of apoplastocyanin (apoPC) were investigated by using a photoinduced triggering system combined with the transient grating and transient lens methods. The thermodynamic quantities, enthalpy, heat capacity, partial volume, and thermal expansion volume changes during the protein folding reaction were measured in time domain for the first time. An interesting observation is the positive enthalpy changes during the folding process. This positive enthalpy change must be compensated by positive entropy changes, which could be originated from the dehydration effect of hydrophobic residues and/or the translational entropy gain of bulk water molecules. Observed negative heat capacity change was explained by the dehydration effect of hydrophilic residues and/or motional confinement of amino acid side chains and water molecules in apoPC. The signs of the volume change and thermal expansion volume were different for two processes and these changes were interpreted in terms of the different relative contributions of the hydration and the dehydration of the hydrophilic residues. These results indicated two-step hydrophobic collapses in the early stage of the apoPC folding, but the nature of the dynamics was different.     

Tuning secondary structure and self-assembly of amphiphilic peptides

Self-assembly is one of nature's mechanisms by which higher order structures are obtained. Two of the main driving forces for self-assembly, hydrophobic interactions and hydrogen bonding, are both present within amphiphilic peptides. Here, it is demonstrated how the intricately interconnected folding and assembly behavior of an N-terminally acylated peptide, with the sequence GANPNAAG, has been tuned by varying its hydrophobic tail and thermal history. The change in interplay between hydrophobic forces and peptide folding allowed the occurrence of different types of aggregation, from soluble peptides with a random coil conformation to aggregated peptides arranged in a beta-sheet assembly, which form helically twisted bilayer ribbons.