Hydrophobicity of amino acid subgroups in proteins

Protein folding studies often utilize areas and volumes to assess the hydrophobic contribution to conformational free energy (Richards, F.M. Annu. Rev. Biophys. Bioeng. 6:151-176, 1977). We have calculated the mean area buried upon folding for every chemical group in each residue within a set of X-ray elucidated proteins. These measurements, together with a standard state cavity size for each group, are documented in a table. It is observed that, on average, each type of group buries a constant fraction of its standard state area. The mean area buried by most, though not all, groups can be closely approximated by summing contributions from three characteristic parameters corresponding to three atom types: (1) carbon or sulfur, which turn out to be 86% buried, on average; (2) neutral oxygen or nitrogen, which are 40% buried, on average; and (3) charged oxygen or nitrogen, which are 32% buried, on average.     

Domains in folding of model proteins.

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

Prediction of the three-dimensional structure of proteins using the electrostatic screening model and hierarchic condensation

We describe a method for predicting the three-dimensional (3-D) structure of proteins from their sequence alone. The method is based on the electrostatic screening model for the stability of the protein main-chain conformation. The free energy of a protein as a function of its conformation is obtained from the potentials of mean force analysis of high-resolution x-ray protein structures. The free energy function is simple and contains only 44 fitted coefficients. The minimization of the free energy is performed by the torsion space Monte Carlo procedure using the concept of hierarchic condensation. The Monte Carlo minimization procedure is applied to predict the secondary, super-secondary, and native 3-D structures of 12 proteins with 28–110 amino acids. The 3-D structures of the majority of local secondary and super-secondary structures are predicted accurately. This result suggests that control in forming the native-like local structure is distributed along the entire protein sequence. The native 3-D structure is predicted correctly for 3 of 12 proteins composed mainly from the α-helices. The method fails to predict the native 3-D structure of proteins with a predominantly β secondary structure. We suggest that the hierarchic condensation is not an appropriate procedure for simulating the folding of proteins made up primarily from β-strands. The method has been proved accurate in predicting the local secondary and super-secondary structures in the blind ab initio 3-D prediction experiment. Proteins 31:74–96, 1998. © 1998 Wiley-Liss, Inc.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Distance-constraint approach to higher-order structures of globular proteins with empirically determined distances between amino acid residues

An analysis of higher-order structures of globular proteins by means of a distance-constraint approach is presented. Conformations are generated for each of 21 test proteins of small and medium sizes by optimizing an objective functionf=w _ij(d _ij–d _ij)², whered _ij is a distance between residuesi andj in a calculated conformation, d _ij is an assigned distance to the (ij) pair of residues which is determined based on the statistics of known three-dimensional structures of 14 proteins in the earlier study, andw _ij is a weighting factor. d _ij involves information about hydrophobicity and hydrophilicity of each amino acid residue and about connectivity of a polypeptide chain. In these calculations, only the amino acid sequence is used as input data specific to a calculated protein. With respect to higher-order structures regenerated in the optimized conformations, the following properties are analyzed: (a) N14 of a residue, defined as the number of residues surrounding the residue located within a sphere of radius of 14 Å; (b) root-mean-square differences of the global and local conformations from the corresponding X-ray conformations; (c) distance profiles in the short and medium ranges; and (d) distance maps. The effects of supplementary information about locations of secondary structures and disulfide bonds are also examined to discuss the potential ability of this methodology to predict the three-dimensional structures of globular proteins.     

How the folding rates of two‐ and multistate proteins depend on the amino acid properties

Proteins fold by either two‐state or multistate kinetic mechanism. We observe that amino acids play different roles in different mechanism. Many residues that are easy to form regular secondary structures (α helices, β sheets and turns) can promote the two‐state folding reactions of small proteins. Most of hydrophilic residues can speed up the multistate folding reactions of large proteins. Folding rates of large proteins are equally responsive to the flexibility of partial amino acids. Other properties of amino acids (including volume, polarity, accessible surface, exposure degree, isoelectric point, and phase transfer energy) have contributed little to folding kinetics of the proteins. Cysteine is a special residue, it triggers two‐state folding reaction and but inhibits multistate folding reaction. These findings not only provide a new insight into protein structure prediction, but also could be used to direct the point mutations that can change folding rate. Proteins 2014; 82:2375–2382. © 2014 Wiley Periodicals, Inc.     

Sequence-based study of two related proteins with different folding behaviors

Z(SPA-1) is an engineered protein that binds to its parent, the three-helix-bundle Z domain of staphylococcal protein A. Uncomplexed Z(SPA-1) shows a reduced helix content and a melting behavior that is less cooperative, compared with the wild-type Z domain. Here we show that the difference in folding behavior between these two sequences can be partly understood in terms of an off-lattice model with 5-6 atoms per amino acid and a minimalistic potential, in which folding is driven by backbone hydrogen bonding and effective hydrophobic attraction.     

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.     

Lattice simulations of cotranslational folding of single domain proteins

We use lattice protein models and Monte Carlo simulations to study cotranslational folding of small single domain proteins. We show that the assembly of native structure begins during late extrusion stages, but final formation of native state occurs during de novo folding, when all residues are extruded. There are three main results in our study. First, for the sequences displaying two-state refolding mechanism de novo cotranslational folding pathway differs from that sampled in in vitro refolding. The change in folding pathways is due to partial assembly of native interactions during extrusion that results in different starting conditions for in vitro refolding and for de novo cotranslational folding. For small single domain proteins cotranslational folding is slower than in vitro refolding, but is generally fast enough to be completed before the release from a ribosome. Second, we found that until final stages of biosynthesis cotranslational folding is essentially equilibrium. This observation is explained by low stability of structured states for partially extruded chains. Finally, our data suggest that the proteins, which refold in vitro slowly via intermediates, complete their de novo folding after the release from a ribosome. Comparison of our lattice cotranslational simulations with recent experimental and computational studies is discussed.     

Composition-related structural transition of random peptides: insight into the boundary between intrinsically disordered proteins and folded proteins

Previous studies based on bioinformatics showed that there is a sharp distinction of structural features and residue composition between the intrinsically disordered proteins and the folded proteins. What induces such a composition-related structural transition? How do various kinds of interactions work in such processes? In this work, we investigate these problems based on a survey on peptides randomly composed of charged residues (including glutamic acids and lysines) and the residues with different hydrophobicity, such as alanines, glycines, or phenylalanines. Based on simulations using all-atom model and replica-exchange Monte Carlo method, a coil-globule transition is observed for each peptide. The corresponding transition temperature is found to be dependent on the contents of the hydrophobic and charged residues. For several cases, when the mean hydrophobicity is larger than a certain threshold, the transition temperature is higher than the room temperature, and vise versa. These thresholds of hydrophobicity and net charge are quantitatively consistent with the border line observed from the study of bioinformatics. These results outline the basic physical reasons for the compositional distinction between the intrinsically disordered proteins and the folded proteins. Furthermore, the contributions of various interactions to the structural variation of peptides are analyzed based on the contact statistics and the charge-pattern dependence of the gyration radii of the peptides. Our observations imply that the hydrophobicity contributes essentially to such composition-related transitions. Thus, we achieve a better understanding on composition–structure relation of the natural proteins and the underlying physics.     

Folding of Top7 in unbiased all‐atom Monte Carlo simulations

For computational studies of protein folding, proteins with both helical and β‐sheet secondary structure elements are very challenging, as they expose subtle biases of the physical models. Here, we present reproducible folding of a 92 residue α/β protein (residues 3–94 of Top7, PDB ID: 1QYS) in computer simulations starting from random initial conformations using a transferable physical model which has been previously shown to describe the folding and thermodynamic properties of about 20 other smaller proteins of different folds. Top7 is a de novo designed protein with two α‐helices and a five stranded β‐sheet. Experimentally, it is known to be unusually stable for its size, and its folding transition distinctly deviates from the two‐state behavior commonly seen in natural single domain proteins. In our all‐atom implicit solvent parallel tempering Monte Carlo simulations, Top7 shows a rapid transition to a group of states with high native‐like secondary structure, and a much slower subsequent transition to the native state with a root mean square deviation of about 3.5 Å from the experimentally determined structure. Consistent with experiments, we find Top7 to be thermally extremely stable, although the simulations also find a large number of very stable non‐native states with high native‐like secondary structure. Proteins 2013; 81:1446–1456. © 2013 Wiley Periodicals, Inc.     

Distinct character in hydrophobicity of amino acid compositions of mitochondrial proteins

A compact mitochondrial gene contains all essential information about the synthesis of mitochondrial proteins which play their roles in a small compartment of the mitochondrium. Almost no noncoding regions have been found through the gene, but a necessary set of tRNAs for the 20 amino acids is provided for biosynthesis, some of them coding different amino acids from those in a usual cell. Since the gene is so compact that the produced proteins would have some characteristic aspects for the mitochondrium, amino acid compositions of mitochondrial proteins (mt-proteins) were examined in the 20-dimensional composition space. The results show that compositions of proteins translated from the mitochondrial genes have a distinct character having more hydrophobic content than others, which is illustrated by a clustered distribution in the multidimensional composition space. The cluster is located at the tail edge of the global distribution pattern of a Gaussian shape for other various kinds of proteins in the space. The mt-proteins are rich in hydrophobic amino acids as is a membrane protein, but are different from other membrane proteins in a lesser content of Val. A good correlation found between the base and amino acid compositions for the mitochondria was examined in comparison to those of organisms such as thermophilic bacterium having an extreme G-C-rich base composition.     

Empirical lipid propensities of amino acid residues in multispan alpha helical membrane proteins

Characterizing the interactions between amino acid residues and lipid molecules is important for understanding the assembly of transmembrane helices and for studying membrane protein folding. In this study we develop TMLIP (TransMembrane helix-LIPid), an empirically derived propensity of individual residue types to face lipid membrane based on statistical analysis of high-resolution structures of membrane proteins. Lipid accessibilities of amino acid residues within the transmembrane (TM) region of 29 structures of helical membrane proteins are studied with a spherical probe of radius of 1.9 A. Our results show that there are characteristic preferences for residues to face the headgroup region and the hydrocarbon core region of lipid membrane. Amino acid residues Lys, Arg, Trp, Phe, and Leu are often found exposed at the headgroup regions of the membrane, where they have high propensity to face phospholipid headgroups and glycerol backbones. In the hydrocarbon core region, the strongest preference for interacting with lipids is observed for Ile, Leu, Phe and Val. Small and polar amino acid residues are usually buried inside helical bundles and are strongly lipophobic. There is a strong correlation between various hydrophobicity scales and the propensity of a given residue to face the lipids in the hydrocarbon region of the bilayer. Our data suggest a possibly significant contribution of the lipophobic effect to the folding of membrane proteins. This study shows that membrane proteins have exceedingly apolar exteriors rather than highly polar interiors. Prediction of lipid-facing surfaces of boundary helices using TMLIP1 results in a 54% accuracy, which is significantly better than random (25% accuracy). We also compare performance of TMLIP with another lipid propensity scale, kPROT, and with several hydrophobicity scales using hydrophobic moment analysis.     

Optimization of the electrostatic interactions in proteins of different functional and folding type

The 3-dimensional optimization of the electrostatic interactions between the charged amino acid residues was studied by Monte Carlo simulations on an extended representative set of 141 protein structures with known atomic coordinates. The proteins were classified by different functional and structural criteria, and the optimization of the electrostatic interactions was analyzed. The optimization parameters were obtained by comparison of the contribution of charge-charge interactions to the free energy of the native protein structures and for a large number of randomly distributed charge constellations obtained by the Monte Carlo technique. On the basis of the results obtained, one can conclude that the charge-charge interactions are better optimized in the enzymes than in the proteins without enzymatic functions. Proteins that belong to the mixed αβ folding type are electrostatically better optimized than pure α-helical or β-strand structures. Proteins that are stabilized by disulfide bonds show a lower degree of electrostatic optimization. The electrostatic interactions in a native protein are effectively optimized by rejection of the conformers that lead to repulsive charge-charge interactions. Particularly, the rejection of the repulsive contacts seems to be a major goal in the protein folding process. The dependence of the optimization parameters on the choice of the potential function was tested. The majority of the potential functions gave practically identical results.     

Challenges in structure prediction of oligomeric proteins at the united-residue level: searching the multiple-chain energy landscape with CSA and CFMC

A revised version of the Conformational Space Annealing (CSA) global optimization method is developed, with three separate measures of structural similarity, in order to overcome the inability of a single distance measure to evaluate multiple-chain protein structures adequately. A second search method, Conformational Family Monte Carlo (CFMC), involving genetic-type moves, Monte Carlo-with-minimization perturbations, and explicit clustering of the population into conformational families, is adapted to treat multiple-chain proteins. These two methods are applied to two oligomeric proteins, the retro-GCN4 leucine zipper and the synthetic domain-swapped dimer. CFMC proves superior to CSA in its search for low-energy representatives of its conformational families, but both methods encounter difficulty in finding the native packing arrangements in the absence of native-like symmetry constraints, even when native monomers are present in the population.     

Dissecting contact potentials for proteins: relative contributions of individual amino acids

Mimotopes mimic the three-dimensional topology of an antigen epitope, and are frequently recognized by antibodies with affinities comparable to those obtained for the original antibody-antigen interaction. Peptides and anti-idiotypic antibodies are two classes of protein mimotopes that mimic the topology (but not necessarily the sequence) of the parental antigen. In this study, we combine these two classes by selecting mimotopes based on single domain IgNAR antibodies, which display exceptionally long CDR3 loop regions (analogous to a constrained peptide library) presented in the context of an immunoglobulin framework with adjacent and supporting CDR1 loops. By screening an in vitro phage-display library of IgNAR variable domains (V(NAR)s) against the target antigen monoclonal antibody MAb5G8, we obtained four potential mimotopes. MAb5G8 targets a linear tripeptide epitope (AYP) in the flexible signal sequence of the Plasmodium falciparum Apical Membrane Antigen-1 (AMA1), and this or similar motifs were detected in the CDR loops of all four V(NAR)s. The V(NAR)s, 1-A-2, -7, -11, and -14, were demonstrated to bind specifically to this paratope by competition studies with an artificial peptide and all showed enhanced affinities (3-46 nM) compared to the parental antigen (175 nM). Crystallographic studies of recombinant proteins 1-A-7 and 1-A-11 showed that the SYP motifs on these V(NAR)s presented at the tip of the exposed CDR3 loops, ideally positioned within bulge-like structures to make contact with the MAb5G8 antibody. These loops, in particular in 1-A-11, were further stabilized by inter- and intra- loop disulphide bridges, hydrogen bonds, electrostatic interactions, and aromatic residue packing. We rationalize the higher affinity of the V(NAR)s compared to the parental antigen by suggesting that adjacent CDR1 and framework residues contribute to binding affinity, through interactions with other CDR regions on the antibody, though of course definitive support of this hypothesis will rely on co-crystallographic studies. Alternatively, the selection of mimotopes from a large (<4 x 10(8)) constrained library may have allowed selection of variants with even more favorable epitope topologies than present in the original antigenic structure, illustrating the power of in vivo selection of mimotopes from phage-displayed molecular libraries.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

Solvent-induced organization: A physical model of folding myoglobin

The essential features of the in vitro refolding of myoglobin are expressed in a solvable physical model. Alpha helices are taken as the fundamental collective coordinates of the system, while the refolding is assumed to be mainly driven by solvent-induced hydrophobic forces. A quantitative model of these forces is developed and compared with experimental and theoretical results. The model is then tested by being employed in a simulation scheme designed to mimic solvent effects. Realistic dynamic trajectories of myoglobin are shown as it folds from an extended conformation to a close approximation of the native state. Various suggestive features of the process are discussed. The tenets of the model are further tested by folding the single-chain plant protein leghemoglobin. © 1994 Wiley-Liss, Inc.