Physical principles of protein structure and protein folding

Physical principles determining the protein structure and protein folding are reviewed: (i) the molecular theory of protein secondary structure and the method of its prediction based on this theory; (ii) the existence of a limited set of thermodynamically favourable folding patterns of α- and β-regions in a compact globule which does not depend on the details of the amino acid sequence; (iii) the moderns approaches to the prediction of the folding patterns of α- and β-regions in concrete proteins; (iv) experimental approaches to the mechanism of protein folding. The review reflects theoretical and experimental works of the author and his collaborators as well as those of other groups.     

Filling small, empty protein cavities: structural and energetic consequences

Most proteins contain small cavities that can be filled by replacing cavity-lining residues by larger ones. Since shortening mutations in hydrophobic cores tend to destabilize proteins, it is expected that cavity-filling mutations may conversely increase protein stability. We have filled three small cavities in apoflavodoxin and determined by NMR and equilibrium unfolding analysis their impact in protein structure and stability. The smallest cavity (14 A3) has been filled, at two different positions, with a variety of residues and, in all cases, the mutant proteins are locally unfolded, their structure and energetics resembling those of an equilibrium intermediate of the thermal unfolding of the wild-type protein. In contrast, two slightly larger cavities of 20 A3 and 21 A3 have been filled with Val to Ile or Val to Leu mutations and the mutants preserve both the native fold and the equilibrium unfolding mechanism. From the known relationship, observed in shortening mutations, between stability changes and the differential hydrophobicity of the exchanged residues and the volume of the cavities, the filling of these apoflavodoxin cavities is expected to stabilize the protein by approximately 1.5 kcal mol(-1). However, both urea and thermal denaturation analysis reveal much more modest stabilizations, ranging from 0.0 kcal mol(-1) to 0.6 kcal mol(-1), which reflects that the accommodation of single extra methyl groups in small cavities requires some rearrangement, necessarily destabilizing, that lowers the expected theoretical stabilization. As the size of these cavities is representative of that of the typical small, empty cavities found in most proteins, it seems unlikely that filling this type of cavities will give rise to large stabilizations.     

Secondary and tertiary structure formation of the beta-barrel membrane protein OmpA is synchronized and depends on membrane thickness

The mechanism of membrane insertion and folding of a beta-barrel membrane protein has been studied using the outer membrane protein A (OmpA) as an example. OmpA forms an eight-stranded beta-barrel that functions as a structural protein and perhaps as an ion channel in the outer membrane of Escherichia coli. OmpA folds spontaneously from a urea-denatured state into lipid bilayers of small unilamellar vesicles. We have used fluorescence spectroscopy, circular dichroism spectroscopy, and gel electrophoresis to investigate basic mechanistic principles of structure formation in OmpA. Folding kinetics followed a second-order rate law and is strongly depended on the hydrophobic thickness of the lipid bilayer. When OmpA was refolded into model membranes of dilaurylphosphatidylcholine, fluorescence kinetics were characterized by a rate constant that was about fivefold higher than the rate constants of formation of secondary and tertiary structure, which were determined by circular dichroism spectroscopy and gel electrophoresis, respectively. The formation of beta-sheet secondary structure and closure of the beta-barrel of OmpA were correlated with the same rate constant and coupled to the insertion of the protein into the lipid bilayer. OmpA, and presumably other beta-barrel membrane proteins therefore do not follow a mechanism according to the two-stage model that has been proposed for the folding of alpha-helical bundle membrane proteins. These different folding mechanisms are likely a consequence of the very different intramolecular hydrogen bonding and hydrophobicity patterns in these two classes of membrane proteins.     

Describing protein structure: a general algorithm yielding complete helicoidal parameters and a unique overall axis

We present a general and mathematically rigorous algorithm which allows the helicoidal structure of a protein to be calculated starting from the atomic coordinates of its peptide backbone. This algorithm yields a unique curved axis which quantifies the folding of the backbone and a full set of helicoidal parameters describing the location of each peptide unit. The parameters obtained form a complete and independent set and can therefore be used for analyzing, comparing, or reconstructing protein backbone geometry. This algorithm has been implemented in a computer program named P-Curve. Several examples of its possible applications are discussed.     

A database of protein structure families with common folding motifs.

The availability of fast and robust algorithms for protein structure comparison provides an opportunity to produce a database of three-dimensional comparisons, called families of structurally similar proteins (FSSP). The database currently contains an extended structural family for each of 154 representative (below 30% sequence identity) protein chains. Each data set contains: the search structure; all its relatives with 70-30% sequence identity, aligned structurally; and all other proteins from the representative set that contain substructures significantly similar to the search structure. Very close relatives (above 70% sequence identity) rarely have significant structural differences and are excluded. The alignments of remote relatives are the result of pairwise all-against-all structural comparisons in the set of 154 representative protein chains. The comparisons were carried out with each of three novel automatic algorithms that cover different aspects of protein structure similarity. The user of the database has the choice between strict rigid-body comparisons and comparisons that take into account interdomain motion or geometrical distortions; and, between comparisons that require strictly sequential ordering of segments and comparisons, which allow altered topology of loop connections or chain reversals. The data sets report the structurally equivalent residues in the form of a multiple alignment and as a list of matching fragments to facilitate inspection by three-dimensional graphics. If substructures are ignored, the result is a database of structure alignments of full-length proteins, including those in the twilight zone of sequence similarity.(ABSTRACT TRUNCATED AT 250 WORDS)     

Structural and energetic consequences of mutations in a solvated hydrophobic cavity

The structural and energetic consequences of modifications to the hydrophobic cavity of interleukin 1-beta (IL-1beta) are described. Previous reports demonstrated that the entirely hydrophobic cavity of IL-1beta contains positionally disordered water. To gain a better understanding of the nature of this cavity and the water therein, a number of mutant proteins were constructed by site-directed mutagenesis, designed to result in altered hydrophobicity of the cavity. These mutations involve the replacement of specific phenylalanine residues, which circumscribe the cavity, with tyrosine, tryptophan, leucine and isoleucine. Using differential scanning calorimetry to determine the relative stabilities of the wild-type and mutant proteins, we found all of the mutants to be destabilizing. X-ray crystallography was used to identify the structural consequences of the mutations. No clear correlation between the hydrophobicities of the specific side-chains introduced and the resulting stabilities was found.     

Protein structure prediction in genomics

As the number of completely sequenced genomes rapidly increases, including now the complete Human Genome sequence, the post-genomic problems of genome-scale protein structure determination and the issue of gene function identification become ever more pressing. In fact, these problems can be seen as interrelated in that experimentally determining or predicting or the structure of proteins encoded by genes of interest is one possible means to glean subtle hints as to the functions of these genes. The applicability of this approach to gene characterisation is reviewed, along with a brief survey of the reliability of large-scale protein structure prediction methods and the prospects for the development of new prediction methods.     

Symmetric primary and tertiary structure mutations within a symmetric superfold: a solution, not a constraint, to achieve a foldable polypeptide

In previous studies designed to increase the primary structure symmetry within the hydrophobic core of human acidic fibroblast growth factor (FGF-1) a combination of five mutations were accommodated, resulting in structure, stability and folding kinetic properties similar to wild-type (despite the symmetric constraint upon the set of core residues). A sixth mutation in the core, involving a highly conserved Met residue at position 67, appeared intolerant to substitution. Structural analysis suggested that the local packing environment of position 67 involved two regions of apparent insertions that distorted the tertiary structure symmetry inherent in the beta-trefoil architecture. It was postulated that a symmetric constraint upon the primary structure within the core could only be achieved after these insertions had been deleted (concomitantly increasing the tertiary structure symmetry). The deletion of these insertions is now shown to permit mutation of position 67, thereby increasing the primary structure symmetry relationship within the core. Furthermore, despite the imposed symmetric constraint upon both the primary and tertiary structure, the resulting mutant form of FGF-1 is substantially more stable. The apparent inserted regions are shown to be associated with heparin-binding functionality; however, despite a marked reduction in heparin-binding affinity the mutant form of FGF-1 is surprisingly approximately 70 times more potent in 3T3 fibroblast mitogenic assays. The results support the hypothesis that primary structure symmetry within a symmetric protein superfold represents a possible solution, rather than a constraint, to achieving a foldable polypeptide.     

神经网络在蛋白质二级结构预测中的应用

介绍了蛋白质二级结构预测的研究意义,讨论了用在蛋白质二级结构预测方面的神经网络设计问题,并且较详尽地评述了近些年来用神经网络方法在蛋白质二级结构预测中的主要工作进展情况,展望了蛋白质结构预测的前景。     

Accelerated simulation of unfolding and refolding of a large single chain globular protein

We have developed novel strategies for contracting simulation times in protein dynamics that enable us to study a complex protein with molecular weight in excess of 34 kDa. Starting from a crystal structure, we produce unfolded and then refolded states for the protein. We then compare these quantitatively using both established and new metrics for protein structure and quality checking. These include use of the programs Concoord and Darvols. Simulation of protein-folded structure well beyond the molten globule state and then recovery back to the folded state is itself new, and our results throw new light on the protein-folding process. We accomplish this using a novel cooling protocol developed for this work.     

A rapid protein structure alignment algorithm based on a text modeling technique

Structural alignment of proteins is widely used in various fields of structural biology. In order to further improve the quality of alignment, we describe an algorithm for structural alignment based on text modelling techniques. The technique firstly superimposes secondary structure elements of two proteins and then, models the 3D-structure of the protein in a sequence of alphabets. These sequences are utilized by a step-by-step sequence alignment procedure to align two protein structures. A benchmark test was organized on a set of 200 non-homologous proteins to evaluate the program and compare it to state of the art programs, e.g. CE, SAL, TM-align and 3D-BLAST. On average, the results of all-against-all structure comparison by the program have a competitive accuracy with CE and TM-align where the algorithm has a high running speed like 3D-BLAST.     

Enhanced sampling of peptide and protein conformations using replica exchange simulations with a peptide backbone biasing-potential

During replica exchange molecular dynamics (RexMD) simulations, several replicas of a system are simulated at different temperatures in parallel allowing for exchange between replicas at frequent intervals. This technique allows significantly improved sampling of conformational space and is increasingly being used for structure prediction of peptides and proteins. A drawback of the standard temperature RexMD is the rapid increase of the replica number with increasing system size to cover a desired temperature range. In an effort to limit the number of replicas, a new Hamiltonian-RexMD method has been developed that is specifically designed to enhance the sampling of peptide and protein conformations by applying various levels of a backbone biasing potential for each replica run. The biasing potential lowers the barrier for backbone dihedral transitions and promotes enhanced peptide backbone transitions along the replica coordinate. The application on several peptide cases including in all cases explicit solvent indicates significantly improved conformational sampling when compared with standard MD simulations. This was achieved with a very modest number of 5-7 replicas for each simulation system making it ideally suited for peptide and protein folding simulations as well as refinement of protein model structures in the presence of explicit solvent.     

Evolutionary computer programming of protein folding and structure predictions

In order to understand the mechanism of protein folding and to assist the rational de-novo design of fast-folding, non-aggregating and stable artificial enzymes it is very helpful to be able to simulate protein folding reactions and to predict the structures of proteins and other biomacromolecules. Here, we use a method of computer programming called "evolutionary computer programming" in which a program evolves depending on the evolutionary pressure exerted on the program. In the case of the presented application of this method on a computer program for folding simulations, the evolutionary pressure exerted was towards faster finding deep minima in the energy landscape of protein folding. Already after 20 evolution steps, the evolved program was able to find deep minima in the energy landscape more than 10 times faster than the original program prior to the evolution process.     

Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

Water as a conformational editor in protein folding

As molecules approach one another in aqueous solution, desolvation free energy barriers to association are encountered. Experiments suggest these (de)solvation effects contribute to the free energy barriers separating the folded and unfolded states of protein molecules. To explore their influence on the energy landscapes of protein folding reactions, we have incorporated desolvation barriers into a semi-realistic, off-lattice protein model that uses a simplified physico-chemical force-field determined solely by the sequence of amino acids. Monte Carlo sampling techniques were used to study the effects on the thermodynamics and kinetics of folding of a number of systems, diverse in structure and sequence. In each case, desolvation barriers increase the stability of the native conformation and the cooperativity of the major folding/unfolding transition. The folding times of these systems are reduced significantly upon inclusion of desolvation barriers, demonstrating that the particulate nature of the solvent engenders a more defined route to the native fold.     

Structure of POIA1, a homologous protein to the propeptide of subtilisin: implication for protein foldability and the function as an intramolecular chaperone

Solution structure of POIA1 (Pleurotus ostreatus proteinase A inhibitor 1), which functions as an intramolecular chaperone and as an inhibitor to subtilisin, was determined. By making use of the fact that POIA1 is the only structured protein that shows homology to the propeptide of subtilisin, which is unstructured by itself, foldability of this protein was elucidated. It became clear that the evolutionarily conserved residues play two important roles, one for the maintenance of its own structure, and the other for the interaction with subtilisin. Structural softness and mutational tolerance contained in the POIA1 structure makes it an ideal material for designing a foldable protein.     

Novel scales based on hydrophobicity indices for secondary protein structure

This paper is concerned with a branch of computational biology related to protein prediction and analysis of secondary structure of proteins. Although traditional methods use a simple amino acid composition to predict the secondary structure content, hydrophobicity has been recently found to improve the results in this and several related prediction tasks. To this end, we propose and analyze advantages of two new hydrophobicity index-based scales that incorporate information about long-range interactions along the protein sequence and contrast them with currently used raw hydrophobic index values. We also compare three leading hydrophobicity indices, i.e., Eisenberg's, Fauchere-Pliska's, and Cid's, using the proposed scales. The analysis is performed using fuzzy cognitive maps that quantify the strength of relation between the hydrophobicity scales/indices and the protein content values. A set of empirical tests that involve generation of fuzzy cognitive map models for a set of 200 low homology proteins have been performed. The results show that the secondary structure content along the protein sequence is characterized by about 2.5 times stronger relation with the two proposed hydrophobicity scales when compared with the currently used raw index values. The new scales exhibit stronger relation irrespective of the applied hydrobhobicity indices. Analysis of different scales shows superiority of the Eisenberg's hydrophobicity index, when used with the new scales. In contrast, the Fauchere-Pliska's index is found to perform better when compared with the two other indices when using raw hydrophobic index values that disregard the long-range interactions.     

Solvent structure in crystals of trypsin determined by X-ray and neutron diffraction.

The solvent structure in orthorhombic crystals of bovine trypsin has been independently determined by X-ray diffraction to 1.35 A resolution and by neutron diffraction to 2.1 A resolution. A consensus model of the water molecule positions was obtained using oxygen positions identified in the electron density map determined by X-ray diffraction, which were verified by comparison to D2O-H2O difference neutron scattering density. Six of 184 water molecules in the X-ray structure, all with B-factors greater than 50 A2, were found to be spurious after comparison with neutron results. Roughly two-thirds of the water of hydration expected from thermodynamic data for proteins was localized by neutron diffraction; approximately one-half of the water of hydration was located by X-ray diffraction. Polar regions of the protein are well hydrated, and significant D2O-H2O difference density is seen for a small number of water molecules in a second shell of hydration. Hydrogen bond lengths and angles calculated from unconstrained refinement of water positions are distributed about values typically seen in small molecule structures. Solvent models found in seven other bovine trypsin and trypsinogen and rat trypsin structures determined by X-ray diffraction were compared. Internal water molecules are well conserved in all trypsin structures including anionic rat trypsin, which is 65% homologous to bovine trypsin. Of the 22 conserved waters in trypsin, 19 were also found in trypsinogen, suggesting that they are located in regions of the apoprotein that are structurally conserved in the transition to the mature protein. Seven waters were displaced upon activation of trypsinogen. Water structure at crystal contacts is not generally conserved in different crystal forms. Three groups of integral structural water molecules are highly conserved in all solvent structures, including a spline of water molecules inserted between two beta-strands, which may resemble an intermediate in the formation of beta sheets during the folding of a protein.