Pattern recognition in the prediction of protein structure. III. An importance-sampling minimization procedure

A procedure that generates random conformations of a protein chain, and then applies energy minimization to find the structure of lowest energy, is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. Each state corresponds to a rectangular region in the ?, ψ map. The conformation of an entire chain is then represented by a sequence of single-residue conformational states. The distinct “chain-states” in this representation correspond to multidimensional rectangular regions in the conformational space of the whole protein. A set of highly-probable chain-states can be predicted from the amino acid sequence using the pattern recognition procedure developed in the first two articles of this series. The importance-sampling minimization procedure of the present article is then used to explore the regions of conformational space corresponding to each of these chain-states. The importance-sampling procedure generates a number of random conformations within a particular multidimensional rectangular region, sampling most densely from the most probable, or “important,” sections of the ?, ψ map. All values of ? and ψ are allowed, but the less-probable values are sampled less often. To achieve this, the random values of ? and Φ are generated from bivariate gaussian distributions that are determined from known X-ray structures. Separate gaussian distributions are used for proline residues in the α and ? states, for glycine residues in the α, ?, α*, and ?* states, and for ordinary residues involved in 29 different tripeptide conformations. Energy minimization is then applied to the randomly-generated structures to optimize interactions and to improve packing. The final energy values are used to select the best structures. The importance-sampling minimization procedure is tested on the avian pancreatic polypeptide, using chain-states predicted from the amino acid sequence. The conformation having the lowest energy is very similar to the X-ray conformation.     

Pattern recognition in the prediction of protein structure. I. Tripeptide conformational probabilities calculated from the amino acid sequence

A procedure that uses pattern recognition techniques to compute tripeptide conformational probabilities is described. The procedure differs in several respects from the many “secondary structure” prediction algorithms that have been published over the last 20 years. First, the procedure classifies tripeptides into 64 different conformational types, rather than just α, β and coil, as is commonly done. Thus, the procedure can attempt to predict regions of irregular structure. Second, the procedure uses the methods of pattern recognition, which are powerful but conceptually simple. In this approach, amino acid properties are used to map peptide sequences into a multivariate property space. Particular tripeptide conformations tend to map to particular regions of the property space. These regions are represented by multivariate gaussian distributions, where the parameters of the distributions are determined from tripeptides in the protein X-ray data bank. Finally, rather than making simple predictions, the procedure computes probabilities. Tripeptide conformational probabilities are calculated in the multivariate property space using the gaussian distributions. In a prediction, the procedure might find that a particular tripeptide in a protein has a 36% chance of being in the ααα conformation, a 17% chance of being αα?, a 14% chance of being ααα*, etc. The α-helical conformation is thus the most probable, but, in predicting the structure of the protein, a search algorithm should also consider some of the other possibilities. The values of the probability provide a rational basis for selecting from among the possible conformations. The second article of this series describes a procedure that uses the probabilities to direct a search through the conformational space of a protein. The third article of the series describes a procedure that generates actual three-dimensional structures, and minimizes their energies. The three articles together describe a complete procedure, termed “pattern recognition-based importance-sampling minimization” (PRISM), for predicting protein structure from amino acid sequence.     

Pattern recognition strategies for molecular surfaces. II. Surface complementarity

Fuzzy logic based algorithms for the quantitative treatment of complementarity of molecular surfaces are presented. Therein, the overlapping surface patches defined in article I1 of this series are used. The identification of complementary surface patches can be considered as a first step for the solution of molecular docking problems. Standard technologies can then be used for further optimization of the resulting complex structures. The algorithms are applied to 33 biomolecular complexes. After the optimization with a downhill simplex method, for all these complexes one structure was found, which is in very good agreement with the experimental results.     

Pattern recognition of the multiplet structure of NMR spectra

A new method of analysis of high-resolution NMR spectra was suggested, and an algorithm and the PAREMUS program package for assignment of patterns of the spectral components based on pattern recognition theory were developed. High effectiveness of the method has been exemplified by determination of the values and relative signs of the interring¹H−¹H and¹³C−¹H spin-spin coupling constants in 1,2,3-trichloronaphthalene. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 3, pp. 444–451, March, 1997.     

Protein structure prediction and biomolecular recognition: from protein sequence to peptidomimetic design with the human beta3 integrin

Computational tools can bridge the gap between sequence and protein 3D structure based on the notion that information is to be retrieved from the databases and that knowledge-based methods can help in approaching a solution of the protein-folding problem. To this aim our group has implemented neural network-based predictors capable of performing with some success in different tasks, including predictions of the secondary structure of globular and membrane proteins, the topology of membrane proteins and porins and stable alpha-helical segments suited for protein design. Moreover we have developed methods for predicting contact maps in proteins and the probability of finding a cysteine in a disulfide bridge, tools which can contribute to the goal of predicting the 3D structure starting from the sequence (the so called ab initio prediction). All our predictors take advantage of evolution information derived from the structural alignments of homologous (evolutionary related) proteins and taken from the sequence and structure databases. When it is necessary to build models for proteins of unknown spatial structure, which have very little homology with other proteins of known structure, non-standard techniques need to be developed and the tools for protein structure predictions may help in protein modeling. The results of a recent simulation performed in our lab highlights the role of high performing computing technology and of tools of computational biology in protein modeling and peptidomimetic design.     

Pattern recognition strategies for molecular surfaces: III. Binding site prediction with a neural network

An algorithm for the identification of possible binding sites of biomolecules, which are represented as regions of the molecular surface, is introduced. The algorithm is based on the segmentation of the molecular surface into overlapping patches as described in the first article of this series.1 The properties of these patches (calculated on the basis of physical and chemical properties) are used for the analysis of the molecular surfaces of 7821 proteins and protein complexes. Special attention is drawn to known protein binding sites. A binding site identification algorithm is realized on the basis of the calculated data using a neural network strategy. The neural network is able to classify surface patches as protein-protein, protein-DNA, protein-ligand, or nonbinding sites. To show the capability of the algorithm, results of the surface analysis and the predictions are presented and discussed with representative examples.     

Statistical mechanical treatment of protein conformation. III. Prediction of protein conformation based on a three-state model.

The method proposed for the evaluation of statistical weights in paper I, and the three-state model [alpha-helical (alpha), extended (epsilon), and other (c) states] formulated in paper II, have been used to develop a procedure to predict the backbone conformations of proteins, based on the concept of the predominant role played by shortrange interactions in determining protein conformation. Conformational probability profiles, in which the probabilities of formation of three consecutive alpha-helical conformations (triad) and of four consecutive extended conformations (tetrad) have been defined relative to their average values over the whole molecule, are calculated for 19 proteins, of which 16 had been used in paper I to evaluate the set of statistical weights of the 20 naturally occurring amino acids. By comparing these conformational probability profiles to experimental x-ray observations, the following results have been obtained: 80% of the alpha-helical regions and 72% of the extended conformational regions have been predicted correctly for the 19 proteins. The percentage of residues predicted correctly is in the range of 53 to 90% for the alpha-helical conformation and in the range of 63 to 88% for the extended conformation for the 19 proteins in the two-state models [alpha-helical (alpha) and other (c) states, and extended (epsilon) and other (c) states]. In the three-state model, the percentage of residues predicted correctly is in the range of 47% to 77 for 19 proteins. These results suggest that the assumption of the dominance of short-range interactions, on which the predictive scheme is based, is a reasonable one. The present predictive method is compared with that of other authors.     

Effects of protein conformation in docking: improved pose prediction through protein pocket adaptation

Computational methods for docking ligands have been shown to be remarkably dependent on precise protein conformation, where acceptable results in pose prediction have been generally possible only in the artificial case of re-docking a ligand into a protein binding site whose conformation was determined in the presence of the same ligand (the “cognate” docking problem). In such cases, on well curated protein/ligand complexes, accurate dockings can be returned as top-scoring over 75% of the time using tools such as Surflex-Dock. A critical application of docking in modeling for lead optimization requires accurate pose prediction for novel ligands, ranging from simple synthetic analogs to very different molecular scaffolds. Typical results for widely used programs in the “cross-docking case” (making use of a single fixed protein conformation) have rates closer to 20% success. By making use of protein conformations from multiple complexes, Surflex-Dock yields an average success rate of 61% across eight pharmaceutically relevant targets. Following docking, protein pocket adaptation and rescoring identifies single pose families that are correct an average of 67% of the time. Consideration of the best of two pose families (from alternate scoring regimes) yields a 75% mean success rate.     

Heterogeneity in the conformation of different protein fractions from the human erythrocyte membrane.

We have isolated 5 families of proteins from human red blood cell membranes and characterized their secondary structure by ultraviolet circular dichroism measurements. The protein families were prepared by selective solubilization from ghosts under nondenaturing conditions. We find that the intact ghost has a mean alpha-helix fraction of 0.37, whereas a low-ionic-strength extract (bands 1, 2, 5, "spectrin") has a substantially higher helix fraction, 0.55. Further extraction of the ghosts with para-chloromercuribenzoate yields bands 2.1, 4.1, 4.2, and 6; their helix content is only 0.17. Finally, the major intrinsic protein, band 3, was solubilized by a non-ionic detergent. Its helix fraction is 0.38.     

The molecular structure and conformation of acetamides in the vapour phase: Part II. 2-Iodoacetamide

2-Iodoacetamide has been studied by electron diffraction, utilizing a new nozzle construction. A skew conformation with a dihedral angle of 126.3(1.1)° from syn (C-I bond eclipsing the C-N bond), and a gauche conformation with a dihedral angle of 42.3(1.6) both fit the experimental data almost equally well. However, comparison with the X-ray structure and the results for the two models indicate a slight preference for the skew form.The most important structural parameters are: r_g(CO) = 1.222(3)Å, r_g(C-N) = 1.370(3)Å, r_g(C-C) = 1.515(4) Å, r_g(C-I) = 2.160(4) Å, ∠_αOCC = 120.0(6)°, ∠_αNCC = 116.9(4)° and ∠_αCCl = 117.3(4)°. Parenthesized values are one standard deviation.     

All-atom structure prediction and folding simulations of a stable protein

We present results from all-atom, fully unrestrained ab initio folding simulations for a stable protein with nontrivial secondary structure elements and a hydrophobic core. The construct, "trpcage", is a 20-residue sequence optimized by the Andersen group at University of Washington and is currently the smallest protein that displays two-state folding properties. Compared over the well-defined regions of the experimental structure, our prediction has a remarkably low 0.97 A Calpha root-mean-square-deviation (rmsd) and 1.4 A for all heavy atoms. The simulated structure family displays additional features that are suggested by experimental data, yet are not evident in the family of NMR-derived structures.     

Trends in template/fragment-free protein structure prediction

Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward.     

Incorporation of FT-IR spectral data in a computer-assisted prediction of globular protein structure

Currently, much effort is being directed to the determination of the three-dimensional structure of proteins. Two classes of research are of interest; spectrometric techniques which include Fourier transform infrared (FT-IR) spectrometry, and non-spectrometric prediction schemes. The spectra obtained using FT-IR spectrometry, are analyzed to determine the percentages of alpha-helices, beta-pleated sheets, and non-structured coils in a protein. Unfortunately, FT-IR, as well as other spectrometric techniques, cannot be used to determine the exact secondary structure of a protein reliably. Non-spectrometric prediction methods yield information on the exact secondary structure, but are not always accurate. Most prediction methods relate the primary amino acid sequence to the secondary structure of a protein, allowing sequential secondary structure information for the protein examined to be obtained. The goal of this research is to incorporate FT-IR with a prediction method, resulting in an improvement in the accuracy of the prediction.     

Statistical mechanical treatment of protein conformation. II. A three-state model for specific-sequence copolymers of amino acids.

A one-dimensional three-state Ising model [involving alpha-helical (alpha), extended (epsilon), and coil (or other) (c) states] for specific-sequence copolymers of amino acids ahs been formulated in order to treat the conformational states of proteins. This model involves four parameters (wh,iota, vh, iota, v episilon, iota, and uc, iota), and requires a 4 X 4 matrix for generating statistical weights. Some problems in applying this model to a specific-sequence copolymer of amino acids are discussed. A nearest-neighbor approximation for treating this three-state model is also formulated; it requires a 3 X 3 matrix, in which the same four parameters appear, but (as with the 4 X 4 matrix treatment) only three parameters (wh, uh, and v epsilon) are required if relative statistical weights are used. The relationship between the present three-state model (3 X 3 matrix treatment) and models of the helix--coil transition is discussed. Then, the three-state model (3 X 3 matrix treatment) is incorporated into an earlier (Tanaka--Scheraga) model of the helix-coil transition, in which asymmetric nucleation of helical sequences is taken into account. A method for calculating molecular averages and conformational-sequence probabilities, P(iota/eta/(rho)), i.e., the probability of finding a sequence of eta residues in a specific conformational state (rho), starting at the iotath position of the chain, is described. Two alternative methods for calculating P(iota/eta/(rho)), that can be applied to a model involving any number of states, are proposed and presented; one is the direct matrix-multiplication method, and the other uses a first-order a priori probability and a conditional probability. In this paper, these calculations are performed with the nearest-neighbor model, and without the feature of asymmetric nucleation. Finally, it is indicated how the three-state model and the methods for computing P(iota/eta/(rho)) can be applied to predict protein conformation.     

Guided macro-mutation in a graded energy based genetic algorithm for protein structure prediction

Protein structure prediction is considered as one of the most challenging and computationally intractable combinatorial problem. Thus, the efficient modeling of convoluted search space, the clever use of energy functions, and more importantly, the use of effective sampling algorithms become crucial to address this problem. For protein structure modeling, an off-lattice model provides limited scopes to exercise and evaluate the algorithmic developments due to its astronomically large set of data-points. In contrast, an on-lattice model widens the scopes and permits studying the relatively larger proteins because of its finite set of data-points. In this work, we took the full advantage of an on-lattice model by using a face-centered-cube lattice that has the highest packing density with the maximum degree of freedom. We proposed a graded energy—strategically mixes the Miyazawa–Jernigan (MJ) energy with the hydrophobic-polar (HP) energy—based genetic algorithm (GA) for conformational search. In our application, we introduced a 2 × 2 HP energy guided macro-mutation operator within the GA to explore the best possible local changes exhaustively. Conversely, the 20 × 20 MJ energy model—the ultimate objective function of our GA that needs to be minimized—considers the impacts amongst the 20 different amino acids and allow searching the globally acceptable conformations. On a set of benchmark proteins, our proposed approach outperformed state-of-the-art approaches in terms of the free energy levels and the root-mean-square deviations.     

The structure of the flavonoids from Rhodiola algida. II

Summary New flavonoid glycosides have been obtained from the roots ofRhodiola algida: rhodalgin (I), composition C₂₀H₁₈O₁₁, mp 239–240°C; acetylrhodalgin (II) C₂₂H₂₀O₁₂, mp 223–224°C; diacetylrhodalgin (III), C₂₄H₂₂O₁₃, mp 208–209°C; and triacetylrhodalgin (IV), C₂₆H₂₄O₁₄, mp 230–231°C.It has been established that they have the following structures: (I), 3,4,5,7,8-pentahydroxyflavone 8-O--L-arabinopyranoside; (II), 3,4,5,7,8-pentahydroxyflavone 8-O-(3-O-acetyl--L-arabinopyranoside; (III), 3,4,5,7,8-pentahydroxyflavone 8-O-(2,3-di-O-acetyl)--D-xylopyranoside; and (IV), 3,4,5,7,8-pentahydroxyflavone 8-O-(2,34-tri-O-acetyl)--D-xylopyranoside. The -L-arabinopyranose and -D-xylopyranose are present in these compounds in the C1 conformations.In the performance of this investigation, the authors consulted O. S. Chizhov, and M. B. Zoltarev (N. D. Zelinskii Institute of Organic Chemistry of the Academy of Sciences of the USSR) and V. I. Sheichenko (All-Union Institute of Medicinal plants).All-Union Scientific-Research Institute of Medicinal Plants. Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 712–720. November–December, 1975.     

Folding funnels: the key to robust protein structure prediction

Natural proteins fold because their free energy landscapes are funneled to their native states. The degree to which a model energy function for protein structure prediction can avoid the multiple minima problem and reliably yield at least low-resolution predictions is also dependent on the topography of the energy landscape. We show that the degree of funneling can be quantitatively expressed in terms of a few averaged properties of the landscape. This allows us to optimize simplified energy functions for protein structure prediction even in the absence of homology information. Here we outline the optimization procedure in the context of associative memory energy functions originally introduced for tertiary structure recognition and demonstrate that even partially funneled landscapes lead to qualitatively correct, low-resolution predictions.