■ Abstract Comparative modeling predicts the three-dimensional structure of a given protein sequence (target) based primarily on its alignment to one or more pro- teins of known structure (templates). The prediction process consists of fold assign- ment, target-template alignment, model building, and model evaluation. The number of protein sequences that can be modeled and the accuracy of the predictions are in- creasing steadily because of the growth in the number of known protein structures and because of the improvements in the modeling software. Further advances are nec- essary in recognizing weak sequence-structure similarities, aligning sequences with structures, modeling of rigid body shifts, distortions, loops and side chains, as well as detecting errors in a model. Despite these problems, it is currently possible to model with useful accuracy significant parts of approximately one third of all known protein sequences. The use of individual comparative models in biology is already rewarding and increasingly widespread. A major new challenge for comparative modeling is the integration of it with the torrents of data from genome sequencing projects as well as from functional and structural genomics. In particular, there is a need to develop an automated, rapid, robust, sensitive, and accurate comparative modeling pipeline applicable to whole genomes. Such large-scale modeling is likely to encourage new kinds of applications for the many resulting models, based on their large number and completeness at the level of the family, organism, or functional network.

Comparative protein structure modeling of genes and genomes

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 A RMSD error for the mainchain N, C(alpha), C, and O atoms; the average accuracies were 0.59 +/- 0.05, 1.16 +/- 0.10, and 2.61 +/- 0.16 A, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 A, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.

/pdf/modeling-of-loops-in-protein-structures-39225473o2.pdf

Modeling of loops in protein structures.

A prerequisite to understand cell functioning on the system level is the knowledge of three-dimensional protein structures that mediate biochemical interactions. The explosion in the number of available gene sequences set the stage for the next step in genome scale projects, to obtain three dimensional structures for each protein. To achieve this ambitious goal, the costly and slow structure determination experiments are boosted with theoretical approaches. The current state and recent advances in structure modelling approaches are reviewed here, with special emphasis on comparative structure modelling techniques.

Comparative Protein Structure Modelling

Interleukin-5 (IL-5) is a lineage-specific cytokine for eosinophilpoiesis and plays an important part in diseases associated with increased eosinophils, such as asthma. Human IL-5 is a disulphide-linked homodimer with 115 amino-acid residues in each chain. The crystal structure at 2.4 A resolution reveals a novel two-domain structure, with each domain showing a striking similarity to the cytokine fold found in granulocyte macrophage and macrophage colony-stimulating factors, IL-2 (ref. 5), IL-4 (ref. 6), and human and porcine growth hormones. IL-5 is unique in that each domain requires the participation of two chains. The IL-5 structure consists of two left-handed bundles of four helices laid end to end and two short beta-sheets on opposite sides of the molecule. Surprisingly, the C-terminal strand and helix of one chain complete a bundle of four helices and a beta-sheet with the N-terminal three helices and one strand of the other chain. The structure of IL-5 provides a molecular basis for the design of antagonists and agonists that would delineate receptor recognition determinants critical in signal transduction. This structure determination extends the family of the cytokine bundle of four helices and emphasizes its fundamental significance and versatility in recognizing its receptor.

A novel dimer configuration revealed by the crystal structure at 2.4 Å resolution of human interleukin-5

This paper discusses the mathematical formulation of and solution attempts for the so-called protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein given its sequence of amino acids. The dynamic aspect asks about the possible pathways to folding and unfolding, including the stability of the folded protein. 
From a mathematical point of view, there are several main sides to the static problem: 
-- the selection of an appropriate potential energy function;
-- the parameter identification by fitting to experimental data; and
-- the global optimization of the potential.
The dynamic problem entails, in addition, the solution of (because of multiple time scales very stiff) ordinary or stochastic differential equations (molecular dynamics simulation) or (in case of constrained molecular dynamics) of differential-algebraic equations. A theme connecting the static and dynamic aspect is the determination and formation of secondary structure motifs.
The present paper gives a self-contained introduction to the necessary background from physics and chemistry and surveys some of the literature. It also discusses the various mathematical problems arising, some deficiencies of the current models and algorithms, and possible (past and future) attacks to arrive at solutions to the protein-folding problem.

Molecular Modeling of Proteins and Mathematical Prediction of Protein Structure

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

A procedure that finds the most probable conformational states of a protein chain is described. Single-residue conformations are represented in terms of four conformational states, α, ϵ, α*, and ϵ*. The conformation of the entire chain is represented by a sequence of single-residue conformational states; the distinct conformations in this representation are called “chain-states.” The first article in this series described a procedure that computes tripeptide conformational probabilities from the amino acid sequence using pattern recognition techniques. The procedure described in this article uses the tripeptide probabilities to estimate the probabilities of the chain-states. The chain-state probability estimator is a product of conditional and marginal probabilities (obtained from the tripeptide probabilities), with a penalty factor to eliminate conformations containing α-helices and ϵ-strands of excessive length. The probability estimator considers short-range conformational information, medium-range sequence information and some simple long-range information (through the restrictions on helix and strand lengths). Energy minimization calculations can be carried out in the region of conformational space corresponding to a particular chain-state. By selecting the most probable chain-states, the search can be focused on the most probable, or “important,” regions of the conformational space. These energy calculations are described in the third article of the series. The complete procedure described by the three articles is called PRISM, for pattern recognition-based importance sampling minimization.

Pattern recognition in the prediction of protein structure. II. Chain conformation from a probability-directed search 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, ϵ, α*, and ϵ*. Each state corresponds to a rectangular region in the ϕ, 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 ϕ, ψ map. All values of ϕ and ψ are allowed, but the less-probable values are sampled less often. To achieve this, the random values of ϕ 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 ϵ states, for glycine residues in the α, ϵ, α*, and ϵ* 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. III. An importance-sampling minimization procedure

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

Pattern recognition in the prediction of protein structure. II. Chain conformation from a probability-directed search procedure

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