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Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. The proposed method takes into account the circular nature of the angular data using trigonometric spline which is more efficient compared to existing methods. This collective density estimation approach is widely applicable when there is a need to estimate multiple density functions from different populations with common features. Moreover, the coefficients of adaptive basis expansion for the fitted densities provide a low-dimensional representation that is useful for visualization, clustering, and classification of the densities. The proposed method provides a novel and unique perspective to two important and challenging problems in protein structure research: structure-based protein classification and angular-sampling-based protein loop structure prediction. Keywords: Bivariate splines, Log-spline density estimation, Protein structure, Ramachandran distribution, Roughness penalty, Trigonometric B-spline, Protein classification, SCOP

Accurately modeling protein loops is an important step to predict three-dimensional structures as well as to understand functions of many proteins. Because of their high flexibility, modeling the three-dimensional structures of loops is difficult and is usually treated as a “mini protein folding problem” under geometric constraints. In the past decade, there has been remarkable progress in template-free loop structure modeling due to advances of computational methods as well as stably increasing number of known structures available in PDB. This mini review provides an overview on the recent computational approaches for loop structure modeling. In particular, we focus on the approaches of sampling loop conformation space, which is a critical step to obtain high resolution models in template-free methods. We review the potential energy functions for loop modeling, loop buildup mechanisms to satisfy geometric constraints, and loop conformation sampling algorithms. The recent loop modeling results are also summarized.

The most significant advance in modeling GPCR active states has been the β2-adrenergic receptor–Gs complex as this essentially transforms active-state modeling into homology modeling. Various different molecular dynamics-based approaches for modeling active states are presented, and a number of key applications discussed. These simulations have given insights into the activation pathway, conformational changes, dimerization, hydration, the ionic lock, ligand binding, protonation, and sodium binding. Crystallography and simulations have shown that the presence of agonist alone is unlikely to be sufficient to form the active state and that restraints applied to the G protein-binding region are required. The role of various microswitches in activation is discussed, including the controversial rotamer toggle switch. The importance of explicitly simulating experimental molecular probes to understand activation is highlighted, along with the need to ensure that such molecules are well parameterized. Approaches to loop modeling are discussed. We argue that the role of successful virtual screening against active models should not be overestimated as the main conformational changes on activation occur in the intracellular region.

This review will focus on the construction, refinement, and validation of G-protein-coupled receptor (GPCR) structural models for the purpose of structure-based virtual screening (SBVS) and ligand design. The review will present a comparative analysis of GPCR crystal structures and their implication on GPCR (homology) modeling. The challenges associated with steps along the modeling workflow will be discussed: the use of experimental anchors to steer the modeling procedure, amino acid sequence alignment and template selection, receptor structure refinement, loop modeling, ligand-binding mode prediction, and virtual screening for novel ligands. An overview of several successful structure-based ligand discovery and design studies shows that receptor models, despite structural inaccuracies, can be efficiently used to find novel ligands for GPCRs. Moreover, the recently solved GPCR crystal structures have further increased the opportunities in structure-based ligand discovery for this pharmaceutically important protein family.

The observation of a limited secondary-structural alphabet in native proteins, with significant sequence preferences, has profoundly influenced the fields of protein design and structure prediction (Simons et al., 1997; Verschueren et al., 2011). In the era of structural genomics, as the size of the structural dataset continues to grow rapidly, it is becoming possible to extend this analysis to tertiary structural motifs and their sequences. For a hypothetical tertiary motif, the rate of its utilization in natural proteins may be used to assess its designability - the ease with which the motif can be realized with natural amino acids. This requires a structural similarity search methodology, which rather than looking for global topological agreement (more appropriate for functional categorization of proteins or domains), identifies detailed geometric matches. In this chapter we introduce such a method, called MaDCaT, and demonstrate its use by assessing the designability landscapes of two tertiary structural motifs. We also show that such analysis can establish structure/sequence links by providing the sequence constraints necessary to encode designable motifs. As a logical extension of their secondary-structure counterparts, statistics of tertiary structural preferences will likely prove extremely useful in de novo protein design and structure prediction.

The prediction of protein secondary structures is an intermediate goal for determining its tertiary structure. The analysis on the performance of several secondary structure prediction methods in different structural classes shows that all the methods predict the secondary structure of all-α proteins more accurately than other classes. The successful prediction of the structural class and schemes developed for each class may help to improve the accuracy levels of secondary structure predictive schemes in globular proteins. Deciphering the native conformation of a protein from its amino acid sequence, termed, as “protein folding problem,” is one of the long-standing challenges in molecular and computational biology. Several methods have been proposed to predict the structural class, secondary structure content, location of secondary structures, and modeling tertiary structures. These methods have also been proposed for predicting the secondary structure content of a protein based on amino acid composition and residue-pair composition. The concept of “amino acid composition” plays a major role in predicting the structural class of globular proteins, and it is defined as the statistical preference of each of the amino acid residues occurring in protein molecules. Further these methods have been proposed to predict the secondary structures, and the success rate is limited with their own advantages and disadvantages.

Publisher Summary This chapter describes the extraction of structural information from protein sequence. The deduced sequences of proteins provide invaluable insights into the functions of those proteins and the evolution of the organisms producing those proteins. Structures of proteins in solution determined by nuclear magnetic resonance (NMR) provide invaluable information about the dynamics and mobilities of proteins. Usually, those regions assigned high mobility by NMR accord with those having high B values in crystal structures. The refinement of protein structures by energy minimization involves many empirical formulas that only approximate the exact functions. Fold recognition relies heavily on the more sophisticated methods of sequence comparison. The assessments of success in CASP4 considered 52 target domains from the 40 target proteins in four subcategories. All loops are considered for replacement in homolog and fold modeling using database fragment searches. It is found that CHARMM is used to adjust the conformations of loops to match ends of helices and strands.

Publisher Summary Each protein is a sequence of amino acids bound into linear chains that adopts a specific folded 3D shape. Each shape provides valuable clues to the protein's function. The chapter reviews the basic structure of proteins and discusses how evolutionary algorithms (EAs) have been used to solve three protein-folding subproblems: minimalist models, side-chain packing, and docking. Ab initio methods try to predict the fold without using structure information from any other protein for comparison. The greatest success in protein folding studies is achieved when use can be made of the known structure of a homologous protein (i.e., one similar in structure) via common evolutionary descent. As the number of known structures increases, the probability of resolving the conformation of other unsolved proteins will likewise increase. The three major aspects to homology-based modeling are amino acid sequence alignment, generation of loop conformations as needed, and predicting the conformations of the side chains. The side-chain packing problem (SCPP) deals only with the last part of this modeling procedure. Docking problem solutions predict how two organic molecules will energetically and physically bind together. The chapter presents evidence that EAs are both effective and computationally efficient search strategies that show great promise for solving a wide variety of bioinformatics problems.

Publisher Summary Considerable amount of structural data on 3D protein structure has established structure comparison as an essential technique for understanding protein sequence, structure, function, and evolution. The goal is to predict 3D protein structures from amino acid sequence information alone. A major step toward this goal is to determine a method for discovering common protein structures in databases such as the Protein Data Bank, so that a better understanding of protein structure and function can be pieced together. Structure comparison algorithms are used to identify a set of residue equivalencies between two proteins based on their 3D coordinates. This set of equivalencies is called a structure alignment, and it allows the superposition of one protein structure onto the other after rigid rotation and/or translation. Structure alignments can indicate if two proteins share the same fold , or structural unit. Structure alignment is also used as the gold standard for evaluating protein structure prediction methods. This chapter focuses on the application of evolutionary computation to protein structure similarity problems and provides an example of a hybridization of evolutionary algorithms and other optimization techniques. The combination of these approaches offers a new and exciting method for protein structure comparison with increased specificity and sensitivity compared with previous methods.

Publisher Summary In this chapter, some methods currently employed in the prediction of tertiary structure from the protein sequence are presented. There are many different methods to attack the problem of predicting protein structure. If the protein is a member of a family of closely related proteins, the structure can be postulated through homology analysis. If this is not the case, a sequential approach can be envisioned in which the secondary elements are predicted from the primary sequence and then the different topological orientations of these elements are examined and judged using some energy-function description of the protein. Other methods are based on the observation that protein structures are tightly packed with almost no vacant space in the interior or core of the protein. Such a tight packing of the amino acids then suggests that the arrangements of the polypeptide chain can be restricted to the points of a lattice, greatly reducing the number of possible orientations. These methods do not differentiate between secondary and tertiary structure nor depend on previously determined protein structures.

Publisher Summary In the absence of high-resolution structural data, it is possible to construct a three-dimensional model of a protein if a related protein of known structure is used as a template. This homology-based modeling is predicated on the assumption that the overall folds of functionally related protein regions are more highly conserved than the amino acid sequences. This chapter describes the methods used to generate homology-based models and demonstrates the way electrophysiologic data can be used to refine the models and test the modeling predictions. The development of a model is described in the chapter, starting with the test protein sequence. It discusses the way the best reference protein can be selected, the way insertions and deletions can be modeled in the sequence, and the way the ligand can be generated in the binding domain. It also discusses the energy minimization procedures including refinement of the initial models and illustrates the modeling process using the cyclic nucleotide binding domain of the retina cyclic nucleotide-gated channel (CNGC) β subunit. Electrophysiologic data are used to reline molecular models and generate testable hypotheses about ligand recognition.

Publisher Summary Currently, the studies of linkers of regular secondary structures seeks an understanding of the non-regular regions through a systematic classification scheme. The method, as any other earlier method, depends strongly upon an effective secondary structural assignment method. For this purpose, various secondary structural definitions, including DSSP, SSTRUC, and STRIDE have been studied on a standard data set. STRIDE that has slightly improved assignment over other methods have been chosen. Such analyses of linker regions should certainly pave the way for the improvement of present loop modeling procedures. The methods adapted in the chapter of clustering based on a-carbon distances and in turn backbone and side chain torsions has demonstrated the existence of possible structural motifs within well defined linker regions. The method is not quite exhaustive to account for data outside the clusters and its limitations arise because of non-standard way of defining limits of the clusters. Nevertheless, the method does seem to bring out the structural differences among various linkers. The analyses presented on mainly -α proteins from the CATH database has resulted in two major clusters of three residue linkers among helices (H–L3–H) and few of the helical proteins have same angle of orientation of helices within a cluster.

Publisher Summary The comparison of protein sequences and structures is a critical first step for a wide range of tasks that include, for example, the identification of related proteins––finding common protein folds during data bank searches (fold recognition), phylogenetic reconstruction––based on data from aligned macromolecular sequences, and protein modeling. In protein modeling, an estimate of the atomic coordinates for a protein is based on the accurate alignment of its sequence to one or more tertiary structures from related proteins. If a protein of known sequence, but unknown structure, can be matched to one of the common folds, it is possible to model the three-dimensional structure of the protein and often learn more about its function. This chapter describes the environment-specific amino acid substitutions. Another source of information that can be applied to scoring matches between a structure and a sequence is reflected in the contacts that occur among side chains within the protein structure and how the conservation of these contacts varies among related proteins.

Publisher Summary This chapter discusses the protein structure prediction and neural networks. To define the three dimensional structure of a protein backbone, it suffices to list the phi and psi angles. This makes the prediction of the conformation relatively well defined task: find a mapping from the space of amino acid sequences to a space of dihedral angle sequences, which will correctly map protein sequences onto their three dimensional structures. An empirical way of defining the mapping is to look at the proteins with a known sequence and a known structure and try to extract the information required for the mapping from them. This task can be approached from different viewpoints, using statistical methods, pattern matching, or artificial neural network techniques. Neural network techniques have been successfully used in the prediction of the secondary structure of the globular proteins. Although secondary structures are normally defined by the presence or absence of certain hydrogen bonds among amino acid residues, they could also be described by the dihedral angles of the backbone. When the protein chain adopts a certain secondary structure, the angles are forced to corresponding canonical values. Thus, predicting the secondary structure is equivalent to predicting the classification of the backbone dihedral angles into classes corresponding to helix, sheet, coil, and bend-structures.

Publisher Summary The cloning and sequencing of the G-protein coupled receptors (GPCRs) has revealed a superfamily of GPCR proteins that activate various guanine-nucleotide binding (G) proteins. Throughout this chapter, a distinction is made among the GPCRs on the basis of the chemical nature of their ligands. Bacteriorhodopsin (BR), the major light-sensitive protein of the purple membrane of Halobacterium halobium , has been the first membrane bound protein found to be organized into seven transmembrane spanning domains. Although BR is not a GPCR, the sensory receptors require an intermediary G-protein called transducin to activate the second messenger system. To identify the hydrophobic segments in the GPCR primary sequences, various theoretical methods, such as hydrophobicity profiles, hydrophobic moments, helix amphiphilicity, and secondary structure prediction can be applied. The N-terminal segment length varies to extreme across the GPCR families. Protein chemistry experiments have identified various N-glycosylation sites. The intracellular loops and C-terminal fragments have been shown to affect signal transduction through coupling to the G-protein. Throughout all GPCRs, they are characterized by a heavy content of basic amino acid residues. A number of recently proposed structural models for the non-peptide GPCRs suggest schematic 2-dimensional (2D) representations, 3D models limited to selected helices or highly refined 3D models that sometimes incorporate the connecting loops. Very few modeling reports have been expanded to include the challenge of loop modeling. The internal proline residues impose a curving effect in the helices, molding the transmembrane domains in an overall oblong shape. It has long been speculated that a receptor conformational change, triggered by agonist binding, would be responsible for initiating the resulting transduction mechanism. Variations on the familiar non-peptide GPCR structural theme have been reported in very few peptide receptors.

Publisher Summary This chapter discusses the methodology for the modeling of protein structures from one or more homologous known structures. To perform comparative modeling, knowledge of at least one experimental structure for a member of the homologous family is essential. The amino acid sequence is needed for those proteins whose structure is known. The more structures and amino acid sequences that are available, the more accurate the molecular modeling of the structure of a new protein of interest is likely to be. The amino acid sequence of the new protein to be modeled is also essential. When more than one experimental structure is known, the first step is to superimpose these structures in three dimensions. The purpose is to overlap the molecules so that the common features of the structure, called “structurally conserved regions” (SCRs), coincide. Once the structures are properly superimposed, it is clear that the overlapped structures can be divided into SCRs, where all the known structures have the same conformation, and structurally variable regions (SVRs), where each of the molecules has a different conformation. The next step is to align the amino acid sequences for the known structures.

Publisher Summary The prediction of protein secondary structure is a well-defined digital and linear problem. It is digital because the conformational state that each amino acid residue can adopt is assumed to be either a helix β strand or a coil so that correctly predicted residues are easily countable. It is linear because prediction is carried out to locate secondary-structure elements along the primary structure. This chapter presents the correspondence between two one-dimensional digital series of primary and secondary structures. Secondary-structure prediction is considered as one of the major obstacles in the process of elucidating protein structure. The reason for this difficulty lies in the fact that in protein folding, secondary structures are formed in a “context-dependent” manner. Thus, the prediction methods based on the local-sequence information are dominant. Prediction methods published recently, some of which are novel and others improvements in existing methods, are all of the local-sequence type. One of the new methods is the neural network approach, which is a computer learning algorithm developed for pattern recognition. Another new method is based on homology. In this method, weak and local sequence similarities with proteins of known structure are accumulated, and the majority of the secondary structure at corresponding residue sites is predicted. A different way to use sequence similarity data is to incorporate various sequence data homologous with a target sequence. Proteins belonging to the same evolutionary family share the same 3-D structure, and therefore the same secondary structure as well. Homologous sequence data available from a sequence database improves prediction accuracy.

Publisher Summary This chapter demonstrates the use of alignments obtained from comparison of the protein three-dimensional structures as a standard against which to test an automatic method for the pair wise alignment of protein sequences. Optimal global alignment methods allow the best overall score for the comparison of the two sequences to be obtained including a consideration of gaps. The protein three-dimensional structure determines its biological activity. It is therefore of crucial importance when two or more protein sequences are aligned that those residues defining a common tertiary fold, together with any common catalytic and binding residues, are correctly equivalent. To be useful, a protein sequence alignment method must at least align those residues that are performing equivalent structural roles in the two proteins. The multiple alignments of four or more sequences cannot, in practice, be performed by a rigorous method because even when gaps are not explicitly considered, the number of segment comparisons that must be made is of the order of the product of the sequence lengths. Algorithms for multiple sequence alignment therefore seek to identify an optimum alignment by considering only a small number of the total possible residue or segment comparisons.

Publisher Summary This chapter investigates the anatomy and taxonomy of protein structures. A protein is a polypeptide chain made up of amino acid residues linked together in a definite sequence. Amino acids are “handed,” and naturally occurring proteins contain only L-amino acids. A simple mnemonic for that purpose is the “corncrib.” The sequence of side chains determines all that is unique about a particular protein, including its biological function and its specific three-dimensional structure. The major possible routes to knowledge of three-dimensional protein structure are prediction from the amino acid sequence and analysis of spectroscopic measurements such as circular dichroism, laser Raman spectroscopy, and nuclear magnetic resonance. The analysis and discussion of protein structure is based on the results of three-dimensional X-ray crystallography of globular proteins. The basic elements of protein structures are discussed. The most useful level at which protein structures are to be categorized is the domain, as there are many cases of multiple-domain proteins in which each separate domain resembles other entire smaller proteins. The simplest type of stable protein structure consists of polypeptide backbone wrapped more or less uniformly around the outside of a single hydrophobic core. The outline of the taxonomy is also provided in the chapter.