Small libraries of protein fragments model native protein structures accurately

Construct a variable-length fragment library for de novo protein structure prediction

Although remarkable achievements, such as AlphaFold2, have been made in end-to-end structure prediction, fragment libraries remain essential for de novo protein structure prediction, which can help explore and understand the protein-folding mechanism. In this work, we developed a variable-length fragment library (VFlib). In VFlib, a master structure database was first constructed from the Protein Data Bank through sequence clustering. The hidden Markov model (HMM) profile of each protein in the master structure database was generated by HHsuite, and the secondary structure of each protein was calculated by DSSP. For the query sequence, the HMM-profile was first constructed. Then, variable-length fragments were retrieved from the master structure database through dynamically variable-length profile-profile comparison. A complete method for chopping the query HMM-profile during this process was proposed to obtain fragments with increased diversity. Finally, secondary structure information was used to further screen the retrieved fragments to generate the final fragment library of specific query sequence. The experimental results obtained with a set of 120 nonredundant proteins show that the global precision and coverage of the fragment library generated by VFlib were 55.04% and 94.95% at the RMSD cutoff of 1.5 Å, respectively. Compared with the benchmark method of NNMake, the global precision of our fragment library had increased by 62.89% with equivalent coverage. Furthermore, the fragments generated by VFlib and NNMake were used to predict structure models through fragment assembly. Controlled experimental results demonstrate that the average TM-score of VFlib was 16.00% higher than that of NNMake.

Universal Architectural Concepts Underlying Protein Folding Patterns

What is the architectural “basis set” of the observed universe of protein structures? Using information-theoretic inference, we answer this question with a dictionary of 1,493 substructures—called concepts—typically at a subdomain level, based on an unbiased subset of known protein structures. Each concept represents a topologically conserved assembly of helices and strands that make contact. Any protein structure can be dissected into instances of concepts from this dictionary. We dissected the Protein Data Bank and completely inventoried all the concept instances. This yields many insights, including correlations between concepts and catalytic activities or binding sites, useful for rational drug design; local amino-acid sequence–structure correlations, useful for ab initio structure prediction methods; and information supporting the recognition and exploration of evolutionary relationships, useful for structural studies. An interactive site, Proçodic, at http://lcb.infotech.monash.edu.au/prosodic (click), provides access to and navigation of the entire dictionary of concepts and their usages, and all associated information. This report is part of a continuing programme with the goal of elucidating fundamental principles of protein architecture, in the spirit of the work of Cyrus Chothia.

Deep Learning in Protein Structural Modeling and Design

Deep learning is catalyzing a scientific revolution fueled by big data, accessible toolkits, and powerful computational resources, impacting many fields, including protein structural modeling. Protein structural modeling, such as predicting structure from amino acid sequence and evolutionary information, designing proteins toward desirable functionality, or predicting properties or behavior of a protein, is critical to understand and engineer biological systems at the molecular level. In this review, we summarize the recent advances in applying deep learning techniques to tackle problems in protein structural modeling and design. We dissect the emerging approaches using deep learning techniques for protein structural modeling and discuss advances and challenges that must be addressed. We argue for the central importance of structure, following the "sequence → structure → function" paradigm. This review is directed to help both computational biologists to gain familiarity with the deep learning methods applied in protein modeling, and computer scientists to gain perspective on the biologically meaningful problems that may benefit from deep learning techniques.

Topology-independent and global protein structure alignment through an FFT-based algorithm

MOTIVATION

Protein structure alignment is one of the fundamental problems in computational structure biology. A variety of algorithms have been developed to address this important issue in the past decade. However, due to their heuristic nature, current structure alignment methods may suffer from suboptimal alignment and/or over-fragmentation and thus lead to a biologically wrong alignment in some cases. To overcome these limitations, we have developed an accurate topology-independent and global structure alignment method through an FFT-based exhaustive search algorithm, which is referred to as FTAlign.

RESULTS

Our FTAlign algorithm was extensively tested on six commonly used datasets and compared with seven state-of-the-art structure alignment approaches, TMalign, DeepAlign, Kpax, 3DCOMB, MICAN, SPalignNS and CLICK. It was shown that FTAlign outperformed the other methods in reproducing manually curated alignments and obtained a high success rate of 96.7 and 90.0% on two gold-standard benchmarks, MALIDUP and MALISAM, respectively. Moreover, FTAlign also achieved the overall best performance in terms of biologically meaningful structure overlap (SO) and TMscore on both the sequential alignment test sets including MALIDUP, MALISAM and 64 difficult cases from HOMSTRAD, and the non-sequential sets including MALIDUP-NS, MALISAM-NS, 199 topology-different cases, where FTAlign especially showed more advantage for non-sequential alignment. Despite its global search feature, FTAlign is also computationally efficient and can normally complete a pairwise alignment within one second.

AVAILABILITY AND IMPLEMENTATION

http://huanglab.phys.hust.edu.cn/ftalign/.

Biophysical prediction of protein-peptide interactions and signaling networks using machine learning

In mammalian cells, much of signal transduction is mediated by weak protein-protein interactions between globular peptide-binding domains (PBDs) and unstructured peptidic motifs in partner proteins. The number and diversity of these PBDs (over 1,800 are known), low binding affinities, and sensitivity of binding properties to minor sequence variation represent a substantial challenge to experimental and computational analysis of PBD specificity and the networks PBDs create. Here we introduce a bespoke machine learning approach, hierarchical statistical mechanical modelling (HSM), capable of accurately predicting the affinities of PBD-peptide interactions across multiple protein families. By synthesizing biophysical priors within a modern machine learning framework, HSM outperforms existing computational methods and high-throughput experimental assays. HSM models are interpretable in familiar biophysical terms at three spatial scales: the energetics of protein-peptide binding, the multi-dentate organization of protein-protein interactions, and the global architecture of signaling networks.

Computational reconstruction of atomistic protein structures from coarse-grained models

Three-dimensional protein structures, whether determined experimentally or theoretically, are often too low resolution. In this mini-review, we outline the computational methods for protein structure reconstruction from incomplete coarse-grained to all atomistic models. Typical reconstruction schemes can be divided into four major steps. Usually, the first step is reconstruction of the protein backbone chain starting from the C-alpha trace. This is followed by side-chains rebuilding based on protein backbone geometry. Subsequently, hydrogen atoms can be reconstructed. Finally, the resulting all-atom models may require structure optimization. Many methods are available to perform each of these tasks. We discuss the available tools and their potential applications in integrative modeling pipelines that can transfer coarse-grained information from computational predictions, or experiment, to all atomistic structures.

Investigating the Formation of Structural Elements in Proteins Using Local Sequence-Dependent Information and a Heuristic Search Algorithm

Structural elements inserted in proteins are essential to define folding/unfolding mechanisms and partner recognition events governing signaling processes in living organisms. Here, we present an original approach to model the folding mechanism of these structural elements. Our approach is based on the exploitation of local, sequence-dependent structural information encoded in a database of three-residue fragments extracted from a large set of high-resolution experimentally determined protein structures. The computation of conformational transitions leading to the formation of the structural elements is formulated as a discrete path search problem using this database. To solve this problem, we propose a heuristically-guided depth-first search algorithm. The domain-dependent heuristic function aims at minimizing the length of the path in terms of angular distances, while maximizing the local density of the intermediate states, which is related to their probability of existence. We have applied the strategy to two small synthetic polypeptides mimicking two common structural motifs in proteins. The folding mechanisms extracted are very similar to those obtained when using traditional, computationally expensive approaches. These results show that the proposed approach, thanks to its simplicity and computational efficiency, is a promising research direction.

Supersecondary Structures and Fragment Libraries

The use of smotifs and fragment libraries has proven useful to both simplify and increase the quality of protein models. Here, we present Profrager, a tool that automatically generates putative structural fragments to reproduce local motifs of proteins given a target sequence. Profrager is highly customizable, allowing the user to select the number of fragments per library, the ranking method is able to generate fragments of all sizes, and it was recently modified to include the possibility of output exclusively smotifs.

Navigating Among Known Structures in Protein Space

Present-day protein space is the result of 3.7 billion years of evolution, constrained by the underlying physicochemical qualities of the proteins. It is difficult to differentiate between evolutionary traces and effects of physicochemical constraints. Nonetheless, as a rule of thumb, instances of structural reuse, or focusing on structural similarity, are likely attributable to physicochemical constraints, whereas sequence reuse, or focusing on sequence similarity, may be more indicative of evolutionary relationships. Both types of relationships have been studied and can provide meaningful insights to protein biophysics and evolution, which in turn can lead to better algorithms for protein search, annotation, and maybe even design.In broad strokes, studies of protein space vary in the entities they represent, the similarity measure comparing these entities, and the representation used. The entities can be, for example, protein chains, domains, supra-domains, or smaller protein sub-parts denoted themes. The measures of similarity between the entities can be based on sequence, structure, function, or any combination of these. The representation can be global, encompassing the whole space, or local, focusing on a particular region surrounding protein(s) of interest. Global representations include lists of grouped proteins, protein networks, and maps. Networks are the abstraction that is derived most directly from the similarity data: each node is the protein entity (e.g., a domain), and edges connect similar domains. Selecting the entities, the similarity measure, and the abstraction are three intertwined decisions: the similarity measures allow us to identify the entities, and the selection of entities influences what is a meaningful similarity measure. Similarly, we seek entities that are related to each other in a way, for which a simple representation describes their relationships succinctly and accurately. This chapter will cover studies that rely on different entities, similarity measures, and a range of representations to better understand protein structure space. Scholars may use publicly available navigators offering a global representation, and in particular the hierarchical classifications SCOP, CATH, and ECOD, or a local representation, which encompass structural alignment algorithms. Alternatively, scholars can configure their own navigator using existing tools. To demonstrate this DIY (do it yourself) approach for navigating in protein space, we investigate substrate-binding proteins. By presenting sequence similarities among this large and diverse protein family as a network, we can infer that one member (pdb ID 4ntl; of yet unknown function) may bind methionine and suggest a putative binding mechanism.

Biotite: a unifying open source computational biology framework in Python

BACKGROUND

As molecular biology is creating an increasing amount of sequence and structure data, the multitude of software to analyze this data is also rising. Most of the programs are made for a specific task, hence the user often needs to combine multiple programs in order to reach a goal. This can make the data processing unhandy, inflexible and even inefficient due to an overhead of read/write operations. Therefore, it is crucial to have a comprehensive, accessible and efficient computational biology framework in a scripting language to overcome these limitations.

RESULTS

We have developed the Python package Biotite: a general computational biology framework, that represents sequence and structure data based on NumPyndarrays. Furthermore the package contains seamless interfaces to biological databases and external software. The source code is freely accessible at https://github.com/biotite-dev/biotite .

CONCLUSIONS

Biotite is unifying in two ways: At first it bundles popular tasks in sequence analysis and structural bioinformatics in a consistently structured package. Secondly it adresses two groups of users: novice programmers get an easy access to Biotite due to its simplicity and the comprehensive documentation. On the other hand, advanced users can profit from its high performance and extensibility. They can implement their algorithms upon Biotite, so they can skip writing code for general functionality (like file parsers) and can focus on what their software makes unique.

SAFlex: A structural alphabet extension to integrate protein structural flexibility and missing data information

In this paper, we describe SAFlex (Structural Alphabet Flexibility), an extension of an existing structural alphabet (HMM-SA), to better explore increasing protein three dimensional structure information by encoding conformations of proteins in case of missing residues or uncertainties. An SA aims to reduce three dimensional conformations of proteins as well as their analysis and comparison complexity by simplifying any conformation in a series of structural letters. Our methodology presents several novelties. Firstly, it can account for the encoding uncertainty by providing a wide range of encoding options: the maximum a posteriori, the marginal posterior distribution, and the effective number of letters at each given position. Secondly, our new algorithm deals with the missing data in the protein structure files (concerning more than 75% of the proteins from the Protein Data Bank) in a rigorous probabilistic framework. Thirdly, SAFlex is able to encode and to build a consensus encoding from different replicates of a single protein such as several homomer chains. This allows localizing structural differences between different chains and detecting structural variability, which is essential for protein flexibility identification. These improvements are illustrated on different proteins, such as the crystal structure of an eukaryotic small heat shock protein. They are promising to explore increasing protein redundancy data and obtain useful quantification of their flexibility.

LRFragLib: an effective algorithm to identify fragments for de novo protein structure prediction

Motivation

The quality of fragment library determines the efficiency of fragment assembly, an approach that is widely used in most de novo protein-structure prediction algorithms. Conventional fragment libraries are constructed mainly based on the identities of amino acids, sometimes facilitated by predicted information including dihedral angles and secondary structures. However, it remains challenging to identify near-native fragment structures with low sequence homology.

Results

We introduce a novel fragment-library-construction algorithm, LRFragLib, to improve the detection of near-native low-homology fragments of 7-10 residues, using a multi-stage, flexible selection protocol. Based on logistic regression scoring models, LRFragLib outperforms existing techniques by achieving a significantly higher precision and a comparable coverage on recent CASP protein sets in sampling near-native structures. The method also has a comparable computational efficiency to the fastest existing techniques with substantially reduced memory usage.

Availability and Implementation

The source code is available for download at http://166.111.152.91/Downloads.html.

Contact

hgong@tsinghua.edu.cn.

Supplementary information

Supplementary data are available at Bioinformatics online.

Knowledge-based prediction of protein backbone conformation using a structural alphabet

Libraries of structural prototypes that abstract protein local structures are known as structural alphabets and have proven to be very useful in various aspects of protein structure analyses and predictions. One such library, Protein Blocks, is composed of 16 standard 5-residues long structural prototypes. This form of analyzing proteins involves drafting its structure as a string of Protein Blocks. Predicting the local structure of a protein in terms of protein blocks is the general objective of this work. A new approach, PB-kPRED is proposed towards this aim. It involves (i) organizing the structural knowledge in the form of a database of pentapeptide fragments extracted from all protein structures in the PDB and (ii) applying a knowledge-based algorithm that does not rely on any secondary structure predictions and/or sequence alignment profiles, to scan this database and predict most probable backbone conformations for the protein local structures. Though PB-kPRED uses the structural information from homologues in preference, if available. The predictions were evaluated rigorously on 15,544 query proteins representing a non-redundant subset of the PDB filtered at 30% sequence identity cut-off. We have shown that the kPRED method was able to achieve mean accuracies ranging from 40.8% to 66.3% depending on the availability of homologues. The impact of the different strategies for scanning the database on the prediction was evaluated and is discussed. Our results highlight the usefulness of the method in the context of proteins without any known structural homologues. A scoring function that gives a good estimate of the accuracy of prediction was further developed. This score estimates very well the accuracy of the algorithm (R2 of 0.82). An online version of the tool is provided freely for non-commercial usage at http://www.bo-protscience.fr/kpred/.

Complex evolutionary footprints revealed in an analysis of reused protein segments of diverse lengths

We question a central paradigm: namely, that the protein domain is the “atomic unit” of evolution. In conflict with the current textbook view, our results unequivocally show that duplication of protein segments happens both above and below the domain level among amino acid segments of diverse lengths. Indeed, we show that significant evolutionary information is lost when the protein is approached as a string of domains. Our finer-grained approach reveals a far more complicated picture, where reused segments often intertwine and overlap with each other. Our results are consistent with a recursive model of evolution, in which segments of various lengths, typically smaller than domains, “hop” between environments. The fit segments remain, leaving traces that can still be detected.

Proteins share similar segments with one another. Such “reused parts”—which have been successfully incorporated into other proteins—are likely to offer an evolutionary advantage over de novo evolved segments, as most of the latter will not even have the capacity to fold. To systematically explore the evolutionary traces of segment “reuse” across proteins, we developed an automated methodology that identifies reused segments from protein alignments. We search for “themes”—segments of at least 35 residues of similar sequence and structure—reused within representative sets of 15,016 domains [Evolutionary Classification of Protein Domains (ECOD) database] or 20,398 chains [Protein Data Bank (PDB)]. We observe that theme reuse is highly prevalent and that reuse is more extensive when the length threshold for identifying a theme is lower. Structural domains, the best characterized form of reuse in proteins, are just one of many complex and intertwined evolutionary traces. Others include long themes shared among a few proteins, which encompass and overlap with shorter themes that recur in numerous proteins. The observed complexity is consistent with evolution by duplication and divergence, and some of the themes might include descendants of ancestral segments. The observed recursive footprints, where the same amino acid can simultaneously participate in several intertwined themes, could be a useful concept for protein design. Data are available at http://trachel-srv.cs.haifa.ac.il/rachel/ppi/themes/.

Protein structural motifs in prediction and design

The Protein Data Bank (PDB) has been an integral resource for shaping our fundamental understanding of protein structure and for the advancement of such applications as protein design and structure prediction. Over the years, information from the PDB has been used to generate models ranging from specific structural mechanisms to general statistical potentials. With accumulating structural data, it has become possible to mine for more complete and complex structural observations, deducing more accurate generalizations. Motif libraries, which capture recurring structural features along with their sequence preferences, have exposed modularity in the structural universe and found successful application in various problems of structural biology. Here we summarize recent achievements in this arena, focusing on subdomain level structural patterns and their applications to protein design and structure prediction, and suggest promising future directions as the structural database continues to grow.

Sequence statistics of tertiary structural motifs reflect protein stability

The Protein Data Bank (PDB) has been a key resource for learning general rules of sequence-structure relationships in proteins. Quantitative insights have been gained by defining geometric descriptors of structure (e.g., distances, dihedral angles, solvent exposure, etc.) and observing their distributions and sequence preferences. Here we argue that as the PDB continues to grow, it may become unnecessary to reduce structure into a set of elementary descriptors. Instead, it could be possible to deduce quantitative sequence-structure relationships in the context of precisely-defined complex structural motifs by mining the PDB for closely matching backbone geometries. To validate this idea, we turned to the the task of predicting changes in protein stability upon amino-acid substitution—a difficult problem of broad significance. We defined non-contiguous tertiary motifs (TERMs) around a protein site of interest and extracted sequence preferences from ensembles of closely-matching substructures in the PDB to predict mutational stability changes at the site, ΔΔG_m. We demonstrate that these ensemble statistics predict ΔΔG_m on par with state-of-the-art statistical and machine-learning methods on large thermodynamic datasets, and outperform these, along with a leading structure-based modeling approach, when tested in the context of unbiased diverse mutations. Further, we show that the performance of the TERM-based method is directly related to the amount of available relevant structural data, automatically improving with the growing PDB. This enables a means of estimating prediction accuracy. Our results clearly demonstrate that: 1) statistics of non-contiguous structural motifs in the PDB encode fundamental sequence-structure relationships related to protein thermodynamic stability, and 2) the PDB is now large enough that such statistics are already useful in practice, with their accuracy expected to continue increasing as the database grows. These observations suggest new ways of using structural data towards addressing problems of computational structural biology.

Joint-based description of protein structure: its application to the geometric characterization of membrane proteins

A macroscopic description of a protein structure allows an understanding of the protein conformations in a more simplistic manner. Here, a new macroscopic approach that utilizes the joints of the protein secondary structures as a basic descriptor for the protein structure is proposed and applied to study the arrangement of secondary structures in helical membrane proteins. Two types of dihedral angle, Ω and λ, were defined based on the joint points of the transmembrane (TM) helices and loops, and employed to analyze 103 non-homologous membrane proteins with 3 to 14 TM helices. The Ω-λ plot, which is a distribution plot of the dihedral angles of the joint points, identified the allowed and disallowed regions of helical arrangement. Analyses of consecutive dihedral angle patterns indicated that there are preferred patterns in the helical alignment and extension of TM proteins, and helical extension pattern in TM proteins is varied as the size of TM proteins increases. Finally, we could identify some symmetric protein pairs in TM proteins under the joint-based coordinate and 3-dimensional coordinates. The joint-based approach is expected to help better understand and model the overall conformational features of complicated large-scale proteins, such as membrane proteins.

Minimum action transition paths connecting minima on an energy surface

Dynamics is essential to the biological functions of many bio-molecules, yet our knowledge of dynamics remains fragmented. Experimental techniques for studying bio-molecules either provide high resolution information on static conformations of the molecule or provide low-resolution, ensemble information that does not shed light on single molecule dynamics. In parallel, bio-molecular dynamics occur at time scale that are not yet attainable through detailed simulation methods. These limitations are especially noticeable when studying transition paths. To address this issue, we report in this paper two methods that derive meaningful trajectories for proteins between two of their conformations. The first method, MinActionPath, uses approximations of the potential energy surface for the molecule to derive an analytical solution of the equations of motion related to the concept of minimum action path. The second method, RelaxPath, follows the same principle of minimum action path but implements a more sophisticated potential, including a mixed elastic potential and a collision term to alleviate steric clashes. Using this new potential, the equations of motion cannot be solved analytically. We have introduced a relaxation method for solving those equations. We describe both the theories behind the two methods and their implementations, focusing on the specific techniques we have used that make those implementations amenable to study large molecular systems. We have illustrated the performance of RelaxPath on simple 2D systems. We have also compared MinActionPath and RelaxPath to other methods for generating transition paths on a well suited test set of large proteins, for which the end points of the trajectories as well as an intermediate conformation between those end points are known. We have shown that RelaxPath outperforms those other methods, including MinActionPath, in its ability to generate trajectories that get close to the known intermediates. We have also shown that the structures along the RelaxPath trajectories remain protein-like. Open source versions of the two programs MinActionPath and RelaxPath are available by request.

Critical Features of Fragment Libraries for Protein Structure Prediction

The use of fragment libraries is a popular approach among protein structure prediction methods and has proven to substantially improve the quality of predicted structures. However, some vital aspects of a fragment library that influence the accuracy of modeling a native structure remain to be determined. This study investigates some of these features. Particularly, we analyze the effect of using secondary structure prediction guiding fragments selection, different fragments sizes and the effect of structural clustering of fragments within libraries. To have a clearer view of how these factors affect protein structure prediction, we isolated the process of model building by fragment assembly from some common limitations associated with prediction methods, e.g., imprecise energy functions and optimization algorithms, by employing an exact structure-based objective function under a greedy algorithm. Our results indicate that shorter fragments reproduce the native structure more accurately than the longer. Libraries composed of multiple fragment lengths generate even better structures, where longer fragments show to be more useful at the beginning of the simulations. The use of many different fragment sizes shows little improvement when compared to predictions carried out with libraries that comprise only three different fragment sizes. Models obtained from libraries built using only sequence similarity are, on average, better than those built with a secondary structure prediction bias. However, we found that the use of secondary structure prediction allows greater reduction of the search space, which is invaluable for prediction methods. The results of this study can be critical guidelines for the use of fragment libraries in protein structure prediction.

Barbiturates Bind in the GLIC Ion Channel Pore and Cause Inhibition by Stabilizing a Closed State

Barbiturates induce anesthesia by modulating the activity of anionic and cationic pentameric ligand-gated ion channels (pLGICs). Despite more than a century of use in clinical practice, the prototypic binding site for this class of drugs within pLGICs is yet to be described. In this study, we present the first X-ray structures of barbiturates bound to GLIC, a cationic prokaryotic pLGIC with excellent structural homology to other relevant channels sensitive to general anesthetics and, as shown here, to barbiturates, at clinically relevant concentrations. Several derivatives of barbiturates containing anomalous scatterers were synthesized, and these derivatives helped us unambiguously identify a unique barbiturate binding site within the central ion channel pore in a closed conformation. In addition, docking calculations around the observed binding site for all three states of the receptor, including a model of the desensitized state, showed that barbiturates preferentially stabilize the closed state. The identification of this pore binding site sheds light on the mechanism of barbiturate inhibition of cationic pLGICs and allows the rationalization of several structural and functional features previously observed for barbiturates.

Tertiary alphabet for the observable protein structural universe

Here, we systematically decompose the known protein structural universe into its basic elements, which we dub tertiary structural motifs (TERMs). A TERM is a compact backbone fragment that captures the secondary, tertiary, and quaternary environments around a given residue, comprising one or more disjoint segments (three on average). We seek the set of universal TERMs that capture all structure in the Protein Data Bank (PDB), finding remarkable degeneracy. Only ∼600 TERMs are sufficient to describe 50% of the PDB at sub-Angstrom resolution. However, more rare geometries also exist, and the overall structural coverage grows logarithmically with the number of TERMs. We go on to show that universal TERMs provide an effective mapping between sequence and structure. We demonstrate that TERM-based statistics alone are sufficient to recapitulate close-to-native sequences given either NMR or X-ray backbones. Furthermore, sequence variability predicted from TERM data agrees closely with evolutionary variation. Finally, locations of TERMs in protein chains can be predicted from sequence alone based on sequence signatures emergent from TERM instances in the PDB. For multisegment motifs, this method identifies spatially adjacent fragments that are not contiguous in sequence-a major bottleneck in structure prediction. Although all TERMs recur in diverse proteins, some appear specialized for certain functions, such as interface formation, metal coordination, or even water binding. Structural biology has benefited greatly from previously observed degeneracies in structure. The decomposition of the known structural universe into a finite set of compact TERMs offers exciting opportunities toward better understanding, design, and prediction of protein structure.

Characterization and Prediction of Protein Flexibility Based on Structural Alphabets

Motivation. To assist efforts in determining and exploring the functional properties of proteins, it is desirable to characterize and predict protein flexibilities. Results. In this study, the conformational entropy is used as an indicator of the protein flexibility. We first explore whether the conformational change can capture the protein flexibility. The well-defined decoy structures are converted into one-dimensional series of letters from a structural alphabet. Four different structure alphabets, including the secondary structure in 3-class and 8-class, the PB structure alphabet (16-letter), and the DW structure alphabet (28-letter), are investigated. The conformational entropy is then calculated from the structure alphabet letters. Some of the proteins show high correlation between the conformation entropy and the protein flexibility. We then predict the protein flexibility from basic amino acid sequence. The local structures are predicted by the dual-layer model and the conformational entropy of the predicted class distribution is then calculated. The results show that the conformational entropy is a good indicator of the protein flexibility, but false positives remain a problem. The DW structure alphabet performs the best, which means that more subtle local structures can be captured by large number of structure alphabet letters. Overall this study provides a simple and efficient method for the characterization and prediction of the protein flexibility.

Inverse Kinematics in Biology: The Protein Loop Closure Problem

Assembling fragments from known protein structures is a widely used approach to construct structural models for new proteins. We describe an application of this idea to an important inverse kinematics problem in structural biology: the loop closure problem. We have developed an algorithm for generating the conformations of candidate loops that fit in a gap of given length in a protein structure framework. Our method proceeds by concatenating small fragments of protein chosen from small libraries of representative fragments. Our approach has the advantages of ab initio methods since we are able to enumerate all candidate loops in the discrete approximation of the conformational space accessible to the loop, as well as the advantages of database search approach since the use of fragments of known protein structures guarantees that the backbone conformations are physically reasonable. We test our approach on a set of 427 loops, varying in length from four residues to 14 residues. The quality of the candidate loops is evaluated in terms of global coordinate root mean square (cRMS). The top predictions vary between 0.3 and 4.2 Å for four-residue loops and between 1.5 and 3.1 Å for 14-residue loops, respectively.

Protein flexibility in the light of structural alphabets

Protein structures are valuable tools to understand protein function. Nonetheless, proteins are often considered as rigid macromolecules while their structures exhibit specific flexibility, which is essential to complete their functions. Analyses of protein structures and dynamics are often performed with a simplified three-state description, i.e., the classical secondary structures. More precise and complete description of protein backbone conformation can be obtained using libraries of small protein fragments that are able to approximate every part of protein structures. These libraries, called structural alphabets (SAs), have been widely used in structure analysis field, from definition of ligand binding sites to superimposition of protein structures. SAs are also well suited to analyze the dynamics of protein structures. Here, we review innovative approaches that investigate protein flexibility based on SAs description. Coupled to various sources of experimental data (e.g., B-factor) and computational methodology (e.g., Molecular Dynamic simulation), SAs turn out to be powerful tools to analyze protein dynamics, e.g., to examine allosteric mechanisms in large set of structures in complexes, to identify order/disorder transition. SAs were also shown to be quite efficient to predict protein flexibility from amino-acid sequence. Finally, in this review, we exemplify the interest of SAs for studying flexibility with different cases of proteins implicated in pathologies and diseases.

Customised fragments libraries for protein structure prediction based on structural class annotations

Background

Since experimental techniques are time and cost consuming, in silico protein structure prediction is essential to produce conformations of protein targets. When homologous structures are not available, fragment-based protein structure prediction has become the approach of choice. However, it still has many issues including poor performance when targets’ lengths are above 100 residues, excessive running times and sub-optimal energy functions. Taking advantage of the reliable performance of structural class prediction software, we propose to address some of the limitations of fragment-based methods by integrating structural constraints in their fragment selection process.

Results

Using Rosetta, a state-of-the-art fragment-based protein structure prediction package, we evaluated our proposed pipeline on 70 former CASP targets containing up to 150 amino acids. Using either CATH or SCOP-based structural class annotations, enhancement of structure prediction performance is highly significant in terms of both GDT_TS (at least +2.6, p-values < 0.0005) and RMSD (−0.4, p-values < 0.005). Although CATH and SCOP classifications are different, they perform similarly. Moreover, proteins from all structural classes benefit from the proposed methodology. Further analysis also shows that methods relying on class-based fragments produce conformations which are more relevant to user and converge quicker towards the best model as estimated by GDT_TS (up to 10% in average). This substantiates our hypothesis that usage of structurally relevant templates conducts to not only reducing the size of the conformation space to be explored, but also focusing on a more relevant area.

Conclusions

Since our methodology produces models the quality of which is up to 7% higher in average than those generated by a standard fragment-based predictor, we believe it should be considered before conducting any fragment-based protein structure prediction. Despite such progress, ab initio prediction remains a challenging task, especially for proteins of average and large sizes. Apart from improving search strategies and energy functions, integration of additional constraints seems a promising route, especially if they can be accurately predicted from sequence alone.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0576-2) contains supplementary material, which is available to authorized users.

Building a better fragment library for de novo protein structure prediction

Fragment-based approaches are the current standard for de novo protein structure prediction. These approaches rely on accurate and reliable fragment libraries to generate good structural models. In this work, we describe a novel method for structure fragment library generation and its application in fragment-based de novo protein structure prediction. The importance of correct testing procedures in assessing the quality of fragment libraries is demonstrated. In particular, the exclusion of homologs to the target from the libraries to correctly simulate a de novo protein structure prediction scenario, something which surprisingly is not always done. We demonstrate that fragments presenting different predominant predicted secondary structures should be treated differently during the fragment library generation step and that exhaustive and random search strategies should both be used. This information was used to develop a novel method, Flib. On a validation set of 41 structurally diverse proteins, Flib libraries presents both a higher precision and coverage than two of the state-of-the-art methods, NNMake and HHFrag. Flib also achieves better precision and coverage on the set of 275 protein domains used in the two previous experiments of the the Critical Assessment of Structure Prediction (CASP9 and CASP10). We compared Flib libraries against NNMake libraries in a structure prediction context. Of the 13 cases in which a correct answer was generated, Flib models were more accurate than NNMake models for 10. “Flib is available for download at: http://www.stats.ox.ac.uk/research/proteins/resources”.

Comparative modeling of proteins

Much of the biochemistry that underlies health, medicine, and numerous biotechnology applications is regulated by proteins, whereby the ability of proteins to effect such processes is dictated by the three-dimensional structural assembly of the proteins. Thus, a detailed understanding of biochemistry requires not only knowledge of the constituent sequence of proteins, but also a detailed understanding of how that sequence folds spatially. Three-dimensional analysis of protein structures is thus proving to be a critical mode of biological and medical discovery in the early twenty-first century, providing fundamental insight into function that produces useful biochemistry and dysfunction that leads to disease. The large number of distinct proteins precludes rigorous laboratory characterization of the complete structural proteome, but fortunately efficient in silico structure prediction is possible for many proteins that have not been experimentally characterized. One technique that continues to provide accurate and efficient protein structure predictions, called comparative modeling, has become a critical tool in many biological disciplines. The discussion herein is an updated version of a previous 2008 treatise focusing on the general philosophy of comparative modeling methods and on specific strategies for successfully achieving reliable and accurate models. The chapter discusses basic aspects of template selection, sequence alignment, spatial alignment, loop and gap modeling, side chain modeling, structural refinement and validation, and provides an important new discussion on automated computational tools for protein structure prediction.

Dynameomics: data-driven methods and models for utilizing large-scale protein structure repositories for improving fragment-based loop prediction

Protein function is intimately linked to protein structure and dynamics yet experimentally determined structures frequently omit regions within a protein due to indeterminate data, which is often due protein dynamics. We propose that atomistic molecular dynamics simulations provide a diverse sampling of biologically relevant structures for these missing segments (and beyond) to improve structural modeling and structure prediction. Here we make use of the Dynameomics data warehouse, which contains simulations of representatives of essentially all known protein folds. We developed novel computational methods to efficiently identify, rank and retrieve small peptide structures, or fragments, from this database. We also created a novel data model to analyze and compare large repositories of structural data, such as contained within the Protein Data Bank and the Dynameomics data warehouse. Our evaluation compares these structural repositories for improving loop predictions and analyzes the utility of our methods and models. Using a standard set of loop structures, containing 510 loops, 30 for each loop length from 4 to 20 residues, we find that the inclusion of Dynameomics structures in fragment-based methods improves the quality of the loop predictions without being dependent on sequence homology. Depending on loop length, ∼ 25-75% of the best predictions came from the Dynameomics set, resulting in lower main chain root-mean-square deviations for all fragment lengths using the combined fragment library. We also provide specific cases where Dynameomics fragments provide better predictions for NMR loop structures than fragments from crystal structures. Online access to these fragment libraries is available at http://www.dynameomics.org/fragments.

Exploring representations of protein structure for automated remote homology detection and mapping of protein structure space

BACKGROUND

Due to rapid sequencing of genomes, there are now millions of deposited protein sequences with no known function. Fast sequence-based comparisons allow detecting close homologs for a protein of interest to transfer functional information from the homologs to the given protein. Sequence-based comparison cannot detect remote homologs, in which evolution has adjusted the sequence while largely preserving structure. Structure-based comparisons can detect remote homologs but most methods for doing so are too expensive to apply at a large scale over structural databases of proteins. Recently, fragment-based structural representations have been proposed that allow fast detection of remote homologs with reasonable accuracy. These representations have also been used to obtain linearly-reducible maps of protein structure space. It has been shown, as additionally supported from analysis in this paper that such maps preserve functional co-localization of the protein structure space.

METHODS

Inspired by a recent application of the Latent Dirichlet Allocation (LDA) model for conducting structural comparisons of proteins, we propose higher-order LDA-obtained topic-based representations of protein structures to provide an alternative route for remote homology detection and organization of the protein structure space in few dimensions. Various techniques based on natural language processing are proposed and employed to aid the analysis of topics in the protein structure domain.

RESULTS

We show that a topic-based representation is just as effective as a fragment-based one at automated detection of remote homologs and organization of protein structure space. We conduct a detailed analysis of the information content in the topic-based representation, showing that topics have semantic meaning. The fragment-based and topic-based representations are also shown to allow prediction of superfamily membership.

CONCLUSIONS

This work opens exciting venues in designing novel representations to extract information about protein structures, as well as organizing and mining protein structure space with mature text mining tools.

The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems

The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows the study of single protein properties, DNA-RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the ongoing developments.

Bioinformatic analysis of the protein/DNA interface

To investigate the principles driving recognition between proteins and DNA, we analyzed more than thousand crystal structures of protein/DNA complexes. We classified protein and DNA conformations by structural alphabets, protein blocks [de Brevern, Etchebest and Hazout (2000) (Bayesian probabilistic approach for predicting backbone structures in terms of protein blocks. Prots. Struct. Funct. Genet., 41:271-287)] and dinucleotide conformers [Svozil, Kalina, Omelka and Schneider (2008) (DNA conformations and their sequence preferences. Nucleic Acids Res., 36:3690-3706)], respectively. Assembling the mutually interacting protein blocks and dinucleotide conformers into 'interaction matrices' revealed their correlations and conformer preferences at the interface relative to their occurrence outside the interface. The analyzed data demonstrated important differences between complexes of various types of proteins such as transcription factors and nucleases, distinct interaction patterns for the DNA minor groove relative to the major groove and phosphate and importance of water-mediated contacts. Water molecules mediate proportionally the largest number of contacts in the minor groove and form the largest proportion of contacts in complexes of transcription factors. The generally known induction of A-DNA forms by complexation was more accurately attributed to A-like and intermediate A/B conformers rare in naked DNA molecules.

Detecting protein candidate fragments using a structural alphabet profile comparison approach

Predicting accurate fragments from sequence has recently become a critical step for protein structure modeling, as protein fragment assembly techniques are presently among the most efficient approaches for de novo prediction. A key step in these approaches is, given the sequence of a protein to model, the identification of relevant fragments - candidate fragments - from a collection of the available 3D structures. These fragments can then be assembled to produce a model of the complete structure of the protein of interest. The search for candidate fragments is classically achieved by considering local sequence similarity using profile comparison, or threading approaches. In the present study, we introduce a new profile comparison approach that, instead of using amino acid profiles, is based on the use of predicted structural alphabet profiles, where structural alphabet profiles contain information related to the 3D local shapes associated with the sequences. We show that structural alphabet profile-profile comparison can be used efficiently to retrieve accurate structural fragments, and we introduce a fully new protocol for the detection of candidate fragments. It identifies fragments specific of each position of the sequence and of size varying between 6 and 27 amino-acids. We find it outperforms present state of the art approaches in terms (i) of the accuracy of the fragments identified, (ii) the rate of true positives identified, while having a high coverage score. We illustrate the relevance of the approach on complete target sets of the two previous Critical Assessment of Techniques for Protein Structure Prediction (CASP) rounds 9 and 10. A web server for the approach is freely available at http://bioserv.rpbs.univ-paris-diderot.fr/SAFrag.

Exploring fold space preferences of new-born and ancient protein superfamilies

The evolution of proteins is one of the fundamental processes that has delivered the diversity and complexity of life we see around ourselves today. While we tend to define protein evolution in terms of sequence level mutations, insertions and deletions, it is hard to translate these processes to a more complete picture incorporating a polypeptide's structure and function. By considering how protein structures change over time we can gain an entirely new appreciation of their long-term evolutionary dynamics. In this work we seek to identify how populations of proteins at different stages of evolution explore their possible structure space. We use an annotation of superfamily age to this space and explore the relationship between these ages and a diverse set of properties pertaining to a superfamily's sequence, structure and function. We note several marked differences between the populations of newly evolved and ancient structures, such as in their length distributions, secondary structure content and tertiary packing arrangements. In particular, many of these differences suggest a less elaborate structure for newly evolved superfamilies when compared with their ancient counterparts. We show that the structural preferences we report are not a residual effect of a more fundamental relationship with function. Furthermore, we demonstrate the robustness of our results, using significant variation in the algorithm used to estimate the ages. We present these age estimates as a useful tool to analyse protein populations. In particularly, we apply this in a comparison of domains containing greek key or jelly roll motifs.

Probabilistic search and energy guidance for biased decoy sampling in ab initio protein structure prediction

Adequate sampling of the conformational space is a central challenge in ab initio protein structure prediction. In the absence of a template structure, a conformational search procedure guided by an energy function explores the conformational space, gathering an ensemble of low-energy decoy conformations. If the sampling is inadequate, the native structure may be missed altogether. Even if reproduced, a subsequent stage that selects a subset of decoys for further structural detail and energetic refinement may discard near-native decoys if they are high energy or insufficiently represented in the ensemble. Sampling should produce a decoy ensemble that facilitates the subsequent selection of near-native decoys. In this paper, we investigate a robotics-inspired framework that allows directly measuring the role of energy in guiding sampling. Testing demonstrates that a soft energy bias steers sampling toward a diverse decoy ensemble less prone to exploiting energetic artifacts and thus more likely to facilitate retainment of near-native conformations by selection techniques. We employ two different energy functions, the associative memory Hamiltonian with water and Rosetta. Results show that enhanced sampling provides a rigorous testing of energy functions and exposes different deficiencies in them, thus promising to guide development of more accurate representations and energy functions.

A homology/ab initio hybrid algorithm for sampling near-native protein conformations

One of the major challenges for protein tertiary structure prediction strategies is the quality of conformational sampling algorithms, which can effectively and readily search the protein fold space to generate near-native conformations. In an effort to advance the field by making the best use of available homology as well as fold recognition approaches along with ab initio folding methods, we have developed Bhageerath-H Strgen, a homology/ab initio hybrid algorithm for protein conformational sampling. The methodology is tested on the benchmark CASP9 dataset of 116 targets. In 93% of the cases, a structure with TM-score ≥ 0.5 is generated in the pool of decoys. Further, the performance of Bhageerath-H Strgen was seen to be efficient in comparison with different decoy generation methods. The algorithm is web enabled as Bhageerath-H Strgen web tool which is made freely accessible for protein decoy generation (http://www.scfbio-iitd.res.in/software/Bhageerath-HStrgen1.jsp).

Recurrent structural motifs in non-homologous protein structures

We have extracted an extensive collection of recurrent structural motifs (RSMs), which consist of sequentially non-contiguous structural motifs (4–6 residues), each of which appears with very similar conformation in three or more mutually unrelated protein structures. We find that the proteins in our set are covered to a substantial extent by the recurrent non-contiguous structural motifs, especially the helix and strand regions. Computational alanine scanning calculations indicate that the average folding free energy changes upon alanine mutation for most types of non-alanine residues are higher for amino acids that are present in recurrent structural motifs than for amino acids that are not. The non-alanine amino acids that are most common in the recurrent structural motifs, i.e., phenylalanine, isoleucine, leucine, valine and tyrosine and the less abundant methionine and tryptophan, have the largest folding free energy changes. This indicates that the recurrent structural motifs, as we define them, describe recurrent structural patterns that are important for protein stability. In view of their properties, such structural motifs are potentially useful for inter-residue contact prediction and protein structure refinement.

Local conformational changes in the DNA interfaces of proteins

When a protein binds to DNA, a conformational change is often induced so that the protein will fit into the DNA structure. Therefore, quantitative analyses were conducted to understand the conformational changes in proteins. The results showed that conformational changes in DNA interfaces are more frequent than in non-interfaces, and DNA interfaces have more conformational variations in the DNA-free form. As expected, the former indicates that interaction with DNA has some influence on protein structure. The latter suggests that the intrinsic conformational flexibility of DNA interfaces is important for adjusting their conformation for DNA. The amino acid propensities of the conformationally changed regions in DNA interfaces indicate that hydrophilic residues are preferred over the amino acids that appear in the conformationally unchanged regions. This trend is true for disordered regions, suggesting again that intrinsic flexibility is of importance not only for DNA binding but also for interactions with other molecules. These results demonstrate that fragments destined to be DNA interfaces have an intrinsic flexibility and are composed of amino acids with the capability of binding to DNA. This information suggests that the prediction of DNA binding sites may be improved by the integration of amino acid preference for DNA and one for disordered regions.

Toward optimal fragment generations for ab initio protein structure assembly

Fragment assembly using structural motifs excised from other solved proteins has shown to be an efficient method for ab initio protein-structure prediction. However, how to construct accurate fragments, how to derive optimal restraints from fragments, and what the best fragment length is are the basic issues yet to be systematically examined. In this work, we developed a gapless-threading method to generate position-specific structure fragments. Distance profiles and torsion angle pairs are then derived from the fragments by statistical consistency analysis, which achieved comparable accuracy with the machine-learning-based methods although the fragments were taken from unrelated proteins. When measured by both accuracies of the derived distance profiles and torsion angle pairs, we come to a consistent conclusion that the optimal fragment length for structural assembly is around 10, and at least 100 fragments at each location are needed to achieve optimal structure assembly. The distant profiles and torsion angle pairs as derived by the fragments have been successfully used in QUARK for ab initio protein structure assembly and are provided by the QUARK online server at http://zhanglab.ccmb. med.umich.edu/QUARK/.

Structure based function prediction of proteins using fragment library frequency vectors

The function of the protein is primarily dictated by its structure. Therefore it is far more logical to find the functional clues of the protein in its overall 3-dimensional fold or its global structure. In this paper, we have developed a novel Support Vector Machines (SVM) based prediction model for functional classification and prediction of proteins using features extracted from its global structure based on fragment libraries. Fragment libraries have been previously used for abintio modelling of proteins and protein structure comparisons. The query protein structure is broken down into a collection of short contiguous backbone fragments and this collection is discretized using a library of fragments. The input feature vector is frequency vector that counts the number of each library fragment in the collection of fragments by all-to-all fragment comparisons. SVM models were trained and optimised for obtaining the best 10-fold Cross validation accuracy for classification. As an example, this method was applied for prediction and classification of Cell Adhesion molecules (CAMs). Thirty-four different fragment libraries with sizes ranging from 4 to 400 and fragment lengths ranging from 4 to 12 were used for obtaining the best prediction model. The best 10-fold CV accuracy of 95.25% was obtained for library of 400 fragments of length 10. An accuracy of 87.5% was obtained on an unseen test dataset consisting of 20 CAMs and 20 NonCAMs. This shows that protein structure can be accurately and uniquely described using 400 representative fragments of length 10.

Assessing protein conformational sampling methods based on bivariate lag-distributions of backbone angles

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model that should be considered to accurately parameterize the joint distribution of the angles? and What is the order of the local sequence-structure dependency that should be considered by a prediction method? We assess the model fits for different methods using bivariate lag-distributions of the dihedral/planar angles. Moreover, the main information across the lags can be extracted using a technique called Lag singular value decomposition (LagSVD), which considers the joint distribution of the dihedral/planar angles over different lags using a nonparametric approach and monitors the behavior of the lag-distribution of the angles using singular value decomposition. As a result, we developed graphical tools and numerical measurements to compare and evaluate the performance of different model fits. Furthermore, we developed a web-tool (http://www.stat.tamu.edu/∼madoliat/LagSVD) that can be used to produce informative animations.

Reducing the dimensionality of the protein-folding search problem

How does a folding protein negotiate a vast, featureless conformational landscape and adopt its native structure in biological real time? Motivated by this search problem, we developed a novel algorithm to compare protein structures. Procedures to identify structural analogs are typically conducted in three-dimensional space: the tertiary structure of a target protein is matched against each candidate in a database of structures, and goodness of fit is evaluated by a distance-based measure, such as the root-mean-square distance between target and candidate. This is an expensive approach because three-dimensional space is complex. Here, we transform the problem into a simpler one-dimensional procedure. Specifically, we identify and label the 11 most populated residue basins in a database of high-resolution protein structures. Using this 11-letter alphabet, any protein's three-dimensional structure can be transformed into a one-dimensional string by mapping each residue onto its corresponding basin. Similarity between the resultant basin strings can then be evaluated by conventional sequence-based comparison. The disorder → order folding transition is abridged on both sides. At the onset, folding conditions necessitate formation of hydrogen-bonded scaffold elements on which proteins are assembled, severely restricting the magnitude of accessible conformational space. Near the end, chain topology is established prior to emergence of the close-packed native state. At this latter stage of folding, the chain remains molten, and residues populate natural basins that are approximated by the 11 basins derived here. In essence, our algorithm reduces the protein-folding search problem to mapping the amino acid sequence onto a restricted basin string.

Local structural differences in homologous proteins: specificities in different SCOP classes

The constant increase in the number of solved protein structures is of great help in understanding the basic principles behind protein folding and evolution. 3-D structural knowledge is valuable in designing and developing methods for comparison, modelling and prediction of protein structures. These approaches for structure analysis can be directly implicated in studying protein function and for drug design. The backbone of a protein structure favours certain local conformations which include α-helices, β-strands and turns. Libraries of limited number of local conformations (Structural Alphabets) were developed in the past to obtain a useful categorization of backbone conformation. Protein Block (PB) is one such Structural Alphabet that gave a reasonable structure approximation of 0.42 Å. In this study, we use PB description of local structures to analyse conformations that are preferred sites for structural variations and insertions, among group of related folds. This knowledge can be utilized in improving tools for structure comparison that work by analysing local structure similarities. Conformational differences between homologous proteins are known to occur often in the regions comprising turns and loops. Interestingly, these differences are found to have specific preferences depending upon the structural classes of proteins. Such class-specific preferences are mainly seen in the all-β class with changes involving short helical conformations and hairpin turns. A test carried out on a benchmark dataset also indicates that the use of knowledge on the class specific variations can improve the performance of a PB based structure comparison approach. The preference for the indel sites also seem to be confined to a few backbone conformations involving β-turns and helix C-caps. These are mainly associated with short loops joining the regular secondary structures that mediate a reversal in the chain direction. Rare β-turns of type I’ and II’ are also identified as preferred sites for insertions.

Comparative modeling and protein-like features of hydrophobic-polar models on a two-dimensional lattice

Lattice models of proteins have been extensively used to study protein thermodynamics, folding dynamics, and evolution. Our study considers two different hydrophobic-polar (HP) models on the 2D square lattice: the purely HP model and a model where a compactness-favoring term is added. We exhaustively enumerate all the possible structures in our models and perform the study of their corresponding folds, HP arrangements in space and shapes. The two models considered differ greatly in their numbers of structures, folds, arrangements, and shapes. Despite their differences, both lattice models have distinctive protein-like features: (1) Shapes are compact in both models, especially when a compactness-favoring energy term is added. (2) The residue composition is independent of the chain length and is very close to 50% hydrophobic in both models, as we observe in real proteins. (3) Comparative modeling works well in both models, particularly in the more compact one. The fact that our models show protein-like features suggests that lattice models incorporate the fundamental physical principles of proteins. Our study supports the use of lattice models to study questions about proteins that require exactness and extensive calculations, such as protein design and evolution, which are often too complex and computationally demanding to be addressed with more detailed models.