Algorithms for optimal protein structure alignment

Bi-alignments with affine gaps costs

Background

Commonly, sequence and structure elements are assumed to evolve congruently, such that homologous sequence positions correspond to homologous structural features. Assuming congruent evolution, alignments based on sequence and structure similarity can therefore optimize both similarities at the same time in a single alignment. To model incongruent evolution, where sequence and structural features diverge positionally, we recently introduced bi-alignments. This generalization of sequence and structure-based alignments is best understood as alignments of two distinct pairwise alignments of the same entities: one modeling sequence similarity, the other structural similarity.

Results

Optimal bi-alignments with affine gap costs (or affine shift cost) for two constituent alignments can be computed exactly in quartic space and time. Even bi-alignments with affine shift and gap cost, as well as bi-alignment with sub-additive gap cost are optimized efficiently. Affine gap-cost bi-alignment of large proteins (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 930$$\end{document}∼930 aa) can be computed.

Conclusion

Affine cost bi-alignments are of practical interest to study shifts of protein sequences and protein structures relative to each other.

Availability

The affine cost bi-alignment algorithm has been implemented in Python 3 and Cython. It is available as free software from https://github.com/s-will/BiAlign/releases/tag/v0.3 and as bioconda package bialign.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13015-022-00219-7.

GADP-align: A genetic algorithm and dynamic programming-based method for structural alignment of proteins

Introduction: Similarity analysis of protein structure is considered as a fundamental step to give insight into the relationships between proteins. The primary step in structural alignment is looking for the optimal correspondence between residues of two structures to optimize the scoring function. An exhaustive search for finding such a correspondence between two structures is intractable.

Methods: In this paper, a hybrid method is proposed, namely GADP-align, for pairwise protein structure alignment. The proposed method looks for an optimal alignment using a hybrid method based on a genetic algorithm and an iterative dynamic programming technique. To this end, the method first creates an initial map of correspondence between secondary structure elements (SSEs) of two proteins. Then, a genetic algorithm combined with an iterative dynamic programming algorithm is employed to optimize the alignment.

Results: The GADP-align algorithm was employed to align 10 ‘difficult to align’ protein pairs in order to evaluate its performance. The experimental study shows that the proposed hybrid method produces highly accurate alignments in comparison with the methods using exactly the dynamic programming technique. Furthermore, the proposed method prevents the local optimal traps caused by the unsuitable initial guess of the corresponding residues.

Conclusion: The findings of this paper demonstrate that employing the genetic algorithm along with the dynamic programming technique yields highly accurate alignments between a protein pair by exploring the global alignment and avoiding trapping in local alignments.

Multi-criteria protein structure comparison and structural similarities analysis using pyMCPSC

Protein Structure Comparison (PSC) is a well developed field of computational proteomics with active interest from the research community, since it is widely used in structural biology and drug discovery. With new PSC methods continuously emerging and no clear method of choice, Multi-Criteria Protein Structure Comparison (MCPSC) is commonly employed to combine methods and generate consensus structural similarity scores. We present pyMCPSC, a Python based utility we developed to allow users to perform MCPSC efficiently, by exploiting the parallelism afforded by the multi-core CPUs of today’s desktop computers. We show how pyMCPSC facilitates the analysis of similarities in protein domain datasets and how it can be extended to incorporate new PSC methods as they are becoming available. We exemplify the power of pyMCPSC using a case study based on the Proteus_300 dataset. Results generated using pyMCPSC show that MCPSC scores form a reliable basis for identifying the true classification of a domain, as evidenced both by the ROC analysis as well as the Nearest-Neighbor analysis. Structure similarity based “Phylogenetic Trees” representation generated by pyMCPSC provide insight into functional grouping within the dataset of domains. Furthermore, scatter plots generated by pyMCPSC show the existence of strong correlation between protein domains belonging to SCOP Class C and loose correlation between those of SCOP Class D. Such analyses and corresponding visualizations help users quickly gain insights about their datasets. The source code of pyMCPSC is available under the GPLv3.0 license through a GitHub repository (https://github.com/xulesc/pymcpsc).

Efficient Multicriteria Protein Structure Comparison on Modern Processor Architectures

Fast increasing computational demand for all-to-all protein structures comparison (PSC) is a result of three confounding factors: rapidly expanding structural proteomics databases, high computational complexity of pairwise protein comparison algorithms, and the trend in the domain towards using multiple criteria for protein structures comparison (MCPSC) and combining results. We have developed a software framework that exploits many-core and multicore CPUs to implement efficient parallel MCPSC in modern processors based on three popular PSC methods, namely, TMalign, CE, and USM. We evaluate and compare the performance and efficiency of the two parallel MCPSC implementations using Intel's experimental many-core Single-Chip Cloud Computer (SCC) as well as Intel's Core i7 multicore processor. We show that the 48-core SCC is more efficient than the latest generation Core i7, achieving a speedup factor of 42 (efficiency of 0.9), making many-core processors an exciting emerging technology for large-scale structural proteomics. We compare and contrast the performance of the two processors on several datasets and also show that MCPSC outperforms its component methods in grouping related domains, achieving a high F-measure of 0.91 on the benchmark CK34 dataset. The software implementation for protein structure comparison using the three methods and combined MCPSC, along with the developed underlying rckskel algorithmic skeletons library, is available via GitHub.

Dynamic Programming Used to Align Protein Structures with a Spectrum Is Robust

Several efficient algorithms to conduct pairwise comparisons among large databases of protein structures have emerged in the recent literature. The central theme is the design of a measure between the C_α atoms of two protein chains, from which dynamic programming is used to compute an alignment. The efficiency and efficacy of these algorithms allows large-scale computational studies that would have been previously impractical. The computational study herein shows that the structural alignment algorithm eigen-decomposition alignment with the spectrum (EIGAs) is robust against both parametric and structural variation.

Improved algorithms for matching r-separated sets with applications to protein structure alignment

The Largest Common Point-set (LCP) and the Pattern Matching (PM) problems have received much attention in the fields of pattern matching, computer vision and computational biology. Perhaps, the most important application of these problems is the protein structural alignment, which seeks to find a superposition of a pair of input proteins that maximizes a given protein structure similarity metric. Although it has been shown that LCP and PM are both tractable problems, the running times of existing algorithms are high-degree polynomials. Here, we present novel methods for finding approximate and exact threshold-LCP and threshold-PM for r-separated sets, in general, and protein 3D structures, in particular. Improved running times of our methods are achieved by building upon several different, previously published techniques.

DALIX: optimal DALI protein structure alignment

We present a mathematical model and exact algorithm for optimally aligning protein structures using the DALI scoring model. This scoring model is based on comparing the interresidue distance matrices of proteins and is used in the popular DALI software tool, a heuristic method for protein structure alignment. Our model and algorithm extend an integer linear programming approach that has been previously applied for the related, but simpler, contact map overlap problem. To this end, we introduce a novel type of constraint that handles negative score values and relax it in a Lagrangian fashion. The new algorithm, which we call DALIX, is applicable to any distance matrix-based scoring scheme. We also review options that allow to consider fewer pairs of interresidue distances explicitly because their large number hinders the optimization process. Using four known data sets of varying structural similarity, we compute many provably score-optimal DALI alignments. This allowed, for the first time, to evaluate the DALI heuristic in sound mathematical terms. The results indicate that DALI usually computes optimal or close to optimal alignments. However, we detect a subset of small proteins for which DALI fails to generate any significant alignment, although such alignments do exist.

On the difference in quality between current heuristic and optimal solutions to the protein structure alignment problem

The importance of pairwise protein structural comparison in biomedical research is fueling the search for algorithms capable of finding more accurate structural match of two input proteins in a timely manner. In recent years, we have witnessed rapid advances in the development of methods for approximate and optimal solutions to the protein structure matching problem. Albeit slow, these methods can be extremely useful in assessing the accuracy of more efficient, heuristic algorithms. We utilize a recently developed approximation algorithm for protein structure matching to demonstrate that a deep search of the protein superposition space leads to increased alignment accuracy with respect to many well-established measures of alignment quality. The results of our study suggest that a large and important part of the protein superposition space remains unexplored by current techniques for protein structure alignment.

A new size-independent score for pairwise protein structure alignment and its application to structure classification and nucleic-acid binding prediction

A structure alignment program aligns two structures by optimizing a scoring function that measures structural similarity. It is highly desirable that such scoring function is independent of the sizes of proteins in comparison so that the significance of alignment across different sizes of the protein regions aligned is comparable. Here, we developed a new score called SP-score that fixes the cutoff distance at 4 Å and removed the size dependence using a normalization prefactor. We further built a program called SPalign that optimizes SP-score for structure alignment. SPalign was applied to recognize proteins within the same structure fold and having the same function of DNA or RNA binding. For fold discrimination, SPalign improves sensitivity over TMalign for the chain-level comparison by 12% and over DALI for the domain-level comparison by 13% at the same specificity of 99.6%. The difference between TMalign and SPalign at the chain level is due to the inability of TMalign to detect single domain similarity between multidomain proteins. For recognizing nucleic acid binding proteins, SPalign consistently improves over TMalign by 12% and DALI by 31% in average value of Mathews correlation coefficients for four datasets. SPalign with default setting is 14% faster than TMalign. SPalign is expected to be useful for function prediction and comparing structures with or without domains defined. The source code for SPalign and the server are available at http://sparks.informatics.iupui.edu.

OPTIMAL PAIRWISE ALIGNMENT OF FIXED PROTEIN STRUCTURES IN SUBQUADRATIC TIME

The problem of finding an optimal structural alignment for a pair of superimposed proteins is often amenable to the Smith–Waterman dynamic programming algorithm, which runs in time proportional to the product of lengths of the sequences being aligned. While the quadratic running time is acceptable for computing a single alignment of two fixed protein structures, the time complexity becomes a bottleneck when running the Smith–Waterman routine multiple times in order to find a globally optimal superposition and alignment of the input proteins. We present a subquadratic running time algorithm capable of computing an alignment that optimizes one of the most widely used measures of protein structure similarity, defined as the number of pairs of residues in two proteins that can be superimposed under a predefined distance cutoff. The algorithm presented in this article can be used to significantly improve the speed–accuracy tradeoff in a number of popular protein structure alignment methods.

Optimizing a widely used protein structure alignment measure in expected polynomial time

Protein structure alignment is an important tool in many biological applications, such as protein evolution studies, protein structure modeling, and structure-based, computer-aided drug design. Protein structure alignment is also one of the most challenging problems in computational molecular biology, due to an infinite number of possible spatial orientations of any two protein structures. We study one of the most commonly used measures of pairwise protein structure similarity, defined as the number of pairs of atoms in two proteins that can be superimposed under a predefined distance cutoff. We prove that the expected running time of a recently published algorithm for optimizing this (and some other, derived measures of protein structure similarity) is polynomial.

On complexity of protein structure alignment problem under distance constraint

We study the well known LCP (Largest Common Point-Set) under Bottleneck Distance Problem. Given two proteins a and b (as sequences of points in 3D space) and a distance cutoff σ, the goal is to find a spatial superposition and an alignment that maximizes the number of pairs of points from a and b that can be fit under the distance σ from each other. The best to date algorithms for approximate and exact solution to this problem run in time O(n^8) and O(n^32), respectively, where n represents the protein length. This work improves the runtime of the approximation algorithm and the algorithm for absolute optimum for both order-dependent and order-independent alignments. More specifically, our algorithms for near-optimal and optimal sequential alignments run in time O(^7 log n) and O(n^14 log n), respectively. For non-sequential alignments, corresponding running times are O(n^7.5) and O(n^14.5).

Novel computational approaches to polypharmacology as a means to define responses to individual drugs

Polypharmacology, which focuses on designing therapeutics to target multiple receptors, has emerged as a new paradigm in drug discovery. Polypharmacological effects are an attribute of most, if not all, drug molecules. The efficacy and toxicity of drugs, whether designed as single- or multitarget therapeutics, result from complex interactions between pharmacodynamic, pharmacokinetic, genetic, epigenetic, and environmental factors. Ultimately, to predict a drug response phenotype, it is necessary to understand the change in information flow through cellular networks resulting from dynamic drug-target interactions and the impact that this has on the complete biological system. Although such is a future objective, we review recent progress and challenges in computational techniques that enable the prediction and analysis of in vitro and in vivo drug-response phenotypes.

A spectral approach to protein structure alignment

A new intrinsic geometry based on a spectral analysis is used to motivate methods for aligning protein folds. The geometry is induced by the fact that a distance matrix can be scaled so that its eigenvalues are positive. We provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach and use it to motivate two alignment algorithms. The first uses eigenvalues alone and dynamic programming to quickly compute a fold alignment. Family identification results are reported for the Skolnick40 and Proteus300 data sets. The second algorithm extends our spectral method by iterating between our intrinsic geometry and the 3D geometry of a fold to make high-quality alignments. Results and comparisons are reported for several difficult fold alignments. The second algorithm's ability to correctly identify fold families in the Skolnick40 and Proteus300 data sets is also established.