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da Silva LSA, Seman LO, Camponogara E, Mariani VC, Dos Santos Coelho L. Bilinear optimization of protein structure prediction: An exact approach via AB off-lattice model. Comput Biol Med 2024; 176:108558. [PMID: 38754216 DOI: 10.1016/j.compbiomed.2024.108558] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Revised: 04/25/2024] [Accepted: 05/05/2024] [Indexed: 05/18/2024]
Abstract
Protein structure prediction (PSP) remains a central challenge in computational biology due to its inherent complexity and high dimensionality. While numerous heuristic approaches have appeared in the literature, their success varies. The AB off-lattice model, which characterizes proteins as sequences of A (hydrophobic) and B (hydrophilic) beads, presents a simplified perspective on PSP. This work presents a mathematical optimization-based methodology capitalizing on the off-lattice AB model. Dissecting the inherent non-linearities of the energy landscape of protein folding allowed for formulating the PSP as a bilinear optimization problem. This formulation was achieved by introducing auxiliary variables and constraints that encapsulate the nuanced relationship between the protein's conformational space and its energy landscape. The proposed bilinear model exhibited notable accuracy in pinpointing the global minimum energy conformations on a benchmark dataset presented by the Protein Data Bank (PDB). Compared to traditional heuristic-based methods, this bilinear approach yielded exact solutions, reducing the likelihood of local minima entrapment. This research highlights the potential of reframing the traditionally non-linear protein structure prediction problem into a bilinear optimization problem through the off-lattice AB model. Such a transformation offers a route toward methodologies that can determine the global solution, challenging current PSP paradigms. Exploration into hybrid models, merging bilinear optimization and heuristic components, might present an avenue for balancing accuracy with computational efficiency.
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Affiliation(s)
- Luiza Scapinello Aquino da Silva
- Electrical Engineering Graduate Program (PPGEE), Federal University of Parana (UFPR), Coronel Francisco Heraclito dos Santos, Curitiba, 81530-000, Paraná, Brazil.
| | - Laio Oriel Seman
- Department of Automation and Systems Engineering, Federal University of Santa Catarina (UFSC), Engenheiro Agronômico Andrei Cristian Ferreira, Florianópolis, 88040-900, Santa Catarina, Brazil
| | - Eduardo Camponogara
- Department of Automation and Systems Engineering, Federal University of Santa Catarina (UFSC), Engenheiro Agronômico Andrei Cristian Ferreira, Florianópolis, 88040-900, Santa Catarina, Brazil
| | - Viviana Cocco Mariani
- Electrical Engineering Graduate Program (PPGEE), Federal University of Parana (UFPR), Coronel Francisco Heraclito dos Santos, Curitiba, 81530-000, Paraná, Brazil; Mechanical Engineering Graduate Program (PGMec), Federal University of Parana (UFPR), Coronel Francisco Heraclito dos Santos, Curitiba, 81530-000, Paraná, Brazil
| | - Leandro Dos Santos Coelho
- Electrical Engineering Graduate Program (PPGEE), Federal University of Parana (UFPR), Coronel Francisco Heraclito dos Santos, Curitiba, 81530-000, Paraná, Brazil
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Zhang L, Ma H, Qian W, Li H. Sequence-based protein structure optimization using enhanced simulated annealing algorithm on a coarse-grained model. J Mol Model 2020; 26:250. [PMID: 32833195 DOI: 10.1007/s00894-020-04490-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Accepted: 07/30/2020] [Indexed: 12/28/2022]
Abstract
The understanding of protein structure is vital to determine biological function. We presented an enhanced simulated annealing (ESA) algorithm to investigate protein three-dimensional (3D) structure on a coarse-grained model. Inside the algorithm, we adjusted exploration equations to achieve good search intensity. To that end, our algorithm used (i) a multivariable disturbance operator for diversification of solution, (ii) a sign function to improve randomness of solution, and (iii) taking remainder operation performed on floating-point number to tackle out-of-range solution. By monitoring energy value throughout the simulation, the energy-optimal state can be found. The ESA algorithm was tested on artificial and real protein sequences with different lengths. The results show that our algorithm outperforms conventional simulated annealing algorithm and can compete with the reported algorithms before. Especially, our algorithm can obtain folding conformations with specific structural features. Further analysis shows that simulating trajectory of seeking the lowest energy can exhibit thermodynamic behavior of protein folding. Graphical Abstract.
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Affiliation(s)
- Lizhong Zhang
- College of Medicine and Biological Information Engineering, Northeastern University, Shenyang, 110169, China.,College of Computer Science and Technology, Shenyang University of Chemical Technology, Shenyang, 110142, China
| | - He Ma
- College of Medicine and Biological Information Engineering, Northeastern University, Shenyang, 110169, China. .,Key Laboratory of Medical Image Computing, Ministry of Education, Northeastern University, Shenyang, 110169, China.
| | - Wei Qian
- Department of Electrical and Computer Engineering, College of Engineering, University of Texas, El Paso, TX, 79968, USA
| | - Haiyan Li
- College of Pharmaceutical and Bioengineering, Shenyang University of Chemical Technology, Shenyang, 110142, China
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Zhang L, Ma H, Qian W, Li H. Protein structure optimization using improved simulated annealing algorithm on a three-dimensional AB off-lattice model. Comput Biol Chem 2020; 85:107237. [PMID: 32109854 DOI: 10.1016/j.compbiolchem.2020.107237] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2018] [Revised: 02/11/2020] [Accepted: 02/15/2020] [Indexed: 01/01/2023]
Abstract
This paper proposed an improved simulated annealing (ISA) algorithm for protein structure optimization based on a three-dimensional AB off-lattice model. In the algorithm, we provided a general formula used for producing initial solution, and designed a multivariable disturbance term, relating to the parameters of simulated annealing and a tuned constant, to generate neighborhood solution. To avoid missing optimal solution, storage operation was performed in searching process. We applied the algorithm to test artificial protein sequences from literature and constructed a benchmark dataset consisting of 10 real protein sequences from the Protein Data Bank (PDB). Otherwise, we generated Cα space-filling model to represent protein folding conformation. The results indicate our algorithm outperforms the five methods before in searching lower energies of artificial protein sequences. In the testing on real proteins, our method can achieve the energy conformations with Cα-RMSD less than 3.0 Å from the PDB structures. Moreover, Cα space-filling model may simulate dynamic change of protein folding conformation at atomic level.
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Affiliation(s)
- Lizhong Zhang
- College of Medicine and Biological Information Engineering, Northeastern University, Shenyang 110169, China; College of Computer Science and Technology, Shenyang University of Chemical Technology, Shenyang 110142, China
| | - He Ma
- College of Medicine and Biological Information Engineering, Northeastern University, Shenyang 110169, China; Key Laboratory of Medical Image Computing (Northeastern University), Ministry of Education, Shenyang 110169, China.
| | - Wei Qian
- Department of Electrical and Computer Engineering, College of Engineering, University of Texas, El Paso TX 79968, USA
| | - Haiyan Li
- College of Pharmaceutical and Bioengineering, Shenyang University of Chemical Technology, Shenyang 110142, China
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Protein folding optimization using differential evolution extended with local search and component reinitialization. Inf Sci (N Y) 2018. [DOI: 10.1016/j.ins.2018.04.072] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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Zhou C, Sun C, Wang B, Wang X. An improved stochastic fractal search algorithm for 3D protein structure prediction. J Mol Model 2018; 24:125. [PMID: 29725774 DOI: 10.1007/s00894-018-3644-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2017] [Accepted: 03/28/2018] [Indexed: 12/14/2022]
Abstract
Protein structure prediction (PSP) is a significant area for biological information research, disease treatment, and drug development and so on. In this paper, three-dimensional structures of proteins are predicted based on the known amino acid sequences, and the structure prediction problem is transformed into a typical NP problem by an AB off-lattice model. This work applies a novel improved Stochastic Fractal Search algorithm (ISFS) to solve the problem. The Stochastic Fractal Search algorithm (SFS) is an effective evolutionary algorithm that performs well in exploring the search space but falls into local minimums sometimes. In order to avoid the weakness, Lvy flight and internal feedback information are introduced in ISFS. In the experimental process, simulations are conducted by ISFS algorithm on Fibonacci sequences and real peptide sequences. Experimental results prove that the ISFS performs more efficiently and robust in terms of finding the global minimum and avoiding getting stuck in local minimums.
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Affiliation(s)
- Changjun Zhou
- Key Laboratory of Advanced Design and Intelligent Computing (Dalian University), Ministry of Education, Dalian, 116622, China.
| | - Chuan Sun
- Key Laboratory of Advanced Design and Intelligent Computing (Dalian University), Ministry of Education, Dalian, 116622, China
| | - Bin Wang
- Key Laboratory of Advanced Design and Intelligent Computing (Dalian University), Ministry of Education, Dalian, 116622, China
| | - Xiaojun Wang
- Key Laboratory of Advanced Design and Intelligent Computing (Dalian University), Ministry of Education, Dalian, 116622, China
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Amorim AR, Neves LA, Valêncio CR, Roberto GF, Zafalon GFD. An approach for COFFEE objective function to global DNA multiple sequence alignment. Comput Biol Chem 2018; 75:39-44. [PMID: 29738913 DOI: 10.1016/j.compbiolchem.2018.04.012] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2016] [Revised: 03/29/2018] [Accepted: 04/20/2018] [Indexed: 10/17/2022]
Abstract
Multiple sequence alignment (MSA) is one of the most important tasks in bioinformatics and it can be used to prediction of structures or functions of unknown proteins and to phylogenetic tree reconstruction. There are many heuristics to perform multiple sequence alignment, as Progressive Alignment, Ant Colony, Genetic Algorithms, among others. Along the years, some tools were proposed to perform MSA and MSA-GA is one of them. The MSA-GA is a tool based on Genetic Algorithm to perform multiple sequence alignment and its results are generally better than other well-known tools in bioinformatics, as Clustal W. The COFFEE objective function was implemented in the MSA-GA in order to allow it to produce better alignments to less similar sequence sets of proteins. Nonetheless, the COFFEE objective function is not suited do perform multiple sequence alignment of nucleotides. Thus, we have modified the COFFEE objective function, previously implemented in the MSA-GA, to allow it to obtain better results also to sequences of nucleotides. Our results have shown that our approach has achieved better results in all cases when compared with standard COFFEE and most of cases when compared with WSP for all test cases from BAliBase and BRAliBase. Moreover, our results are more reliable because their standard deviations have less variation.
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Affiliation(s)
- Anderson Rici Amorim
- Department of Computer Science and Statistics, São Paulo State University, Rua Cristovão Colombo 2265, São José do Rio Preto, São Paulo, Brazil
| | - Leandro Alves Neves
- Department of Computer Science and Statistics, São Paulo State University, Rua Cristovão Colombo 2265, São José do Rio Preto, São Paulo, Brazil
| | - Carlos Roberto Valêncio
- Department of Computer Science and Statistics, São Paulo State University, Rua Cristovão Colombo 2265, São José do Rio Preto, São Paulo, Brazil
| | - Guilherme Freire Roberto
- Department of Computer Science and Statistics, São Paulo State University, Rua Cristovão Colombo 2265, São José do Rio Preto, São Paulo, Brazil
| | - Geraldo Francisco Donegá Zafalon
- Department of Computer Science and Statistics, São Paulo State University, Rua Cristovão Colombo 2265, São José do Rio Preto, São Paulo, Brazil.
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Lin J, Zhong Y, Li E, Lin X, Zhang H. Multi-agent simulated annealing algorithm with parallel adaptive multiple sampling for protein structure prediction in AB off-lattice model. Appl Soft Comput 2018. [DOI: 10.1016/j.asoc.2017.09.037] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
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8
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Selection of appropriate metaheuristic algorithms for protein structure prediction in AB off-lattice model: a perspective from fitness landscape analysis. Inf Sci (N Y) 2017. [DOI: 10.1016/j.ins.2017.01.020] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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9
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Differential evolution for protein folding optimization based on a three-dimensional AB off-lattice model. J Mol Model 2016; 22:252. [DOI: 10.1007/s00894-016-3104-z] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2016] [Accepted: 09/01/2016] [Indexed: 10/20/2022]
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10
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Protein folding optimization based on 3D off-lattice model via an improved artificial bee colony algorithm. J Mol Model 2015; 21:261. [DOI: 10.1007/s00894-015-2806-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Accepted: 08/30/2015] [Indexed: 12/30/2022]
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