{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T01:04:38Z","timestamp":1781053478344,"version":"3.54.1"},"reference-count":60,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,12,4]],"date-time":"2019-12-04T00:00:00Z","timestamp":1575417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Protein folding problem (PFP) consists of determining the functional three-dimensional structure of a target protein. PFP is an optimization problem where the objective is to find the structure with the lowest Gibbs free energy. It is significant to solve PFP for use in medical and pharmaceutical applications. Hybrid simulated annealing algorithms (HSA) use a kind of simulated annealing or Monte Carlo method, and they are among the most efficient for PFP. The instances of PFP can be classified as follows: (a) Proteins with a large number of amino acids and (b) peptides with a small number of amino acids. Several HSA have been positively applied for the first case, where I-Tasser has been one of the most successful in the CASP competition. PEP-FOLD3 and golden ratio simulated annealing (GRSA) are also two of these algorithms successfully applied to peptides. This paper presents an enhanced golden simulated annealing (GRSA2) where soft perturbations (collision operators), named \u201con-wall ineffective collision\u201d and \u201cintermolecular ineffective collision\u201d, are applied to generate new solutions in the metropolis cycle. GRSA2 is tested with a dataset for peptides previously proposed, and a comparison with PEP-FOLD3 and I-Tasser is presented. According to the experimentation, GRSA2 has an equivalent performance to those algorithms.<\/jats:p>","DOI":"10.3390\/axioms8040136","type":"journal-article","created":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T03:16:36Z","timestamp":1575515796000},"page":"136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["GRSA Enhanced for Protein Folding Problem in the Case of Peptides"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9307-0734","authenticated-orcid":false,"given":"Juan","family":"Frausto-Sol\u00eds","sequence":"first","affiliation":[{"name":"Divisi\u00f3n de estudios de posgrado e investigaci\u00f3n, Tecnol\u00f3gico Nacional de M\u00e9xico, Instituto Tecnol\u00f3gico de Ciudad Madero, Madero 89440, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9448-1946","authenticated-orcid":false,"given":"Juan Paulo","family":"S\u00e1nchez-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Divisi\u00f3n de estudios de posgrado e investigaci\u00f3n, Tecnol\u00f3gico Nacional de M\u00e9xico, Instituto Tecnol\u00f3gico de Ciudad Madero, Madero 89440, Mexico"},{"name":"Direcci\u00f3n de Inform\u00e1tica, Electr\u00f3nica y Telecomunicaciones, Universidad Polit\u00e9cnica del Estado de Morelos, Boulevard Cuauhn\u00e1huac 566, Jiutepec 62574, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fanny G.","family":"Maldonado-Nava","sequence":"additional","affiliation":[{"name":"Divisi\u00f3n de estudios de posgrado e investigaci\u00f3n, Tecnol\u00f3gico Nacional de M\u00e9xico, Instituto Tecnol\u00f3gico de Ciudad Madero, Madero 89440, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juan J.","family":"Gonz\u00e1lez-Barbosa","sequence":"additional","affiliation":[{"name":"Divisi\u00f3n de estudios de posgrado e investigaci\u00f3n, Tecnol\u00f3gico Nacional de M\u00e9xico, Instituto Tecnol\u00f3gico de Ciudad Madero, Madero 89440, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.tibtech.2013.10.008","article-title":"Protein Folding and de Novo Protein Design for Biotechnological Applications","volume":"32","author":"Khoury","year":"2014","journal-title":"Trends Biotechnol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1126\/science.181.4096.223","article-title":"Principles that Govern the Folding of Protein Chains","volume":"181","author":"Anfinsen","year":"1973","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1039\/C6MB00866F","article-title":"Screening Methods for Identifying Pharmacological Chaperones","volume":"13","author":"Shin","year":"2017","journal-title":"Mol. 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