[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123913-en":3,"doc-seo-123913-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123913,4398048950312,"Violet","https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908",8,"Research & Report","Mathematical and Machine Learning Approaches for Classification of Protein Secondary Structure Elements from Ca Coordinates - Academic Article","Determining Secondary Structure Elements (SSEs) for proteins is a critical intermediate step for experimental tertiary structure determination. Common tools such as DSSP and STRIDE rely on atomic details, including hydrogen-bond information, and can struggle when spatial atomic data are missing. To mitigate this, three Ca-atom-based classification approaches were developed: a mathematical method, a deep learning method, and an ensemble of five machine learning models. All methods were benchmarked against each other and against PCASSO.","biomolecules  \nArticle  \nMathematical and Machine Learning Approaches for Classification of Protein Secondary Structure Elements from Ca Coordinates  \nAli Sekmen 1, Kamal Al Nasr 1,*, Bahadir Bilgin 1,2, Ahmet Bugra Koku 2,3 and Christopher Jones 1  \nCitation: Sekmen, A.; Al Nasr, K.; Bilgin, B.; Koku, A.B.; Jones, C. Mathematical and Machine Learning Approaches for Classification of Protein Secondary Structure Elements from Ca Coordinates. Biomolecules 2023, 13, 923. [https://](https://)[ ](https://)[doi.org/10.3390/biom13060923](doi.org/10.3390/biom13060923)  \nAcademic Editors: Jose M. Guisan, Yung-Chuan Liu and Antonio Zuorro  \nReceived: 3 May 2023  \nRevised: 16 May 2023  \nAccepted: 16 May 2023  \nPublished: 31 May 2023  \nCopyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Department of Computer Science, Tennessee State University, Nashville, TN 37209, USA;  \n[asekmen@tnstate.edu](asekmen@tnstate.edu) (A.S.); [bbilgin@tnstate.edu](bbilgin@tnstate.edu) (B.B.); [cjone141@tnstate.edu](cjone141@tnstate.edu) (C.J.)  \n2 Department of Mechanical Engineering, Middle East Technical University, Ankara 06800, Türkiye; [kbugra@metu.edu.tr](kbugra@metu.edu.tr)  \n3 Center for Robotics and AI, Middle East Technical University, Ankara 06800, Türkiye  \n* Correspondence: [kalnasr@tnstate.edu](kalnasr@tnstate.edu)  \nAbstract: Determining Secondary Structure Elements (SSEs) for any protein is crucial as an intermediate step for experimental tertiary structure determination. SSEs are identified using popular tools such as DSSP and STRIDE. These tools use atomic information to locate hydrogen bonds to identify SSEs. When some spatial atomic details are missing, locating SSEs becomes a hinder. To address the problem, when some atomic information is missing, three approaches for classifying SSE types using Ca atoms in protein chains were developed: (1) a mathematical approach,(2) a deep learning approach, and (3) an ensemble of five machine learning models. The proposed methods were compared against each other and with a state-of-the-art approach, PCASSO.  \nKeywords: protein structure modeling; protein secondary structure; secondary structure identification; machine learning; protein trace; mathematical modeling  \n1. Introduction  \nProteins form 3D structures, via atomic and molecular interactions, that determine their functions such as material or signal transporting, cell adhesion, and cell cycle [1,2]. Primary structures (sequences of amino acids in polypeptide chains) are known for a large set of proteins. However, only a small portion of them (\u003C0.1%) have known tertiary structures (folding of a polypeptide chain into a 3D shape) and quaternary structures (special 3D arrangements of all polypeptide chains of a protein) via experimentation. Secondary structures (repeated patterns of folding of the protein backbone) are important to analyze relationship between primary and tertiary structures. Once the structure of a protein is determined, it is uploaded into a publicly available database such as Protein Data Bank (PDB) [3,4], which had 205 K proteins as of May 2023.  \nThere are three experimental techniques used for determining 3D structures of proteins: X-ray crystallography [5–7], Nuclear Magnetic Resonance (NMR) spectroscopy [8,9], and Cryo-electron microscopy (Cryo-EM) [5,10,11] .  \n• In a crystal, atoms and molecules arrange themselves in regular arrays and X-ray crystallography technology, which has been in use since the 1950s, utilizes this fact to generate atomic and molecular structure of the crystal. In order to determine the atomic structure of a protein, it first needs to be crystallized. However, protein crystallization is a difficult","cbCail9hmWsCtHPJ","https://ap.wps.com/l/cbCail9hmWsCtHPJ","pdf",1293939,1,18,"English","en",105,"# Introduction\n## Protein structure levels and the role of secondary structure\n## Experimental methods for protein 3D structure\n## Computational modeling and its limitations\n# Methods for SSE classification from Ca coordinates\n## Mathematical approach\n## Deep learning approach\n## Ensemble of five machine learning models\n# Comparison and benchmarking","[{\"question\":\"Why is Secondary Structure Element (SSE) classification important in protein structure determination?\",\"answer\":\"SSEs provide an essential intermediate representation that supports experimental determination of tertiary protein structures.\"},{\"question\":\"What problem arises when atomic details are missing in SSE identification tools?\",\"answer\":\"Tools like DSSP and STRIDE depend on atomic information and hydrogen-bond localization; missing spatial atomic data makes SSE detection hindered.\"},{\"question\":\"Which approaches were developed to classify SSE types using Ca atoms, and how were they evaluated?\",\"answer\":\"Three Ca-based approaches were proposed: a mathematical approach, a deep learning approach, and an ensemble of five machine learning models. They were compared with each other and against the state-of-the-art method PCASSO.\"}]","Mathematical and Machine Learning Approaches for Classification of Protein Secondary Structure Elements from Ca Coordinates - Academic Article | PDF",1785819209,45,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"mathematical-and-machine-learning-approaches-for-classification-of-protein-secondary-structure-elements-from-ca-coordinates-academic-article","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/mathematical-and-machine-learning-approaches-for-classification-of-protein-secondary-structure-elements-from-ca-coordinates-academic-article/123913/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-04",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"Why is Secondary Structure Element (SSE) classification important in protein structure determination?","Question",{"text":76,"@type":77},"SSEs provide an essential intermediate representation that supports experimental determination of tertiary protein structures.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What problem arises when atomic details are missing in SSE identification tools?",{"text":81,"@type":77},"Tools like DSSP and STRIDE depend on atomic information and hydrogen-bond localization; missing spatial atomic data makes SSE detection hindered.",{"name":83,"@type":74,"acceptedAnswer":84},"Which approaches were developed to classify SSE types using Ca atoms, and how were they evaluated?",{"text":85,"@type":77},"Three Ca-based approaches were proposed: a mathematical approach, a deep learning approach, and an ensemble of five machine learning models. 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