{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:53:32Z","timestamp":1760234012579,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,3,21]],"date-time":"2021-03-21T00:00:00Z","timestamp":1616284800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/M026981\/1"],"award-info":[{"award-number":["EP\/M026981\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Machine learning (ML)-based algorithms are playing an important role in cancer diagnosis and are increasingly being used to aid clinical decision-making. However, these commonly operate as \u2018black boxes\u2019 and it is unclear how decisions are derived. Recently, techniques have been applied to help us understand how specific ML models work and explain the rational for outputs. This study aims to determine why a given type of cancer has a certain phenotypic characteristic. Cancer results in cellular dysregulation and a thorough consideration of cancer regulators is required. This would increase our understanding of the nature of the disease and help discover more effective diagnostic, prognostic, and treatment methods for a variety of cancer types and stages. Our study proposes a novel explainable analysis of potential biomarkers denoting tumorigenesis in non-small cell lung cancer. A number of these biomarkers are known to appear following various treatment pathways. An enhanced analysis is enabled through a novel mathematical formulation for the regulators of mRNA, the regulators of ncRNA, and the coupled mRNA\u2013ncRNA regulators. Temporal gene expression profiles are approximated in a two-dimensional spatial domain for the transition states before converging to the stationary state, using a system comprised of coupled-reaction partial differential equations. Simulation experiments demonstrate that the proposed mathematical gene-expression profile represents a best fit for the population abundance of these oncogenes. In future, our proposed solution can lead to the development of alternative interpretable approaches, through the application of ML models to discover unknown dynamics in gene regulatory systems.<\/jats:p>","DOI":"10.3390\/s21062190","type":"journal-article","created":{"date-parts":[[2021,3,21]],"date-time":"2021-03-21T23:47:41Z","timestamp":1616370461000},"page":"2190","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Novel Coupled Reaction-Diffusion System for Explainable Gene Expression Profiling"],"prefix":"10.3390","volume":"21","author":[{"given":"Muhamed Wael","family":"Farouq","sequence":"first","affiliation":[{"name":"Department of Statistics, Mathematics and Insurance, University of Ain Shams, Cairo 11566, Egypt"},{"name":"School of Computing, Edinburgh Napier University, Edinburgh EH11 4BN, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2133-0757","authenticated-orcid":false,"given":"Wadii","family":"Boulila","sequence":"additional","affiliation":[{"name":"RIADI Laboratory, National School of Computer Sciences, University of Manouba, Manouba 2010, Tunisia"},{"name":"IS Department, College of Computer Science and Engineering, Taibah University, Medina 42353, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0559-8289","authenticated-orcid":false,"given":"Zain","family":"Hussain","sequence":"additional","affiliation":[{"name":"College of Medicine and Veterinary Medicine, University of Edinburgh, Edinburgh EH8 9YL, UK"}]},{"given":"Asrar","family":"Rashid","sequence":"additional","affiliation":[{"name":"Midland Doctors, Derby DE73 7HA, UK"}]},{"given":"Moiz","family":"Shah","sequence":"additional","affiliation":[{"name":"NHS Greater Glasgow and Clyde, Glasgow G12 0XH, UK"}]},{"given":"Sajid","family":"Hussain","sequence":"additional","affiliation":[{"name":"Albany Gastroenterology Consultants, Albany, NY 12206, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7063-6870","authenticated-orcid":false,"given":"Nathan","family":"Ng","sequence":"additional","affiliation":[{"name":"College of Medicine and Veterinary Medicine, University of Edinburgh, Edinburgh EH8 9YL, UK"}]},{"given":"Dominic","family":"Ng","sequence":"additional","affiliation":[{"name":"Faculty of Biology, Medicine and Health, University of Manchester, Manchester M13 9PL, UK"}]},{"given":"Haris","family":"Hanif","sequence":"additional","affiliation":[{"name":"Faculty of Biology, Medicine and Health, University of Manchester, Manchester M13 9PL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2316-3334","authenticated-orcid":false,"given":"Mohamad Guftar","family":"Shaikh","sequence":"additional","affiliation":[{"name":"NHS Greater Glasgow and Clyde, Glasgow G12 0XH, UK"}]},{"given":"Aziz","family":"Sheikh","sequence":"additional","affiliation":[{"name":"College of Medicine and Veterinary Medicine, University of Edinburgh, Edinburgh EH8 9YL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8080-082X","authenticated-orcid":false,"given":"Amir","family":"Hussain","sequence":"additional","affiliation":[{"name":"School of Computing, Edinburgh Napier University, Edinburgh EH11 4BN, UK"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,21]]},"reference":[{"key":"ref_1","unstructured":"Brazma, A., Parkinson, H., Schlitt, T., and Shojatalab, M. 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