{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T21:20:32Z","timestamp":1777411232822,"version":"3.51.4"},"reference-count":57,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T00:00:00Z","timestamp":1739836800000},"content-version":"vor","delay-in-days":88,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62273153"],"award-info":[{"award-number":["62273153"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021171","name":"Guangdong Basic and Applied Basic Research Foundation","doi-asserted-by":"publisher","award":["2024A1515010900"],"award-info":[{"award-number":["2024A1515010900"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,11,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Modelling biological systems depends on the availability of data and components of the system at hand. As our understanding of these systems evolves, the ability to gradually refine models by adding new components of different formalisms covering stochastic, discrete, deterministic, and uncertainty without starting from scratch becomes essential. However, there remains a significant gap in the availability of methodologies and tool support for incrementally modelling and analysing complex biological systems in a flexible and intuitive manner. In this paper, we employ fuzzy hybrid Petri nets as a powerful expressive tool for presenting an incremental modelling and analysis protocol of biological systems. We demonstrate the utility of our protocol through a case study on cholesterol and lipoprotein metabolism and hypercholesterolemia therapy. Our model not only captures the underlying biochemical processes, but also quantitatively analyses how cholesterol levels are regulated, offering insights into potential therapeutic strategies for diseases associated with elevated cholesterol levels. The results confirm the validity and flexibility of our approach in representing complex biological processes and therapeutic interventions.<\/jats:p>","DOI":"10.1093\/bib\/bbaf029","type":"journal-article","created":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T12:47:11Z","timestamp":1739882831000},"source":"Crossref","is-referenced-by-count":1,"title":["Incremental modelling and analysis of biological systems with fuzzy hybrid Petri nets"],"prefix":"10.1093","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8878-5871","authenticated-orcid":false,"given":"George","family":"Assaf","sequence":"first","affiliation":[{"name":"Department of Computer Science , Brandenburg University of Technology Cottbus-Senftenberg, 03013 Cottbus,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9415-0496","authenticated-orcid":false,"given":"Fei","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Software Engineering , South China University of Technology, No. 381 Wushan Road, Guangzhou 510006, P.R.","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Monika","family":"Heiner","sequence":"additional","affiliation":[{"name":"Department of Computer Science , Brandenburg University of Technology Cottbus-Senftenberg, 03013 Cottbus,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,2,18]]},"reference":[{"key":"2025021812465937400_ref1","volume-title":"Systems Biology: Properties of Reconstructed Networks","author":"Bernhard","year":"2006"},{"key":"2025021812465937400_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-10669-9","volume-title":"Discrete, Continuous, and Hybrid Petri Nets","author":"David","year":"2010"},{"key":"2025021812465937400_ref3","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/B978-0-12-801213-0.00007-1","article-title":"BioModel engineering with Petri nets","author":"Bl\u00e4tke","year":"2015"},{"key":"2025021812465937400_ref4","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/978-3-030-31304-3_17","article-title":"Biochemical reaction networks with fuzzy kinetic parameters in snoopy","volume-title":"Proc. CMSB 2019","author":"Assaf","year":"2019"},{"key":"2025021812465937400_ref5","article-title":"Simulative analysis of coloured extended stochastic Petri nets","author":"Rohr","year":"2017"},{"key":"2025021812465937400_ref7","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1089\/10665270252833208","article-title":"Modeling and simulation of genetic regulatory systems: a literature review","volume":"9","author":"de Jong","year":"2002","journal-title":"J Comput Biol"},{"key":"2025021812465937400_ref8","doi-asserted-by":"publisher","first-page":"3327","DOI":"10.1105\/tpc.107.054700","article-title":"Network inference, analysis, and modeling in systems biology","volume":"19","author":"R\u00e9ka","year":"2007","journal-title":"Plant Cell"},{"key":"2025021812465937400_ref9","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1016\/j.bej.2006.11.002","article-title":"Kinetic modeling using S-systems and lin-log approaches","volume":"33","author":"Feng-Sheng","year":"2007","journal-title":"Biochem Eng J"},{"key":"2025021812465937400_ref10","doi-asserted-by":"publisher","DOI":"10.1093\/bib\/bbae344","article-title":"A novel deep machine learning algorithm with dimensionality and size reduction approaches for feature elimination: thyroid cancer diagnoses with randomly missing data","volume":"25","author":"Onder","year":"2024","journal-title":"Brief Bioinform"},{"key":"2025021812465937400_ref11","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1186\/s12859-024-05729-2","article-title":"Deep self-supervised machine learning algorithms with a novel feature elimination and selection approaches for blood test-based multi-dimensional health risks classification","volume":"25","author":"Onder","year":"2024","journal-title":"BMC Bioinformatics"},{"key":"2025021812465937400_ref12","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1186\/1471-2105-8-433","article-title":"Incremental and unifying modelling formalism for biological interaction networks","volume":"8","author":"Yartseva","year":"2007","journal-title":"BMC Bioinformatics"},{"key":"2025021812465937400_ref13","doi-asserted-by":"publisher","first-page":"5","DOI":"10.3233\/ISB-2010-0415","article-title":"Cell illustrator 4.0: a computational platform for systems biology","volume":"10","author":"Masao","year":"2010","journal-title":"In Silico Biol"},{"key":"2025021812465937400_ref14","doi-asserted-by":"publisher","first-page":"i583","DOI":"10.1093\/bioinformatics\/bty272","article-title":"The kappa platform for rule-based modeling","volume":"34","author":"Boutillier","year":"2018","journal-title":"Bioinformatics"},{"key":"2025021812465937400_ref15","doi-asserted-by":"publisher","DOI":"10.26127\/BTUOpen-5851","article-title":"Fuzzy coloured Petri nets for modelling biological systems with uncertain kinetic parameters","author":"Assaf","year":"2022"},{"key":"2025021812465937400_ref16","doi-asserted-by":"publisher","first-page":"53","DOI":"10.3233\/FI-2018-1674","article-title":"Adaptive and bio-semantics of continuous Petri nets: choosing the appropriate interpretation","volume":"160","author":"Herajy","year":"2018","journal-title":"Fundam Inf"},{"key":"2025021812465937400_ref17","doi-asserted-by":"publisher","DOI":"10.3390\/pr6080134","article-title":"An integrated mathematical model of cellular cholesterol biosynthesis and lipoprotein metabolism","volume":"6","author":"Pool","year":"2018","journal-title":"Processes"},{"key":"2025021812465937400_ref18","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0264903","article-title":"A mathematical model of in vitro hepatocellular cholesterol and lipoprotein metabolism for hyperlipidemia therapy","volume":"17","author":"Efremov","year":"2022","journal-title":"PloS One"},{"key":"2025021812465937400_ref19","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1093\/emboj\/19.5.819","article-title":"Crystal structure of the catalytic portion of human HMG-CoA reductase: insights into regulation of activity and catalysis","volume":"19","author":"Istvan","year":"2000","journal-title":"EMBO J"},{"key":"2025021812465937400_ref20","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1111\/j.1520-037X.2003.01691.x","article-title":"The intestinal absorption of biliary and dietary cholesterol as a drug target for lowering the plasma cholesterol level","volume":"6","author":"Turley","year":"2003","journal-title":"Prev Cardiol"},{"key":"2025021812465937400_ref21","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.jtbi.2014.01.013","article-title":"A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway","volume":"349","author":"Bhattacharya","year":"2014","journal-title":"J Theor Biol"},{"key":"2025021812465937400_ref22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1146\/annurev.cb.01.110185.000245","article-title":"Receptor-mediated endocytosis: concepts emerging from the ldl receptor system","volume":"1","author":"Goldstein","year":"1985","journal-title":"Annu Rev Cell Biol"},{"key":"2025021812465937400_ref23","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1146\/annurev.ge.24.120190.001025","article-title":"The LDL receptor locus in familial hypercholesterolemia: mutational analysis of a membrane protein","volume":"24","author":"Hobbs","year":"1990","journal-title":"Annu Rev Genet"},{"key":"2025021812465937400_ref24","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1007\/978-3-642-31131-4_22","article-title":"Snoopy \u2013 a unifying Petri net tool","volume-title":"Proc. PETRI NETS 2012","author":"Heiner","year":"2012"},{"key":"2025021812465937400_ref25","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1186\/s12918-018-0568-8","article-title":"Fuzzy Petri nets for modelling of uncertain biological systems","volume":"12","author":"Liu","year":"2018","journal-title":"Brief Bioinform"},{"key":"2025021812465937400_ref26","doi-asserted-by":"publisher","first-page":"942","DOI":"10.1016\/j.nahs.2012.05.004","article-title":"Hybrid representation and simulation of stiff biochemical networks","volume":"6","author":"Herajy","year":"2012","journal-title":"J Nonlinear Anal: Hybrid Syst"},{"key":"2025021812465937400_ref27","volume-title":"Computational Steering of Multi-Scale Biochemical Networks","author":"Herajy","year":"2013"},{"key":"2025021812465937400_ref28","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/978-3-642-40465-8_7","article-title":"Hybrid Petri nets for modelling the eukaryotic cell cycle","author":"Herajy","year":"2013"},{"key":"2025021812465937400_ref29","doi-asserted-by":"publisher","DOI":"10.3389\/fenvs.2015.00053","article-title":"Modeling and simulation of multi-scale environmental systems with generalized hybrid Petri nets","volume":"3","author":"Herajy","year":"2015","journal-title":"Front Environ Sci"},{"key":"2025021812465937400_ref30","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/978-3-319-47151-8_2","article-title":"Accelerated simulation of hybrid biological models with quasi-disjoint deterministic and stochastic subnets","volume-title":"Hybrid Systems Biology: 5th International Workshop, HSB 2016","author":"Herajy","year":"2016"},{"key":"2025021812465937400_ref31","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1186\/s12918-017-0449-6","article-title":"Snoopy\u2019s hybrid simulator: a tool to construct and simulate hybrid biological models","volume":"11","author":"Herajy","year":"2017","journal-title":"BMC Syst Biol"},{"key":"2025021812465937400_ref32","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.nahs.2017.09.002","article-title":"Efficient modelling of yeast cell cycles based on multisite phosphorylation using coloured hybrid Petri nets with marking-dependent arc weights","volume":"27","author":"Herajy","year":"2018","journal-title":"Nonlinear Anal: Hybrid Syst"},{"key":"2025021812465937400_ref33","doi-asserted-by":"publisher","first-page":"2340","DOI":"10.1021\/j100540a008","article-title":"Exact stochastic simulation of coupled chemical reactions","volume":"81","author":"Gillespie","year":"1977","journal-title":"J Phys Chem"},{"key":"2025021812465937400_ref34","volume-title":"Markov Processes: An Introduction for Physical Scientists","author":"Gillespie","year":"1991"},{"key":"2025021812465937400_ref35","doi-asserted-by":"publisher","first-page":"1725","DOI":"10.1109\/TCBB.2022.3213914","article-title":"Assessment of prediction uncertainty quantification methods in systems biology","volume":"20","author":"Villaverde","year":"2023","journal-title":"IEEE\/ACM Trans Comput Biol Bioinform"},{"key":"2025021812465937400_ref36","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1186\/s12918-018-0568-8","article-title":"Modeling biological systems with uncertain kinetic data using fuzzy continuous Petri nets","volume":"12","author":"Liu","year":"2018","journal-title":"BMC Syst Biol"},{"key":"2025021812465937400_ref37","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1093\/bib\/bbz114","article-title":"Hybrid modelling of biological systems using fuzzy continuous Petri nets","volume":"22","author":"Liu","year":"2019","journal-title":"Brief Bioinform"},{"key":"2025021812465937400_ref38","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.tcs.2021.04.011","article-title":"Colouring fuzziness for systems biology","volume":"875","author":"Assaf","year":"2021","journal-title":"Theor Comput Sci"},{"key":"2025021812465937400_ref39","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf Control"},{"key":"2025021812465937400_ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.xpro.2023.102651","article-title":"Protocol for biomodel engineering of unilevel to multilevel biological models using colored Petri nets","volume":"4","author":"Liu","year":"2023","journal-title":"STAR Protocols"},{"key":"2025021812465937400_ref41","article-title":"Manual for colored Petri nets in Snoopy","author":"Liu","year":"2012"},{"key":"2025021812465937400_ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2021.104533","article-title":"A Petri nets-based framework for whole-cell modeling","volume":"210","author":"Liu","year":"2021","journal-title":"Biosystems"},{"key":"2025021812465937400_ref43","doi-asserted-by":"publisher","DOI":"10.1186\/s12859-019-2690-z","article-title":"Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking","volume":"20","author":"Gilbert","year":"2019","journal-title":"BMC Bioinformatics"},{"key":"2025021812465937400_ref44","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1007\/978-3-030-51831-8_16","article-title":"Efficient unfolding of coloured Petri nets using interval decision diagrams","volume-title":"Proc. PETRI NETS 2020","author":"Schwarick","year":"2020"},{"key":"2025021812465937400_ref45","doi-asserted-by":"publisher","first-page":"2884","DOI":"10.1016\/j.tcs.2010.06.030","article-title":"IDD-based model validation of biochemical networks","volume":"412","author":"Schwarick","year":"2011","journal-title":"Theor Comput Sci"},{"key":"2025021812465937400_ref46","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1093\/bib\/bbx150","article-title":"Coloured Petri nets for multilevel, multiscale, and multidimensional modelling of biological systems","volume":"20","author":"Liu","year":"2019","journal-title":"Brief Bioinform"},{"key":"2025021812465937400_ref47","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1002\/9781119716600.ch2","article-title":"Petri nets for systems biology modelling and analysis","author":"Liu","year":"2022"},{"key":"2025021812465937400_ref48","doi-asserted-by":"publisher","DOI":"10.1177\/1177625007001000","article-title":"Computational systems biology in cancer: modeling methods and applications","volume":"1","author":"Wayne","year":"2007","journal-title":"Gene Regul Syst Biol"},{"key":"2025021812465937400_ref49","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1186\/1742-4682-9-46","article-title":"Dynamics of glucose and insulin concentration connected to the $\\beta $-cell cycle: model development and analysis","volume":"9","author":"Gallenberger","year":"2012","journal-title":"Theor Biol Med Model"},{"key":"2025021812465937400_ref50","doi-asserted-by":"publisher","first-page":"106507","DOI":"10.1016\/j.compchemeng.2019.06.032","article-title":"A multi-scale model for low-density lipoprotein cholesterol (LDL-C) regulation in the human body: application to quantitative systems pharmacology","volume":"130","author":"Toroghi","year":"2019","journal-title":"Comput Chem Eng"},{"key":"2025021812465937400_ref51","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1186\/1752-0509-6-130","article-title":"A whole-body mathematical model of cholesterol metabolism and its age-associated dysregulation","volume":"6","author":"McAuley","year":"2012","journal-title":"BMC Syst Biol"},{"key":"2025021812465937400_ref52","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1057\/jos.2012.20","article-title":"Verification and validation of simulation models","volume":"7","author":"Sargent","year":"2013","journal-title":"J Simul"},{"key":"2025021812465937400_ref53","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/978-3-319-15099-4_3","volume-title":"Measures of Quality for Model Validation","author":"Murray-S","year":"2015"},{"key":"2025021812465937400_ref54","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/s10270-019-00754-9","article-title":"A framework for FMI-based co-simulation of human\u2013machine interfaces","volume":"19","author":"Maurizio","year":"2020","journal-title":"Softw Syst Model"},{"key":"2025021812465937400_ref55","doi-asserted-by":"publisher","first-page":"235","DOI":"10.3384\/ecp14096235","article-title":"Model-based integration platform for FMI co-simulation and heterogeneous simulations of cyber-physical systems","volume-title":"Proceedings of the 10th International Modelica Conference","author":"Neema","year":"2014"},{"key":"2025021812465937400_ref56","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1007\/978-3-319-19488-2_10","article-title":"Charlie \u2013 an extensible Petri net analysis tool","volume-title":"Proc. PETRI NETS 2015","author":"Heiner","year":"2015"},{"key":"2025021812465937400_ref57","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/978-3-642-38697-8_21","article-title":"MARCIE - model checking and reachability analysis done effiCIEntly","volume-title":"Proc. PETRI NETS 2013","author":"Heiner","year":"2013"},{"key":"2025021812465937400_ref58","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1093\/jpp\/rgab002","article-title":"Bile acid sequestrants: a review of mechanism and design","volume":"73","author":"Feng","year":"2021","journal-title":"J Pharm Pharmacol"}],"container-title":["Briefings in Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bib\/article-pdf\/26\/1\/bbaf029\/61938933\/bbaf029.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bib\/article-pdf\/26\/1\/bbaf029\/61938933\/bbaf029.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T12:47:15Z","timestamp":1739882835000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bib\/article\/doi\/10.1093\/bib\/bbaf029\/8020207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,22]]},"references-count":57,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,11,22]]}},"URL":"https:\/\/doi.org\/10.1093\/bib\/bbaf029","relation":{},"ISSN":["1467-5463","1477-4054"],"issn-type":[{"value":"1467-5463","type":"print"},{"value":"1477-4054","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,1]]},"published":{"date-parts":[[2024,11,22]]},"article-number":"bbaf029"}}