{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"institution":[{"name":"bioRxiv"}],"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:10:13Z","timestamp":1792786213079,"version":"4.5.0"},"posted":{"date-parts":[[2025,9,29]]},"group-title":"Systems Biology","reference-count":59,"publisher":"openRxiv","license":[{"start":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T00:00:00Z","timestamp":1759104000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"name":"Fondation CHU Sainte-Justine","id":[{"id":"https:\/\/ror.org\/0122m4141","id-type":"ROR","asserted-by":"crossref"}]},{"name":"Vanier Canada Graduate Scholarship"},{"name":"National Institutes of Health","award":["R01 AI170115"],"award-info":[{"award-number":["R01 AI170115"]}]},{"award":["Computational Immunology"],"award-info":[{"award-number":["Computational Immunology"]}],"id":[{"id":"https:\/\/ror.org\/0517h6h17","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2026,9,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                <jats:p>The inherent heterogeneity of complex biological systems makes it difficult to experimentally and clinically explore individual outcomes. Mechanistic mathematical models are essential tools for studying such heterogeneity. Thus, there is increasing interest in integrating newer mechanistic model-based techniques, like virtual patient cohorts and virtual clinical trials, within experimental and regulatory pipelines to probe relationships that may be difficult or impossible to ascertain through traditional wet-lab or clinical experimentation alone. Approximate Bayesian Computation (ABC) is an attractive method for generating virtual patient cohorts and running virtual clinical trials. However, ABC-based approaches can become computationally demanding when stringent acceptance criteria are imposed. In response, we developed a model-based technique called trajectory-matching random-walk feasibility sampling (TM-RWFS) that captures the variability of complex biological systems by constraining model trajectories between the upper and lower bounds of available data to generate heterogeneity. By testing the method\u2019s performance on existing mechanistic models, we show that TM-RWS generates parameter sets whose simulated trajectories reproduce the observed variability in biological systems of varying complexity while maintaining computational efficiency. Thus, TM-RWFS is a fast, new approach for generating heterogeneity in mechanistic mathematical models with implications for model-based experimental design, virtual patient cohorts, and virtual clinical trials.<\/jats:p>","DOI":"10.1101\/2025.09.26.678800","type":"posted-content","created":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T19:45:13Z","timestamp":1759175113000},"source":"Crossref","is-referenced-by-count":1,"title":["Trajectory matching-random walk feasibility sampling for simulating heterogeneous dynamics in mechanistic models"],"prefix":"10.64898","author":[{"given":"Fatemeh","family":"Beigmohammadi","sequence":"first","affiliation":[{"name":"Sainte-Justine University Hospital Research Centre, Montr\u00e9al, Qu\u00e9bec, Canada"},{"name":"Department of Mathematics and Statistics, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, Qu\u00e9bec, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jordan J.A.","family":"Weaver","sequence":"additional","affiliation":[{"name":"Department of Pediatrics, University of Tennessee Health Science Center, Memphis, TN USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sol\u00e8ne","family":"Hegarty-Cremer","sequence":"additional","affiliation":[{"name":"Sainte-Justine University Hospital Research Centre, Montr\u00e9al, Qu\u00e9bec, Canada"},{"name":"Department of Mathematics and Statistics, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, Qu\u00e9bec, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cailan","family":"Jeynes-Smith","sequence":"additional","affiliation":[{"name":"Department of Pediatrics, University of Tennessee Health Science Center, Memphis, TN USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7092-6904","authenticated-orcid":false,"given":"Amber M.","family":"Smith","sequence":"additional","affiliation":[{"name":"Department of Pediatrics, University of Tennessee Health Science Center, Memphis, TN USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4852-4770","authenticated-orcid":false,"given":"Morgan","family":"Craig","sequence":"additional","affiliation":[{"name":"Sainte-Justine University Hospital Research Centre, Montr\u00e9al, Qu\u00e9bec, Canada"},{"name":"Department of Mathematics and Statistics, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, Qu\u00e9bec, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"54368","reference":[{"key":"2026092502101359000_2025.09.26.678800v3.1","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s11481-009-9164-4","article-title":"Heterogeneity of microglial activation in the innate immune response in the brain","volume":"4","year":"2009","journal-title":"Journal of neuroimmune pharmacology"},{"key":"2026092502101359000_2025.09.26.678800v3.2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1818210116"},{"key":"2026092502101359000_2025.09.26.678800v3.3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2015.08.027"},{"key":"2026092502101359000_2025.09.26.678800v3.4","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1038\/s41586-021-03739-1","article-title":"Age-related immune response heterogeneity to SARS-CoV-2 vaccine BNT162b2","volume":"596","year":"2021","journal-title":"Nature"},{"key":"2026092502101359000_2025.09.26.678800v3.5","first-page":"1156","article-title":"Virtual Clinical Trial Reveals Significant Clinical Potential of Targeting Tumor-Associated Macrophages and Microglia to Treat Glioblastoma","volume":"14","year":"2025","journal-title":"CPT: Pharmacometrics & Systems Pharmacology"},{"key":"2026092502101359000_2025.09.26.678800v3.6","doi-asserted-by":"crossref","unstructured":"Deng, X. , Farhang-Sardroodi, S. & Craig, M. Predicting age-related determinants of heterogeneous outcomes to COVID-19 mRNA vaccines through mathematical modelling. medRxiv, 2025.2002.2014.25322308 (2025).","DOI":"10.1101\/2025.02.14.25322308"},{"key":"2026092502101359000_2025.09.26.678800v3.7","doi-asserted-by":"publisher","DOI":"10.1371\/journal.ppat.1009753"},{"key":"2026092502101359000_2025.09.26.678800v3.8","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btaa1026"},{"key":"2026092502101359000_2025.09.26.678800v3.9","doi-asserted-by":"publisher","DOI":"10.1002\/psp4"},{"key":"2026092502101359000_2025.09.26.678800v3.10","doi-asserted-by":"crossref","first-page":"1174647","DOI":"10.3389\/fsysb.2023.1174647","article-title":"A practical guide for the generation of model-based virtual clinical trials","volume":"3","year":"2023","journal-title":"Frontiers in Systems Biology"},{"key":"2026092502101359000_2025.09.26.678800v3.11","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1038\/s41746-024-01188-4","article-title":"From virtual patients to digital twins in immuno-oncology: lessons learned from mechanistic quantitative systems pharmacology modeling","volume":"7","year":"2024","journal-title":"NPJ Digital Medicine"},{"key":"2026092502101359000_2025.09.26.678800v3.12","doi-asserted-by":"crossref","unstructured":"Braniff, N. et al. An integrated quantitative systems pharmacology virtual population approach for calibration with oncology efficacy endpoints. CPT: Pharmacometrics & Systems Pharmacology (2025).","DOI":"10.1002\/psp4.13270"},{"key":"2026092502101359000_2025.09.26.678800v3.13","doi-asserted-by":"publisher","DOI":"10.1007\/s10928-022-09826-8"},{"key":"2026092502101359000_2025.09.26.678800v3.14","doi-asserted-by":"publisher","DOI":"10.1016\/j.pbiomolbio.2018.06.002"},{"key":"2026092502101359000_2025.09.26.678800v3.15","doi-asserted-by":"publisher","DOI":"10.1093\/bib\/bby043"},{"key":"2026092502101359000_2025.09.26.678800v3.16","doi-asserted-by":"crossref","first-page":"713118","DOI":"10.3389\/fphys.2021.713118","article-title":"Clinically-driven virtual patient cohorts generation: an application to aorta","volume":"12","year":"2021","journal-title":"Frontiers in Physiology"},{"key":"2026092502101359000_2025.09.26.678800v3.17","doi-asserted-by":"publisher","DOI":"10.1093\/genetics\/162.4.2025"},{"key":"2026092502101359000_2025.09.26.678800v3.18","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asp052"},{"key":"2026092502101359000_2025.09.26.678800v3.19","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-ecolsys-102209-144621"},{"key":"2026092502101359000_2025.09.26.678800v3.20","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1016\/j.tree.2010.04.001","article-title":"Approximate Bayesian computation (ABC) in practice","volume":"25","year":"2010","journal-title":"Trends in ecology & evolution"},{"key":"2026092502101359000_2025.09.26.678800v3.21","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1007\/s11222-011-9288-2","article-title":"Approximate Bayesian computational methods","volume":"22","year":"2012","journal-title":"Statistics and computing"},{"key":"2026092502101359000_2025.09.26.678800v3.22","doi-asserted-by":"crossref","first-page":"S85","DOI":"10.1002\/jae.3950080507","article-title":"Indirect inference","volume":"8","year":"1993","journal-title":"Journal of applied econometrics"},{"key":"2026092502101359000_2025.09.26.678800v3.23","first-page":"1","article-title":"Bayesian synthetic likelihood","volume":"27","year":"2018","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"2026092502101359000_2025.09.26.678800v3.24","doi-asserted-by":"publisher","DOI":"10.1534\/genetics.109.102509"},{"key":"2026092502101359000_2025.09.26.678800v3.25","doi-asserted-by":"crossref","first-page":"6767","DOI":"10.1002\/2014WR015386","article-title":"Approximate bayesian computation using markov chain monte carlo simulation: Dream (abc)","volume":"50","year":"2014","journal-title":"Water Resources Research"},{"key":"2026092502101359000_2025.09.26.678800v3.26","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9884.00117"},{"key":"2026092502101359000_2025.09.26.678800v3.27","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1020281327116","article-title":"An introduction to MCMC for machine learning","volume":"50","year":"2003","journal-title":"Machine learning"},{"key":"2026092502101359000_2025.09.26.678800v3.28","unstructured":"Bernardo, J. et al. in Bayesian Statistics 7: Proceedings of the Seventh Valencia International Meeting. 181 (Citeseer)."},{"key":"2026092502101359000_2025.09.26.678800v3.29","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0306899100"},{"key":"2026092502101359000_2025.09.26.678800v3.30","doi-asserted-by":"publisher","DOI":"10.1101\/2025.06.24.661262"},{"key":"2026092502101359000_2025.09.26.678800v3.31","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1098\/rsif.2008.0172","article-title":"Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems","volume":"6","year":"2009","journal-title":"Journal of the Royal Society Interface"},{"key":"2026092502101359000_2025.09.26.678800v3.32","doi-asserted-by":"crossref","first-page":"e2019WR025474","DOI":"10.1029\/2019WR025474","article-title":"Improving simulation efficiency of MCMC for inverse modeling of hydrologic systems with a Kalman-inspired proposal distribution","volume":"56","year":"2020","journal-title":"Water Resources Research"},{"key":"2026092502101359000_2025.09.26.678800v3.33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2012.02.005"},{"key":"2026092502101359000_2025.09.26.678800v3.34","doi-asserted-by":"publisher","DOI":"10.1111\/j.1461-0248.2011.01640.x"},{"key":"2026092502101359000_2025.09.26.678800v3.35","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2006.00553.x"},{"key":"2026092502101359000_2025.09.26.678800v3.36","doi-asserted-by":"crossref","first-page":"e68864","DOI":"10.7554\/eLife.68864","article-title":"Dynamically linking influenza virus infection kinetics, lung injury, inflammation, and disease severity","volume":"10","year":"2021","journal-title":"Elife"},{"key":"2026092502101359000_2025.09.26.678800v3.37","unstructured":"Lovly, C. M. , Salama, A. K. & Salgia, R. in American Society of Clinical Oncology educational book. American Society of Clinical Oncology. Annual Meeting. e585."},{"key":"2026092502101359000_2025.09.26.678800v3.38","doi-asserted-by":"crossref","first-page":"e85004","DOI":"10.1371\/journal.pone.0085004","article-title":"Inter-and intra-patient heterogeneity of response and progression to targeted therapy in metastatic melanoma","volume":"9","year":"2014","journal-title":"PloS one"},{"key":"2026092502101359000_2025.09.26.678800v3.39","doi-asserted-by":"crossref","first-page":"141","DOI":"10.3389\/fbioe.2020.00141","article-title":"Conducting a virtual clinical trial in HER2-negative breast cancer using a quantitative systems pharmacology model with an epigenetic modulator and immune checkpoint inhibitors","volume":"8","year":"2020","journal-title":"Frontiers in Bioengineering and Biotechnology"},{"key":"2026092502101359000_2025.09.26.678800v3.40","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1703355114"},{"key":"2026092502101359000_2025.09.26.678800v3.41","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1002\/cpt.1987","article-title":"Quantitative systems pharmacology approaches for immuno-oncology: adding virtual patients to the development paradigm","volume":"109","year":"2021","journal-title":"Clinical Pharmacology & Therapeutics"},{"key":"2026092502101359000_2025.09.26.678800v3.42","first-page":"374","article-title":"A quantitative systems pharmacology model of Gaucher disease type 1 provides mechanistic insight into the response to substrate reduction therapy with eliglustat","volume":"9","year":"2020","journal-title":"CPT: pharmacometrics & systems pharmacology"},{"key":"2026092502101359000_2025.09.26.678800v3.43","doi-asserted-by":"publisher","DOI":"10.1016\/J.DRUDIS.2023.103605"},{"key":"2026092502101359000_2025.09.26.678800v3.44","doi-asserted-by":"crossref","unstructured":"Polasek, T. M. & Rostami-Hodjegan, A. Virtual Twins: Understanding the Data Required for Model-Informed Precision Dosing. Clinical Pharmacology & Therapeutics 107 (2020).","DOI":"10.1002\/cpt.1778"},{"key":"2026092502101359000_2025.09.26.678800v3.45","doi-asserted-by":"crossref","unstructured":"Alfonso, S. , Jenner, A. L. & Craig, M. Translational approaches to treating dynamical diseases through in silico clinical trials. Chaos: An Interdisciplinary Journal of Nonlinear Science 30 (2020).","DOI":"10.1063\/5.0019556"},{"key":"2026092502101359000_2025.09.26.678800v3.46","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-0716-2265-0_8"},{"key":"2026092502101359000_2025.09.26.678800v3.47","doi-asserted-by":"publisher","DOI":"10.1101\/2025.04.26.649406"},{"key":"2026092502101359000_2025.09.26.678800v3.48","unstructured":"Volterra, V. Variazioni e ffuttuazioni del numero d\u2019individui in specie animali conviventi. (Societ\u00e0 anonima tipografica\u201d Leonardo da Vinci\u201d, 1926)."},{"key":"2026092502101359000_2025.09.26.678800v3.49","unstructured":"Lotka, A. J. Elements of physical biology. (Williams & Wilkins, 1925)."},{"key":"2026092502101359000_2025.09.26.678800v3.50","doi-asserted-by":"publisher","DOI":"10.1137\/18m1213403"},{"key":"2026092502101359000_2025.09.26.678800v3.51","doi-asserted-by":"publisher","DOI":"10.1038\/mt.2009.205"},{"key":"2026092502101359000_2025.09.26.678800v3.52","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.3389\/fmicb.2018.01554","article-title":"Influenza virus infection model with density dependence supports biphasic viral decay","volume":"9","year":"2018","journal-title":"Frontiers in microbiology"},{"key":"2026092502101359000_2025.09.26.678800v3.53","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.3934\/mbe.2015.12.1237","article-title":"Treatment strategies for combining immunostimulatory oncolytic virus therapeutics with dendritic cell injections","volume":"12","year":"2015","journal-title":"Mathematical Biosciences & Engineering"},{"key":"2026092502101359000_2025.09.26.678800v3.54","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-statistics-030718-104938"},{"key":"2026092502101359000_2025.09.26.678800v3.55","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2013.03.018"},{"key":"2026092502101359000_2025.09.26.678800v3.56","article-title":"pyABC: Efficient and robust easy-to-use approximate Bayesian computation","year":"2022","journal-title":"arXiv preprint"},{"key":"2026092502101359000_2025.09.26.678800v3.57","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/bty361"},{"key":"2026092502101359000_2025.09.26.678800v3.58","doi-asserted-by":"crossref","first-page":"841","DOI":"10.3934\/mbe.2015.12.841","article-title":"Quantitative impact of immunomodulation versus oncolysis with cytokine-expressing virus therapeutics","volume":"12","year":"2015","journal-title":"Mathematical Biosciences & Engineering"},{"key":"2026092502101359000_2025.09.26.678800v3.59","first-page":"110","article-title":"Weak convergence and optimal scaling of random walk Metropolis algorithms","volume":"7","year":"1997","journal-title":"The annals of applied probability"}],"container-title":[],"original-title":[],"link":[{"URL":"https:\/\/syndication.highwire.org\/content\/doi\/10.1101\/2025.09.26.678800","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T09:10:23Z","timestamp":1790327423000},"score":1,"resource":{"primary":{"URL":"http:\/\/biorxiv.org\/lookup\/doi\/10.1101\/2025.09.26.678800"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,29]]},"references-count":59,"URL":"https:\/\/doi.org\/10.1101\/2025.09.26.678800","relation":{},"subject":[],"published":{"date-parts":[[2025,9,29]]},"subtype":"preprint"}}