{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T18:49:09Z","timestamp":1791571749406,"version":"4.3.4"},"reference-count":40,"publisher":"Public Library of Science (PLoS)","issue":"10","license":[{"start":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:00:00Z","timestamp":1791504000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["OCE-2019589"],"award-info":[{"award-number":["OCE-2019589"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Institute of Health","award":["P41GM109824"],"award-info":[{"award-number":["P41GM109824"]}]},{"DOI":"10.13039\/100000925","name":"John Templeton Foundation","doi-asserted-by":"publisher","award":["62825"],"award-info":[{"award-number":["62825"]}],"id":[{"id":"10.13039\/100000925","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    Building multiscale biological models requires the integration of independently developed submodels, which means moving shared variables between them and coordinating when each submodel runs. Existing tools typically address isolated biological mechanisms with specific numerical methods, rarely specify which variables each model reads and writes, how those variables are translated, and how model updates are synchronized. We present Process Bigraph, a framework for composing and simulating multiscale models. Process Bigraph generalizes the architectural ideas previously used in the Vivarium software into a shared specification that describes process interfaces, hierarchical data structures, composition patterns, and orchestration patterns. The paper explains how the framework is organized and why it makes biological models easier to understand, reuse, and build on; S1 Text provides the formal specification. We introduce Vivarium 2.0 as an open-source implementation of the process bigraph framework. We demonstrate its utility with Spatio-Flux, a standalone library of microbial ecosystem simulations that combine kinetic equations, dynamic flux balance analysis, and different spatial processes. These simulations illustrated how the framework effectively integrates diverse biological processes, leading to emergent spatially organized population dynamics. Finally, we discuss implications for emerging multiscale modeling standards.\n                    <jats:bold>Availability and implementation:<\/jats:bold>\n                    Vivarium 2.0 is a suite of software libraries that include: (1) bigraph-schema, for defining and operating on data types within a hierarchical JSON-based format; (2) process-bigraph, for defining process interfaces, composite simulations, and executing them; and (3) viva-superpowers, for AI-assisted construction and composition of process bigraphs. Spatio-Flux is a reference application used in this paper to demonstrate the framework\u2019s utility. S1 Text provides detailed descriptions of these software libraries. All software is open-source and available at:\n                    <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/github.com\/vivarium-collective\" xlink:type=\"simple\">https:\/\/github.com\/vivarium-collective<\/jats:ext-link>\n                    .\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1014819","type":"journal-article","created":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T17:52:06Z","timestamp":1791568326000},"page":"e1014819","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Process bigraphs and the architecture of compositional systems biology"],"prefix":"10.1371","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1279-2474","authenticated-orcid":true,"given":"Eran","family":"Agmon","sequence":"first","affiliation":[{"name":"Center for Cell Analysis and Modeling, University of Connecticut Health","place":["Farmington, Connecticut, United States of America"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ryan K.","family":"Spangler","sequence":"additional","affiliation":[{"name":"Center for Cell Analysis and Modeling, University of Connecticut Health","place":["Farmington, Connecticut, United States of America"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,10,9]]},"reference":[{"issue":"16","key":"pcbi.1014819.ref001","doi-asserted-by":"crossref","first-page":"164115","DOI":"10.1063\/1.2062048","article-title":"On the origins of approximations for stochastic chemical kinetics","volume":"123","author":"EL Haseltine","year":"2005","journal-title":"J Chem Phys"},{"issue":"3","key":"pcbi.1014819.ref002","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1016\/S0006-3495(02)73903-9","article-title":"Dynamic flux balance analysis of diauxic growth in Escherichia coli","volume":"83","author":"R Mahadevan","year":"2002","journal-title":"Biophys J"},{"issue":"18","key":"pcbi.1014819.ref003","doi-asserted-by":"crossref","first-page":"2044","DOI":"10.1093\/bioinformatics\/btn352","article-title":"Integrating metabolic, transcriptional regulatory and signal transduction models in Escherichia coli","volume":"24","author":"MW Covert","year":"2008","journal-title":"Bioinformatics"},{"issue":"12","key":"pcbi.1014819.ref004","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1005236","article-title":"Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology","volume":"12","author":"JC Schaff","year":"2016","journal-title":"PLoS Comput Biol"},{"issue":"11","key":"pcbi.1014819.ref005","doi-asserted-by":"crossref","first-page":"5030","DOI":"10.1038\/s41596-021-00593-3","article-title":"A metabolic modeling platform for the computation of microbial ecosystems in time and space (COMETS)","volume":"16","author":"I Dukovski","year":"2021","journal-title":"Nat Protoc"},{"issue":"2","key":"pcbi.1014819.ref006","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.cell.2012.05.044","article-title":"A whole-cell computational model predicts phenotype from genotype","volume":"150","author":"JR Karr","year":"2012","journal-title":"Cell"},{"issue":"6502","key":"pcbi.1014819.ref007","doi-asserted-by":"crossref","DOI":"10.1126\/science.aav3751","article-title":"Simultaneous cross-evaluation of heterogeneous E. coli datasets via mechanistic simulation","volume":"369","author":"DN Macklin","year":"2020","journal-title":"Science"},{"issue":"2","key":"pcbi.1014819.ref008","doi-asserted-by":"crossref","first-page":"167351","DOI":"10.1016\/j.jmb.2021.167351","article-title":"Building Structural Models of a Whole Mycoplasma Cell","volume":"434","author":"M Maritan","year":"2022","journal-title":"J Mol Biol"},{"issue":"2","key":"pcbi.1014819.ref009","doi-asserted-by":"crossref","DOI":"10.1016\/j.cell.2021.12.025","article-title":"Fundamental behaviors emerge from simulations of a living minimal cell","volume":"185","author":"ZR Thornburg","year":"2022","journal-title":"Cell"},{"key":"pcbi.1014819.ref010","doi-asserted-by":"crossref","first-page":"1106495","DOI":"10.3389\/fchem.2023.1106495","article-title":"Molecular dynamics simulation of an entire cell","volume":"11","author":"JA Stevens","year":"2023","journal-title":"Front Chem"},{"key":"pcbi.1014819.ref011","doi-asserted-by":"crossref","unstructured":"Rackauckas C, Ma Y, Martensen J, Warner C, Zubov K, Supekar R. 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