Process bigraphs and the architecture of compositional systems biology.

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. Availability and implementation: 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's utility. S1 Text provides detailed descriptions of these software libraries. All software is open-source and available at: https://github.com/vivarium-collective.