PhysiBoSS: Multiscale Tissue Modeling

• PhysiBoSS is an open-source computational framework that integrates agent-based modeling with stochastic Boolean networks for simulating tissue dynamics.
• The framework couples PhysiCell's spatial cell mechanics with MaBoSS's rapid, noisy intracellular signaling to capture complex cell behaviors.
• Its practical applications include modeling tumor apoptosis, cell-cycle regulation, and cancer invasion, enhancing reproducibility and collaborative research.

PhysiBoSS is an open-source computational framework engineered for the multiscale modeling of complex biological tissues, coupling agent-based models of cell populations with continuous-time stochastic Boolean network representations of intracellular signaling. By integrating spatial cell mechanics and dynamics (via PhysiCell) with rapid and noisy intracellular decision-making (via MaBoSS), PhysiBoSS enables the study of how genetic, molecular, and microenvironmental cues collectively shape tissue-scale phenotypes in both physiological and pathological contexts (Noel et al., 7 Aug 2025, Ruscone et al., 2024).

1. Core Architecture: Coupling Agent-Based and Boolean Network Dynamics

PhysiBoSS combines the center-based, off-lattice agent-based modeling provided by PhysiCell (C++, for 2D/3D tissues) with per-cell stochastic Boolean networks simulated by MaBoSS. Each cell (agent) in the simulation maintains its own independent Boolean network, in which nodes represent gene or protein states ($x_i \in \{0,1\}$).

At each simulation step, a cell updates its Boolean network state $x(t) = (x_1(t), ..., x_n(t))$ using a Gillespie-style continuous-time, asynchronous update:

$$x_i(t+\Delta t) = f_i(x_1(t),...,x_n(t)) + \eta_i(t)$$

Here, $f_i$ is a logical update function and $\eta_i$ represents stochasticity as a Poissonian term. Transition propensities $a_j = c_j h_j(x)$ are calculated from rate constants $c_j$ and Boolean conditions $h_j(x)$. This stochastic network update, as implemented in MaBoSS, captures rare but biologically crucial decisions (e.g., apoptosis from DNA damage) at realistic population scales.

Simultaneously, PhysiCell manages phenotypic processes such as cell growth, division, motility, mechanical interactions, and death. Chemical substrates (oxygen, cytokines, drugs) diffuse according to reaction–diffusion PDEs:

$$\frac{\partial C}{\partial t} = D \nabla^2 C - \lambda C + S(x, t)$$

where $D$ is the diffusion coefficient, $\lambda$ the decay rate, and $S(x,t)$ cellular source/sink terms (Noel et al., 7 Aug 2025, Ruscone et al., 2024).

2. Continuous-Time Boolean Network Modeling with MaBoSS

MaBoSS encodes intracellular signaling using continuous-time stochastic Boolean networks, interpreting each node’s state transition as a Markov jump process. For $N$ nodes $X_i$, each transitions $0\to1$ and $1\to0$ at rates $\lambda_i^+(X)$ and $\lambda_i^-(X)$, piecewise functions of logical parent nodes:

$rate\_up(i) = \begin{cases}k_i^{on} & \text{if }f_i(X_{parents})=1\0&\text{otherwise}\end{cases}$

$rate\_down(i) = \begin{cases}k_i^{off}&\text{if }f_i(X_{parents})=0\0&\text{otherwise}\end{cases}$

The global state exit rate is

$$\Lambda(X)=\sum_{i=1}^N [\lambda_i^+(X)(1-X_i)+\lambda_i^-(X)X_i]$$

Update times are exponentially distributed, and node flips are chosen probabilistically. Intracellular inputs from the microenvironment (e.g., TNF, oxygen) are mapped to network nodes, and designated outputs control cell behaviors such as apoptosis, cell-cycle transitions, and secretion (Ruscone et al., 2024).

3. Model Development Workflow and Configuration

Construction of PhysiBoSS models involves coordinated definition of external and internal cell processes. The standard workflow comprises:

• XML-based model configuration specifying microenvironmental parameters, spatial cell layouts, and simulation settings.
• Boolean network specification for each cell type (.bnd for structure, .cfg for parameters).
• Input mapping: external variables (substrate concentrations, cell contact signals) thresholded and assigned to specific network nodes.
• Output mapping: network node states mapped to cell phenotype changes (death rates, cycle transitions, motility).
• Setting update intervals, time-scaling between Boolean and agent-based modules, and tuning stochasticity (e.g., intracellular_dt, scaling, time_stochasticity).
• Custom C++ modules can be incorporated for advanced behaviors (e.g., novel adhesion or kinetics).
• Simulation execution is supported via command line or PhysiCell Studio GUI; results are output to CSV, MAT, SVG, or VTP formats for downstream visualization and analysis (Noel et al., 7 Aug 2025, Ruscone et al., 2024).

4. PhysiBoSS-Models: Database, Versioning, and Workflow Automation

The PhysiBoSS-Models database is a curated, community-driven repository designed for systematic sharing, discovery, and reuse of multiscale models built on PhysiBoSS. Each contributed model adheres to a standard file layout, including:

• Framework source pinned to validated commits (src/physicell, src/physiboss)
• Custom modules (modules/)
• Configuration files (config/), Boolean networks (bnets/)
• Rich metadata (metadata/model.yml) and documentation

Automated continuous integration compiles models across Linux, macOS, and Windows, with version tags (v1.0.0, etc.) ensuring exact reproducibility. All published results are validated against checksums, parameter sets, and reference steady-state distributions; every new submission undergoes CI-based consistency checks (Noel et al., 7 Aug 2025).

A Python API (physioboss_models) enables search, download, configuration, and simulation from notebook environments. Additionally, PhysiCell Studio (v2024+) provides GUI access to the entire model collection. This design eliminates manual dependency management and source compilation for model deployment.

5. Practical Applications and Example Use Cases

PhysiBoSS-Models includes models for diverse biological contexts, such as:

• TNF-mediated tumor death: exploring the apoptotic response as a function of cytokine pulse amplitude/duration, with endpoints like time-series of “Caspase3_Active.”
• Cell-cycle regulatory networks: integrating checkpoints at the single-cell level with tissue-scale proliferation dynamics.
• T-cell differentiation: mapping of extracellular cues to fate commitment via Boolean logic.
• Cancer invasion models (e.g., “MultiscaleCancerInvasion”): parameter sweeps (MMP secretion, for instance) reveal transitions between solitary and collective invasion, with results visualized as 3D scatter plots of cell positions colored by Boolean network states.

All models in the database are fully reproducible; researchers can reproduce published figures or perform novel analyses by loading and running simulations with minimal scripting (Noel et al., 7 Aug 2025, Ruscone et al., 2024).

6. Standardization, Validation, and Extensions

PhysiBoSS-Models enforces uniform folder structure, schema-validated metadata, and code-style for each deposited model. Automated test scripts validate expected simulation outputs so updates remain stable across versions. Git tags support reproducible workflows, and open-source visibility fosters collaboration and benchmarking.

Model calibration best practices include standalone MaBoSS runs for timescale alignment, data-driven threshold/rate selection for environmental mappings, and comparison of single-cell and population-level simulation outputs against experimental data. The database enables sensitivity/mutant screens and can be extended with add-ons such as PhysiPKPD for pharmacokinetics, UPMaBoSS for population models without spatial dynamics, and omics-driven parameterization. Planned future directions include interactive dashboards and support for pure PhysiCell models (Noel et al., 7 Aug 2025, Ruscone et al., 2024).

7. Significance and Outlook

PhysiBoSS addresses key multiscale modeling challenges by integrating agent-based cell mechanics, chemical microenvironments, and continuous-time logical signaling at organotypic scales. By lowering the overhead for model assembly, sharing, and validation, PhysiBoSS-Models catalyzes collaborative modeling efforts and accelerates hypothesis-driven computational biology. The design philosophy aims to make sophisticated tissue simulations as accessible as running simple ODE solvers, supporting research into disease, immune interactions, and synthetic tissue engineering (Noel et al., 7 Aug 2025, Ruscone et al., 2024).