Topologically-based parameter inference for agent-based model selection from spatiotemporal cellular data

Advances in spatiotemporal single-cell imaging have enabled detailed observations of cell population dynamics and intercellular interactions. However, translating these rich data sets into mechanistic insight remains a significant challenge. Agent-based models (ABMs) are a bottom-up computational framework for investigating the emergent behavior of cell populations that can arise from rules defining the interactions between individual neighboring cells, while topological data analysis (TDA) provides robust descriptors of spatial organization. We present TOPAZ (TOpologically-based Parameter inference for Agent-based model optimiZation), a computational pipeline that integrates TDA with approximate Bayesian computation (ABC), approximate approximate Bayesian computation (AABC), and Bayesian model selection to identify biologically plausible ABMs from spatiotemporal cellular data. TOPAZ uses persistent homology to quantify spatial features of cell trajectories and combines this topological information with parameter inference via ABC and AABC and model comparison using the Bayesian information criterion. We validate TOPAZ using simulations of collective fibroblast movement, demonstrating its ability to accurately recover model parameters and distinguish between a baseline ABM and an extended model that incorporates an alignment interaction. Our results and open-source code demonstrate the utility of TOPAZ as an extensible framework for mechanistic inference and model discrimination in spatial single-cell analysis.Author summary: Understanding how individual cells coordinate to produce complex collective behaviors is a major challenge in computational biology, especially with the increasing availability of high-resolution, spatiotemporal single-cell data. While agent-based models (ABMs) offer a flexible framework for simulating cell behaviors and interactions, they are often difficult to calibrate and compare. Topological data analysis (TDA), on the other hand, captures spatial organization in a robust and scale-invariant way but lacks mechanistic interpretability. In this work, we present TOPAZ (TOpologically-based Parameter inference for Agent-based model optimiZation), a novel computational pipeline that integrates TDA with approximate Bayesian computation, approximate approximate Bayesian computation, and Bayesian model selection to infer biologically meaningful parameters and identify the most plausible ABM from spatiotemporal cellular data. We benchmark TOPAZ using synthetic data from ABMs of collective cell movement in dense fibroblast populations. Our results show that TOPAZ can distinguish between competing mechanistic hypotheses, namely the presence or absence of alignment interactions among neighboring cells. This approach provides a powerful and extensible framework for model inference and selection with the potential to enable deeper insights into the mechanisms driving complex emergent behaviors in cell populations.