Parallelization and High-Performance Computing Enables Automated Statistical Inference of Multi-scale Models

Mechanistic understanding of multi-scale biological processes, such as cell proliferation in a changing biological tissue, is readily facilitated by computational models. While tools exist to construct and simulate multi-scale models, the statistical inference of the unknown model parameters remains an open problem. Here, we present and benchmark a parallel approximate Bayesian computation sequential Monte Carlo (pABC SMC) algorithm, tailored for high-performance computing clusters. pABC SMC is fully automated and returns reliable parameter estimates and confidence intervals. By running the pABC SMC algorithm for ∼10⁶ hr, we parameterize multi-scale models that accurately describe quantitative growth curves and histological data obtained in vivo from individual tumor spheroid growth in media droplets. The models capture the hybrid deterministic-stochastic behaviors of 10⁵–10⁶ of cells growing in a 3D dynamically changing nutrient environment. The pABC SMC algorithm reliably converges to a consistent set of parameters. Our study demonstrates a proof of principle for robust, data-driven modeling of multi-scale biological systems and the feasibility of multi-scale model parameterization through statistical inference.