Trajectory-matching ABC-MCMC for simulating heterogeneous dynamics in mechanistic models

The inherent heterogeneity of complex biological systems makes it difficult to experimentally and clinically explore individual outcomes within them. Mechanistic mathematical models are essential tools for studying such heterogeneity. Thus, there is increasing interest in integrating newer mechanistic model-based techniques, like virtual patient cohorts and virtual clinical trials, within experimental and regulatory pipelines to probe relationships that may be difficult or impossible to ascertain through traditional wetlab or clinical experimentation alone. Computational approaches like Approximate Bayesian Computation (ABC) are attractive methods for generating virtual patient cohorts and running virtual clinical trials. Among the various ABC approaches, ABC combined with Markov chain Monte Carlo (ABC-MCMC) is widely used to improve sampling efficiency and guarantee convergence to the approximate posterior. However, ABC-MCMC must meet the acceptance criteria of both approaches, which results in a high rejection rate. In response, we developed a model-based technique called trajectory-matching ABC-MCMC (TM-ABC-MCMC). TM-ABC-MCMC captures the variability of complex biological systems by constraining model trajectories between the upper and lower bounds of available data to generate heterogeneity in model parameters. By testing the method's performance on existing mechanistic models and comparing to existing ABC-MCMC algorithms, we show that TM-ABC-MCMC accurately reproduces the observed noise in biological systems of varying complexity, all while maintaining computational efficiency. Thus, TM-ABC-MCMC is a new approach for generating heterogeneity in mechanistic mathematical models with implications for model-based experimental design, virtual patient cohorts, and virtual clinical trials.