A stochastic generalization of the manifold boundary approximation method (MBAM) with application to a mechanistic radiobiological model of cell survival.

The manifold boundary approximation method (MBAM) is a powerful method for compressing many-parameter models into reduced-order models that retain predictive power and interpretability. Current MBAM implementations are built on automatic differentiation (AD) for calculating the sensitivity of predictions with respect to parameters. AD techniques are well-established for deterministic computations, but their extension to stochastic computations is less developed. Consequently, applications of MBAM thus far have mostly been restricted to deterministic models. In this work, we adapt a recent generalization of AD to enable MBAM for stochastic multi-parameter models. We benchmark the approach on a two-parameter Gillespie simulation for a reversible binding reaction. In the 'macroscopic' limit of large molecule numbers and long reaction times, the results from stochastic MBAM agree with those of deterministic MBAM applied to the mass-action kinetic limit of the Gillespie simulation. Finally, we apply stochastic MBAM to the mechanistic DNA repair and survival (MEDRAS) model of cell survival in the presence of radiation. We analyze three scenarios: exposure to sparsely ionizing radiation, exposure to densely ionizing radiation, and exposure to a combination of sparsely and densely ionizing radiation. The resulting reduced-order models for the first two scenarios have mechanistic interpretations as limiting linear-quadratic descriptions for monoenergetic exposures. The reduced-order model for the third scenario is a newly-discovered parsimonious descriptor of biological effectiveness for mixed-quality radiation, rigorously grounded in radiobiological mechanism.