Gradient matching accelerates mixed-effects inferencefor biochemical networks

Single-cell time series data frequently display considerable variability across a cell population. The current gold standard for inferring parameter distributions across cell populations is the Global Two Stage (GTS) approach for nonlinear mixed-effects (NLME) models. However, this method is computationally intensive, as it makes repeated use of non-convex optimization that in turn requires numerical integration of the underlying system. Here, we propose the Gradient Matching GTS (GMGTS) method as an efficient alternative to GTS. Gradient matching offers an integration-free approach to parameter estimation that is particularly powerful for dynamical systems that are linear in the unknown parameters, such as biochemical networks modeled by mass action kinetics. Here, we harness the power of gradient matching by integrating it into the GTS framework. To this end, we significantly expand the capabilities of gradient matching via uncertainty propagation calculations and the development of an iterative estimation scheme for partially observed systems. Through comparisons of GMGTS with GTS in different inference setups, we demonstrate that our method provides a significant computational advantage, thereby facilitating the use of complex NLME models in systems biology applications.