A data-driven optimal control method for endoplasmic reticulum membrane compartmentalization in budding yeast cells

In this paper, we propose a variational data assimilation approach for including data measurements in the simulation of the mobility of fluorescently labeled molecules in the yeast endoplasmic reticulum. The modeling framework aims to provide numerical evidence for compartmentalization in the endoplasmic reticulum. Experimental data are collected and an optimal control problem is formulated as a regularized inverse problem. To our knowledge, this is the first attempt to introduce an optimization formulation constrained by partial differential equations to study the kinetics of fluorescently labeled molecules in budding yeast. We derive the optimality conditions and use an optimize-then-discretize approach. A gradient descent algorithm allows accurate estimation of unknown key parameters in different cellular compartments. The numerical results support the empirical barrier index theory suggesting the presence of a physical diffusion barrier that compartmentalizes the endoplasmic reticulum membrane by limiting the exchange of proteins between the mother and its growing bud. We report several numerical experiments on real data and geometry, with the aim of illustrating the accuracy and efficiency of the method. Furthermore, a relationship between the size ratio of mother and bud compartments and the barrier index ratio is provided.