Feasible parameter space characterization with adaptive sparse grids for nonlinear systems biology models

Mathematical models are commonly used to interrogate and control biological systems. However, such models are often uncertain and sloppy, with multiple parameter sets equally capable of reproducing the experimental data. These features make systems biology models unreliable when used to support a model-based control strategy. Multi-scenario control can help account for this uncertainty, but a computationally feasible method for characterizing all data-consistent regions of the global parameter space is necessary. Herein, we propose a tool for multi-scenario control in which sparse grid-based optimization is paired with a grid focusing algorithm to characterize acceptable regions of the uncertain parameter space. The grid focusing algorithm is first demonstrated on a test function before being applied within a multi-scenario control framework to an uncertain model of cell differentiation. The results show the algorithm´s ability to identify disparate low-cost regions of the parameter space and selectively increase the grid resolution in these areas to help determine appropriate model scenarios for the multi-scenario controller. While particularly relevant to biological systems, this approach is broadly applicable to the control of any uncertain system.