Mathematical basis and toolchain for hierarchical optimization of biochemical networks

Biological signalling systems are complex, and efforts to build mechanistic models must confront a huge parameter space, indirect and sparse data, and frequently encounter multiscale and multiphysics phenomena. We present HOSS, a framework for Hierarchical Optimization of Systems Simulations, to address such problems. HOSS operates by breaking down extensive systems models into individual pathway blocks organized in a nested hierarchy. At the first level, dependencies are solely on signalling inputs, and subsequent levels rely only on the preceding ones. We demonstrate that each independent pathway in every level can be efficiently optimized. Once optimized, its parameters are held constant while the pathway serves as input for succeeding levels. We develop an algorithmic approach to identify the necessary nested hierarchies for the application of HOSS in any given biochemical network. Furthermore, we devise two parallelizable variants that generate numerous model instances using stochastic scrambling of parameters during initial and intermediate stages of optimization. Our results indicate that these variants produce superior models and offer an estimate of solution degeneracy. Additionally, we showcase the effectiveness of the optimization methods for both abstracted, event-based simulations and ODE-based models.Author summary: Biochemical pathway models integrate quantitative and qualitative data to understand cell functioning, disease effects, and to test treatments in silico. Constructing and optimizing these models is challenging due to the complexity and multitude of variables and parameters involved. Although hundreds of biochemical models have been developed and are available in repositories, they are rarely reused. To enhance the utilization of these models in biomedicine, we propose HOSS, an innovative hierarchical model optimization method. HOSS takes advantage of the modular structure of pathway models by breaking down large mechanistic computational models into smaller modules. These modules are then optimized progressively, starting with input modules and following causality paths. This method significantly reduces the computational burden as each step involves solving a simpler problem. By making the optimization process more manageable, HOSS accelerates the lifecycle of biochemical models and promotes their broader use in biomedical research and applications.