Implementing biological hybrid systems: Allowing composition and avoiding stiffness

The theory of hybrid systems allows us to model biological functions with many interactive processes, describe complexity and hierarchy levels, and consider behavior law changes. However, we need to develop an implementation to simulate these models. The BioRica framework allows a non-ambiguous implementation, and, as shown here, the QSS method (Quantized States Systems) helps us to approach complex systems in a more efficient way. This method allows us to numerically solve stiff differential equations by separately choosing the temporal partition for each sub-model and variable, depending on how fast it changes over time. With that, one obtains more accurate solutions and decreases the number of computations compared to classic methods. Moreover, QSS does not need to store trajectories and interpolate when mode transitions occur between partition times. Herein, we exhibit a translation from BioRica to QSS models, which preserves the semantics. We implement QSS method with BioRica, and illustrate with applications in Biology, the Tyson model of cell cycle, and examples in Engineering.