Merdan Sarmis, Jean-Marie C Bouteiller, Nicolas Ambert, Arnaud Legendre, Serge Bischoff, Olivier Haeberlé and Michel Baudry
In systems biology, systems of kinetic reactions are generally used to model and simulate various biochemical pathways. These reactions are translated into ordinary differential equations, which are computationally resolved by numerical algorithms. Computation performance, defined by how fast the algorithm converges to a numerical solution of the system of ordinary differential equations, critically depends on the choice of the appropriate algorithm. In this paper, we compared several algorithms used to solve ordinary differential equations applied to several kinetic models that describe the dynamic behavior of receptors and ion channels found in chemical synapses of the Central Nervous System; we provide a simplified method to determine the performances of these ordinary differential equation solvers, in order to provide a benchmark for algorithm selection. This method will facilitate the choice of the most efficient algorithm for a given kinetic model with a minimum number of tests. Our results provide a tool for identifying optimal solvers for any biological bilinear kinetic models under various experimental conditions. This comparison also underscored the complexity of biological kinetic models and illustrates how their input dependency could interfere with performance. Despite these challenges, our simplified method helps to select the best solvers for any synaptic receptors kinetic models described, with a bilinear system with minimal a priori information on the solver structure and the model.
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