Quantitative Modeling in Systems Biology: How to Develop Relevant Models

Since 1990s, Petri nets have been used in systems biology for quantitative modeling. Despite the increasing number of models developed during this period, doubts remain about their biological relevance. Although biological systems predominantly exhibit intracellular or cellular structures, the models rely largely on deterministic predictions, failing to capture the inherent randomness and uncertainties of such systems. The question arises whether these models accurately describe the dynamic behavior of biological systems. This paper introduces a methodology for selecting the appropriate modeling paradigms in systems biology. Initially, we construct a Petri net model and perform deterministic, stochastic, and fuzzy stochastic simulations. Then we perform various statistical tests to measure the discrepancies between the simulation results. Based on scale-density analysis, we determine the modeling approach that best approximates the biological system. Finally, we compare the results of the statistical tests and the scale-density analysis to identify the optimal modeling approach. We applied the proposed methodology to the synthesis of spinal motor neuron protein from the spinal motor neuron-2 gene. Analysis revealed significant discrepancies between the simulation results of different modeling paradigms. Due to the sparse nature of the underlying drug-disease network, we conclude that the fuzzy stochastic paradigm provides the most biologically relevant results. We predict drug combinations that could lead to an up to 149-fold increase in spinal motor neuron protein levels, indicating a promising treatment for the disease. This methodology has potential for application to other gene-drug-disease networks and broader biological systems.