Comparison of parameters estimation methods based on the systems biology model of breast cancer

Breast cancer is the most common malignant disease in women. The kinase mammalian target of rapamycin (mTOR) and mitogen-activated protein kinase (MAPK) have been generally demonstrated to play important roles in the proliferation of breast cancer. Therefore, this study constructed a systematic biology model based on the mTOR/MAPK pathway obtained from the canonical pathway database of ingenuity pathway analysis (IPA) and built a system of ordinary differential equations (ODEs) based on the law of mass action to describe the temporal dynamics of concentration for each protein. However, the optimization of parameters for ODE models is generally essential and challenging. Here, three classical optimization methods, genetic algorithm (GA), particle swarm optimization (PSO), and simulated annealing (SA), are employed on the systematic model to optimize the key parameters of ODEs. Furthermore, we compared their optimization effects respectively. The results suggested that the performance of PSO algorithm is the best for optimize the key parameters of the model.