2012 年 78 巻 790 号 p. 1279-1291
Mathematical description of biological processes, including cell growth, cell differentiation, cell response to stress, and cell damage and death could be beneficial to the characterization, quantitative evaluation, design and optimization of the relevant processes. In this study, a mathematical model with reaction kinetic formulation was proposed and developed to describe the process of cell differentiation with cell growth. Basic equations and analytical solutions for the numbers of undifferentiated and differentiated cells were obtained. A parameter study of the model constants, rate constants of cell growth and differentiation, was performed to analyze the model characteristics. An experiment with a rat pheochromocytoma cell line PC12 as nerve cells was also performed to evaluate time-series changes in the numbers of undifferentiated and differentiated cells. The rate constants were determined by inverse problem analysis based on the experiment with PC12 cells. The prediction by the model well simulated the characteristics of the experiment, proving that the present reaction kinetic model successfully represents cell differentiation with cell growth. Therefore, the cell growth and differentiation can be appropriately characterized by the rate constants, regarded as specific characteristics of cells.