A Multiphysics Model of In Vitro Transcription Coupling Enzymatic Reaction and Precipitation Formation

Multiphysics modeling, which integrates the models studied in different disciplines so far, is an indispensable approach toward a comprehensive understanding of biological systems composed of diverse phenomena. However, the variety of the models is narrower than the actual diverse phenomena because of the difficulty in coupling independent models separately studied in different disciplines for the actual coupled phenomena. In this study, we develop a mathematical model coupling an enzymatic reaction and mineralization formation. As a test case, we selected an in vitro transcription system where a transcription reaction occurs along with the precipitation formation of magnesium pyrophosphate (Mg2PPi). To begin, we experimentally elucidated how the transcription reaction and the precipitation formation are coupled. In the analysis, we applied a Michaelis-Menten-type equation to the transcription reaction and a semiempirical equation describing the correlation between the induction period and the supersaturation ratio to the precipitation formation, respectively. Based on the experimental results, we then integrated these two models. These models were connected by supersaturation that increases as the transcription reaction proceeds and becomes the driving force of the precipitation. We believe that our modeling approach could significantly contribute to the development of newer multiphysics models in systems biology such as bone metabolic networks.