Non-linear modeling and control of Mitochondrial Dynamics

Mitochondrial Dynamics (MD) has recently emerged as one of the most interesting topics in biology since the intricate connection between energy production and MD regulates cells development and function. On the other hand, the impairment of such mechanism is strictly related to the emergence of various diseases, among which neurodegenerative disorders. In this work, we provide a simple, yet complete, and well-posed mathematical model to describe the MD and the related phenomena through a population-dynamics approach, together with the ATP-energy turnover, which is an important step to unravel the underlying dynamics of the whole cell system and has a key role in its quality control. With the tools of system theory, we highlight the positiveness of the system and the presence of non-zero equilibria and compute bounds for the involved system state quantities. Furthermore, we consider a situation of impairment in the MD and design a control law, based on input-output linearization and state-feedback control able to allow a damaged system to compensate for the defect and behave as a nominal one. In this scenario, we test two different protocols that could be suggestive for treatment strategies.