Towards feedback control of the cell-cycle across a population of yeast cells

Cells are defined by their unique ability to self-replicate through cell division. This periodic process is known as the cell-cycle and it happens with a defined period in each cell. The budding yeast divides asymmetrically with a mother cell generating multiple daughter cells. Within the cell population each cell divides with the same period but asynchronously. Here, we investigate the problem of synchronising the cell-cycle across a population of yeast cells through a microfluidics-based feedback control platform. We propose a theoretical and experimental approach for cell-cycle control by considering a yeast strain that can be forced to start the cell-cycle by changing growth medium. The duration of the cell-cycle is strictly linked to the cell volume growth, hence a hard constraint in the controller design is to prevent excessive volume growth. We experimentally characterised the yeast strain and derived a simplified phase-oscillator model of the cell-cycle. We then designed and implemented three impulsive control strategies to achieve maximal synchronisation across the population and assessed their control performance by numerical simulations. The first two controllers are based on event-triggered strategies, while the third uses a model predictive control (MPC) algorithm to select the sequence of control impulses while satisfying built-in constraints on volume growth. We compared the three strategies by computing two cost functions: one quantifying the level of synchronisation across the cell population and the other volume growth during the process. We demonstrated that the proposed control approaches can effectively achieve an acceptable trade-off between two conflicting control objectives: (i) obtaining maximal synchronisation of the cell cycle across the population while (ii) minimizing volume growth. The results can be used to implement effective strategies to unfold the biological mechanisms controlling cell cycle and volume growth in yeast cells.