Measuring regulatory network inheritance in dividing yeast cells using ordinary differential equations

Quantifying the inheritance of regulatory networks among proteins during asymmetric cell division remains a challenge due to the complexity of these systems and the lack of robust mathematical definitions for inheritance. We propose a novel statistical framework called ODEinherit to measure how much a mother cell’s regulatory network explains its daughter’s trajectories, addressing this gap. Using time-lapse microscopy, we tracked the expression dynamics of six proteins across 85 dividing S. cerevisiae cells, observed over eight hours at 12-minute intervals. Our framework employs a two-step approach. First, we estimate an ordinary differential equation (ODE) system for each cell to characterize protein interactions, introducing novel adjustments for non-oscillatory time series and leveraging multi-cell data. Second, we assess inheritance by clustering cells based on cycling markers and quantifying how well a mother’s regulatory network predicts her daughter’s. Preliminary findings suggest stage-dependent differences in inheritance rates, paving the way for applications in cellular stress response and cell-fate prediction studies across generations.