Moving horizon estimation of Amnioserosa cell dynamics during Drosophila dorsal closure

Dorsal closure is a morphogenetic process similar to wound healing, whereby a gap in the epithelium is closed through the coordination of the elongation of epidermal cells and contraction of Amnioserosa cells (AS). Throughout the early stages of this process, the AS cells exhibit fluctuations of their apical area which provides an ideal system to understand contractile epithelia, both in terms of the cellular mechanisms and how tissue behavior emerges from the activity of individual cells. In this work, we present a vertex-based model to explore the dynamics of Amnioserosa cells and provide insights into the regulation of dorsal closure. Towards this end, moving horizon estimation is used to predict the mechanics of AS cell oscillations and contractions modeled as a quasi-linear parameter-varying system with bounded unknown parameters. We perform estimation through the minimization of the least-squares moving horizon cost with respect to both state variables and unknown parameters simultaneously. For simulation purposes, data from the work published in [13] are used to evaluate the performance of moving-horizon estimation as compared to the extended Kalman filter. The comparative analysis reveals that the moving-horizon approach performs better than those provided by the Kalman filtering and with an increased robustness to measurement and process noises.