Hybrid System Models of Biological Cell Network Signaling and Di erentiation

We present a piecewise linear switch which faithfully represents the e ect of certain protein concentrations on others, in a biological control mechanism for cell di erentiation known as Delta-Notch signaling. This switch is shown to be a good approximation to the Hill Equation and sigmoid switching curve, which are widely accepted models for biological switches. In addition, the switch allows us to use a mathematically tractable piecewise linear hybrid system model as an analysis tool for the dynamics of Delta-Notch signaling in a network of cells. In this paper, we give an overview of the biological system under study, we present the hybrid system model of the cell network, perform a convergence analysis, and validate with simulation results.