UC Irvine

The spatial organization of tissues is often determined by long-range signals, morphogens, through the concentration-dependent manner. The morphogen-mediated patterning is a great foundation, but inadequate to explain the effects of tissue growth and stochasticity, the two prevalent phenomena, in pattern formation. In this thesis, we use multi-scale models to study those questions. In Chapter 2, we study how pattern scales to tissue size in Drosophila wing disc and find the scaling is through the feedback control on receptors and co-receptors of the morphogen. In Chapter 3, we study how different types of noise affect the dynamics of spatial pattern in the epithelium and we find the balanced levels of different types of noise is essential to the tissue homeostasis. In Chapter 4, we discuss both effects of growth and noise in the zebrafish hindbrain pattern. Despite the noise causes variability, growth improves the precision of the pattern. In Chapter 5, we develop a numerical method for solving stiff reaction-diffusion equations which provides a necessary tool for solving modeling problems.