Qixuan Wang, University of California, Irvine
Many biological processes in cell and developmental systems require an intricate and well-coordinated regu-lation of spatial-temporal dynamics at multi-scales. How to incorporate the dynamics at different scales in one system is a big challenge in modeling of developmental systems. We developed several multi-scale models for different systems to study the spatial-temporal dynamics in system development, pattern formation and cell migration. These model systems include: 1) a 3D model for hair follicle development and wave propagation, where follicle growth is regulated by the coupling of activator/inhibitor signaling that is described by stochas-tic PDE, and we show that the co-option of these signals into skin macro-environment produces wave-like coupled hair growth; 2) hybrid models for pattern formation during embryo development, with gene regu-lation network described by stochastic PDE/ODE and cells modeled by sub-cellular element method, where we explore how global information incorporated chemical signaling directs cell fate decision making and guides cell movement; 3) models for amoebae cells and mini aqua robots swimming in viscous fluid, where we either use techniques from complex analysis in a 2D model or asymptotic analysis on 3D linked-sphere type models, so to explore how various modes of cyclic deformations lead to cell movement in viscous fluid.