Sequential pattern formation as a front instability problem

  • SPEAKER : Lei-Han Tang
  • INSTITUTE : Beijing Computational Science Research Center & HKBU
  • DATE : October 14(Wed), 2015
  • TIME : 17:30-18:00
  • PLACE : Rm 1503(Bldg#I,5th), Korea Institute for Advanced Study, South Korea
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ABSTRACT : Pattern formation is a fundamental process in embryogenesis and development. In his seminal paper half a century ago, Turing proposed a mechanism for spontaneous pattern formation in biological systems that involve the diffusion of two types of morphogens (“activator” and “inhibitor”) whose interaction stimulates their own synthesis. Starting from random initial perturbations, the Turing model typically generates patterns via the development of finitewavelength dynamical instabilities in confined geometries. Recently, a collaboration led by Terry Hwa at UCSD and Jiandong Huang at HKU conducted experiments of pattern formation in open geometry through control of the synthetic chemotactic circuit of bacteria[1]. A key feature of the system is a concentration-dependent diffusivity of the active species which can be tuned in the experiment through control of gene expression. Theoretical analysis of the traveling wave solution reveals key parameters that span the phase diagram of the system[2]. Very recently, we carried out linear stability analysis of the traveling wave which yields a localized mode. Depending on the sharpness of the motility variation in space, either a Hopf bifurcation or a first order transition to a pulsating front solution can be observed[3]. The autonomous diffusion control together with the open, expanding geometries offered by growing biological systems, give rise to novel strategies to generate well-defined patterns in space and time. References 1. Chenli Liu et al., Science 334, 238 (2011). 2. Xiongfei Fu et al., Phys. Rev. Lett. 108, 198102 (2012). 3. Moritz Zehl, Min Tang and Lei-Han Tang, in preparation.

The 3rd East Asia Joint Seminar on Statistical Physics