The 3rd East Asia Joint Seminar on Statistical Physics
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
PLACE | Rm 1503(Bldg#I,5th), Korea Institute for Advanced Study, South Korea
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 (ˇ°activatorˇ± and
ˇ°inhibitorˇ±) 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. 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.
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. 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.
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.