Reception to follow.
Breaking symmetry in spatially distributed networks is a fascinating dynamical systems problem and is of fundamental interest to developmental biology. We will discuss two types of local interaction that underlie formation of gene expression patterns in multi-cellular organisms: diffusion and cell-to-cell contact signaling. We will first present new insights on a diffusion-driven mechanism for pattern formation and propose a synthetic gene network architecture built upon this mechanism. We will then discuss contact-mediated inhibition – a mechanism responsible for segmentation and fate-specification. We will introduce a broad dynamical model to represent this mechanism and reveal the key properties of the model that are necessary for pattern formation. Our approach is to describe the spatial configuration of the cells with a contact graph, and to exploit graph symmetries to partition the vertices into classes of cells with equal fates. We will present a dynamical systems procedure to determine whether steady-state patterns structured according to candidate partitions exist and conclude by exhibiting patterns for several graph structures.
Murat Arcak is an associate professor at UC Berkeley in the Electrical Engineering and Computer Sciences Department. He received the B.S. degree from the Bogazici University in Istanbul (1996) and the M.S. and Ph.D. degrees from the University of California, Santa Barbara (1997 and 2000). His research is in dynamical systems and control theory with applications to biological networks, power systems, communication networks, and cooperative robotics. Prior to joining Berkeley in 2008, he was a faculty member at the Rensselaer Polytechnic Institute. He received a NSF CAREER Award in 2003, the Donald P. Eckman Award in 2006, and the SIAM Control and Systems Theory Prize in 2007. He is a member of SIAM and a fellow of IEEE.