In the Modes Lab we are driven by questions and problems where geometry and topology play together in biological and biophysical settings. Much of our work falls under two larger umbrellas: complex spatial networks and spontaneous strain driven morphogenesis, together with a number of smaller projects that fit these themes to varying degrees. Rich topology comes for free in the setting of complex networks and higher-order structures such as simplicial complexes, but when these networks are embedded in real space, geometry can play a critical role. On the other hand, epithelial morphogenesis is, on its surface, entirely about the geometry of complex shape transitions and establishment during morphogenesis. However, we are advancing a model of morphogenesis that is primarily driven by in-plane gradients of active cell behaviors rather than apico-basal gradients. In such a model, topological defects in the spontaneous strain field created by in-plane activities become powerful organizers and drivers of shape outcomes.
In the realm of complex spatial networks, we are especially interested in the establishment of complex distribution networks during organogenesis. It is particularly striking when two or more separate, intertwined networks co-service the same tissue volume, as occurs for example with the sinusoidal and bile canalicular networks in the liver or the vascular and ductal networks in the pancreas. In addition to the explicit modeling and analysis of these systems, we also find that it is of critical importance to advance the fundamental, theoretical understanding of spatially embedded networks, where characteristics, metrics, and modeling approaches have lagged far behind those found in their abstract, purely topological, non-geometric brethren, the social and relational networks and their ilk.
On the side of spontaneous strain-driven morphogenesis, we are pushing forward the theoretical underpinnings of these ideas by marrying the theory of tissue mechanics and vertex models with the theory of shape programmable exotic materials, in which we have played an important foundational role. At the same time, we are applying our approach to understand the eversion of the Drosophila wing disc, the establishment of the Drosophila cephalic furrow, and the formation of the zebrafish optic cup, among other tissues.
Our group seeks to leverage principles and methods of applied topology and geometry in order to better understand complex biological phenomena, with particular interest in the role of network complexity and the shape-organizing power of topological defects in such systems. Generally speaking, we are excited by any new ideas, systems, or collaborations that demand the coupling of topology, geometry, and biophysics. In the future, we will also seek to build a bridge between the network side of our work and the topologically-driven shape outcome side in order to capture the complex volumetric morphologies of many organelles within the cells and mesoscale tissue structure beyond.