Cellular polarization plays a critical during cellular differentiation, development, and cellular migration through the establishment of a long-lived cell-front and cell-rear. Although mechanisms of polarization vary across cells types, some common biochemical players have emerged, namely the RhoGTPases Rac and Rho. The low diffusion coefficient of the active form of these molecules combined with their mutual inhibitory interaction dynamics have led to a prototypical pattern-formation system that can polarizes cell through a non-Turing pattern formation mechanism termed wave-pinning. We investigate the effects of paxillin, a master regulator of adhesion dynamics, on the Rac-Rho system through a positive feedback loop that amplifies Rac activation. We find that paxillin feedback onto the Rac-Rho system produces cells that (i) self-polarize in the absence of any input signal (i.e., paxllin feedback causes a Turing instability) and (ii) become arrested due to the development of multiple protrusive regions. The former effect is a positive finding that can be related to certain cell-types, while the latter outcome is likely an artefact of the model. In order to minimize the effects of this artefact and produce cells that can both self-polarize as well as migrate for extended periods of time, we revisit some of model's parameter values and use lessons from previous models of polarization. This approach allows us to draw conclusions about the biophysical properties and spatiotemporal dynamics of molecular systems required for autonomous decision making during cellular migration.
Cell division is a vital mechanism for cell proliferation, but it often breaks its symmetry during animal development. Symmetry-breaking of cell division, such as the orientation of the cell division axis and asymmetry of daughter cell sizes, regulates morphogenesis and cell fate decision during embryogenesis, organogenesis, and stem cell division in a range of organisms. Despite its significance in development and disease, the mechanisms of symmetry-breaking of cell division remain unclear. Previous studies heavily focused on the mechanism of symmetry-breaking at metaphase of mitosis, wherein a localized microtubule-motor protein activity pulls the mitotic spindle. Recent studies found that cortical flow, the collective migration of the cell surface actin-myosin network, plays an independent role in the symmetry-breaking of cell division after anaphase. Using nematode C. elegans embryos, we identified extrinsic and intrinsic cues that pattern cortical flow during early embryogenesis. Each cue specifies distinct cellular arrangements and is involved in a critical developmental event such as the establishment of the left-right body axis, the dorsal-ventral body axis, and the formation of endoderm. Our research started to uncover the regulatory mechanisms underlying the cortical flow patterning during early embryogenesis.
What does mathematics, materials science, biology, and quantum
information science have in common? It turns out, there are many
connections worth exploring. I this talk, I will focus on graphs and random
walks, starting from the classical mathematical constructs and moving on to
quantum descriptions and applications. We will see how the notions of graph
entropy and KL divergence appear in the context of characterizing
polycrystalline material microstructures and predicting their performance
under mechanical deformation, while also allowing to measure adaptation in
cancer networks and entanglement of quantum states. We will discover
unified conditions under which master equations for classical random walks
exhibit nonlocal and non-diffusive behavior and see how quantum walks allow
to realize the coveted exponential speedup in quantum Hamiltonian
simulations. Recent classical and quantum breakthroughs and open questions
will be discussed.