UC Santa Barbara

In this thesis, we study aspects of active matter with the aim of application to biological systems and processes such as morphogenesis, using tools and ideas from condensedmatter physics, non-equilibrium physics, topology, and geometry.

We begin by examining the origin of local nematic order and extensile stress. Wedevelop a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, and show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key assumption of the model is that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations.

Assuming the existence of active stresses and local nematic order, for example generated via the noise mechanism discussed here, we study the dynamics of 2D activenematics, for which topological defects play a key role. We employ the power of complex analysis to study defects in the deep nematic limit where the nematic texture is determined by the defect positions. In particular, the polarization of a defect is not an independent degree of freedom, but rather is directly determined by the position of all of the other defects. Relaxational dynamics leads to a set of coupled ordinary differential equations for the defect positions. We discover novel dynamical aspects of defects, including a position-dependent “collective mobility” matrix, and non-central and non- reciprocal pair-wise interactions. We consider extensions and applications of this model, including excited states, continuum model, and different geometries and topologies, as well as for active polar fluids and its orientation dynamics. In particular, we highlight that for contractile (extensile) active nematic systems, +1 vortices (asters) should emerge as bound states of a pair of +1/2 defects, which has been recently observed.

Combining what we have learned about defect dynamics and inspired by recent experiments that highlight the role of nematic defects on the morphogenesis of epithelialtissues, we develop a minimal framework to study the dynamics of an active nematic on a curved surface which itself deforms in response to the nematic field. Allowing also the geometry of the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. Applying this framework to the dynamics of cultured murine neural progenitor cells (NPCs) in an ex-vivo setting, we find that cells accumulate at positive defects and form mounds, and that cells are depleted at negative defects. In contrast, applying this to the dynamics of a basal marine invertebrate Hydra in an in-vivo setting, we show that a bound +1 defect state surrounded by two −1/2 defects can create a stationary ring configuration of tentacles, consistent with observations.