In this talk, I will present two recent pieces of research that are connected by the common theme of multiscale models for motile microorganisms. 

In the first part, I will discuss the orientational dynamics of microscopic organisms, such as bacteria, swimming in biofluids with properties that differ from those of isotropic Newtonian fluids, instead exhibiting characteristics of liquid crystals. These environments have a preferred direction, which forces the swimmers to align with it. However, certain types of bacteria can overcome this external torque and swim across the preferred direction. I will present a nonlinear PDE system that couples liquid crystal hydrodynamics with a model of a prototypical microswimmer. This model identifies the conditions for non-trivial reorientation dynamics and allows for deriving the homogenized limit, effectively describing the dynamics of the microswimmer colony. This is the joint work with I. Aronson (PSU), L. Berlyand (PSU), H. Chi (PSU), A. Yip (Purdue U.), and L. Zhang (SJTU). 

In the second part of the talk, I will focus on a computational model that describes how motile cancer cells interact with the extracellular matrix (ECM) during the initial invasion phase, including ECM degradation and mechanical remodeling. The model highlights the role of elastic interactions in the dynamics of cell clusters, including their shapes, sizes, and orientations. These results are joint work with O. Kim (Virginia Tech), Y. Klymenko (Indiana U.), M. Alber (UCR), and I. Aranson (PSU).