Computational modeling of cell membrane mechanics from sub-cellular to tissue length scales

Author(s): Vasan, Ritvik | Advisor(s): Rangamani, Padmini | Abstract: Cell and tissue movement are essential to embryonic development, cancer metastasis, wound healing, cargo delivery etc. These movements span multiple length scales — collective cell behavior occurs at ~ 10^-2m, membrane trafficking occurs at ~ 10^-8m, and the growth of the actin cytoskeleton occurs at ~ 10^-10m. The forces needed to drive movement begins with actin polymerization and other molecular motors, enabling local deformations that can translate into movement across length scales. Experimental methods for quantification of such forces are often difficult to implement in a high-throughput context and can be disruptive. In this work, we present mathematical and computational models to understand the relationship between cell movements and forces at two different length scales. At the sub-cellular length scale, we use Helfrich-energy theory in an axisymmetric and continuum framework to probe traction stress distributions generated along membrane tubules and buds. After discussing the applicability of this model to predict traction stresses from 2D electron micrograph (EM) images of membrane bud shapes, we then use a 3D Finite Element Model (FEM) to analyze a spontaneous symmetry breaking instability of the membrane neck during the pinching step of membrane trafficking. We draw similarities with classical buckling in many thin elastic structures, and proceed to analyze the effect of helical loading to compare against polymers like Dynamin. We then pair a continuum membrane mechanics model with an agent based model of filament dynamics to show that actin filaments self-organize to promote axial force production towards the base of the endocytic pit. At the tissue length scale, we use a vertex model of colony morphogenesis to validate a data-driven force-inference toolkit applicable to time-series 2D images of cell monolayers. We show that including a regularization term in the opitimization formulation boosts model prediction across time. We also discuss the potential for high-throughput imaging to model pipelines through machine learning algorithms for segmentation, generation, and meshing of cellular structures. Our models identify mechanisms of cell movement at two different length scales, enabling future work to establish the contribution of endocytic pathways in directing cell topologies and tissue morphogenesis.