Deformation of Cell Nuclei

In this thesis we investigate the role of the cell nucleus in processes that involve nucleus deformation. To begin with, we mathematically model the motion of molecular motors, using an asymmetric particle model, as a method to describe one force generation mechanism within a cell. This model is used to explore the effects of molecular motors working in tandem while attached to a single object, such as the cell nucleus. We then move on to developing a analysis tool for use with images of nucleus deformation. This computational tool uses a simulated annealing energy minimisation method with classical elasticity to determine the deformation of the nucleus between images, and from the deformation field, make predictions about the traction force on the surface of the nucleus which caused the observed deformations. We begin by treating the nucleus as a homogeneous elastic solid and calculating the traction force to cause the deformations observed of nuclei as they pass through channels containing constrictions. We then developed a second model of the nucleus, where it is instead treated as a thin homogeneous elastic shell. The shell model of the nucleus was then applied to the same images of nuclei passing through channels, and the resulting traction forces compared with the solid model results. Both the solid and shell models of the nucleus were then developed further to calculate the traction force on a deforming nucleus, when using three dimensional images in the form of a series of z stacks as input. We also combine the traction force calculations with an iterative method to calculate Poisson’s ratio from experimental images and compared this with previously published data of nuclei.