Mathematical modelling of cell migration and biological systems driven by cell proliferation
by Rebecca Chisholm
Abstract: Mathematical biology is an emerging field. As the name suggests, the aim of this discipline is to model biological systems using mathematics to provide new insight and make predictions about the biology. To maintain realism and to generate models that are biologically accurate requires close collaboration between biologists and mathematicians.
Throughout my PhD candidature I had the opportunity to collaborate with experimentalists on a number of projects. Each project relates to a different field of biological research. The aim of each collaboration was to use mathematical modelling to gain new biological insight into the system of interest. Furthermore each project involved modelling the fundamental cell behaviours of either cell migration or cell proliferation.
During this seminar I will briefly describe four mathematical models of biological systems including:
(1) short time-scale cell migration, where a cell undergoes one cycle of protrusion, adhesion and detachment, to understand the difference in biphasic cell migration speed with and without proteolysis;
(2) morphogen gradient formation in a growing tissue that does not support diffusion, to determine the circumstances under which a morphogen gradient can form;
(3) sequential segmentation in velvet worms;
(4) the growth of the gubernaculum during the descent of the testes to understand the role of the gubernaculum core in growth.