Mathematical Modeling of Phagocytosis and Cell Swimming

Abstract

This is a collection of work that I have done during my PhD research at the Universityof Minnesota. There are two parts dedicated to the two projects I was involved in, one on the mechanics of cell swimming, and the other on the signaling dynamics of phagocytosis. The abstracts are included below. Abstract for Actin Waves in Frustrated PhagocytosisPhagocytosis is a complex process by which phagocytes such as lymphocytes or macrophages engulf and destroy foreign bodies called pathogens in a tissue. The process is triggered by the detection of antibodies that trigger signaling mechanisms that control the changes of the cellular cytoskeleton needed for engulfment of the pathogen. A mathematical model of the entire process would be extremely complicated, because the signaling and cytoskeletal changes produce large mechanical deformations of the cell. Recent experiments have used a confinement technique that leads to a process called frustrated phagocytosis, in which the membrane does not deform, but rather, signaling triggers actin waves that propagate along the boundary of the cell. This eliminates the large-scale deformations and facilitates modeling of the wave dynamics. Herein we develop a model of the actin dynamics observed in frustrated phagocytosis and show that it can replicate the experimental observations. We identify the key components that control the actin waves and make a number of experimentally-testable predictions. In particular, we predict that diffusion coefficients of membrane-bound species must be larger behind the wavefront to replicate the internal structure of the waves. Our model is a first step toward a more complete model of phagocytosis, and provides insights into circular dorsal ruffles as well. Abstract for ”Cell Swimming Driven by Cortical Tension Gradients”Recent experimental work has shown that numerous cell types can use different modes to move in different environments. Some cells crawl and some swim, but many can do both, and understanding how they interrogate their environment and determine how to move in response is central to understanding basic processes ranging from early development to cancer metastasis. Cell movement usually involves shapes changes, ranging from the massive changes in fibroblast movement in the ECM to the more refined gliding movement of keratocytes on smooth surfaces. In vivo tissues can contain fluid-filled regions, and there cells can move by cyclic shape deformations or strokes, i.e., by swimming. However, it is also known that cells can swim without shape changes, simply by maintaining a tension gradient in the cell membrane and cortex. This is called tension-driven movement, and previous work has demonstrated how static tension gradients can lead to movement. We will derive the differential equations governing cell swimming, review the results developed earlier, and - using a finite element approximation of the solution to the resulting equations - extend them here by studying how the shape and speed of a moving cell are affected by (i) the interaction of normal and tangential cortical forces (ii) the interior and exterior viscosities of the surrounding fluid and (iii) the vertical domain size.