Discrete 3-Dimensional Modeling of Tumor Cell Growth and Migration

Abstract

A variety of genetic factors causing up-regulation or down-regulation of key enzymes have been attributed to affect the malignancy of tumors. Yet, the ability to predict the aggressiveness of tumors in terms of their growth rate and metastatic potential is fairly limited. We hypothesize that the genetic and enzymatic factors only indirectly influence tumor growth and metastasis and that these processes are primarily physical in nature. This is based on observations that the physical state of a cell plays a major role in determining its fate - division, survival, migration and apoptosis. The physical state of a cell (shape and size) is a direct function of the physical properties of the cell such as the osmotic pressure, the cytoskeletal stiffness and the strength of inter-cellular and cell-matrix bonding. We have developed a computational model describing the physical state of discrete cells in a 3-dimensional tissue environment as a function of the physical properties of cells. Using this model and a cell shape dependent cell death and division rate we recreate the conditions for cell turnover and tissue homeostasis. We then probe the influence of changes in a cell's physical properties on its division rate and apoptosis. The changes in physical properties that cause an uncontrolled growth and division of cells can be identified. Cells with these characteristics correspond in nature to tumor cells. Computer simulations based on this model provide information on the growth rate of particular tumors with cells displaying specific physical properties as well as the shape evolution of these tumors. The identification of changes in physical properties of a cell that drive tumor cell growth and division helps isolate key genetic and enzymatic factors that influence these properties and the mechanism by which they drive tumor progression.