Skip to main content
Article thumbnail
Location of Repository

A mathematical model for the onset of avascular tumor growth in response to the loss of p53 function

By Howard A. Levine, Michael W. Smiley, Anna L. Tucker and Marit Nilsen-Hamilton

Abstract

We present a mathematical model for the formation of an avascular tumor based on the loss by gene mutation of the tumor suppressor function of p53. The wild type p53 protein regulates apoptosis, cell expression of growth factor and matrix metalloproteinase, which are regulatory functions that many mutant p53 proteins do not possess. The focus is on a description of cell movement as the transport of cell population density rather than as the movement of individual cells. In contrast to earlier works on solid tumor growth, a model is proposed for the initiation of tumor growth. The central idea, taken from the mathematical theory of dynamical systems, is to view the loss of p53 function in a few cells as a small instability in a rest state for an appropriate system of differential equations describing cell movement. This instability is shown (numerically) to lead to a second, spatially inhomogeneous, solution that can be thought of as a solid tumor whose growth is nutrient diffusion limited. In this formulation, one is led to a system of nine partial differential equations. We show computationally that there can be tumor states that coexist with benign states and that are highly unstable in the sense that a slight increase in tumor size results in the tumor occupying the sample region while a slight decrease in tumor size results in its ultimate disappearance

Topics: Original Research
Publisher: Libertas Academica
OAI identifier: oai:pubmedcentral.nih.gov:2675492
Provided by: PubMed Central
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://www.pubmedcentral.nih.g... (external link)
  • Suggested articles

    Citations

    1. (2004). A history of the study of solid tumour growth: the contribution of mathematical modelling
    2. (1992). A mathematical model for the growth and classification of a solid tumor: a new approach via nonlinear elasticity theory using strain-energy functions,
    3. (2005). Cancer: Two in one,
    4. (1982). Chemotaxis of aortic endot helial cells in response to fi bronectin Cancer Res.,
    5. (2004). Dynamics and porcessivity of 40S ribosome scanning on mRNA in yeast,
    6. (1996). Ecological models, permanence and spatial heterogeneity,
    7. (1993). Enhanced degradation of p53 protein in HPV-t and BPV-1 E6 immortalized human mammary epithelial cells,
    8. (1995). Growth of nonnecrotic tumors in the presence and absence of inhibitors,
    9. (1991). Loss of a tumor suppressor gene function is correlated with downregulation of chondrocyte-specific collagen expression in Syrian hamster embrio cells,
    10. (1992). Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids.
    11. (1996). Mathematical models of prevascular spheroid development and catastrophe-theoretic description of rapid metastatic growth/tumor remission,
    12. (2003). Mathematical models of tumor growth: from empirical description to biological mechanism,
    13. (1989). Mathematical models of tumor growth. IV. Effects of a necrotic core,
    14. (2004). Multiple reversals of competitive dominance in ecological reserves via external habitat degradation
    15. (1984). On interacting populations that disperse to avoid crowding: The effect of a sedentary colony,
    16. (1998). On the effects of spatial heterogeneity on the persistence of interacting species,
    17. (1989). On the uniqueness and stability of positive solutions in the Lotka-Volterra competition model with diffusion,
    18. (1991). Permanence for nonautonomous predator-prey systems,
    19. (1993). Permanence in ecological systems with spatial heterogeneity
    20. (1999). Quantitative relationship among integrin-ligand binding, adhesion, and signaling via focal adhesion kinase and extracellular signalregulated kinase 2,
    21. (2001). The influence of growth-induced stress from the surrounding medium on the development of multicell spheroids,

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.