Estimating the Selective Advantage of Mutant p53 Tumour Cells to Repeated Rounds of Hypoxia

Abstract

The tumour suppressor gene, p53, plays an important role in tumour development. Under low levels of oxygen (hypoxia), cells expressing wild-type p53 undergo programmed cell death (apoptosis), whereas cells expressing mutations in the p53 gene may survive and express angiogenic growth factors that stimulate tumour vascularization. Given that cells expressing mutations in the p53 gene have been observed in many forms of human tumour, it is important to understand how both wild-type and mutant cells react to hypoxic conditions. In this paper a mathematical model is presented to investigate the effects of alternating periods of hypoxia and normoxia (normal oxygen levels) on a population of wild-type and mutant p53 tumour cells. The model consists of three coupled ordinary differential equations that describe the densities of the two cell types and the oxygen concentration and, as such, may describe the growth of avascular tumours in vitro and/or in vivo. Numerical and analytical techniques are used to determine how changes in the system parameters influence the time at which mutant cells become dominant within the population. A feedback mechanism, which switches off the oxygen supply when the total cell density exceeds a threshold value, is introduced into the model to investigate the impact that vessel collapse (and the associated hypoxia) has on the time at which the mutant cells become dominant within vascular tumours growing in vivo. Using the model we can predict the time it takes for a subpopulation of mutant p53 tumour cells to become the dominant population within either an avascular tumour or a localized region of a vascular tumour. Based on independent experimental results, our model suggests that the mutant population becomes dominant more quickly in vivo than in vitro (12 days vs 17 days).

Competition and natural selection in a mathematical model of cancer

“…Thompson and Royds (1999), using data from Graber et al (1996), estimated parameter values for the function for two different cancer cell lines in culture-a 'wild-type' and a mutant that under-expresses p53 (Table 1). These values, also used by Gammack et al (2001), suggest that tumor cells are remarkably insensitive to changes in oxygen availability and therefore vascularization [see Fig. 2(a)].…”

“…Values for parameters A i , B i , σ i ,ĉ i1 ,ĉ i2 , p i and q i can be obtained empirically (see Section 3). Equation (2) is similar to the model of Gammack et al (2001) [see also Thompson and Royds (1999)] except for the lack of a logistic crowding term omitted here because model (2) is meant to express dynamics of a small tumor for which exponential growth is a sufficient approximation. The dependence of oxygen concentration on vascularization is assumed to be…”

“…Similarly, bothĉ 1 andĉ 2 in Table 1 are probably lower bounds; indeed, substantial increases in either one, up to say 10 or more, have little effect on the overall form of the functions and may represent more realistic behavior in vivo. Gammack et al (2001) and Thompson and Royds (1999). Values forĉ have been converted from percent to mmHg.…”

Numerical Solution of a Model for Brain Cancer Progression After Therapy

“…Net cellular proliferation is a function of available nutrient, as experimentally quantified in [7,15]. Migratory cells do not grow, but die at a constant per capita rate.…”

Explicit Separation of Growth and Motility in a New Tumor Cord Model

“…While some simple mutations offer a clear selective advantage (e.g., the loss of the p53 tumor suppressor gene as a mechanism to dramatically increase survival in any environment Gammack et al, 2001), more complex genetic transformations involving a large number of mutations working in concert to create a new phenotype are much more difficult to analyze experimentally. It is in this area that mathematical models of cancer offer the greatest potential for contributing to oncological research.…”