Modeling of Cell Cycle Distortion and p16ink4a Significance in Human Papillomavirus-Infected Cells and Novel Use of Partial Differential Equations in Epidemiology Modeling

Abstract

The role of human papillomavirus (HPV) as a causative agent for epithelial cancers is well-known, but many open questions remain regarding the downstream gene regulatory effects of viral proteins E6 and E7 on the cell cycle. Here, we extend a cell cycle model originally presented by Gerard and Goldbeter in order to capture the effects of E6 and E7 on key actors in the cell cycle. Results suggest that E6 is sufficient to reverse p53-induced quiescence, while E7 is sufficient to reverse p16INK4a-induced quiescence; both E6 and E7 are necessary when p53 and p16INK4a are both active. Moreover, E7 appears to play a role as a "growth factor substitute", inducing cell division in the absence of growth factor. Low levels of E7 may permit regular cell division, but the results suggest that higher levels of E7 dysregulate the cell cycle in ways that may destabilize the cellular genome.

In the second project, we additionally explore factors related to susceptibility to apoptosis in HPV-positive cells, with results suggesting that while p16INK4a may be important in preventing apoptosis in such cells, this is unlikely to be due to stabilization of the cell cycle. The mechanisms explored here provide opportunities for developing new treatment targets that take advantage of the cell cycle regulatory system to prevent HPV-related cancer effects. In particular, suppression of p16INK4a activity may be a valuable target as an adjuvant to chemotherapy in HPV-positive cancers.

Additionally, we present a novel implementation of the standard SIR epidemiology model, refined to use partial differential equations instead of the usual ordinary differential equations. This enables the model to more easily consider factors like differing levels of vulnerability in a given population or different states of disease progression without needing to explicitly add more equations to the system. Case studies illustrating the use of this new framework are given, and some speculation on ways in which this model may be made further abstract are included at the end.