A Mathematical Model of Cell Cycle Dysregulation Due to Human Papillomavirus Infection

Understanding the mechanisms of HPV-related carcinogenesis: Implications for cell cycle dynamics

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 Gérard and Goldbeter (2009) 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. 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.

A Model for the Proliferation–Quiescence Transition in Human Cells

The process of revitalising quiescent cells in order for them to proliferate plays a pivotal role in the repair of worn-out tissues as well as for tissue homeostasis. This process is also crucial in the growth, development and well-being of higher multi-cellular organisms such as mammals. Deregulation of proliferation-quiescence transition is related to many diseases, such as cancer. Recent studies have revealed that this proliferation–quiescence process is regulated tightly by the Rb−E2F bistable switch mechanism. Based on experimental observations, in this study, we formulate a mathematical model to examine the effect of the growth factor concentration on the proliferation–quiescence transition in human cells. Working with a non-dimensionalised model, we prove the positivity, boundedness and uniqueness of solutions. To understand model solution behaviour close to bifurcation points, we carry out bifurcation analysis, which is further illustrated by the use of numerical bifurcation analysis, sensitivity analysis and numerical simulations. Indeed, bifurcation and numerical analysis of the model predicted a transition between bistable and stable states, which are dependent on the growth factor concentration parameter (GF). The derived predictions confirm experimental observations.

Mathematical analysis of a SIPC age-structured model of cervical cancer

Human Papillomavirus (HPV), which is the main causal factor of cervical cancer, infects normal cervical cells on the specific cell's age interval, i.e., between the G₁ to S phase of cell cycle. Hence, the spread of the viruses in cervical tissue not only depends on the time, but also the cell age. By this fact, we introduce a new model that shows the spread of HPV infections on the cervical tissue by considering the age of cells and the time. The model is a four dimensional system of the first order partial differential equations with time and age independent variables, where the cells population is divided into four sub-populations, i.e., susceptible cells, infected cells by HPV, precancerous cells, and cancer cells. There are two types of the steady state solution of the system, i.e., disease-free and cancerous steady state solutions, where the stability is determined by using Fatou's lemma and solving some integral equations. In this case, we use a non-standard method to calculate the basic reproduction number of the system. Lastly, we use numerical simulations to show the dynamics of the age-structured system.

Principles of epithelial homeostasis control during persistent human papillomavirus infection and its deregulation at the cervical transformation zone

Human papillomaviruses establish a reservoir of infection in the epithelial basal layer. To do this they limit their gene expression to avoid immune detection and modulate epithelial homeostasis pathways to inhibit the timing of basal cell delamination and differentiation to favour persistence. For low-risk Alpha papillomaviruses, which cause benign self-limiting disease in immunocompetent individuals, it appears that cell competition at the lesion edge restricts expansion. These lesions may be considered as self-regulating homeostatic structures, with epithelial cells of the hair follicles and sweat glands, which are proposed targets of the Beta and Mu papillomaviruses, showing similar restrictions to their expansion across the epithelium as a whole. In the absence of immune control, which facilitates deregulated viral gene expression, such lesions can expand, leading to problematic papillomatosis in afflicted individuals. By contrast, he high-risk Alpha HPV types can undergo deregulated viral gene expression in immunocompetent hosts at a number of body sites, including the cervical transformation zone (TZ) where they can drive the formation of neoplasia. Homeostasis at the TZ is poorly understood, but involves two adjacent epithelial cell population, one of which has the potential to stratify and to produce a multilayed squamous epithelium. This process of metaplasia involves a specialised cell type known as the reserve cell, which has for several decades been considered as the cell of origin of cervical cancer. It is becoming clear that during evolution, HPV gene products have acquired functions directly linked to their requirements to modify the normal processes of epithelial homestasis at their various sites of infection. These protein functions are beginning to provide new insight into homeostasis regulation at different body sites, and are likely to be central to our understanding of HPV epithelial tropisms.

Epithelial stratification shapes infection dynamics

Infections of stratified epithelia contribute to a large group of common diseases, such as dermatological conditions and sexually transmitted diseases. To investigate how epithelial structure affects infection dynamics, we develop a general ecology-inspired model for stratified epithelia. Our model allows us to simulate infections, explore new hypotheses and estimate parameters that are difficult to measure with tissue cell cultures. We focus on two contrasting pathogens: Chlamydia trachomatis and Human papillomaviruses (HPV). Using cervicovaginal parameter estimates, we find that key infection symptoms can be explained by differential interactions with the layers, while clearance and pathogen burden appear to be bottom-up processes. Cell protective responses to infections (e.g. mucus trapping) generally lowered pathogen load but there were specific effects based on infection strategies. Our modeling approach opens new perspectives for 3D tissue culture experimental systems of infections and, more generally, for developing and testing hypotheses related to infections of stratified epithelia.