Biology subjects

Hillen, T.

Publications and source records attributed to Hillen, T..

5 recordsLinked to original sources

bioRxiv2018

A Stochastic Model for Cancer Metastasis: Branching Stochastic Process with Settlement

We introduce a new stochastic model for metastatic growth, which takes the form of a branching stochastic process with settlement. The moving particles are interpreted as clusters of cancer cells while stationary particles correspond to micro-tumors and metastases. The analysis of expected particle location, their locational variance, the furthest particle distribution, and the extinction probability leads to a common type of differential equation, namely, a non-local integro-differential equation with distributed delay. We prove global existence and uniqueness results for this type of equation. The solutions asymptotic behavior for long time is characterized by an explicit index, a metastatic reproduction number R0: metastases spread for R0 > 1 and become extinct for R0 < 1. Using metastatic data from mouse experiments, we show the suitability of our framework to model metastatic cancer.

cancer biology↗

bioRxiv2017

Effects of G2 checkpoint dynamics on the low-dose hyper-radiosensitivity

We develop and analyze a system of differential equations to investigate the effects of G2 checkpoint dynamics on the low-dose hyper-radiosensitivity. In experimental studies, it has been found that certain cell lines are more sensitive to low-dose radiation than would be expected from the classical Linear Quadratic model (LQ model). In fact, it is frequently observed that cells incur more damage at a low dose (say 0.3 Gy) than at higher dose (say 1 Gy). This effect has been termed hyper-radiosensitivity (HRS). The HRS is followed by a period of relative radioresistance (per unit dose) of cell kill over the dose range of ~ 0.5 - 1 Gy. This latter phenomenon is termed increased radioresistance (IRR). These effects depend on the type of cells and on their phase in the cell cycle. Here we focus on the HRS phenomenon by fitting a model for the cell cycle that includes G2-checkpoint dynamics and radiation treatment to surviving fraction data for different cell lines including glioma cells, prostate cancer cells, as well as to cell populations that are enriched in certain phases of the cell cycle. The HRS effect is measured in the literature through [Formula], the ratio of slope s, of the surviving fraction curve at zero dose to slope of the corresponding LQ model. We derive an explicit formula for this ratio and we show that it corresponds very closely to experimental observations. Finally, we can identify the dependence of this ratio on the surviving fraction at 2 Gy. It was speculated in the literature that such a relation exists. Our theoretical analysis will help to more systematically identify the HRS in cell lines and opens doors to analyze its use in cancer treatment.\n\nPACS and mathematical subject classification numbers as needed.

cancer biology↗

bioRxiv2016

Aggregation of biological particles under radial directional guidance.

Many biological environments display an almost radially-symmetric structure, allowing proteins, cells or animals to move in an oriented fashion. Motivated by specific examples of cell movement in tissues, pigment protein movement in pigment cells and animal movement near watering holes, we consider a class of radially-symmetric anisotropic diffusion problems, which we call the star problem. The corresponding diffusion tensor D(x) is radially symmetric with isotropic diffusion at the origin. We show that the anisotropic geometry of the environment can lead to strong aggregations and blow-up at the origin. We classify the nature of aggregation and blow-up solutions and provide corresponding numerical simulations. A surprising element of this strong aggregation mechanism is that it is entirely based on geometry and does not derive from chemotaxis, adhesion or other well known aggregating mechanisms. We use these aggregate solutions to discuss the process of pigmentation changes in animals, cancer invasion in an oriented fibrous habitat (such as collagen fibres), and sheep distributions around watering holes.\n\nJTB classification21.050, 21.160, 52.250, 71.060

systems biology↗

bioRxiv2016

A Reaction-Diffusion Model for Radiation-InducedBystander Effects

We develop and analyze a reaction-diffusion model to investigate the dynamics of the lifespan of a bystander signal emitted when cells are exposed to radiation. Experimental studies by Mothersill and Seymour 1997, using malignant epithelial cell lines, found that an emitted bystander signal can still cause bystander effects in cells even 60h after its emission. Several other experiments have also shown that the signal can persist for months and even years. Also, bystander effects have been hypothesized as one of the factors responsible for the phenomenon of low-dose hyper-radiosensitivity and increased radioresistance (HRS/IRR). Here, we confirm this hypothesis with a mathematical model, which we fit to Joiners data on HRS/IRR in a T98G glioma cell line. Furthermore, we use phase plane analysis to understand the full dynamics of the signals lifespan. We find that both single and multiple radiation exposure can lead to bystander signals that either persist temporarily or permanently. We also found that, in an heterogeneous environment, the size of the domain exposed to radiation and the number of radiation exposures can determine whether a signal will persist temporarily or permanently. Finally, we use sensitivity analysis to identify those cell parameters that affect the signals lifespan and the signal-induced cell death the most.

cancer biology↗

bioRxiv2016

A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis

Cellular adhesion provides one of the fundamental forms of biological interaction between cells and their surroundings, yet the continuum modelling of cellular adhesion has remained mathematically challenging. In 2006, Armstrong et al. proposed a mathematical model in the form of an integro-partial differential equation. Although successful in applications, a derivation from an underlying stochastic random walk has remained elusive. In this work we develop a framework by which non-local models can be derived from a space-jump process. We show how the notions of motility and a cell polarization vector can be naturally included. With this derivation we are able to include microscopic biological properties into the model. We show that particular choices yield the original Armstrong model, while others lead to more general models, including a doubly non-local adhesion model and non-local chemotaxis models. Finally, we use random walk simulations to confirm that the corresponding continuum model represents the mean field behaviour of the stochastic random walk.

systems biology↗