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A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies

G. Kapitanov (2012)

Mathematical Modelling of Natural Phenomena

There is evidence that cancer develops when cells acquire a sequence of mutations that alter normal cell characteristics. This sequence determines a hierarchy among the cells, based on how many more mutations they need to accumulate in order to become cancerous. When cells divide, they exhibit telomere loss and differentiate, which defines another cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model, which combines...

A Maturity-Structured Mathematical Model of Mutation, Acquisition in the Absence of Homeostatic Regulation

S. N. Gentry, R. Ashkenazi, T. L. Jackson (2009)

Mathematical Modelling of Natural Phenomena

Most mammalian tissues are organized into a hierarchical structure of stem, progenitor, and differentiated cells. Tumors exhibit similar hierarchy, even if it is abnormal in comparison with healthy tissue. In particular, it is believed that a small population of cancer stem cells drives tumorigenesis in certain malignancies. These cancer stem cells are derived from transformed stem cells or mutated progenitors that have acquired stem-cell qualities, specifically the ability to self-renew. Similar...

An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development

Ph. Laurençot, Ch. Walker (2008)

Mathematical Modelling of Natural Phenomena

Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces. In this paper we investigate a mathematical model that has been shown to display these structures when solved numerically. The model consists of an ordinary differential equation coupled with a partial differential equation involving a first-order hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to admit global weak solutions.

Mathematical Models of Dividing Cell Populations: Application to CFSE Data

H.T. Banks, W. Clayton Thompson (2012)

Mathematical Modelling of Natural Phenomena

Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental tool which can be used in conjunction with mathematical modeling to quantify the dynamic behavior of a population of lymphocytes. In this survey we begin by providing an overview of the mathematically relevant aspects of the data collection procedure. We then present an overview of the large body of mathematical models, along with their assumptions and uses,...

Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach

R. Kerner (2011)

Mathematical Modelling of Natural Phenomena

An analysis of all possible icosahedral viral capsids is proposed. It takes into account the diversity of coat proteins and their positioning in elementary pentagonal and hexagonal configurations, leading to definite capsid size. We show that the self-organization of observed capsids during their production implies a definite composition and configuration of elementary building blocks. The exact number of different protein dimers is related to the...

The Use of CFSE-like Dyes for Measuring Lymphocyte Proliferation : Experimental Considerations and Biological Variables

B.J.C. Quah, A.B. Lyons, C.R. Parish (2012)

Mathematical Modelling of Natural Phenomena

The measurement of CFSE dilution by flow cytometry is a powerful experimental tool to measure lymphocyte proliferation. CFSE fluorescence precisely halves after each cell division in a highly predictable manner and is thus highly amenable to mathematical modelling. However, there are several biological and experimental conditions that can affect the quality of the proliferation data generated, which may be important to consider when modelling dye...

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