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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...
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...
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.
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,...
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 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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