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Displaying 21 –
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100
In this work, we introduce a new software created to study hematopoiesis at the cell
population level with the individually based approach. It can be used as an interface between theoretical
works on population dynamics and experimental observations. We show that this software
can be useful to study some features of normal hematopoiesis as well as some blood diseases such
as myelogenous leukemia. It is also possible to simulate cell communication and the formation of
cell colonies in the bone marrow.
...
We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical...
A nonlinear system of two delay differential equations is proposed to model
hematopoietic stem cell dynamics. Each equation describes the evolution of a
sub-population, either proliferating or nonproliferating. The nonlinearity
accounting for introduction of nonproliferating cells in the proliferating phase
is assumed to depend upon the total number of cells. Existence and stability
of steady states are investigated. A Lyapunov functional is built to obtain the
global asymptotic stability of the...
The paper is devoted to mathematical modelling of erythropoiesis,
production of red blood cells in the bone marrow.
We discuss intra-cellular regulatory networks which determine
self-renewal and differentiation of erythroid progenitors.
In the case of excessive self-renewal, immature cells can fill
the bone marrow resulting in the development of leukemia.
We introduce a parameter characterizing the strength of mutation.
Depending on its value, leukemia will or will not develop.
The simplest...
A large variety of complex
spatio-temporal patterns emerge from the processes occurring in
biological systems, one of them being the result of propagating
phenomena. This wave-like structures
can be modelled via reaction-diffusion equations. If a solution of
a reaction-diffusion equation represents a travelling wave, the
shape of the solution will be the same at all time and the speed
of propagation of this shape will be a constant. Travelling wave
solutions of reaction-diffusion systems have been...
The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure and...
The calculus of looping sequences is a formalism for describing the
evolution of biological systems by means of term rewriting rules. In
this paper we enrich this calculus with a type discipline which
preserves some biological properties depending on the minimum and
the maximum number of elements of some type requested by the present elements. The type
system enforces these properties and typed reductions guarantee that
evolution preserves them. As an example, we model the hemoglobin
structure...
Cell motility is an integral part of a diverse set of biological processes. The quest for
mathematical models of cell motility has prompted the development of automated approaches
for gathering quantitative data on cell morphology, and the distribution of molecular
players involved in cell motility. Here we review recent approaches for quantifying cell
motility, including automated cell segmentation and tracking. Secondly, we present our own
novel...
In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell....
Viruses are obligate intracellular parasites that rely on the host cell for expansion.
With the development of global analyses techniques like transcriptomics, proteomics and
siRNA library screening of complete cellular gene sets, a large range of host cell factors
have been discovered that either support or restrict virus growth. Here we summarize some
of the recent findings and focus our discussion on the hepatitis C virus and the human
immunodeficiency...
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
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