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Epidermal wound healing is a complex process that repairs injured tissue. The complexity
of this process increases when bacteria are present in a wound; the bacteria interaction
determines whether infection sets in. Because of underlying physiological problems
infected wounds do not follow the normal healing pattern. In this paper we present a
mathematical model of the healing of both infected and uninfected wounds. At the core of
our model is an...
We discuss theoretical and experimental approaches to three distinct
developmental systems that illustrate how theory can influence experimental work
and vice-versa. The chosen systems – Drosophila melanogaster,
bacterial pattern formation, and pigmentation patterns – illustrate the
fundamental physical processes of signaling, growth and cell division, and cell
movement involved in pattern formation and development. These systems exemplify
the current state of theoretical and experimental understanding...
Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated analogy...
In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.
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