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Collective motion of cells: from experiments to models
Swarming or collective motion of living entities is one of the most common
and spectacular manifestations of living systems having been extensively
studied in recent years. A number of general principles have been established.
The interactions at the level of cells are quite different from those among
individual animals therefore the study of collective motion of cells is likely
to reveal some specific important features which are overviewed in this paper.
In addition to presenting the most appealing results from the quickly growing
related literature we also deliver a critical discussion of the emerging
picture and summarize our present understanding of collective motion at the
cellular level. Collective motion of cells plays an essential role in a number
of experimental and real-life situations. In most cases the coordinated motion
is a helpful aspect of the given phenomenon and results in making a related
process more efficient (e.g., embryogenesis or wound healing), while in the
case of tumor cell invasion it appears to speed up the progression of the
disease. In these mechanisms cells both have to be motile and adhere to one
another, the adherence feature being the most specific to this sort of
collective behavior. One of the central aims of this review is both presenting
the related experimental observations and treating them in the light of a few
basic computational models so as to make an interpretation of the phenomena at
a quantitative level as well.Comment: 24 pages, 25 figures, 13 reference video link
Lattice gas cellular automata model for rippling and aggregation in myxobacteria
A lattice-gas cellular automaton (LGCA) model is used to simulate rippling
and aggregation in myxobacteria. An efficient way of representing cells of
different cell size, shape and orientation is presented that may be easily
extended to model later stages of fruiting body formation. This LGCA model is
designed to investigate whether a refractory period, a minimum response time, a
maximum oscillation period and non-linear dependence of reversals of cells on
C-factor are necessary assumptions for rippling. It is shown that a refractory
period of 2-3 minutes, a minimum response time of up to 1 minute and no maximum
oscillation period best reproduce rippling in the experiments of {\it
Myxoccoccus xanthus}. Non-linear dependence of reversals on C-factor is
critical at high cell density. Quantitative simulations demonstrate that the
increase in wavelength of ripples when a culture is diluted with non-signaling
cells can be explained entirely by the decreased density of C-signaling cells.
This result further supports the hypothesis that levels of C-signaling
quantitatively depend on and modulate cell density. Analysis of the
interpenetrating high density waves shows the presence of a phase shift
analogous to the phase shift of interpenetrating solitons. Finally, a model for
swarming, aggregation and early fruiting body formation is presented
Current quantization and fractal hierarchy in a driven repulsive lattice gas
Driven lattice gases are widely regarded as the paradigm of collective
phenomena out of equilibrium. While such models are usually studied with
nearest-neighbor interactions, many empirical driven systems are dominated by
slowly decaying interactions such as dipole-dipole and Van der Waals forces.
Motivated by this gap, we study the non-equilibrium stationary state of a
driven lattice gas with slow-decayed repulsive interactions at zero
temperature. By numerical and analytical calculations of the particle current
as a function of the density and of the driving field, we identify (i) an
abrupt breakdown transition between insulating and conducting states, (ii)
current quantization into discrete phases where a finite current flows with
infinite differential resistivity, and (iii) a fractal hierarchy of
excitations, related to the Farey sequences of number theory. We argue that the
origin of these effects is the competition between scales, which also causes
the counterintuitive phenomenon that crystalline states can melt by increasing
the density
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