299 research outputs found
Instantaneous cell migration velocity may be ill-defined
Cell crawling is critical to biological development, homeostasis and disease.
In many cases, cell trajectories are quasi-random-walk. In vitro assays on flat
surfaces often described such quasi-random-walk cell trajectories as
approximations to a solution of a Langevin process. However, experiments show
quasi-diffusive behavior at small timescales, indicating that instantaneous
velocity and velocity autocorrelations are not well-defined. We propose to
characterize mean-squared cell displacement using a modified F\"urth equation
with three temporal and spatial regimes: short- and long-time/range diffusion
and intermediate time/range ballistic motion. This analysis collapses
mean-squared displacements of previously published experimental data onto a
single-parameter family of curves, allowing direct comparison between movement
in different cell types, and between experiments and numerical simulations. Our
method also show that robust cell-motility quantification requires an
experiment with a maximum interval between images of a few percent of the
cell-motion persistence time or less, and a duration of a few
orders-of-magnitude longer than the cell-motion persistence time or more.Comment: 5 pages, plus Supplemental materia
Simulations of viscous shape relaxation in shuffled foam clusters
We simulate the shape relaxation of foam clusters and compare them with the
time exponential expected for Newtonian fluid. Using two-dimensional Potts
Model simulations, we artificially create holes in a foam cluster and shuffle
it by applying shear strain cycles. We reproduce the experimentally observed
time exponential relaxation of cavity shapes in the foam as a function of the
number of strain steps. The cavity rounding up results from local rearrangement
of bubbles, due to the conjunction of both a large applied strain and local
bubble wall fluctuations
Computer Simulations of Cell Sorting Due to Differential Adhesion
The actions of cell adhesion molecules, in particular, cadherins during embryonic development and morphogenesis more generally, regulate many aspects of cellular interactions, regulation and signaling. Often, a gradient of cadherin expression levels drives collective and relative cell motions generating macroscopic cell sorting. Computer simulations of cell sorting have focused on the interactions of cells with only a few discrete adhesion levels between cells, ignoring biologically observed continuous variations in expression levels and possible nonlinearities in molecular binding. In this paper, we present three models relating the surface density of cadherins to the net intercellular adhesion and interfacial tension for both discrete and continuous levels of cadherin expression. We then use then the Glazier-Graner-Hogeweg (GGH) model to investigate how variations in the distribution of the number of cadherins per cell and in the choice of binding model affect cell sorting. We find that an aggregate with a continuous variation in the level of a single type of cadherin molecule sorts more slowly than one with two levels. The rate of sorting increases strongly with the interfacial tension, which depends both on the maximum difference in number of cadherins per cell and on the binding model. Our approach helps connect signaling at the molecular level to tissue-level morphogenesis
Shape-velocity correlation defines polarization in migrating cell simulations
Cell migration plays essential roles in development, wound healing, diseases,
and in the maintenance of a complex body. Experiments in collective cell
migration generally measure quantities such as cell displacement and velocity.
The observed short-time diffusion regime for mean square displacement in
single-cell migration experiments on flat surfaces calls into question the
definition of cell velocity and the measurement protocol. Theoretical results
in stochastic modeling for single-cell migration have shown that this fast
diffusive regime is explained by a white noise acting on displacement on the
direction perpendicular to the migrating cell polarization axis (not on
velocity). The prediction is that only the component of velocity parallel to
the polarization axis is a well-defined quantity, with a robust measurement
protocol. Here, we ask whether we can find a definition of a migrating-cell
polarization that is able to predict the cell's subsequent displacement, based
on measurements of its shape. Supported by experimental evidence that cell
nucleus lags behind the cell center of mass in a migrating cell, we propose a
robust parametrization for cell migration where the distance between cell
nucleus and the cell's center of mass defines cell shape polarization. We
tested the proposed methods by applying to a simulation model for
three-dimensional cells performed in the CompuCell3D environment, previously
shown to reproduce biological cells kinematics migrating on a flat surface
Velocities of Mesenchymal Cells May be Ill-Defined
The dynamics of single cell migration on flat surfaces is usually modeled by
a Langevin-like problem consisting of ballistic motion for short periods and
random walk. for long periods. Conversely, recent studies have revealed a
previously neglected random motion at very short intervals, what would rule out
the possibility of defining the cell instantaneous velocity and a robust
measurement procedure. A previous attempt to address this issue considered an
anisotropic migration model, which takes into account a polarization
orientation along which the velocity is well-defined, and a direction
orthogonal to the polarization vector that describes the random walk. Although
the numerically and analytically calculated mean square displacement and
auto-correlation agree with experimental data for that model, the velocity
distribution peaks at zero, which contradicts experimental observations of a
constant drift in the polarization direction. Moreover, Potts model simulations
indicate that instantaneous velocity cannot be measured for any direction.
Here, we consider dynamical equations for cell polarization, which is
measurable and introduce a polarization-dependent displacement, circumventing
the problem of ill defined instantaneous velocity. Polarization is a
well-defined quantity, preserves memory for short intervals, and provides a
robust measurement procedure for characterizing cell migration. We consider
cell polarization dynamics to follow a modified Langevin equation that yields
cell displacement distribution that peaks at positive values, in agreement with
experiments and Potts model simulations. Furthermore, displacement
autocorrelation functions present two different time scales, improving the
agreement between theoretical fits and experiments or simulations
Growth laws and self-similar growth regimes of coarsening two-dimensional foams: Transition from dry to wet limits
We study the topology and geometry of two dimensional coarsening foams with
arbitrary liquid fraction. To interpolate between the dry limit described by
von Neumann's law, and the wet limit described by Marqusee equation, the
relevant bubble characteristics are the Plateau border radius and a new
variable, the effective number of sides. We propose an equation for the
individual bubble growth rate as the weighted sum of the growth through
bubble-bubble interfaces and through bubble-Plateau borders interfaces. The
resulting prediction is successfully tested, without adjustable parameter,
using extensive bidimensional Potts model simulations. Simulations also show
that a selfsimilar growth regime is observed at any liquid fraction and
determine how the average size growth exponent, side number distribution and
relative size distribution interpolate between the extreme limits. Applications
include concentrated emulsions, grains in polycrystals and other domains with
coarsening driven by curvature
Dibaryons as axially symmetric skyrmions
Dibaryons configurations are studied in the framework of the bound state
soliton model. A generalized axially symmetric ansatz is used to determine the
soliton background. We show that once the constraints imposed by the symmetries
of the lowest energy torus configuration are satisfied all spurious states are
removed from the dibaryon spectrum. In particular, we show that the lowest
allowed state in the channel carries the quantum numbers of the H
particle. We find that, within our approximations, this particle is slightly
bound in the model. We discuss, however, that vacuum effects neglected in the
present calculation are very likely to unbind the H.Comment: 24 pages, LaTeX, TAN-FNT-93-12 (it replaces old version which was
truncated
Ecosystem engineer morphological traits and taxon identity shape biodiversity across the euphotic-mesophotic transition
Funding was provided by a Leverhulme Trust Research Project grant (no. RPG-2018-113) to H.L.B., G.A.T. and I.D.W.S., an Engineering and Physical Sciences Research Council grant (no. EP/L017008/1) to G.A.T. and I.D.W.S., and a São Paulo Research Foundation (FAPESP) individual grant (no. 2016/14017-0) to G.H.P.F.The euphotic-mesophotic transition is characterized by dramatic changes in environmental conditions, which can significantly alter the functioning of ecosystem engineers and the structure of their associated communities. However, the drivers of biodiversity change across the euphotic-mesophotic transition remain unclear. Here, we investigated the mechanisms affecting the biodiversity-supporting potential of free-living red coralline algae-globally important habitat creators-towards mesophotic depths. Across a 73 m depth gradient, we observed a general decline in macrofaunal biodiversity (fauna abundance, taxon richness and alpha diversity), but an increase in beta-diversity (i.e. variation between assemblages) at the deepest site (86 m depth, where light levels were less than 1% surface irradiance). We identified a gradient in abundance decline rather than distinct ecological shifts, driven by a complex interaction between declining light availability, declining size of the coralline algal host individuals and a changing host taxonomy. However, despite abundance declines, high between-assemblage variability at deeper depths allowed biodiversity-supporting potential to be maintained, highlighting their importance as coastal refugia.PostprintPeer reviewe
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