44 research outputs found
A purely mechanical model with asymmetric features for early morphogenesis of rod-shaped bacteria micro-colony
To model the morphogenesis of rod-shaped bacterial micro-colony, several
individual-based models have been proposed in the biophysical literature. When
studying the shape of micro-colonies, most models present interaction forces
such as attraction or filial link. In this article, we propose a model where
the bacteria interact only through non-overlapping constraints. We consider the
asymmetry of the bacteria, and its influence on the friction with the
substrate. Besides, we consider asymmetry in the mass distribution of the
bacteria along their length. These two new modelling assumptions allow us to
retrieve mechanical behaviours of micro-colony growth without the need of
interaction such as attraction. We compare our model to various sets of
experiments, discuss our results, and propose several quantifiers to compare
model to data in a systematic way
Modelling adhesion-independent cell migration
A two-dimensional mathematical model for cells migrating without adhesion
capabilities is presented and analyzed. Cells are represented by their cortex,
which is modelled as an elastic curve, subject to an internal pressure force.
Net polymerization or depolymerization in the cortex is modelled via local
addition or removal of material, driving a cortical flow. The model takes the
form of a fully nonlinear degenerate parabolic system. An existence analysis is
carried out by adapting ideas from the theory of gradient flows. Numerical
simulations show that these simple rules can account for the behavior observed
in experiments, suggesting a possible mechanical mechanism for
adhesion-independent motility.Comment: 22 pages and 9 figure
Asymptotic preserving schemes for nonlinear kinetic equations leading to volume-exclusion chemotaxis in the diffusive limit
In this work we first prove, by formal arguments, that the diffusion limit of
nonlinear kinetic equations, where both the transport term and the turning
operator are density-dependent, leads to volume-exclusion chemotactic
equations. We generalise an asymptotic preserving scheme for such nonlinear
kinetic equations based on a micro-macro decomposition. By properly
discretizing the nonlinear term implicitly-explicitly in an upwind manner, the
scheme produces accurate approximations also in the case of strong
chemosensitivity. We show, via detailed calculations, that the scheme presents
the following properties: asymptotic preserving, positivity preserving and
energy dissipation, which are essential for practical applications. We extend
this scheme to two dimensional kinetic models and we validate its efficiency by
means of 1D and 2D numerical experiments of pattern formation in biological
systems.Comment: 30 pages, 8 figure
Multispecies cross-diffusions: from a nonlocal mean-field to a porous medium system without self-diffusion
Systems describing the long-range interaction between individuals have
attracted a lot of attention in the last years, in particular in relation with
living systems. These systems are quadratic, written under the form of
transport equations with a nonlocal self-generated drift. We establish the
localisation limit, that is the convergence of nonlocal to local systems, when
the range of interaction tends to 0. These theoretical results are sustained by
numerical simulations. The major new feature in our analysis is that we do not
need diffusion to gain compactness, at odd with the existing literature. The
central compactness result is provided by a full rank assumption on the
interaction kernels. In turn, we prove existence of weak solutions for the
resulting system, a cross-diffusion system of quadratic type
A purely mechanical model with asymmetric features for early morphogenesis of rod-shaped bacteria micro-colony
International audienceTo model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as attraction or filial link. In this article, we propose a model where the bacteria interact only through non-overlapping constraints. We consider the asymmetry of the bacteria, and its influence on the friction with the substrate. Besides, we consider asymmetry in the mass distribution of the bacteria along their length. These two new modelling assumptions allow us to retrieve mechanical behaviours of micro-colony growth without the need of interaction such as attraction. We compare our model to various sets of experiments, discuss our results, and propose several quantifiers to compare model to data in a systematic way
Particle interactions mediated by dynamical networks: assessment of macroscopic descriptions
We provide a numerical study of the macroscopic model of [3] derived from an
agent-based model for a system of particles interacting through a dynamical
network of links. Assuming that the network remodelling process is very fast,
the macroscopic model takes the form of a single aggregation diffusion equation
for the density of particles. The theoretical study of the macroscopic model
gives precise criteria for the phase transitions of the steady states, and in
the 1-dimensional case, we show numerically that the stationary solutions of
the microscopic model undergo the same phase transitions and bifurcation types
as the macroscopic model. In the 2-dimensional case, we show that the numerical
simulations of the macroscopic model are in excellent agreement with the
predicted theoretical values. This study provides a partial validation of the
formal derivation of the macroscopic model from a microscopic formulation and
shows that the former is a consistent approximation of an underlying particle
dynamics, making it a powerful tool for the modelling of dynamical networks at
a large scale
Modelling adhesion-independent cell migration
International audienceA two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net polymerization or depoly-merization in the cortex is modelled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility
Continuum model for linked fibers with alignment interactions
International audienceWe introduce an individual-based model for fiber elements having the ability to cross-link or unlink each other and to align with each other at the cross links. We first formally derive a kinetic model for the fiber and cross-links distribution functions. We then consider the fast linking/unlinking regime in which the model can be reduced to the fiber distribution function only and investigate its diffusion limit. The resulting macroscopic model consists of a system of nonlinear diffusion equations for the fiber density and mean orientation. In the case of a homogeneous fiber density, we show that the model is elliptic
"Još jedan osvrt na pitanje izbora šarana za daljnji uzgoj"
We extend the live-cell motility Filament Based Lamellipodium Model (FBLM) to incorporate the forces exerted on the lamellipodium of the cells due to cell-cell collision and cadherin induced cell-cell adhesion. We take into account the nature of these forces via physical and biological constraints and modelling assumptions. We investigate the effect these new components have in the migration and morphology of the cells through particular experiments. We exhibit moreover the similarities between our simulated cells and HeLa cancer cells