Search results for "cell behavior"
showing 10 items of 91 documents
Bifurcation of traveling waves in a Keller–Segel type free boundary model of cell motility
2018
We study a two-dimensional free boundary problem that models motility of eukaryotic cells on substrates. This problem consists of an elliptic equation describing the flow of cytoskeleton gel coupled with a convection-diffusion PDE for the density of myosin motors. The two key properties of this problem are (i) presence of the cross diffusion as in the classical Keller-Segel problem in chemotaxis and (ii) nonlinear nonlocal free boundary condition that involves curvature of the boundary. We establish the bifurcation of the traveling waves from a family of radially symmetric steady states. The traveling waves describe persistent motion without external cues or stimuli which is a signature of …
Axisymmetric solutions for a chemotaxis model of Multiple Sclerosis
2018
In this paper we study radially symmetric solutions for our recently proposed reaction–diffusion–chemotaxis model of Multiple Sclerosis. Through a weakly nonlinear expansion we classify the bifurcation at the onset and derive the amplitude equations ruling the formation of concentric demyelinating patterns which reproduce the concentric layers observed in Balò sclerosis and in the early phase of Multiple Sclerosis. We present numerical simulations which illustrate and fit the analytical results.
Sensitivity to Initial Conditions in an Extended Activator--Inhibitor Model for the Formation of Patterns
2018
Despite simplicity, the synchronous cellular automaton [D.A. Young, Math. Biosci. 72, 51 (1984)] enables reconstructing basic features of patterns of skin. Our extended model allows studying the formatting of patterns and their temporal evolution also on the favourable and hostile environments. As a result, the impact of different types of an environment is accounted for the dynamics of patterns formation. The process is based on two diffusible morphogens, the short-range activator and the long-range inhibitor, produced by differentiated cells (DCs) represented as black pixels. For a neutral environment, the extended model reduces to the original one. However, even the reduced model is stat…
Synchronized rotation in swarms of magnetotactic bacteria.
2017
Self-organizing behavior has been widely reported in both natural and artificial systems, typically distinguishing between temporal organization (synchronization) and spatial organization (swarming). Swarming has been experimentally observed in systems of magnetotactic bacteria under the action of external magnetic fields. Here we present a model of ensembles of magnetotactic bacteria in which hydrodynamic interactions lead to temporal synchronization in addition to the swarming. After a period of stabilization during which the bacteria form a quasiregular hexagonal lattice structure, the entire swarm begins to rotate in a direction opposite to the direction of the rotation of the magnetic …
Magnetic dipole with a flexible tail as a self-propelling microdevice.
2012
By numerical simulations, it is illustrated that a magnetic dipole with a flexible tail behaves as a swimmer in AC magnetic fields. The behavior of the swimmer on long time scales is analyzed and it is shown that due to the flexibility of the tail two kinds of torques arise, the first is responsible for the orientation of the swimmer perpendicularly to the AC field and the second drags the filament in the direction of the rotating field. Due to this, circular trajectories of the swimmer are possible; however, these are unstable. The self-propulsion velocity of this swimmer is higher than the velocities of other magnetic microdevices for comparable values of the magnetoelastic number.
Ballistic phonon transport in dielectric membranes
2006
We have calculated the ballistic phononic heat transport in dielectric membranes as a function of radiator temperature and membrane thickness. The phonon modes of such membranes are known as Lamb-modes from elasticity theory. The striking result is that, for a fixed temperature, the radiated power first decreases with decreasing membrane thickness, but then develops a minimum when the transition to two dimensionality is reached. Further decrease of the membrane thickness in the 2D limit leads to increasing radiated power.
Hydrodynamic synchronization of pairs of puller type magnetotactic bacteria in a high frequency rotating magnetic field.
2019
Ensembles of magnetotactic bacteria are known to interact hydrodynamically and form swarms under the influence of external magnetic fields. We describe the synchronization of puller type magnetotactic bacteria in a rotating magnetic field by representing the bacteria as hydrodynamic force dipoles. Numerical simulations show that at moderate values of the hydrodynamic interaction parameter large ensembles of asynchronously rotating bacteria randomly eject propagating doublets of synchronized bacteria. We quantitatively analyze the dynamics of the doublets and show that an important role in the formation of these propagating structures is played by the parameters characterizing the possible t…
Ewald sum for hydrodynamic interactions of rigid spherical microswimmers
2018
We derive the Ewald sum decomposition of the grand mobility tensor which captures the hydrodynamic interactions in an infinite suspension of rigid spherical microswimmers. The grand mobility tensor connects the motion of an individual swimmer to the active and passive forces and torques acting on all the swimmers, and it is calculated based on a minimal microswimmer model incorporating the swimmers' finite body size. Our results have direct applications to the Stokesian dynamics simulations of an infinite suspension of rigid-bodied microswimmers. They also provide a platform to develop more advanced methods such as particle-mesh-Ewald-sum and accelerated Stokesian dynamics simulations.
Diffusion of magnetotactic bacterium in rotating magnetic field
2011
Swimming trajectory of a magnetotactic bacterium in a rotating magnetic field is a circle. Random reversals of the direction of the bacterium motion induces a random walk of the curvature center of the trajectory. In assumption of the distribution of the switching events according to the Poisson process the diffusion coefficient is calculated in dependence on the frequency of the rotating field and the characteristic time between the switching events. It is confirmed by the numerical simulation of the random walk of the bacterium in the rotating magnetic field.
3D motion of flexible ferromagnetic filaments under a rotating magnetic field.
2020
Ferromagnetic filaments in a rotating magnetic field are studied both numerically and experimentally. The filaments are made from micron-sized ferromagnetic particles linked with DNA strands. It is found that at low frequencies of the rotating field a filament rotates synchronously with the field and beyond a critical frequency it undergoes a transition to a three dimensional regime. In this regime the tips of the filament rotate synchronously with the field on circular trajectories in the plane parallel to the plane of the rotating field. The characteristics of this motion found numerically match the experimental data and allow us to obtain the physical properties of such filaments. We als…