arXiv subjects

Wouter-Jan Rappel

Publications and source records attributed to Wouter-Jan Rappel.

28 records · Page 2Linked to original sources

arXiv2006

Embryonic Pattern Scaling Achieved by Oppositely Directed Morphogen Gradients

Morphogens are proteins, often produced in a localised region, whose concentrations spatially demarcate regions of differing gene expression in developing embryos. The boundaries of expression must be set accurately and in proportion to the size of the one-dimensional developing field; this cannot be accomplished by a single gradient. Here, we show how a pair of morphogens produced at opposite ends of a developing field can solve the pattern-scaling problem. In the most promising scenario, the morphogens effectively interact according to the annihilation reaction $A+B\to\emptyset$ and the switch occurs according to the absolute concentration of $A$ or $B$. In this case embryonic markers across the entire developing field scale approximately with system size; this cannot be achieved with a pair of non-interacting gradients that combinatorially regulate downstream genes. This scaling occurs in a window of developing-field sizes centred at a few times the morphogen decay length.

q-bio.SC↗

arXiv2005

Dynamics of conduction blocks in a model of paced cardiac tissue

We study numerically the dynamics of conduction blocks using a detailed electrophysiological model. We find that this dynamics depends critically on the size of the paced region. Small pacing regions lead to stationary conduction blocks while larger pacing regions can lead to conduction blocks that travel periodically towards the pacing region. We show that this size-dependence dynamics can lead to a novel arrhythmogenic mechanism. Furthermore, we show that the essential phenomena can be captured in a much simpler coupled-map model.

q-bio.TO↗

arXiv2004

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome.

q-bio.TO↗

arXiv2003

Phase field approach for modeling intracellular dynamics

We introduce a phase field approach for diffusion inside and outside a closed cell with damping and with source terms at the interface. The method is compared to exact solutions (where possible) and the more traditional finite element method. It is shown to be very accurate, easy to implement and computationally inexpensive. We apply our method to a recently introduced model for chemotaxis by Rappel et al. [Biophys. J. 83, 1361 (2002)].

cond-mat.stat-mech↗

arXiv2000

Self-organization in systems of self-propelled particles

We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges.In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent.

cond-mat.soft↗

arXiv1999

Self-organized Vortex State in Two-dimensional Dictyostelium Dynamics

We present results of experiments on the dynamics of Dictyostelium discoideum in a novel set-up which constraints cell motion to a plane. After aggregation, the amoebae collect into round ''pancake" structures in which the cells rotate around the center of the pancake. This vortex state persists for many hours and we have explicitly verified that the motion is not due to rotating waves of cAMP. To provide an alternative mechanism for the self-organization of the Dictyostelium cells, we have developed a new model of the dynamics of self-propelled deformable objects. In this model, we show that cohesive energy between the cells, together with a coupling between the self-generated propulsive force and the cell's configuration produces a self-organized vortex state. The angular velocity profiles of the experiment and of the model are qualitatively similar. The mechanism for self-organization reported here can possibly explain similar vortex states in other biological systems.

patt-sol↗

arXiv1999

Phase-Field Model of Dendritic Sidebranching with Thermal Noise

We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show that the simulated fluctuation spectrum of a one-dimensional interface in thermal equilibrium agrees with the exact sharp-interface spectrum up to an irrelevant short-wavelength cutoff comparable to the interface thickness. Simulations of dendritic growth are then carried out in two dimensions to compute sidebranching characteristics (root-mean-square amplitude and mean spacing between sidebranches) as a function of distance behind the tip. These quantities are found to be in good overall quantitative agreement with the predictions of the existing linear WKB theory of noise amplification. The extension of this study to three dimensions remains needed to determine the origin of noise in experiments.

cond-mat.mtrl-sci↗

arXiv1996

Noise Induced Coherence in Neural Networks

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in the thermodynamic limit ($N\to \infty$) a broadband peak and an additional delta-function peak that is absent from the powerspectrum of an isolated element. The powerspectrum of the mean output signal only exhibits the delta-function peak. These results are explained analytically in an exactly soluble oscillator model with global phase coupling.

chao-dyn↗

arXiv1996

Numerical Simulation of Three-Dimensional Dendritic Growth

Dendritic crystal growth in a pure undercooled melt is simulated quantitatively in three dimensions using a phase-field approach. The full non-axisymmetric morphology of the steady-state dendrite tip and $σ^*$ are determined as a function of anisotropy for a crystal with a cubic symmetry. Results are compared to experiment and used to critically test solvability theory.

patt-sol↗

arXiv1995

Coexisting Pulses in a Model for Binary-Mixture Convection

We address the striking coexistence of localized waves (`pulses') of different lengths which was observed in recent experiments and full numerical simulations of binary-mixture convection. Using a set of extended Ginzburg-Landau equations, we show that this multiplicity finds a natural explanation in terms of the competition of two distinct, physical localization mechanisms; one arises from dispersion and the other from a concentration mode. This competition is absent in the standard Ginzburg-Landau equation. It may also be relevant in other waves coupled to a large-scale field.

patt-sol↗