Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields

In vitro angiogenesis assays have shown that tubulogenesis of endothelial cells within biogels, like collagen or fibrin gels, only appears for a critical range of experimental parameter values. These experiments have enabled us to develop and validate a theoretical model in which mechanical interactions of endothelial cells with extracellular matrix influence both active cell migration--haptotaxis--and cellular traction forces. Depending on the number of cells, cell motility and biogel rheological properties, various 2D endothelial patterns can be generated, from non-connected stripe patterns to fully connected networks, which mimic the spatial organization of capillary structures. The model quantitatively and qualitatively reproduces the range of critical values of cell densities and fibrin concentrations for which these cell networks are experimentally observed. We illustrate how cell motility is associated to the self-enhancement of the local traction fields exerted within the biogel in order to produce a pre-patterning of this matrix and subsequent formation of tubular structures, above critical thresholds corresponding to bifurcation points of the mathematical model. The dynamics of this morphogenetic process is discussed in the light of videomicroscopy time lapse sequences of endothelial cells (EAhy926 line) in fibrin gels. Our modeling approach also explains how the progressive appearance and morphology of the cellular networks are modified by gradients of extracellular matrix thickness.     

Electrohydrodynamic instabilities and segregation of polysaccharides in capillary polymer solution electrophoresis

During capillary electrophoresis of negatively charged polysaccharides in polymer solutions as sieving media, concentration fluctuations develop due to electrohydrodynamic instabilities caused by polarization of the polyelectrolytic chains. This leads to deviations from electroneutrality far beyond the Debye layer and segregation of the initially homogeneous sample solution into aggregated sample‐rich domains as verified by epifluorescence videomicroscopy imaging. As a result, anomalous and irregular peak profiles are obtained impeding the characterization of such complex sample mixtures. This effect appears at an electric field strength threshold value that depends on the molecular weight of the solute polymer molecules, pH, type and concentration of the polymer solution sieving media, and buffering conditions. The magnitude increases with increasing field strength and amount of sample injected. The aggregation onset, as evaluated by the value of the threshold potential, is affected by the charge density of the sample polymer molecules and Debye screening effects and investigated through variation of pH and ionic strength, respectively. Exchange of a simple base buffer component for small and multiply charged organic bases markedly increases the electric field strength necessary to trigger the electrohydrodynamic instabilities. Ultimately, the threshold value could be increased more than seven times by addition of an oppositely charged aminodextran polymer, thereby decreasing the analysis time. © 1999 John Wiley & Sons, Inc. Biopoly 49: 515–524, 1999     

Computer Methods in Membrane Biomechanics

The purpose of this paper is twofold: first, to review analytical, experimental, and numerical methods for studying the nonlinear, pseudoelastic behavior of membranes of interest in biomechanics, and second, to present illustrative examples from the literature for a variety of biomembranes (e.g., skin, pericardium, pleura, aneurysms, and cells) as well as elastomeric membranes used in balloon catheters and new cell stretching tests. Although a membrane approach affords great simplifications in comparison to the three-dimensional theory of nonlinear elasticity, associated problems are still challenging. Computer-based methods are essential, therefore, for performing the requisite experiments, analyzing data, and solving boundary and initial value problems. Emphasis is on stable equilibria although material instabilities and elastodynamics are discussed.     

Cytomechanics of cell deformations and migration: from models to experiments

A cytomechanical model bas been proposed to analyse cell-cell interactions and cell migration through chemotaxis. We consider as the leading assumption that the cell cortical tension is locally modified by the protrusive activity of neighbour cells and binding of chemoattractant molecules to membrane receptors respectively. The model derives from the one initially proposed by Alt and Tranquillo (1995), which successfully describes experimentally observed cyclic autonomous cell shape changes. It is based on force balance equations coupling intracellular hydrostatic pressure and cell cortex contraction. Considering the protrusive dynamics of L929 fibroblats observed by videomicroscopy, we simulated the influence of neighbouring protrusions on a cell spontaneous pulsating behaviour. We further investigated the role of an extracellular gradient as another kind of external stimulus. The model illustrates how binding of chemoattractant molecules can induce a cell morphological instability that, above an intracellular stress threshold, will break the cell-substratum attachment. As a result, realistic cell chemotaxis can be simulated.     

Spatial instabilities and local oscillations in a lattice gas Lotka–Volterra model

 We analyze the evolution of spatially inhomogeneous perturbations in a lattice gas model for a prey-predator population. Starting with the master equation of the model, decoupled by means of a mean field approximation, spatial instabilities are seen to take place in a region of the phase diagram. This is in qualitative agreement with local oscillations already observed in computer simulations. We determine the transition line that separates the homogeneous region from the inhomogeneous region and we study the spatio-temporal self-organized structures that appear inside the inhomogeneous region. Received 3 November 1995; received in revised form 26 January 1996     

SPOTTED HYAENA WHOOPS: FREQUENT INCIDENCE OF VOCAL INSTABILITIES IN A MAMMALIAN LOUD CALL

ABSTRACT

Spotted hyaena Crocuta crocuta whoops are loud calls normally produced in a sequence termed a bout. Whoops are produced by hyaenas irrespective of age or sex to display identity and convey information about the location of the caller. The majority (91%, n=460) of whoops produced by spotted hyaenas, from two geographically separate populations in southern Africa and one population in eastern Africa, showed pronounced nonlinear phenomena, predominantly subharmonics. Whoops produced by males and females had a similarly high probability of sub- harmonics, and 91.5% of the 78 bouts examined contained calls with subharmonics. These results provide evidence that nonlinear vocal phenomena are a common feature of hyaena whoops. The presence of subharmonics in whoops may be enhanced by vocal tract resonances when the fundamental frequency and first formant in the calls are close or coincide. Vocal membranes may also play a role. The high incidence of subharmonics in whoops may enhance individual recognition by adding structural complexity to calls. As 33 of 34 individually known spotted hyaenas examined in this study produced whoops containing subharmonics, it is unlikely that the production of subharmonics is confined to calls from individuals of a particular social status, sex, size, or level of developmental asymmetry, as proposed for nonlinear phenomena in the calls of other mammalian species, although variation in structural features of subharmonics may convey information about these characteristics.     

A theoretical model of sinusoidal forearm tracking with delayed visual feedback

We present a phenomenological model to an experiment, where a person is systematically confronted with a delayed effect of her or his reaction to a time-periodic external signal. The model equations are derived from purely macroscopic considerations. Applying methods developed in the realm of synergetics we can analyze the first instability in the person's behaviour semi-analytically. A careful numerical study is devoted to the higher order instabilities and a comparison between experiment and the results obtained from our model is performed in detail.     

Spontaneous oscillations in two 2-component cells coupled by diffusion

Mathematical examples are presented of oscillators with two variables which do not oscillate in isolation, but which do oscillate stably when coupled with a twin via difiusion. Two examples are presented, the LefeverPrigogine Brusselator and a system used to model glycolytic oscillations. The mathematical method is not the usual bifurcation theory, but rather a type of singular perturbation theory combined with bifurcation theory. For both examples, it is shown that all stationary solutions are unstable for appropriate parameter settings. In the case of the Brusselator, it is further shown that there exist limit cycles; i.e. stable oscillations, in this parameter range. A numerical example is presented.Partially supported by NSF