Insights into collective cell behaviour from populations of coupled chemical oscillators.

Biological systems such as yeast show coordinated activity driven by chemical communication between cells. Here, we show how experiments with coupled chemical oscillators can provide insights into collective behaviour in cellular systems. Two methods of coupling the oscillators are described: exchange of chemical species with the surrounding solution and computer-controlled illumination of a light-sensitive catalyst. The collective behaviour observed includes synchronisation, dynamical quorum sensing (a density dependent transition to population-wide oscillations), and chimera states, where oscillators spontaneously split into coherent and incoherent groups. At the core of the different types of behaviour lies an intracellular autocatalytic signal and an intercellular communication mechanism that influences the autocatalytic growth

Spatial Symmetry Breaking in the Belousov-Zhabotinsky Reaction with Light-Induced Remote Communication

Domains containing spiral waves form on a stationary background in a photosensitive Belousov-Zhabotinsky reaction with light-induced alternating nonlocal feedback. Complex behavior of colliding and splitting wave fragments is found with feedback radii comparable to the spiral wavelength. A linear stability analysis of the uniform stationary states in an Oregonator model reveals a spatial symmetry breaking instability. Numerical simulations show behavior in agreement with that found experimentally and also predict a variety of other new patterns

The Christiansen Effect in Saturn's narrow dusty rings and the spectral identification of clumps in the F ring

Stellar occultations by Saturn's rings observed with the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft reveal that dusty features such as the F ring and the ringlets in the Encke and the Laplace Gaps have distinctive infrared transmission spectra. These spectra show a narrow optical depth minimum at wavelengths around 2.87 microns. This minimum is likely due to the Christiansen Effect, a reduction in the extinction of small particles when their (complex) refractive index is close to that of the surrounding medium. Simple Mie-scattering models demonstrate that the strength of this opacity dip is sensitive to the size distribution of particles between 1 and 100 microns across. Furthermore, the spatial resolution of the occultation data is sufficient to reveal variations in the transmission spectra within and among these rings. For example, in both the Encke Gap ringlets and F ring, the opacity dip weakens with increasing local optical depth, which is consistent with the larger particles being concentrated near the cores of these rings. The strength of the opacity dip varies most dramatically within the F ring; certain compact regions of enhanced optical depth lack an opacity dip and therefore appear to have a greatly reduced fraction of grains in the few-micron size range.Such spectrally-identifiable structures probably represent a subset of the compact optically-thick clumps observed by other Cassini instruments. These variations in the ring's particle size distribution can provide new insights into the processes of grain aggregation, disruption and transport within dusty rings. For example, the unusual spectral properties of the F-ring clumps could perhaps be ascribed to small grains adhering onto the surface of larger particles in regions of anomalously low velocity dispersion.Comment: 42 pages, 15 figures, accepted for publication in Icarus. A few small typographical errors fixed to match correction in proof

Experimental observation of extreme multistability in an electronic system of two coupled R\"{o}ssler oscillators

We report the first experimental observation of extreme multistability in a controlled laboratory investigation. Extreme multistability arises when infinitely many attractors coexist for the same set of system parameters. The behavior was predicted earlier on theoretical grounds, supported by numerical studies of models of two coupled identical or nearly identical systems. We construct and couple two analog circuits based on a modified coupled R\"{o}ssler system and demonstrate the occurrence of extreme multistability through a controlled switching to different attractor states purely through a change in initial conditions for a fixed set of system parameters. Numerical studies of the coupled model equations are in agreement with our experimental findings.Comment: to be published in Phys. Rev.

On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation

In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the hamiltonian system $u_{xx} + f(u) = 0$ and the asymptotic speed of propagation of fronts of the reaction diffusion equation. Based on this conjecture an explicit expression for the speed of the front is given. We give a counterexample to this conjecture and conclude that additional restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

Statin Drugs Plus Th1 Cytokines Potentiate Apoptosis and Ras Delocalization in Human Breast Cancer Lines and Combine with Dendritic Cell-Based Immunotherapy to Suppress Tumor Growth in a Mouse Model of HER-2 Disease

A dendritic cell-based, Type 1 Helper T cell (Th1)-polarizing anti-Human Epidermal Growth Factor Receptor-2 (HER-2) vaccine supplied in the neoadjuvant setting eliminates disease in up to 30% of recipients with HER-2-positive (HER-2) ductal carcinoma in situ (DCIS). We hypothesized that drugs with low toxicity profiles that target signaling pathways critical for oncogenesis may work in conjunction with vaccine-induced immune effector mechanisms to improve efficacy while minimizing side effects. In this study, a panel of four phenotypically diverse human breast cancer lines were exposed in vitro to the combination of Th1 cytokines Interferon-gamma (IFN-γ) and Tumor Necrosis Factor-alpha (TNF-α) and lipophilic statins. This combination was shown to potentiate multiple markers of apoptotic cell death. The combination of statin drugs and Th1 cytokines minimized membrane K-Ras localization while maximizing levels in the cytoplasm, suggesting a possible means by which cytokines and statin drugs might cooperate to maximize cell death. A combined therapy was also tested in vivo through an orthotopic murine model using the neu-transgenic TUBO mammary carcinoma line. We showed that the combination of HER-2 peptide-pulsed dendritic cell (DC)-based immunotherapy and simvastatin, but not single agents, significantly suppressed tumor growth. Consistent with a Th1 cytokine-dependent mechanism, parenterally administered recombinant IFN-γ could substitute for DC-based immunotherapy, likewise inhibiting tumor growth when combined with simvastatin. These studies show that statin drugs can amplify a DC-induced effector mechanism to improve anti-tumor activity