Transition from traveling to standing waves in the 4:1 resonant Belousov-Zhabotinsky reaction.

We report a transition from traveling to standing domain walls in a parametrically forced two-dimensional oscillatory Belousov-Zhabotinsky chemical reaction in 4:1 resonance. Our experimental results demonstrate spatiotemporal solutions not predicted by previous analytic results of the complex Ginzburg-Landau amplitude equation and numerical results from reaction-diffusion models. In addition to the stationary pi fronts at high forcing amplitudes, the 4:1 resonant patterns we observe include stationary pi/2 fronts.

Period doubling in a periodically forced Belousov-Zhabotinsky reaction.

Using an open-flow reactor periodically perturbed with light, we observe subharmonic frequency locking of the oscillatory Belousov-Zhabotinsky chemical reaction at one-sixth the forcing frequency (6:1) over a region of the parameter space of forcing intensity and forcing frequency where the Farey sequence dictates we should observe one-third the forcing frequency (3:1). In this parameter region, the spatial pattern also changes from slowly moving traveling waves to standing waves with a smaller wavelength. Numerical simulations of the FitzHugh-Nagumo equations show qualitative agreement with the experimental observations and indicate that the oscillations in the experiment are a result of period doubling.

Resonant and nonresonant patterns in forced oscillators.

Uniform oscillations in spatially extended systems resonate with temporal periodic forcing within the Arnold tongues of single forced oscillators. The Arnold tongues are wedge-like domains in the parameter space spanned by the forcing amplitude and frequency, within which the oscillator's frequency is locked to a fraction of the forcing frequency. Spatial patterning can modify these domains. We describe here two pattern formation mechanisms affecting frequency locking at half the forcing frequency. The mechanisms are associated with phase-front instabilities and a Turing-like instability of the rest state. Our studies combine experiments on the ruthenium catalyzed light-sensitive Belousov-Zhabotinsky reaction forced by periodic illumination, and numerical and analytical studies of two model systems, the FitzHugh-Nagumo model and the complex Ginzburg-Landau equation, with additional terms describing periodic forcing.

Polarized secretory trafficking directs cargo for asymmetric dendrite growth and morphogenesis.

Proper growth of dendrites is critical to the formation of neuronal circuits, but the cellular machinery that directs the addition of membrane components to generate dendritic architecture remains obscure. Here, we demonstrate that post-Golgi membrane trafficking is polarized toward longer dendrites of hippocampal pyramidal neurons in vitro and toward apical dendrites in vivo. Small Golgi outposts partition selectively into longer dendrites and are excluded from axons. In dendrites, Golgi outposts concentrate at branchpoints where they engage in post-Golgi trafficking. Within the cell body, the Golgi apparatus orients toward the longest dendrite, and this Golgi polarity precedes asymmetric dendrite growth. Manipulations that selectively block post-Golgi trafficking halt dendrite growth in developing neurons and cause a shrinkage of dendrites in mature pyramidal neurons. Further, disruption of Golgi polarity produces neurons with symmetric dendritic arbors lacking a single longest principal dendrite. These results define a novel polarized organization of neuronal secretory trafficking and demonstrate a mechanistic link between directed membrane trafficking and asymmetric dendrite growth.

Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction.

We examine the effects of controlled, slowly varying spatial inhomogeneities on spiral wave dynamics in the light sensitive Belousov-Zhabotinsky chemical reaction-diffusion system. We measure the speed of the grain boundary that separates two spirals, the speed of the lower frequency spiral being swept away by the grain boundary, and the speed of the slow drift of the highest frequency spiral. The grain boundary speeds are shown to be related to the frequency of rotation and wave number of the spiral pattern, as predicted from analysis of the complex Ginzburg-Landau equation [M. Hendrey, Phys. Rev. Lett.10.1103/PhysRevLett.82.859 82, 859 (1999); M. Hendrey,, Phys. Rev. E10.1103/PhysRevE.61.4943 61, 4943 (2000)].

Front dynamics in an oscillatory bistable Belousov-Zhabotinsky chemical reaction.

We observe breathing front dynamics which select three distinct types of bistable patterns in the 2:1 resonance regime of the periodically forced oscillatory Belousov-Zhabotinsky reaction. We measure the curvature-driven shrinking of a circular domain R approximately t(1/2) at forcing frequencies below a specific value, and show that the fast time scale front oscillations (breathing) drive this slow time scale shrinking. Above a specific frequency, we observe fronts of higher curvature grow instead of shrink and labyrinth patterns form. Just below the transition frequency is a relatively narrow range of frequencies where the curvature-driven coarsening is balanced by a competing front interaction, which leads to a pattern of localized structures. The length scale of the localized structure and labyrinth patterns is set by the front interactions.

BLOCH-front turbulence in a periodically forced Belousov-Zhabotinsky reaction.

Experiments on a periodically forced Belousov-Zhabotinsky chemical reaction show front breakup into a state of spatiotemporal disorder involving continual events of spiral-vortex nucleation and destruction. Using the amplitude equation for forced oscillatory systems and the normal form equations for a curved front line, we identify the mechanism of front breakup and explain the experimental observations.

Resonance tongues and patterns in periodically forced reaction-diffusion systems.

Various resonant and near-resonant patterns form in a light-sensitive Belousov-Zhabotinsky (BZ) reaction in response to a spatially homogeneous time-periodic perturbation with light. The regions (tongues) in the forcing frequency and forcing amplitude parameter plane where resonant patterns form are identified through analysis of the temporal response of the patterns. Resonant and near-resonant responses are distinguished. The unforced BZ reaction shows both spatially uniform oscillations and rotating spiral waves, while the forced system shows patterns such as standing-wave labyrinths and rotating spiral waves. The patterns depend on the amplitude and frequency of the perturbation, and also on whether the system responds to the forcing near the uniform oscillation frequency or the spiral wave frequency. Numerical simulations of a forced FitzHugh-Nagumo reaction-diffusion model show both resonant and near-resonant patterns similar to the BZ chemical system.

Localization and extinction of bacterial populations under inhomogeneous growth conditions.

The transition from localized to systemic spreading of bacteria, viruses, and other agents is a fundamental problem that spans medicine, ecology, biology, and agriculture science. We have conducted experiments and simulations in a simple one-dimensional system to determine the spreading of bacterial populations that occurs for an inhomogeneous environment under the influence of external convection. Our system consists of a long channel with growth inhibited by uniform ultraviolet (UV) illumination except in a small "oasis", which is shielded from the UV light. To mimic blood flow or other flow past a localized infection, the oasis is moved with a constant velocity through the UV-illuminated "desert". The experiments are modeled with a convective reaction-diffusion equation. In both the experiment and model, localized or extinct populations are found to develop, depending on conditions, from an initially localized population. The model also yields states where the population grows everywhere. Further, the model reveals that the transitions between localized, extended, and extinct states are continuous and nonhysteretic. However, it does not capture the oscillations of the localized population that are observed in the experiment.