Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator.

We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.

Extended source model for diffusive coupling.

Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources.

Tunable diffusive lateral inhibition in chemical cells.

The Belousov-Zhabotinsky (BZ) reaction has become the prototype of nonlinear chemical dynamics. Microfluidic techniques provide a convenient method for emulsifying BZ solutions into monodispersed drops with diameters of tens to hundreds of microns, providing a unique system in which reaction-diffusion theory can be quantitatively tested. In this work, we investigate monolayers of microfluidically generated BZ drops confined in close-packed two-dimensional (2D) arrays through experiments and finite element simulations. We describe the transition from oscillatory to stationary chemical states with increasing coupling strength, controlled by independently varying the reaction chemistry within a drop and diffusive flux between drops. For stationary drops, we studied how the ratio of stationary oxidized to stationary reduced drops varies with coupling strength. In addition, using simulation, we quantified the chemical heterogeneity sufficient to induce mixed stationary and oscillatory patterns.

Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets.

We study the dynamical behavior of one-dimensional arrays of ∼100 µm diameter aqueous droplets containing the oscillatory Belousov-Zhabotinsky (BZ) reaction, separated by narrow gaps of a fluorinated oil. In this closed system, the malonic acid concentration decreases as the reaction proceeds. Starting with a low initial malonic acid concentration, we observe a series of attractors as a function of time in the following order: anti-phase attractors; in-phase attractors, which evolve into traveling waves; and mixed modes that contain either regions of in-phase droplets separated by anti-phase oscillators, or in-phase oscillators combined with non-oscillatory droplets. Most of the observations are consistent with numerical chemical models of the BZ reaction in which components that participate in the excitatory (bromine dioxide and bromous acid) and inhibitory (bromine) pathways diffuse between the droplets. The models are used to quantitatively assess the inter-drop coupling strength as a function of drop separation, drop size and malonic acid concentration. To experimentally establish the mechanism of excitatory coupling between the BZ droplets, we verify the transport through the fluorinated oil of chlorine dioxide and several weak acids, including malonic acid.

Coalescence in double emulsions.

Coalescence processes in double emulsions, water-in-oil-in-water, are studied by optical microscopy. The time evolution of such systems is determined by the interplay of two coalescence processes, namely, between inner water droplets and between the inner water droplets and the continuous external water phase. The predominance of one of those processes over the other, regulated by the relative amount of hydrophilic and lipophilic surfactants, leads to different evolutions of the system. We present here results for a class of systems whose evolution follows a master behavior. We also implemented a computer simulation where the system is modeled as a spherical cavity filled with smaller Brownian spheres. Collisions between spheres allow coalescence between them with probability P(i), whereas collisions between a sphere and the wall of the cavity allow coalescence with the external phase with probability P(e). The phenomenology observed in the experimental systems is well reproduced by the computer simulation for suitable values of the probability parameters.

Spontaneous two-dimensional spherical colloidal structures.

Two-dimensional spherical crystalline colloidal structures are formed at the interface between water and oil as the result of spontaneous emulsification and colloidal self-assembly. When water droplets are introduced in oil containing a lipophilic surfactant, smaller water droplets of uniform size are spontaneously produced at the spherical interface. Initially of submicrometer size, the small droplets at the interface self-assemble, forming ordered structures, and grow uniformly with time until they reach a size of a few micrometers, maintaining the crystalline structure.

Muscarinic modulation of Cav2.3 (R-type) calcium channels is antagonized by RGS3 and RGS3T.

Ca(2+) influx through voltage-gated R-type (Ca(V)2.3) Ca(2+) channels is important for hormone and neurotransmitter secretion and other cellular events. Previous studies have shown that Ca(V)2.3 is both inhibited and stimulated through signaling mechanisms coupled to muscarinic ACh receptors. We previously demonstrated that muscarinic stimulation of Ca(V)2.3 is blocked by regulator of G protein signaling (RGS) 2. Here we investigated whether muscarinic inhibition of Ca(V)2.3 is antagonized by RGS3. RGS3 is particularly interesting because it contains a lengthy ( approximately 380 residue) amino-terminal domain of uncertain physiological function. Ca(V)2.3, M(2) muscarinic ACh receptors (M(2)R), and various deletion mutants of RGS3, including its native isoform RGS3T, were expressed in HEK293 cells, and agonist-dependent inhibition of Ca(V)2.3 was quantified using whole cell patch-clamp recordings. Full-length RGS3, RGS3T, and the core domain of RGS3 were equally effective in antagonizing inhibition of Ca(V)2.3 through M(2)R. These results identify RGS3 and RGS3T as potential physiological regulators of R-type Ca(2+) channels. Furthermore, they suggest that the signaling activity of RGS3 is unaffected by its extended amino-terminal domain. Confocal microscopy was used to examine the intracellular locations of four RGS3-enhanced green fluorescent protein fusion proteins. The RGS3 core domain was uniformly distributed throughout both cytoplasm and nucleus. By contrast, full-length RGS3, RGS3T, and the amino-terminal domain of RGS3 were restricted to the cytoplasm. These observations suggest that the amino terminus of RGS3 may serve to confine it to the cytoplasmic compartment where it can interact with cell surface receptors, heterotrimeric G proteins, and other signaling proteins.