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Previous experiments demonstrated that a population of HeLa cells starved of glucose or both glucose and serum exhibited a strong heterogeneity in the glycolytic oscillations in terms of the number of oscillatory cells, periods of oscillations, and duration of oscillations. Here, we report numerical simulations of this heterogeneous oscillatory behavior in HeLa cells by using a newly developed mathematical model. It is simple enough that we can apply a mathematical analysis, but capture the core of the glycolytic pathway and the activity of the glucose transporter (GLUT). Lognormal distributions of the values of the four rate constants in the model were obtained from the experimental distributions in the periods of oscillations. Thus, the heterogeneity in the periods of oscillations can be attributed to the difference in the rate constants of the enzymatic reactions. The activity of GLUT is found to determine whether the HeLa cells were oscillatory or non-oscillatory under the same experimental conditions. Simulation with the log-normal distribution of the maximum uptake velocity of glucose and the four randomized rate constants based on the log-normal distributions successfully reproduced the time-dependent number of oscillatory cells (oscillatory ratios) under the two starving conditions. The difference in the initial values of the metabolites has little effect on the simulated results.

We report the first direct observation of glycolytic oscillations in HeLa cervical cancer cells, which we regard as primordial oscillations preserved in living cells. HeLa cells starved of glucose or both glucose and serum exhibited glycolytic oscillations in nicotinamide adenine dinucleotide (NADH), exhibiting asynchronous intercellular behaviors. Also found were spatially homogeneous and inhomogeneous intracellular NADH oscillations in the individual cells. Our results demonstrate that starved HeLa cells may be induced to exhibit glycolytic oscillations by either high-uptake of glucose or the enhancement of a glycolytic pathway (Crabtree effect or the Warburg effect), or both. Their asynchronous collective behaviors in the oscillations were probably due to a weak intercellular coupling. Elucidation of the relationship between the mechanism of glycolytic dynamics in cancer cells and their pathophysiological characteristics remains a challenge in future.

Yeast cells were encapsulated into alginate microparticles of a few hundred micrometers diameter using a centrifuge-based droplet shooting device. We demonstrate the first experimental results of glycolytic oscillations in individual yeast cells immobilized in this way. We investigated both the individual and collective oscillatory behaviors at different cell densities. As the cell density increased, the amplitude of the individual oscillations increased while their period decreased, and the collective oscillations became more synchronized, with an order parameter close to 1 (indicating high synchrony). We also synthesized biphasic-Janus microparticles encapsulating yeast cells of different densities in each hemisphere. The cellular oscillations between the two hemispheres were entrained at both the individual and population levels. Such systems of cells encapsulated into microparticles are useful for investigating how cell-to-cell communication depends on the density and spatial distribution of cells.

Pattern formation in the Belousov-Zhabotinsky reaction experiments carried out by filling capillary glass tubes with catalyst-immobilized gel for the reaction is reported. Under unperturbed and oscillatory conditions, helicoidal waves appear spontaneously. Quantitative structural data of those helices are obtained by devising an optical tomography technique for extracting rotationally symmetric structures from time-lapse data. Space-time representation of the catalyst oxidation reveals wave transmission phenomenon that is studied further by numerical simulations of a reduced spatial model.

The entropy production sigma is calculated in the time evolution processes toward a Turing-like pattern and a chaotic pattern in a two-dimensional reaction-diffusion system. The contributions of reaction and diffusion to the entropy production are evaluated separately. Though its contribution to total sigma is about 5%, the entropy production in diffusion foretells the moving direction of the dots (reaction spots) and the line-shaped patterns. The entropy production of the entire system sigma depicts well the cooperative dynamics and evolution of chaotic dot patterns. It is suggested that sigma can be a scalar measure for quantitative studies of hierarchic pattern dynamics. The relation is also discussed between the bifurcation parameter and the distance from thermodynamic equilibrium.

The polarization curve of an acid-base interface in a hydrogel medium has a diode characteristic. Two of each such electrolyte diodes can be combined to give an electrolyte transistor. When a salt is added to the alkaline or to the acidic part of a reverse biased electrolyte diode, the current response is highly nonlinear. If the salt is added to the acidic side, even bistability can be observed. This bistability can generate complex oscillations in a base-acid-base electrolyte transistor. These nonlinear effects are studied experimentally and theoretically. While the nonlinear salt effect can be explained with the Nernst-Planck equations, to understand the bistable behavior further investigations are necessary. (c) 1999 American Institute of Physics.

We report on a beating polymer gel that exhibits periodical volume changes (swelling and deswelling) in a closed solution without external stimuli, like autonomous heartbeat. The mechanical oscillation is driven by the chemical energy of the oscillatory Belousov-Zhabotinsky (BZ) reaction. The gel is a copolymer gel of N-isopropylacrylamide (NIPAAm) in which ruthenium tris(2,2(')-bipyridine) [Ru(bpy)(3)], known as a catalyst of the BZ reaction, is covalently bonded to the polymer chain. The poly[NIPAAm-co-Ru(bpy)(3)] gel provides an open system where the BZ reaction proceeds, when immersed in an aqueous solution containing the reactants of the BZ reaction (with the exception of a catalyst). The chemical oscillation in the BZ reaction generates the periodical changes of the charge of Ru(bpy)(3) in the gel network between reduced [Ru(II)] and oxidized [Ru(III)] states. The gel swells at the oxidized state because the hydrophilicity of the polymer chains increases, while at the reduced state the gel deswells. Thus, the chemical energy is transduced into the mechanical energy to drive the polymer gel oscillation with a period of about 5 min, depending on the composition of the surrounding solution. The oscillation mode of the gel depends on its size scaled by the wavelength of the BZ pattern. Sufficiently small bead-like gels demonstrate isotropic beating. A large rectangular gel shows mechanical oscillation with a peristaltic motion coupled with the propagating chemical waves. The dynamic behavior of the chemical and mechanical oscillations have been analyzed with a model simulation. (c) 1999 American Institute of Physics.

Experimental and computational studies of the formation and evolution of scroll waves in three-dimensional excitable media are presented. Scroll waves are initiated in the photosensitive Belousov-Zhabotinsky reaction by perturbing traveling waves transverse to their direction of propagation. Scroll rings are generated by perturbing circular waves, which expand or contract depending on the strength of an imposed excitability gradient and its direction relative to the rotational direction of the scroll wave. (c) 1998 American Institute of Physics.