Unraveling dispersion and buoyancy dynamics around radial A + B → C reaction fronts: microgravity experiments and numerical simulations.

Radial Reaction-Diffusion-Advection (RDA) fronts for A + B → C reactions find wide applications in many natural and technological processes. In liquid solutions, their dynamics can be perturbed by buoyancy-driven convection due to concentration gradients across the front. In this context, we conducted microgravity experiments aboard a sounding rocket, in order to disentangle dispersion and buoyancy effects in such fronts. We studied experimentally the dynamics due to the radial injection of A in B at a constant flow rate, in absence of gravity. We compared the obtained results with numerical simulations using either radial one- (1D) or two-dimensional (2D) models. We showed that gravitational acceleration significantly distorts the RDA dynamics on ground, even if the vertical dimension of the reactor and density gradients are small. We further quantified the importance of such buoyant phenomena. Finally, we showed that 1D numerical models with radial symmetry fail to predict the dynamics of RDA fronts in thicker geometries, while 2D radial models are necessary to accurately describe RDA dynamics where Taylor-Aris dispersion is significant.

Synchronisation of glycolytic activity in yeast cells.

Glycolysis is the central metabolic pathway of almost every cell and organism. Under appropriate conditions, glycolytic oscillations may occur in individual cells as well as in entire cell populations or tissues. In many biological systems, glycolytic oscillations drive coherent oscillations of other metabolites, for instance in cardiomyocytes near anorexia, or in pancreas where they lead to a pulsatile release of insulin. Oscillations at the population or tissue level require the cells to synchronize their metabolism. We review the progress achieved in studying a model organism for glycolytic oscillations, namely yeast. Oscillations may occur on the level of individual cells as well as on the level of the cell population. In yeast, the cell-to-cell interaction is realized by diffusion-mediated intercellular communication via a messenger molecule. The present mini-review focuses on the synchronisation of glycolytic oscillations in yeast. Synchronisation is a quorum-sensing phenomenon because the collective oscillatory behaviour of a yeast cell population ceases when the cell density falls below a threshold. We review the question, under which conditions individual cells in a sparse population continue or cease to oscillate. Furthermore, we provide an overview of the pathway leading to the onset of synchronized oscillations. We also address the effects of spatial inhomogeneities (e.g., the formation of spatial clusters) on the collective dynamics, and also review the emergence of travelling waves of glycolytic activity. Finally, we briefly review the approaches used in numerical modelling of synchronized cell populations.

Complexity of a peroxidase-oxidase reaction model.

The peroxidase-oxidase oscillating reaction was the first (bio)chemical reaction to show chaotic behaviour. The reaction is rich in bifurcation scenarios, from period-doubling to peak-adding mixed mode oscillations. Here, we study a state-of-the-art model of the peroxidase-oxidase reaction. Using the model, we report systematic numerical experiments exploring the impact of changing the enzyme concentration on the dynamics of the reaction. Specifically, we report high-resolution phase diagrams predicting and describing how the reaction unfolds over a quite extended range of enzyme concentrations. Surprisingly, such diagrams reveal that the enzyme concentration has a huge impact on the reaction evolution. The highly intricate dynamical behaviours predicted here are difficult to establish theoretically due to the total absence of an adequate framework to solve nonlinearly coupled differential equations. But such behaviours may be validated experimentally.

Partial synchronisation of glycolytic oscillations in yeast cell populations.

The transition between synchronized and asynchronous behaviour of immobilized yeast cells of the strain Saccharomyces carlsbergensis was investigated by monitoring the autofluorescence of the coenzyme NADH. In populations of intermediate cell densities the individual cells remained oscillatory, whereas on the level of the cell population both a partially synchronized and an asynchronous state were accessible for experimental studies. In the partially synchronized state, the mean oscillatory frequency was larger than that of the cells in the asynchronous state. This suggests that synchronisation occurred due to entrainment by the cells that oscillated more rapidly. This is typical for synchronisation due to phase advancement. Furthermore, the synchronisation of the frequency of the glycolytic oscillations preceded the synchronisation of their phases. However, the cells did not synchronize completely, as the distribution of the oscillatory frequencies only narrowed but did not collapse to a unique frequency. Cells belonging to spatially denser clusters showed a slightly enhanced local synchronisation during the episode of partial synchronisation. Neither the clusters nor a transition from partially synchronized glycolytic oscillations to travelling glycolytic waves did substantially affect the degree of partial synchronisation. Chimera states, i.e., the coexistence of a synchronized and an asynchronous part of the population, could not be found.

Metamaterial-based transmit and receive system for whole-body magnetic resonance imaging at ultra-high magnetic fields.

Magnetic resonance imaging (MRI) at ultra-high fields (UHF), such as 7 T, provides an enhanced signal-to-noise ratio and has led to unprecedented high-resolution anatomic images and brain activation maps. Although a variety of radio frequency (RF) coil architectures have been developed for imaging at UHF conditions, they usually are specialized for small volumes of interests (VoI). So far, whole-body coil resonators are not available for commercial UHF human whole-body MRI systems. The goal of the present study was the development and validation of a transmit and receive system for large VoIs that operates at a 7 T human whole-body MRI system. A Metamaterial Ring Antenna System (MRAS) consisting of several ring antennas was developed, since it allows for the imaging of extended VoIs. Furthermore, the MRAS not only requires lower intensities of the irradiated RF energy, but also provides a more confined and focused injection of excitation energy on selected body parts. The MRAS consisted of several antennas with 50 cm inner diameter, 10 cm width and 0.5 cm depth. The position of the rings was freely adjustable. Conformal resonant right-/left-handed metamaterial was used for each ring antenna with two quadrature feeding ports for RF power. The system was successfully implemented and demonstrated with both a silicone oil and a water-NaCl-isopropanol phantom as well as in vivo by acquiring whole-body images of a crab-eating macaque. The potential for future neuroimaging applications was demonstrated by the acquired high-resolution anatomic images of the macaque's head. Phantom and in vivo measurements of crab-eating macaques provided high-resolution images with large VoIs up to 40 cm in xy-direction and 45 cm in z-direction. The results of this work demonstrate the feasibility of the MRAS system for UHF MRI as proof of principle. The MRAS shows a substantial potential for MR imaging of larger volumes at 7 T UHF. This new technique may provide new diagnostic potential in spatially extended pathologies such as searching for spread-out tumor metastases or monitoring systemic inflammatory processes.

Dynamics of scroll waves in a cylinder jacket geometry.

The dynamics of scroll waves in a narrow cylinder jacket-shaped reactor is investigated experimentally by optical tomography. The fate of the scroll waves of excitation in the Belousov-Zhabotinsky reaction depends on the thickness of the cylinder jacket. While at sufficiently wide cylinder jackets vertically oriented scroll waves remain stable, the probability that the filament of a scroll hits a lateral wall increases as the cylinder jacket narrows. This may lead to the rupture of the initial filament and pinning of the filament ends at the lateral walls. Filaments that pin to opposite lateral walls shrink and reorient to a horizontal orientation; such a reorientation corresponds to a transition from an intramural to a transmural scroll wave. The kinetics of the reorientation and shrinkage of the scrolls were studied. Furthermore, we find that no new filaments were generated upon collision of excitation waves at the side of the cylinder jacket opposite to the scroll wave. Thus, under the studied conditions, we do not observe any new generation of filaments due to a phenomenon like reentry.

Patterns of cell thickness oscillations during directional migration of Physarum polycephalum.

The functional relationship between the velocity of cell locomotion and intracellular spatial patterns of thickness oscillations in the acellular slime mould Physarum polycephalum was studied. The freely migrating plasmodial cells of 300-800 µm length were tadpole-shaped and displayed thickness oscillations along their longitudinal (body) axis. Two distinct patterns of intracellular thickness oscillations were observed in dependence on the locomotive velocity. The first mode consisted of a single travelling wave that propagated from the rear to the front of the cell. This pattern occurred when the plasmodium migrated slowly. The second mode was a multinodal standing wave that was found during events of fast propagation. Transitions between these two types of cell thickness oscillation patterns took place in narrow propagation velocity intervals. We discuss the possible mechanism leading to these patterns, which are conjectured to modulate both the intracellular pressure and the velocity of free locomotion of the cell.

Convective dynamics of traveling autocatalytic fronts in a modulated gravity field.

When traveling in thin solution layers, autocatalytic chemical fronts may be deformed and accelerated by convective currents that develop because of density and surface tension gradients related to concentration and thermal gradients across the front. On earth, both buoyancy and Marangoni related flows can act in solution layers open to the air while only buoyancy effects operate in covered liquid layers. The respective effects of density and surface tension induced convective motions are analysed here by studying experimentally the propagation of autocatalytic fronts in uncovered and covered liquid layers during parabolic flights in which the gravity field is modulated periodically. We find that the velocity and deformation of the front are increased during hyper-gravity phases and reduced in the micro-gravity phase. The experimental results compare well with numerical simulations of the evolution of the concentration of the autocatalytic product coupled to the flow field dynamics described by Navier-Stokes equations.

Nonchaos-Mediated Mixed-Mode Oscillations in an Enzyme Reaction System.

We report numerical evidence of a new type of wide-ranging organization of mixed-mode oscillations (MMOs) in a model of the peroxidase-oxidase reaction, in the control parameter plane defined by the supply of the reactant NADH and the pH of the medium. In classic MMOs, the intervals of distinct periodic oscillations are always separated from each other by windows of chaos. In contrast, in the new unfolding, such windows of chaos do not exist. Chaos-mediated and nonchaos-mediated MMO phases are separated by a continuous transition boundary in the control parameter plane. In addition, for low pH values, we find an exceptionally wide and intricate mosaic of MMO phases that is described by a detailed phase diagram.

Chemotaxis with directional sensing during Dictyostelium aggregation.

We show that the chemotactic movements of colonies of the starving amoeba Dictyostelium discoideum are driven by a force that depends on both the direction of propagation (directional sensing) of reaction-diffusion chemotactic waves and on the gradient of the concentration of the chemoattractant, solving the chemotactic wave paradox. It is shown that the directional sensing of amoebae is due to the sensitivity of the cells to the time variation of the concentration of the chemoattractant combined with its spatial gradient. It is also shown that chemotaxis exclusively driven by local concentration gradient leads to unstable local motion, preventing cells from aggregation. These findings show that the formation of mounds, which initiate multicellularity in Dictyostelium discoideum, is caused by the sensitivity of the amoebae due to three factors, namely, to the direction of propagation of the chemoattractant, to its spatial gradient, and to the emergence of cAMP "emitting centres", responsible for the local accumulation of the amoebae.

Interaction of a pair of parallel scroll waves.

Interactions of pairs of scroll waves in three-dimensional excitable media were studied experimentally in the Belousov-Zhabotinsky reaction by optical tomography. The behavior of two scroll waves depended on the distance d between their filaments. When the interfilament distance was shorter than the wavelength λ of the scroll waves (but larger than the diameter of the spiral core), the filaments repelled each other. Once d ≈ λ, the two scroll waves synchronized, rotating around their filaments with both a common rotation frequency and a common pitch. The interfilament distance of synchronized scroll waves did not change. When fluctuations broke the symmetry of the rotation periods, the scroll with higher rotation frequency displaced the slower rotating one, until the latter was ousted or even annihilated. These behaviors were independent of the sense of rotation (co- or counter-rotating), the filament dynamics (rigidly rotating or meandering tip motion in two-dimensional media), and the presence or absence of a gradient of excitability parallel to the filaments.

Cyclosis-mediated transfer of H2O 2 elicited by localized illumination of Chara cells and its relevance to the formation of pH bands.

Cytoplasmic streaming occurs in most plant cells and is vitally important for large cells as a means of long-distance intracellular transport of metabolites and messengers. In internodal cells of characean algae, cyclosis participates in formation of light-dependent patterns of surface pH and photosynthetic activity, but lateral transport of regulatory metabolites has not been visualized yet. Hydrogen peroxide, being a signaling molecule and a stress factor, is known to accumulate under excessive irradiance. This study was aimed to examine whether H2O2 produced in chloroplasts under high light conditions is released into streaming fluid and transported downstream by cytoplasmic flow. To this end, internodes of Chara corallina were loaded with the fluorogenic probe dihydrodichlorofluorescein diacetate and illuminated locally by a narrow light beam through a thin optic fiber. Fluorescence of dihydrodichlorofluorescein (DCF), produced upon oxidation of the probe by H2O2, was measured within and around the illuminated cell region. In cells exhibiting active streaming, H2O2 first accumulated in the illuminated region and then entered into the streaming cytoplasm, giving rise to the expansion of DCF fluorescence downstream of the illuminated area. Inhibition of cyclosis by cytochalasin B prevented the spreading of DCF fluorescence along the internode. The results suggest that H2O2 released from chloroplasts under high light is transported along the cell with the cytoplasmic flow. It is proposed that the shift of cytoplasmic redox poise and light-induced elevation of cytoplasmic pH facilitate the opening of H(+)/OH(-)-permeable channels in the plasma membrane.

Functional organization of the vascular network of Physarum polycephalum.

The plasmodium of the slime mould Physarum polycephalum forms a transportation network of veins, in which protoplasm is transported due to peristaltic pumping. This network forms a planar, weighted, undirected graph that, for the first time, can be extracted automatically from photographs or movies. Thus, data from real transportation networks have now become available for the investigation of network properties. We determine the local drag of the vein segments and use these data to calculate the transport efficiency. We unravel which veins form the backbone of the transportation network by using a centrality measure from graph theory. The principal vein segments lie on relatively ample cycles of veins, and the most important segments are those that belong simultaneously to two of these principal cycles. Each principal cycle contains a series of smaller cycles of veins of lower transport efficiency, thus reflecting the hierarchical and self-similar structure of the transportation network. Finally, we calculate accessibility maps that show how easily different nodes of the network may be reached from a given reference node.

Twists of opposite handedness on a scroll wave.

The dynamic interaction of scroll waves in the Belousov-Zhabotinsky reaction with a vertically orientated gradient of excitability is studied by optical tomography. This study focuses on scroll waves, whose filaments were oriented almost perpendicular to the gradient. Whereas scroll waves with filaments exactly perpendicular to the gradient remain unaffected, filaments with a component parallel to the gradient develop a twist. Scroll waves with U-shaped filaments exhibit twists starting from both of its ends, resulting in scroll waves whose filaments display a pair of twists of opposite handedness. These twists are separated by a nodal plane where the filament remains straight and untwisted. The experimental findings were reproduced by numerical simulations using the Oregonator model and a linear gradient of excitability almost perpendicular to the orientation of the filament.

Dependence of scroll-wave dynamics on the orientation of a gradient of excitability.

The dynamics of scroll waves with a variable orientation to a vertically oriented gradient of excitability is studied by optical tomography in the ferroin-catalyzed Belousov-Zhabotinsky reaction. An almost perpendicular orientation between the scroll wave and gradient induces a pair of twists of opposite handedness on the scroll wave. The position of the nodal plane formed between the twists is governed by the time delay of the twist formation and therefore leads to a symmetric or asymmetric twisted scroll wave. Larger inclinations between scroll wave and gradient cause a drift of the filament along the reactor wall until it reaches the bottom of the reaction container. In this case, the scroll wave does not twist, suggesting that a drift acts as an alternative mechanism of responding to the gradient.

Desynchronisation of glycolytic oscillations in yeast cell populations.

Glycolytic oscillations of intact yeast cells of the strain Saccharomyces carlsbergensis were investigated at both the levels of cell populations and of individual cells. Individual cells showed glycolytic oscillations even at very low cell densities (e.g. 1.0 x 10(5) cells/ml). By contrast, the collective behaviour on the population level was cell density-dependent: at high cell densities it is oscillatory, but below the threshold density of 1.0 x 10(6) cells/ml the collective dynamics becomes quiescent. We demonstrate that the transition in the collective dynamics is caused by the desynchronisation of the oscillations of individual cells. This is characteristic for a Kuramoto transition. Spatially resolved measurements at low cell densities revealed that even cells that adhere to their neighbours oscillated with their own, independent frequencies and phases.

An extended model for the repression of photosynthesis genes by the AppA/PpsR system in Rhodobacter sphaeroides.

Purple bacteria derive energy from aerobic respiration or photosynthesis depending on the availability of oxygen and light. Under aerobic conditions, photosynthesis genes are specifically repressed by the PpsR protein. In Rhodobacter sphaeroides, the repressive action of PpsR is antagonized by the blue-light and redox-sensitive flavoprotein AppA, which sequesters PpsR under anaerobic conditions into transcriptionally inactive complexes. However, under semi-aerobic conditions, blue-light excitation of AppA causes the AppA-PpsR complexes to dissociate, again leading to a repression of photosynthesis genes. We have recently developed a simple mathematical model suggesting that this phenotype arises from the formation of a maximum in the response curve of reduced PpsR at intermediate oxygen concentrations. However, this model focused mainly on the oxygen-dependent interactions whereas light regulation was only implemented in a simplified manner. In the present study, we incorporate a more detailed mechanism for the light-dependent interaction between AppA and PpsR, which now allows for a direct comparison with experiments. Specifically, we take into account that, upon blue-light excitation, AppA undergoes a conformational change, creating a long-lived signalling state causing the dissociation of the AppA-PpsR complexes. The predictions of the extended model are found to be in good agreement with experimental results on the light-dependent repression of photosynthesis genes under semi-aerobic conditions. We also identify the potential kinetic and stoichiometric constraints that the interplay between light and redox regulation imposes on the functionality of the AppA/PpsR system, especially with respect to a possible bistable response.

Helical deformation of the filament of a scroll wave.

In three-dimensional excitable systems scroll waves may lose their originally straight shape through different instabilities. In experiments, the formation of zigzag-shaped or helical filaments is often observed. Such a deformation may be due to either a twist-induced instability or a 3D meandering instability. We performed a systematic study using a Belousov-Zhabotinsky (BZ) system with a vertical gradient of excitability and determined the necessary twist for the onset of undulation in the filament. Thus, we demonstrate that in the case of a BZ system with a gradient parallel to the filament, the deformation of the filament is induced by a twist-induced instability.

Surfactant-induced gradients in the three-dimensional Belousov-Zhabotinsky reaction.

Scroll waves are prominent patterns formed in three-dimensional excitable media, and they are frequently considered highly relevant for some types of cardiac arrhythmias. Experimentally, scroll wave dynamics is often studied by optical tomography in the Belousov-Zhabotinsky reaction, which produces CO(2) as an undesired product. Addition of small concentrations of a surfactant to the reaction medium is a popular method to suppress or retard CO(2) bubble formation. We show that in closed reactors even these low concentrations of surfactants are sufficient to generate vertical gradients of excitability which are due to gradients in CO(2) concentration. In reactors open to the atmosphere such gradients can be avoided. The gradients induce a twist on vertically oriented scroll waves, while a twist is absent in scroll waves in a gradient-free medium. The effects of the CO(2) gradients are reproduced by a numerical study, where we extend the Oregonator model to account for the production of CO(2) and for its advection against the direction of gravity. The numerical simulations confirm the role of solubilized CO(2) as the source of the vertical gradient of excitability in reactors closed to the atmosphere.

Modeling the light- and redox-dependent interaction of PpsR/AppA in Rhodobacter sphaeroides.

Facultative photosynthetic bacteria switch their energy generation mechanism from respiration to photosynthesis depending on oxygen tension and light. Part of this transition is mediated by the aerobic transcriptional repressor PpsR. In Rhodobacter sphaeroides, the repressive action of PpsR is antagonized by the redox- and blue-light-sensitive flavoprotein AppA which results in a unique phenotype: the repression of photosynthesis genes at intermediate oxygen levels and high light intensity, which is believed to reduce the risk of photooxidative stress. To analyze the underlying mechanism we developed a simple mathematical model based on the AppA-dependent reduction of a disulfide bond in PpsR and the light-sensitive complex formation between the reduced forms of AppA and PpsR. A steady-state analysis shows that high light repression can indeed occur at intermediate oxygen levels if PpsR is reduced on a faster timescale than AppA and if the electron transfer from AppA to PpsR is effectively irreversible. The model further predicts that if AppA copy numbers exceed those of PpsR by at least a factor of two, the transition from aerobic to anaerobic growth mode can occur via a bistable regime. We provide necessary conditions for the emergence of bistability and discuss possible experimental verifications.