Quasi-periodic behaviour in a model for the lithium-induced,electrical oscillations of frog skin

The fact that oscillations can be induced in studies of the maintenance of the electrical potential of frog skin by addition of lithium allowed evaluation of several parameters fundamental to the functioning of the system in vivo (e.g. relative volumes of internal compartments, characteristic times of ionic exchanges between compartments). A realistic model was thus proposed under the form of a set of ordinary differential equations. In the past, numerical simulations using such a model reproduced the periodic experimental oscillations and was able to provide an explanation for the global synchronised oscillations of the whole skin. In that paper, new numerical simulations reproduce the non-periodic oscillations which were observed two decades ago, but not reproduced by the model. Moreover, the dynamical process under which all the local oscillators are synchronised is explained in terms of a tangent bifurcation.     

Cascade Electric Field Enhancement in the Orthogonal-Nanorod Structures

The transverse mode electron oscillations contribute to most of the surface-enhanced Raman scattering (SERS) intensity from the nanorod array substrates. To enhance the transverse mode electron oscillation and improve the SERS enhancements, the local electric field distribution of the orthogonal-nanorod structures, composed of two parallel horizontal nanorods in between two parallel vertical nanorods, has been studied. The local electric fields of the longitudinal mode along the horizontal nanorods act as the excitation for the transverse mode electron oscillations in vertical nanorods, leading to the cascade enhancements of the electric fields around the vertical nanorods. In addition, the plasmon peaks of the longitudinal modes can be tuned by changing the lengths and the widths of the horizontal nanorods and the separations between horizontal and vertical nanorods. These results would be much helpful to engineer SERS substrates to obtain larger SERS enhancements.     

Regulating synchronous oscillations of cerebellar granule cells by different types of inhibition

Synchronous oscillations in neural populations are considered being controlled by inhibitory neurons. In the granular layer of the cerebellum, two major types of cells are excitatory granular cells (GCs) and inhibitory Golgi cells (GoCs). GC spatiotemporal dynamics, as the output of the granular layer, is highly regulated by GoCs. However, there are various types of inhibition implemented by GoCs. With inputs from mossy fibers, GCs and GoCs are reciprocally connected to exhibit different network motifs of synaptic connections. From the view of GCs, feedforward inhibition is expressed as the direct input from GoCs excited by mossy fibers, whereas feedback inhibition is from GoCs via GCs themselves. In addition, there are abundant gap junctions between GoCs showing another form of inhibition. It remains unclear how these diverse copies of inhibition regulate neural population oscillation changes. Leveraging a computational model of the granular layer network, we addressed this question to examine the emergence and modulation of network oscillation using different types of inhibition. We show that at the network level, feedback inhibition is crucial to generate neural oscillation. When short-term plasticity was equipped on GoC-GC synapses, oscillations were largely diminished. Robust oscillations can only appear with additional gap junctions. Moreover, there was a substantial level of cross-frequency coupling in oscillation dynamics. Such a coupling was adjusted and strengthened by GoCs through feedback inhibition. Taken together, our results suggest that the cooperation of distinct types of GoC inhibition plays an essential role in regulating synchronous oscillations of the GC population. With GCs as the sole output of the granular network, their oscillation dynamics could potentially enhance the computational capability of downstream neurons.     

Effect of local anesthetics on the electrical characteristics of an excitable model membrane composed of dioleyl phosphate II. Dynamic response

The effects of local anesthetics (tetracaine, procaine and lidocaine) on self-sustained electrical oscillations were studied for a lipid membrane comprising dioleyl phosphate (DOPH). This model membrane exhibits oscillation of the membrane potential in a manner similar to that of nerve membranes, i.e., repetitive firing, in the presence of an ion-concentration gradient, on the application of d.c. electric current. Relatively weak anesthetics such as procaine and lidocaine increased the frequency of self-sustained oscillation, and finally induced aperiodic, rapid oscillation. The strong anesthetic tetracaine inhibited oscillation.     

Robustness and Coherence of a Three-Protein Circadian Oscillator: Landscape and Flux Perspectives

Three-protein circadian oscillations in cyanobacteria sustain for weeks. To understand how cellular oscillations function robustly in stochastic fluctuating environments, we used a stochastic model to uncover two natures of circadian oscillation: the potential landscape related to steady-state probability distribution of protein concentrations; and the corresponding flux related to speed of concentration changes which drive the oscillations. The barrier height of escaping from the oscillation attractor on the landscape provides a quantitative measure of the robustness and coherence for oscillations against intrinsic and external fluctuations. The difference between the locations of the zero total driving force and the extremal of the potential provides a possible experimental probe and quantification of the force from curl flux. These results, correlated with experiments, can help in the design of robust oscillatory networks.     

A model for self-sustained potential oscillation of lipid bilayer membranes induced by the gel-liquid crystal phase transitions.

To clarify the mechanism of self-sustained oscillation of the electric potential between the two solutions divided by a lipid bilayer membrane, a microscopic model of the membrane system is presented. It is assumed, on the basis of the observed results (Yoshikawa, K., T. Omachi, T. Ishii, Y. Kuroda, and K. liyama. 1985. Biochem. Biophys. Res. Commun. 133:740-744; Ishii, T., Y. Kuroda, T. Omochi, and K. Yoshikawa. 1986. Langmuir. 2:319-321; Toko, K., N. Nagashima, S. liyama, K. Yamafuji, and T. Kunitake. Chem. Lett. 1986:1375-1378), that the gel-liquid crystal phase transition of the membrane drives the potential oscillation. It is studied, by using the model, how and under what condition the repetitive phase transition may occur and induce the potential oscillation. The transitions are driven by the repetitive adsorption and desorption of proton by the membrane surface, actions that are induced the periodic reversal of the direction of protonic current. The essential conditions for the periodic reversal are (a) at least one kind of cations such as Na+ or K+ are included in the system except for proton, and the variation of their permeability across the membrane due to the phase transition is noticeably larger than that of proton permeability; and (b) the phase transition has a hysteresis. When these conditions are fulfilled, the self-sustained potential oscillation may be brought about by adjusting temperature, pH, and the cation concentration in the solutions on both sides of the membrane. Application of electric current across the membrane also induces or modifies the potential oscillation. Periodic, quasiperiodic, and chaotic oscillations appear especially, depending on the value of frequency of the applied alternating current.     

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with halfperiod phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.     

Spontaneous myocardial calcium oscillations: overview with emphasis on ryanodine and caffeine

All mammalian cardiac preparations exhibit the capacity for periodic spontaneous Ca2+ release from the sarcoplasmic reticulum (SR) (Ca2+ oscillations). The occurrence of such oscillations in unstimulated preparations and their periodicity depend on the species and the Ca2+ load on the cell. When the spontaneous frequency of these oscillations exceeds the rate of external simulation, they appear between stimulated contractions and impart a variable Ca2+-dependent component of diastolic tonus and a propensity for extrasystoles and arrhythmias to occur; these diastolic oscillations can also affect systolic function as well. Although enhancing the spontaneous frequency of Ca2+ release, caffeine depresses the oscillation amplitude, whereas ryanodine suppresses both frequency and amplitude. Detailed studies of oscillation characteristics and of the different effects of caffeine and ryanodine on them may provide an understanding of and may be useful for modeling SR Ca2+ uptake and release in intact preparations.     

Bloch Oscillations of Surface Plasmon-Like Modes in Waveguide Arrays That Comprise Perforated Perfect Conductor Layers and Dielectric Layers

This study investigates the optical Bloch oscillations (OBOs) in waveguide arrays that consist of alternative perfect electric conductor (PEC) layers and dielectric layers by performing both numerical simulations and theoretical analyses. In PEC dielectric waveguide arrays (PDWAs), the PEC layers are perforated with square holes to support the surface plasmon-like (SPL) modes. The relative permittivities of the dielectric layers have a constant gradient across the waveguide arrays. The OBOs in the PDWAs arise because of the excitation and coupling of the SPL modes. The ray trajectories that are predicted using Hamiltonian optics are consistent with the simulated results. When the position of incidence is fixed, the period of oscillation varies as the reciprocal of the incident frequency. However, the amplitude of oscillation is almost independent of the frequency. For a fixed incident frequency, the amplitude and period of oscillation increases and decreases, respectively as the position of incidence moves toward the dielectric layers with higher relative permittivities.     

Relationship between Growth and Electric Oscillations in Bean Roots

Extracellular and intracellular electric potentials in bean roots are known to show electric oscillations along the longitudinal axis with a period of several minutes. The relationship between growth and the electric oscillations was studied using roots of adzuki (Phaseolus chrysanthos). We measured surface electric potentials with a multielectrode apparatus while simultaneously measuring elongation using a CCD camera and monitor. Roots having an electric oscillation grew faster than roots with no oscillation. Furthermore, elongation rate was higher in roots with higher oscillation frequency. Oscillation frequency had a strong dependence on temperature; i.e. Q₁₀ was estimated at 1.7. These results suggest a correlation between electric oscillation and elongation.     

Mass-induced oscillations in the femur-tibia control system of stick insects

Attaching an inert mass to a freely moving tibia of an otherwise fixed stick insect Carausius morosus, induces undamped oscillations of the tibia. We describe the use of a rotational pendulum to observe these oscillations applying various amounts of inertia. The dependence of the frequency of these oscillations on the moment of inertia is similar to that of a purely mechanical system. The sequence of the oscillatory behavior can be separated into 3 distinct behavioural states. The transitions between some of these states could be elicited by external stimuli and partly showed characteristics of habituation and dishabituation. With a rotational pendulum on each middle leg, simultaneous oscillations of both legs were measured to investigate coupling effects between the neural control systems of the two legs. In some cases, significant coupling effects could be observed in phase and frequency. In many other cases, no coupling was found. The habituation and dishabituation effects were not transferred between the middle legs.     

Electric oscillation in an excitable model membrane impregnated with lipid analogues

A model membrane constructed from a Millipore filter, whose pores were impregnated with dioleyl phosphate, exhibited an electric self-oscillation under nonequilibrium conditions. The membrane interposed between two solutions with the same KCl concentrations showed no temporal change in membrane potential. However, the potential became oscillatory on application of an electric current to the membrane. The frequency was proportional to the magnitude of the electric current. When both KCl solutions were replaced by NaCl solutions, a similar trend was observed, although the oscillation was not as regular as in the case of KCl. A membrane placed between equimolar solutions of KCl and NaCl, on the other hand, gave rise to an oscillation even without current application. When a membrane was placed between 5 mM KCl and 100 mM KCl, it was found that NaCl added to the 5 mM KCl side had a pronounced effect on the membrane with respect to the frequency response of the oscillation. These results indicate that the dioleyl phosphate membrane discriminates Na+ from K+.     

Mitochondrial metabolism reveals a functional architecture in intact islets of Langerhans from normal and diabetic Psammomys obesus

The cells within the intact islet of Langerhans function as a metabolic syncytium, secreting insulin in a coordinated and oscillatory manner in response to external fuel. With increased glucose, the oscillatory amplitude is enhanced, leading to the hypothesis that cells within the islet are secreting with greater synchronization. Consequently, non-insulin-dependent diabetes mellitus (NIDDM; type 2 diabetes)-induced irregularities in insulin secretion oscillations may be attributed to decreased intercellular coordination. The purpose of the present study was to determine whether the degree of metabolic coordination within the intact islet was enhanced by increased glucose and compromised by NIDDM. Experiments were performed with isolated islets from normal and diabetic Psammomys obesus. Using confocal microscopy and the mitochondrial potentiometric dye rhodamine 123, we measured mitochondrial membrane potential oscillations in individual cells within intact islets. When mitochondrial membrane potential was averaged from all the cells in a single islet, the resultant waveform demonstrated clear sinusoidal oscillations. Cells within islets were heterogeneous in terms of cellular synchronicity (similarity in phase and period), sinusoidal regularity, and frequency of oscillation. Cells within normal islets oscillated with greater synchronicity compared with cells within diabetic islets. The range of oscillatory frequencies was unchanged by glucose or diabetes. Cells within diabetic (but not normal) islets increased oscillatory regularity in response to glucose. These data support the hypothesis that glucose enhances metabolic coupling in normal islets and that the dampening of oscillatory insulin secretion in NIDDM may result from disrupted metabolic coupling.     

On the oscillatory phenomenon in an oil/water interface

A simple theoretical model is presented for simulating the self-sustained oscillations of electric potential and pH at an oil/water interface appearing in a two-phase system composed of 2-nitropropane solution containing picrate acid and an aqueous solution of cetyltrimethylammonium bromide. In the present model, a well-known condition necessary for the occurrence of self-sustained oscillations, i.e., the presence of a positive feedback process far from equilibrium, is taken into account in a set of kinetic equations to describe simplified characters of the following two processes: (i) a cooperative formation of ion pair complexes at the interface, and (ii) supply of picrate anions and cetyltrimethylammonium cations to the interface accompanied by release of ion pair complexes to the organic phase. The numerical solutions of the present equations are shown to reproduce fairly well the characteristic properties of the oscillation of electric potential and pH such as wave forms and frequencies.     

Dependency analysis of frequency and strength of gamma oscillations on input difference between excitatory and inhibitory neurons

It has been found that gamma oscillations and the oscillation frequencies are regulated by the properties of external stimuli in many biology experimental researches. To unveil the underlying mechanism, firstly, we reproduced the experimental observations in an excitatory/inhibitory (E/I) neuronal network that the oscillation became stronger and moved to a higher frequency band (gamma band) with the increasing of the input difference between E/I neurons. Secondly, we found that gamma oscillation was induced by the unbalance between positive and negative synaptic currents, which was caused by the input difference between E/I neurons. When this input difference became greater, there would be a stronger gamma oscillation (i.e., a higher peak power in the power spectrum of the population activity of neurons). Further investigation revealed that the frequency dependency of gamma oscillation on the input difference between E/I neurons could be explained by the well-known mechanisms of inter-neuron-gamma (ING) and pyramidal-interneuron-gamma (PING). Finally, we derived mathematical analysis to verify the mechanism of frequency regulations and the results were consistent with the simulation results. The results of this paper provide a possible mechanism for the external stimuli-regulated gamma oscillations.     

Potential differences in the inferior vena cava and between cava and extravascular electrode at leg contraction in man.

When a voluntary adult male contracted his leg muscles, electric potential differences were recorded between platinum electrodes positioned inside the vena cava or between the vena cava and the grounded skin. Two experiments confirm that potential differences at leg contractions in man have a similar appearance as those in the rat at pain-evoked contractions of leg muscles. Platinum electrodes were used in man. The potential differences obtained are thereafter compared with recordings with Ag-AgCl electrodes in salt-bridges in the rat. Slow potential waves with superimposed irregular potential oscillations are recorded in man as previously found in the rat using platinum or Ag-AgCl electrodes. The findings indicate that vascular-interstitial routes participate in a vascular-interstitial-neuromuscular closed circuit, which is activated at contraction of the muscles.     

Undamped oscillations in prey–predator models on a finite size lattice

Sustained oscillation is frequently observed in population dynamics of biospecies. The oscillation comes not only from deterministic but also from stochastic characteristics. In the present article, we deal with a finite size lattice which contains prey and predator. The interaction between a pair of lattice points is carried out by two different methods; local and global interactions. In the former, interaction occurs between adjacent sites, while in the latter interaction takes place between any pair of lattice sites. It is found that both systems exhibit undamped oscillations. The amplitude of oscillation decreases with the increase of the total lattice sites. In the case of global interaction, we can present a stochastic differential equation which is composed of two factors, i.e., the Lotka–Volterra equation with density dependence and noise term. The quantitative agreement between theory and simulation results of global interaction is almost perfect. The stochastic theory qualitatively expresses characteristics of sustainable oscillation for local interaction.     

Modeling Plasmalemma Ion Transport of the Aquatic Plant Egeria densa

Fresh-water plants generate extraordinarily high electric potential differences at the plasma membrane. For a deeper understanding of the underlying transport processes a mathematical model of the electrogenic plasmalemma ion transport was developed based on experimental data mainly obtained from Egeria densa. The model uses a general nonlinear network approach and assumes coupling of the transporters via membrane potential. A proton pump, an outward-rectifying K⁺ channel, an inward-rectifying K⁺ channel, a Cl⁻ channel and a (2H-Cl)⁺ symporter are considered to be elements of the system. The model takes into consideration the effects of light, external pH and ionic content of the bath medium on ion transport. As a result it does not only satisfactorily describe the membrane potential as a function of these external physiological factors but also succeeds in simulating the effects of specific inhibitors as well as I-V-curves obtained with the patch-clamp technique in the whole cell mode. The quality of the model was checked by stability and sensitivity analyses. Received: 18 March 1996/Revised: 17 July 1996     

Microbial predation in a periodically operated chemostat: a global study of the interaction between natural and externally imposed frequencies.

Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When the chemostat is operated periodically, the interaction of the natural oscillation frequency with the external forcing gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions (local and especially global) between them as the amplitude and frequency of the forcing vary. The transition from low-forcing-amplitude quasiperiodicity to entrainment of the chemostat behavior by strong forcing (involving the concerted closing of resonance horns) is analyzed. We concentrate on certain strong resonance phenomena between the two frequencies and provide an extensive atlas of computed phase portraits for our model system. Our observations corroborate recent mathematical results and case studies of periodically forced chemical oscillators. In particular, the existence and relative succession of several distinct types of global bifurcations resulting in chaotic transients and multistability are studied in detail. The location in the operating diagram of several key codimension 2 local bifurcations of periodic solutions is computed, and their interaction with an interesting feature we name "real-eigenvalues horns" is examined.     

Oscillation period of MEPP frequency at frog neuromuscular junctions is inversely correlated with release efficacy and independent of acute Ca2+ loading

Periodic oscillations in miniature endplate potential (MEPP) frequency have been described at the frog neuromuscular junction. It is assumed that the periodic oscillations in MEPP frequency reflect cytosolic oscillations in intracellular Ca2+ concentration. In the course of a study related to describing the differences between weak and strong neuromuscular junctions by using the post-tetanic potentiation of MEPP frequency, we noted periodic oscillations in MEPP frequency in the first few minutes after a tetanus. The period of this oscillation (i.e. the time interval of one complete oscillation cycle) was inversely related to synaptic release efficacy, as measured by quantal content released per 100 microns of nerve terminal length. Junctions of high release efficacy have an oscillation period of 20 s or less whereas the oscillations in weaker junctions have periods of up to 60 s or longer. This relation is very similar during post-tetanic recovery in either a calcium containing Ringer solution or in a zero calcium-EGTA Ringer solution, indicating that external calcium is not necessary to express the phenomenon. We also found that the oscillations are apparent in resting junctions preceding a tetanus and that they are similar in period and show the same inverse relation to synaptic strength.