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A spatial pattern of the electric potential formed by a characean internodal cell is investigated experimentally. A multi-electrode measuring system is used to pursue the dynamic properties of the pattern. It is shown that periodic low-potential regions are formed after the entire transient increase over the cell when the light is imposed on. Under constant illumination an electric oscillation is found. These experimental data are also discussed by the use of a spectrum analysis; the formation of the pattern is a bifurcation phenomenon of soft-mode instability realizing far from equilibrium, accompanied by sharpening of spectrum of a particular wave mode. A long-range coherence extending over 1 cm is also shown to exist in the high-potential region, where protons are extruded by H + -ATPase molecules existing within the membrane.

The effect of taste substances was investigated for a lipid membrane constructed by casting complexes of synthetic lipid (double-chain ammonium salt) and sodium polystyrenesulfonate on a silicon wafer with a single minute pore. Reproducibility of the electric properties was improved remarkably by the use of the present construction method for the lipid membrane. It was found that this membrane showed a sensitive response to negatively-charged chemicals having strong bitterness such as picric acid because the lipids are positively charged. A membrane with non-equimolar lipid-polymer complexes showed a phase separation between two phases composed of liquid-crystal lipid multi-bilayers and crystal lipid-polymers within a limited temperature range. This membrane in the phase-separation state generated a self-sustained electric oscillation, whose mechanism was explained with the aid of a non-equilibrium theory. The waveform of the oscillation changed by using picric acid on the membrane. This bio-mimetic membrane has the possibility of acting as a biological chemoreceptor.

Self-sustained oscillations of membrane potential in an artificial model membrane, where dioleyl phosphate (DOPH) is infiltrated into pores of a Millipore filter, are investigated both experimentally and theoretically. Spike-like self-oscillations with an extremely long period of about one hour were observed for membranes with large adsorbed amounts of DOPH in the absence of external forces such as electric current and pressure gradient. On the basis of a previously-presented model that DOPH molecules make transitions among three phases composed of oil droplets, spherical micelles and multi- or bilayer leaflets, the occurrence of self-oscillations is explained well by taking account of an accumulation and a release of salt in a pore of the filter.

For an artificial membrane in which dioleyl phosphate (DOPH) is infiltrated into pores of Millipore filter, a relaxation of electric caracitance of the membrane in a solution was investigated after an abrupt change of salt concentration. Relaxation curves of sigmoid types were observed after an increase of salt concentration, while the curves were of exponential types after a decrease. These facts suggest us that hysteresis loops of electric capacitance or this membrane observed for a cyclic variation of salt concentration belong to a different type from the usual ones originating from the first-order phase transition. It is shown that these electric characteristics of the membranes can be explained well on the basis of a model that dioleyl phosphate molecules make transitions among three phases composed of droplets, spherical micells and multi- or bilayer leaflets.

An expression for the amplitude of stable steady self-oscillatory solutions for the inverted bifurcation is obtained by applying bifurcation theory to the BVP equation, which is a model describing nerve excitations. Up to the fifth-power term with respect to the amplitude is included in the calculation, assuming that the amplitude of the steady self-oscillatory solution is of small order. The obtained expression for the inverted-bifurcation can continuously be transformed, leading to an expression for the normal-bifurcation by merely varying one parameter. Further, utilizing that expression and employing the reductive perturbation method in which the amplitude is regarded as an infinitesimal parameter, an expression describing the relaxation phenomenon in the neighborhood of the stable steady solution is derived for the inverted-bifurcation as well as for the normal-bifurcation, the nature of which is close to that of the inverted-bi-furcation. Since this expression has the form of the usual time-dependent Ginzburg-Landau(TDGL) equation and an additional term, the behavior of those bifurcations which considerably differ from the usual normal-bifurcation can well be described by the derived expression.

An early stage of developing eggs of the seaweed Fucus is summarized briefly. A Fucus egg, which is initially apolar, forms a rhizoid 12-14 hours after fertilization. After a latent period when no egg responds to external vectors, the polarity becomes sensitive to some external vectors as a unilateral light. Fucus eggs also tend to form rhizoids to each other when eggs are sufficiently close. As a probable mechanism to explain the rhizoid formation, an electrophoresis mechanism is mentioned in detail.Based on a bridging activity of Ca2+ in the membrane formation, an appearance of sensitivity in Fucus eggs is understood as a kind of bifurction phenomenon far from equilibrium. The appearance of polarity influenced by neighboring eggs is also discussed in terms of a self-organization process through the increasing number of components.

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+.

The effect of bitter substances on the self-sustained electric oscillation of a DOPH (dioleyl phosphate)-Millipore membrane was investigated as a model system of taste reception. Caffeine and theobromine, having higher taste thresholds, had slight effect, but quinine, strychnine and nicotine, exhibiting strong bitterness, increased the frequency of the oscillation. The mode of action of bitter substances on the DOPH-Millipore membrane in the non-oscillatory state suggested that they cause the receptor potential by a change in the phase boundary potential. The intensity of action on the electric potential was associated with the threshold values of bitterness.

Electric spatial patterns of bands formed along the cell wall of the characean internode were studied using a multi-electrode measuring system. The electric potential near the surface of the cell was measured by arranging about 25 electrodes along the cell at approximately 1.6 mm intervals. Since the time required for one scan over the cell length is only 1 s, the temporal change in the spatial pattern of surface electric potential can be readily observed. Oscillations were sometimes found as the electric pattern started to appear after the cell was illuminated. Fourier analysis shows that a single spatial mode arises gradually and then becomes stabilized in an oscillatory manner. A simple electric circuit model comprising three variables, i.e., a membrane potential, an electric current across the membrane and an electromotive force, can simulate well the oscillatory rise of bands. These results imply that the electric spatial pattern observed in characean internodes is a self-organized structure emerging far from equilibrium, known as a dissipative structure. Biophysical mechanisms of band formation are discussed.

The electric spatial pattern is often observed in biological systems. The freshwater alga Chara, composed of giant internodal cells, develops alternating periodic bands of acidic and alkaline regions along the cell wall under illumination. Figure 1 shows the formation of 5 alkaline bands along the cell with 70 mm length. The electric potential near the cell surface and the membrane potential also show a similar pattern, which implies an electric current flowing from the acidic to alkaline zone [1–6]. Since the acidic regions elongate, the formation of pattern is directly related to the growth. The band surrounding the circumferential direction of the cell is formed through a gathering process of many small patches at the cell surface [4]. Electric oscillations sometimes appearing under weak light intensity are coherent in the acidic region [3]. This electrochemical spatial pattern is fairly stable in grown cells, but is unstable in very young cells. Even if one of the bands formed on the cell is diminished by some electro-mechanical perturbations, other bands are scarcely changed [7]; the pattern seems a kind of frozen pattern, which has not been investigated yet in detail, although propagative or oscillatory waves of chemical concentrations have been studied well.

The electric membrane potential as functions of position and time of Characean internode has been studied using a modified water-film electrode technique. Between the low-conductance hyperpolarized region (called the H-region or acidic region) and the high-conductance depolarized region ( D-region), there is a difference in the direction of responses to light-off and -on stimulations. In darkness the membrane potential becomes hyperpolarized in the D-region, whereas it is depolarized in the H-region at the steady state. The potential difference between D- and H- regions, ΔVm, is increased by exposure to pure O2, N2, or CO2-free air. When the amount of water surrounding the internode is limited, the formation of an electric pattern occurs rapidly. In contrast, the recovery is delayed. The membrane potential of the D-region is sometimes hyperpolarized significantly with lowering of the extracellular pH to 7.5, while the potential of the H-region is slightly depolarized. This seems to be an all-or-none type response. However, the electric profile is always homogenized with the pH of 6.8. Thus, the pH around 7.5 may be a threshold level to open/close putative OH− (or H +) channels of the D-region.

A theory is presented on the electrostatic properties of the surface area of phosphatidyl-glycerol monolayers spreading at an air-water interface in the presence of monovalent and divalent cations. In the present theory, the adsorption of monovalent and divalent cations to the membranes is taken into account, besides the dissociation of protons, as a possible cause of the change of surface charge density with the variation of pH or ion concentrations. It is also pointed out that, in the presence of structure-making ions such as Li+ and Na+, the nearest-neighbour interactions between proton dissociation sites become important for the monolayers in the gel state to yield a sharp expansion of the surface area with the increase of pH. The present theory shows quantitative agreements with previously-observed data.

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.

A band-type alternating pattern of acidic and alkaline regions formed along the Characean cell wall is discussed theoretically. The model system is constructed from linear diffusion equations for the concentration of H + outside the internode and in the protoplasm. The plasmalemma is taken as a boundary transporting H + under energy supply by light. The sizes of the protoplasm and extracellular water phase are taken into account explicitly in the present model system to reproduce qualitatively the characteristics observed in various types of experiments. Theoretical analysis shows that the band pattern belongs to dissipative structures emerging far from equilibrium, and is stabilized through the electric current loops produced by locally activated electrogenic H + pumps and spatially separated passive H + influx (or OH − efflux) across the membrane. Both the numerical calculation and the theoretical analysis using a generalized time-dependent Ginzburg-Landau equation reveal the following points: (i) the intemodal cell with a larger vacuole in a smaller size of the extracellular water phase tends to exhibit a clearer band pattern; (ii) the increase in viscosity of the external aqueous medium makes the bands appear more easily and, furthermore, distinctly; (iii) the change in size of the extracellular water phase significantly affects the kinetics of the pattern- formation process. These results are interpreted reasonably by taking account of the electric current circulating between the acidic and alkaline regions.

For an artificial membrane prepared by infiltrating dioleyl phosphate (DOPH) into pores of a Millipore filter, we propose a theoretical model for explaining observed data on electric behavior, such as d.c. current-voltage characteristics and self-sustained oscillations of the electric potential. The model consists of a simple electric circuit composed of electric resistances and capacitances as given functions of internal variables which represent conformational states of DOPH molecules and salt concentration inside the pore concerned. The kinetic equations for these variables are the same as those presented previously for describing a phase transition of DOPH. except for a slight modification taking account of effects of salt accumulation inside the pore. The present theory can describe well the I–V hysteresis and various features of spike-like oscillations with long periods of up to a few hours in the absence of external force and also short-period oscillations with periods of the order of 1 s under pressure difference.

For growing roots of azuki bean (Phaseolus chrysanthos), an electric potential is measured minutely along the surface of the root, together with the surface pH. It was found that the root begins to display a band-type pattern of potential with a spatial period of about 2 cm in a mature region as soon as it grows to about 10 cm in root length, while the surface potential shows only one convex peak around a position 5–20 mm behind a root tip and a succeeding concave peak around 20–35 mm, providing the length of root is shorter than about 10 cm. Since the surface potential takes a relatively positive value on average at the side of the root base compared with that in an elongation zone near the tip, electric current is supposed to flow into the elongation zone, accompanied by some local current loops in the mature region. The present band-type pattern observed first in multi-cell systems seems to be a kind of dissipative structure appearing far from equilibrium, and hence its relationship to growth is discussed.

La resistivite electrique d'un film de phosphate de dioleyl a l'interface entre des solutions de KCl a SmM et 100 mM est etudiee en fonction des transitions de phase

The normalized decay rate R of magnetization due to thermally activated flux creep is typically given by R≃k B T/U c, where k B is the Boltzmann constant, T is the absolute temperature and U c is the effective pinning potential. Some observed data for high-T c superconductors show that R increases with increasing T, while in other studies, R takes a peak at a certain temperature T m below the critical temperature T c, where T m decreases with increasing external magnetic field. These temperature dependences of R are explained systematically on the basis of a recent theory of flux creep developed by the authors.

A correlation dimension and a distribution pattern of spectrum intensities of a self-sustained electric oscillation were studied for an aperiodic oscillation induced by an application of electric current on a membrane of a synthetic lipid, dioleyl phosphate. The estimated dimension showed a remarkable deviation in the presence of taste substances such as quinine (above a certain threshold value) from that in the absence of these taste substances; this deviation was accompanied by a change in spectrum pattern. The present result indicates that the two variables extracted from the aperiodic oscillations will be useful as sensing information in a chemical taste sensor using lipid membranes.

A formal theory of macroscopic pinning force FP is presented from a viewpoint that FP of is a value of Lorentz force FL at a bifurcation point, JT=Jc, above which a nondissipative state fluxoi'd lattice carrying a transport current with the density JT becomes unstable and a dynamic dissipative state called the flux flow appears. It is shown that correlation lengthes among pinned fluxoids diverge at the bifurcation point Jc, as these do in other bifurcation phenomena.

High frequency multi-sensor patterns for instrumental odor monitoring in urban areas close to industrial districts requires adequate analytical strategies, hardware and effective data analysis and control procedures. An approach linking data analysis tools is presented based on unsupervised identification of recurrent patterns from data produced by hybrid instrumental odour monitoring systems. A self-organizing map is built and clustered in order to identify air typologies at a e-nose site; they are interpreted thanks to data fusion of sensorial data from citizen complaints, olfactometric measures, air pollutants and meteorological data. A supervised Kohonen network generates quantitative relationships between multisensor patterns and sparse olfatometric measures on air samples timely collected after complaints or instrumental threshold exceedance, allowing high frequency estimates of odour concentrations.