"Metabolic" action potentials in Acetabularia

Mathematical Models of Electrical Activity in Plants

Electrical activity plays an important role in plant life; in particular, electrical responses can participate in the reception of the action of stressors (local electrical responses and oscillations) and signal transduction into unstimulated parts of the plant (action potential, variation potential and system potential). Understanding the mechanisms of electrical responses and subsequent changes in physiological processes and the prediction of plant responses to stressors requires the elaboration of mathematical models of electrical activity in plant organisms. Our review describes approaches to the simulation of plant electrogenesis and summarizes current models of electrical activity in these organisms. It is shown that there are numerous models of the generation of electrical responses, which are based on various descriptions (from modifications of the classical Hodgkin-Huxley model to detailed models, which consider ion transporters, regulatory processes, buffers, etc.). A moderate number of works simulate the propagation of electrical signals using equivalent electrical circuits, systems of excitable elements with local electrical coupling and descriptions of chemical signal propagation. The transmission of signals from a plasma membrane to intracellular compartments (endoplasmic reticulum, vacuole) during the generation of electrical responses is much less modelled. Finally, only a few works simulate plant physiological changes that are connected with electrical responses or investigate the inverse problem: reconstruction of the type and parameters of stimuli through the analysis of electrical responses. In the conclusion of the review, we discuss future perspectives on the simulation of electrical activity in plants.

Impedance of the electrogenic Cl(-) pump inAcetabularia: Electrical frequency entrainements, voltage-sensitivity, and reaction kinetic interpretation

Reaction kinetic analysis of the electrical properties of the electrogenic Cl(-) pump inAcetabularia has been extended from steady-state to nonsteady-state conditions: electrical frequency responses of theAcetabularia membrane have been measured over the range from 1 Hz to 10 kHz at transmembrane potential differences across the plasmalemma (V m ) between -70 and -240 mV using voltage-clamp techniques. The results are well described by an electrical equivalent circuit with three parallel limbs: a conventional membrane capacitancec m , a steadystate conductanceg o (predominantly of the pump pathway plus a minor passive ion conductance) and a conductanceg s in series with a capacitancec p which are peculiar to the temporal behavior of the pump. The absolute values and voltage sensitivities of these four elements have been determined:c m of about 8 mF m(-2) turned out to be voltage insensitive; it is considered to be normal.g o is voltage sensitive and displays a peak of about 80 S m(-2) around -180 mV. Voltage sensitivity ofg s could not be documented due to large scatter ofg s (around 80 S m(-2)).c p behaved voltage sensitive with a notch of about 20 mF m(-2) around -180 mV, a peak of about 40 mF m(-2) at -120 mV and vanishing at -70 mV. When these data are compared with the predictions of nonsteady-state electrical properties of charge transport systems (U.-P. Hansen, J. Tittor, D. Gradmann, 1983,J. Membrane Biol. in press), model "A" (redistribution of states within the reaction cycle) consistently provides magnitude and voltage sensitivity of the elementsg o ,g s andc p of the equivalent circuit, when known kinetic parameters of the pump are used for the calculations. This analysis results in a density of pump elements in theAcetabularia plasmalemma of about 50 nmol m(-2). The dominating rate constants for the redistribution of the individual states of the pump in the electric field turn out to be in the range of 500 sec(-1), under normal conditions.

Time evolution of the action potential in plant cells

In this paper we extend and reconsider a solitonic model of the actionpotential in biological membranes for the case of plant cells. Aiming togive at least a qualitative description of the K(+),Cl(-) and Ca(2+) driven process of propagation ofthe action potential along plant cells we put forward the hypothesis ofthree scalar fields φ(i) (X), i = 1, 2, 3 which representK(+), Cl(-) and Ca(2+) ions,respectively. The modulus squared of these fields carries the usualquantum-mechanical (probabilistic) interpretation of the wave function. Onthe other hand, the fields are described themselves by the Lagrangiandensities ℒ[Formula: see text]. Moreover, the interaction and self-interaction term ℒ[Formula: see text] between thefields is considered. The Lagrangian densities ℒ[Formula: see text]include a double-well potential (which is proportional toσ(4) (i)) that leads to spontaneous symmetrybreaking which may produce structures with non-zero topological charge, e.g.longitudinal solitons. In order to describe the transversal motion of theions of concern we need to assume only non-uniform solutions of the system of equation of motion. Hence we seek for solutions (travelling waves) whichpreserve the shape and which move without dissipation and in this way wereconstruct the main dynamical features of the action potential in plants.

Simulation of action potential propagation in plants

Action potential is considered to be one of the primary responses of a plant to action of various environmental factors. Understanding plant action potential propagation mechanisms requires experimental investigation and simulation; however, a detailed mathematical model of plant electrical signal transmission is absent. Here, the mathematical model of action potential propagation in plants has been worked out. The model is a two-dimensional system of excitable cells; each of them is electrically coupled with four neighboring ones. Ion diffusion between excitable cell apoplast areas is also taken into account. The action potential generation in a single cell has been described on the basis of our previous model. The model simulates active and passive signal transmission well enough. It has been used to analyze theoretically the influence of cell to cell electrical conductivity and H(+)-ATPase activity on the signal transmission in plants. An increase in cell to cell electrical conductivity has been shown to stimulate an increase in the length constant, the action potential propagation velocity and the temperature threshold, while the membrane potential threshold being weakly changed. The growth of H(+)-ATPase activity has been found to induce the increase of temperature and membrane potential thresholds and the reduction of the length constant and the action potential propagation velocity.

A mathematical model of action potential in cells of vascular plants

A mathematical model of action potential (AP) in vascular plants cells has been worked out. The model takes into account actions of plasmalemma ion transport systems (K(+), Cl(-) and Ca(2+) channels; H(+)- and Ca(2+)-ATPases; 2H(+)/Cl(-) symporter; and H(+)/K(+) antiporter), changes of ion concentrations in the cell and in the extracellular space, cytoplasmic and apoplastic buffer capacities and the temperature dependence of active transport systems. The model of AP simulates a stationary level of the membrane potential and ion concentrations, generation of AP induced by electrical stimulation and gradual cooling and the impact of external Ca(2+) for AP development. The model supports a hypothesis about participation of H(+)-ATPase in AP generation.

Light- and dark-induced action potentials in Physcomitrella patens

Glass microelectrodes were inserted into Physcomitrella patens gametophyte leaves and action potentials (APs) were recorded in response to sudden illumination as well as after darkening, i.e., when the dark-induced membrane depolarization crossed a threshold. Application of 5 mM La(3+) (a calcium channel inhibitor), 10 mM TEA(+) (a potassium channel inhibitor) and increased free Ca(2+) resulted in a loss of excitability. Lack of Ca(2+) in the external medium did not prevent APs from occurring. It was concluded that during light- dark-induced excitation of Physcomitrella patens, APs might rely upon calcium influxes from the intracellular compartments. APs were not blocked by the proton pump inhibitors (DES, DCCD), although the resting potential (RP) diminished significantly.

Electrophysiology of turgor regulation in marine siphonous green algae

We review electrophysiological measures of turgor regulation in some siphonous green algae, primarily the giant-celled marine algae, Valonia and Ventricaria, with particular comparison to the well studied charophyte algae Chara and Lamprothamnium. The siphonous green algae have a less negative plasma membrane potential, and are unlikely to have a proton-based chemiosmotic transport system, dominated by active electrogenic K(+) uptake. We also make note of the unusual cellular structure of the siphonous green algae. Hypertonic stress, due to increased external osmotic pressure, is accompanied by positive-going potential difference (PD), increase in conductance, and slow turgor regulation. The relationship between these is not yet resolved, but may involve changes in K(+ )conductance (G (K)) or active K(+) transport at both membranes. Hypotonic turgor regulation, in response to decreased external osmotic pressure, is approximately 3 times faster than hypertonic turgor regulation. It is accompanied by a negative-going PD, although conductance also increases. The conductance increase and the magnitude of the PD change are strongly correlated with the magnitude of hypotonic stress.

Electrical signal from root to shoot in Sorghum bicolor: induction of leaf opening and evidence for fast extracellular propagation

We have observed earlier that primary leaf opening in Sorghum is a light-dependent process. We now show that giving a short photo-exposure to the roots alone also induced leaf opening over a similar time scale. However, any injury to the primary root inhibited the leaf formation. To check the propagation rate and response in this plant, the excitable properties and capability of conduction of electrical stimulus were investigated by extracellular recordings. Sorghum seedlings (5-7 days) were examined using non-damaging electrical stimuli. We demonstrate that seedlings when stimulated in one organ, the root region, produced a characteristic response, which could be recorded further up from the stimulating region in another organ, the shoot tissue. The minimum period of stimulation was 150 µs and threshold stimulus intensity was 100 µA. The general characteristic electrophysiological properties of the seedlings and the extracellular propagation of electrical signal suggest that S. bicolor exhibit typical excitable properties comparable to neural tissues. Moreover, electrical stimulus given to the root medium could overcome the requirement of photo-exposure to induce primary leaf formation in etiolated seedlings.

Changes in membrane potential and delayed luminescence of Acetabularia acetabulum

This paper examines the effect of changes in membrane potential on the critical parameters of delayed luminescence of Acetabularia acetabulum. We show that these parameters are altered by changes in membrane potential in ways that may reflect concomitant changes in energy storage and energy coupling.

Ultradian rhythms in Desmodium

The leaves of Desmodium gyrans (L.F.) DC show circadian movements in the terminal and ultradian movements of the lateral leaflets. The movements are due to swelling and shrinking of motor cells in special organs. The anatomy of these pulvini is described for the lateral leaflets. Data from electrophysiological recordings using microelectrodes inserted into the lateral pulvini, together with treatments that affect the proton pumps and ion channels, have been used to develop a physiological model of the ultradian leaflet movement. It explains the oscillations in the motor cells as being due to a change between a pump state and depolarization. During the pump state, ions are taken up, causing water influx and swelling of the motor cells. Depolarization causes loss of ions and water efflux (the motor cells shrink). The roles of calcium and the phosphatidyl inositol signal chain are discussed on the basis of experiments using chemical agents that affect these processes. Since calcium oscillations are known to occur in organisms in both time and space, an attempt has been made to simulate the situation in Desmodium pulvini by a model of specially coupled oscillators. Effects of different other treatments of the lateral pulvini are discussed. Oscillations in the minute range seem to be more common and some might be related to turgor regulation and ion uptake comparable to the situation in Desmodium. The ultradian control of the lateral pulvini and the circadian control of the terminal pulvini are apparently based on different mechanisms.

Action potentials in Acetabularia: measurement and simulation of voltage-gated fluxes

Amounts and temporal changes of the release of the tracer ions K+ (86Rb+), 22Na+, and 36Cl- as well as of H+ in the course of action potentials in Acetabularia have been recorded. New results and model calculations confirm in quantitative terms the involvement of three major ion transport systems X in the plasmalemma: Cl- pumps, K+ channels, and Cl- channels (which are marked in the following by the prefixes, P, K and C) with their equilibrium voltages XVe and voltage/time-dependent conductances, which can be described by the following, first approximation. Let the maximum (ohmic) conductance of each of the three populations of transporter species be about the same (pL, KL, CL = 1) but voltage gating be different: the pump (pVe about -200 mV) being inactivated (open, o----closed, c) at positive going transmembrane voltages, Vm; the K+ channels (KVe about -100 mV) are inactivated at negative going Vm; and the Cl- channels (CVe: around 0 mV), which are normally closed (c) at a resting Vm (near pVe) go through an intermediate open (o) state at more positive Vm before they enter a third "shut" state (s) in series. Model calculations, in which voltage sensitivities are expressed by the factor f = exp(VmF/(2RT], simulate the action potential fairly well with the following parameters (pkco: 10/fks-1, pkoc: 1000.f ks-1, Kkco: 200.f ks-1, Kkoc: 2/f ks-1, ckco: 500.f ks-1, fkoc: 5/f ks-1, Cks0: 0.1/f ks-1,Ckos: 20.f ks-1). It is also shown that the charge balance for the huge transient Cl- efflux, which frequently occurs during an action potential, can be accounted for by the observation of a corresponding release of Na+.

Ion fluxes in Acetabularia: vesicular shuttle

Ion flux relations in the unicellular marine alga Acetabularia have been investigated by uptake and washout kinetics of radioactive tracers (22Na+, 42K+, 36Cl- and 86Rb+) in normal cells and in cell segments with altered compartmentation (depleted of vacuole or of cytoplasm). Some flux experiments were supplemented by simultaneous electrophysiological recordings. The main results and conclusions about the steady-state relations are: the plasmalemma is the dominating barrier for translocation of K+ with influx and efflux of about 100 nmol.m-2.sec-1. K+ passes three- to sevenfold more easily than Rb+ does. Under normal conditions, Cl- (the substrate of the electrogenic pump, which dominates the electrical properties of the plasmalemma in the resting state) shows two efflux components of about 17 and 2 mumol.m-2.sec-1, and a cytoplasmic as well as vacuolar [Cl-] of about 420 mM ([Cl-]o = 529 mM). At 4 degrees C, when the pump is inhibited, both influx and efflux, as well as the cellular [Cl-], are significantly reduced. Na+ ([Na+]i: about 70 mM, [Na+]o: 461 mM), which is of minor electrophysiological relevance compared to K+, exhibits rapid and virtually temperature-insensitive (electroneutral) exchange (two components with about 2 and 0.2 mumol.m-2.sec-1 for influx and efflux). Some results with Na+ and Cl- are inconsistent with conventional (noncyclic) compartmentation models: (i) equilibration of the vacuole (with the external medium) can be faster than equilibration of the cytoplasm, (ii) absurd concentration values result when calculated by conventional compartmental analysis, and (iii) large amounts of ions can be released from the cell without changes in the electrical potential of the cytoplasm. These observations can be explained by the particular compartmentation of normal Acetabularia cells (as known by electron micrographs) with about 1 part cytoplasm, 5 parts central vacuole, and 5 parts vacuolar vesicles. These vesicles communicate directly with the central vacuole, with the cytoplasm and with the external medium.

A calcium-activated sodium conductance produces a long-duration action potential in the egg of a nemertean worm

1. The egg of the nemertean worm Cerebratulus lacteus produced an action potential having a duration of about 9 min. We investigated the ionic conductances which accounted for this long-duration action potential. 2. The peak of the action potential was about +50 mV and depended on extracellular Ca2+, while the plateau potential was about +25 mV and depended on extracellular Na+. 3. Under voltage-clamp conditions, depolarization produced two temporally separate inward currents: a fast current which reached a peak at about 10 ms, and a slow current which took up to 1 min to reach its peak and lasted for several min. 4. The fast current was independent of extracellular Na+, but was blocked by removal of extracellular Ca2+. 5. The slow current was not seen when extracellular Na+ was replaced by choline+ or K+. 6. The slow current did not develop in Ca2+-free sea water, and was reduced to about half if Ca2+ was removed after the current had been initiated. 7. Microinjection of EGTA blocked the slow current, and reduced the action potential duration to about 1 min. 8. We concluded that a voltage-activated Ca2+ conductance produced the peak of the action potential, while a Ca2+-activated Na+ conductance produced its plateau.

Determination of transmembrane currents from external potential measurements by the method of regularization

A novel non-invasive technique for measuring the transmembrane currents during action potential depolarizations of stalk segments of the giant unicellular alga Acetabularia mediterranea is described. This involves measurement of spatial samples of the time-dependent potential in the external medium (sea water) and an inverse transformation to give the current distribution at the cell surface. A detailed description of the method of regularization needed to handle this ill-conditioned inversion problem is presented in this paper, along with the results of test experiments to demonstrate its validity. An example of its application to the data recorded from an actual cell is also given.

Potassium channels in Eremosphaera viridis : I. Influence of cations and pH on resting membrane potential and on an action-potential-like response

The dependence of the membrane potential of Eremosphaera viridis on different external concentrations of potassium, sodium, calcium, and protons was compared with the diffusion potential measured in the dark and in the presence of NaN3. In contrast to some other algae, the membrane potential in the light as well as in the dark seemed to be predominantly determined by the calculated diffusion potential and less by an electrogenic pump which, however, seemed to be involved at potassium concentrations >1 mol·m(-3) and at higher pHos (>pH 6). Furthermore, some characteristics of an action-potential-like response (CAP) triggered by light-off, and independent of the membrane-potential threshold value, were determined. The CAP had a delay period of 5.4 s and needed 4.5 s for polarization to a plateau. On average, the plateau held for 8.8 s and the CAP lasted 37.7 s. The peak amplitudes of CAP (P AP) exactly followed the Nernst potential of potassium. Other cations like sodium, calcium and protons did not appreciably affect the peak amplitudes of CAP. From these and other results it can be assumed that the CAP is caused by a temporary opening of potassium channels in the plasma membrane of Eremosphaera (Köhler et al., 1983, Planta 159, 165-171). The release of a CAP by light-off has been partly explained by the participation of a transient increase of proton concentration in the cytoplasm. It was possible to trigger a CAP by external pH changes and by the addition of sodium acetate, thus supporting the hypothesis that a pH decrease in the cytoplasm may be one element of the signal transfer from the photosynthetic system to the potassium channels in the plasmalemma. Calcium also seemed to have an influence on triggering the CAP.

Changes in membrane potential and resistance caused by transient increase of potassium conductance in the unicellular green alga Eremosphaera viridis

The electrophysiological membrane parameters of the unicellular green alga Eremosphaera viridis were determined using an improved computer-supported single-microelectrode technique. These cells developed an average membrane potential of-150 mV in the light and a specific resistance of 1 Ω m(2) with an external potassium concentration of 1.1 mM and pH 5.5. In the dark, many cells showed a less polarized potential of 30-40 mV and a smaller membrane resistance. At potassium concentrations in the external medium higher than 1 mM, the membrane potential strongly depends on the external potassium content apart from a small electrogenic component. At concentrations lower than 1 mM K(+), a dependence of the membrane potential upon external potassium concentrations could not be verified. Inserting the internal ion activities in the Goldmann equation shows that, in this range, the proton conductance seems to be predominant over the potassium conductance. Transient changes in the membrane potential and in the membrane resistance were observed after switching off the light, after addition of 3-(3',4'-dichlorophenyl)-1,1-dimethylurea or N,N'-dicyclohexylcarbodiimide, after a sudden decrease in temperature, and after current pulses. These changes resemble the action potentials (AP) found in other plant cells (Chara, Acetabularia). On average, the AP has a delay period of 5.1 s and a duration of 43.8 s showing a sudden decrease and a slower regeneration. The voltage peak during an AP followed exactly the Nernst potential of potassium over a range of external potassium concentrations from 5 μM to 0.2 M. This is true for depolarization or hyperpolarization, depending on the external K(+)-concentration. Tetraethylammonium-hydrogensulphate, a rather specific inhibitor of K(+) channels in nervous cells, suppressed the AP. The correlation of the appearance of the AP with a short-term opening of potassium channels in the membrane of Eremosphaera is discussed.

Cable properties and compartmentation in Acetabularia

The electrical cable properties of three different compartmentation types of Acetabularia cells have been investigated. These three types were: normal cells, 'stumps' (filled with cytoplasm, no central vacuole) and 'tubes' (cytoplasm depleted vacuoles). The latter two types have been obtained by centrifugation of normal cells. Qualitatively, the characteristic biphasic voltage response upon rectangular current pulses is the same in these three types. Quantitatively, however, the two conductances which can be obtained from the biphasic voltage response as well as the apparent capacity of several F . m-2 which derives from the large time constant of the second phase, are drastically increased in stumps and decreased in tubes compared to normal cells. The resting potential is a few mV more negative in stumps, and more positive in tubes, than in normal cells. Based on the existence of the high resting potential and the apparent large capacity in the non-vacuolated stumps, it is concluded that the electrogenic Cl- pump of Acetabularia is located in the plasmalemma membrane and that the apparent large capacity is not a result of the complicated membraneous organisation of the vacuolar system. Several possibilities are discussed, in relation to the quantitative correlation between intracellular compartmentation and electrical membrane parameters.

Evidence for electrogenic proton extrusion by subepidermal cells of Lemna paucicostata 6746

The cell potential of Lemna paucicostata 6746 was measured between the vacuole and the external solution. The potential in the dark (-202 mV) could be depolarized with 0.1 mM dicyclohexyl carbodiimide (DCCD) or 1 mM arsenate to-81 mV. The hyperpolarization above the latter value is therefore attributed to an ATP-dependent process. The cell potential showed a significant dependence upon the pH of the external solution. The change in the potential induced by a jump in pH between two certain values, was reversible and independent of the mode of performing the pH change (stepwise or at once). The DCCD-or arsenate-depolarized potential did not respond to external pH changes. A 0.1 mM ammonium chloride solution depolarized the cell potential reversibly to-83 mV. This potential-change could be greatly reduced by simultaneous addition of 5 mM Na isobutyrate. The pH sensitivity of the cell potential is ascribed to changes in the rate of proton extrusion upon altering the proton gradient across the plasmalemma. The effects of ammonium and isobutyrate are interpreted as being the consequence of pH shifts at the inner face of the plasmalemma, caused by the permeation of the undissociated form of the weak acid or base. A critical discussion of an alternative interpretation for the ammonium effect is presented.

The role of electrical fields, ions, and the cortex in the morphogenesis of Acetabularia

Electrophysiological and biochemical aspects of polarity determination and morphogenesis were studied in regenerating Acetabularia. The Ca(++), Mg(++) ionophore, A23187, reversibly inhibits the formation of apical structures (whorls and caps) but does not arrest longitudinal growth. This normal growth correlates with normal electrophysiology as reflected in an apico-basal electrical potential gradient and spontaneous recurrent action potentials which propagate from apex to base. However, the ionophore markedly elevates (32)PO 3 (3-) incorporation into the cortical cytoplasm which is normally low apically and rises to a maximum at the base. A molecular model of membrane-dependent morphogenesis is suggested.

Membrane potential changes during transport of hexoses in Lemna gibba G1

The membrane potential (pd) of duck weed (Lemna gibba G1) proved to be energy dependent. At high internal ATP levels of 74 to 105 nmol ATP g(-1) FW, pd was between -175 and -265 mV. At low ATP levels of 23 to 46 nmol ATP g(-1) FW, pd was low, about -90 to -120 mV at pH 5.7, but -180 mV at pH 8. Upon addition of glucose in the dark or by light energy the low pd recovered to the high values. The active component of the pd was depolarized by the addition of hexoses in the dark and in the light. Hexose-dependent depolarization of the pd (=Δ pd) followed a saturation curve similar to active hexose influx kinetics. Depolarization of the pd recovered in the dark even in the presence of the hexoses and with a 10fold enhancement in the light. Depolarization and recovery could be repeated several times with the same cell. Glucose uptake caused a maximum depolarization of 133 mV, fructose uptake half that amount, sucrose had the same effect as glucose. During 3-O-methylglucose and 2-deoxyglucose uptake the depolarizing effect was only slightly lower. The pd remained unchanged in the presence of mannitol. The glucose dependent Δ pd and especially the rate of pd recovery proved to be pH-dependent between pH 4 and pH 8. It was independent of the presence of 1 mM KCl. Although no Δ pH could be measured in the incubation medium, these results can be best explained by a H(+)-hexose cotransport mechanism powered by active H(+) extrusion at the plasmalemma.