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The excitability of plant cells: with a special emphasis on Characean internodal cells.

Now in the further development of science, we want more than just a formula. First we have an observation, then we have numbers that we measure, then we have a law which summarizes all the numbers. But the real glory of science is that we can find a way of thinking such that the law is evident.

--Richard Feynman (in Feynman et al., 1963)

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas expressed in symbols had ever quite found their way out of the equations into their minds.

--James Clerk Maxwell (cited in Agin, 1972)

II. Introduction:

Plants Sense Environmental Cues and Act Appropriately

Every day we can observe the fact that plants respond to the environment. For example, plants respond to gravity. "Remember the little seed in the styrofoam cup: The roots go down and the plants go up" (Fulghum, 1989). Plants also respond to light and temperature. In a perennial garden, each variety flowers at a certain time of the year because the plants are capable of identifying the season by detecting both the day length and the temperature. Plants can also perceive the time of day, and many plants have "sleep movements" where they change the orientation of their leaves so that they maximize the absorption of light during the day and minimize the loss of heat at night. Plants adjust their height and leaf shape depending on whether they are growing in the sun or shade. In this case, they detect the difference in the quality of light (i.e., color distribution) that occurs in full sun compared to shade. Plants can determine the direction of light, and they bend toward the light in a way that presents the maximum surface area to the sun to maximize photosynthesis. After sensing the various environmental stimuli, the sensor region must transmit a signal to the responding region, In theory, this signal can be chemical (e.g., hormonal), physical (e.g., electrical or hydraulic), or both (Kudoyarova et al., 1990; Malone, 1993; Appendix B).

It has been known since Charles Darwin's time that many plants, like animals, respond to mechanical stimulation (Bernard, 1974; Darwin, 1893, 1966; Davies, 1987, 1993a, 1993b; Galston, 1994; Jaffe, 1973, 1976; Jaffe & Galston, 1968; Pickard, 1973; Sibaoka, 1966, 1969; Simons, 1981, 1992; Smith, 1788; Thomson, 1932; Wayne, 1993). Insectivorous plants that live in nitrogen- and mineral-depleted areas get their required nitrogen and minerals by capturing and digesting insects. The sundew immobilizes an insect in its mucilage. Subsequently, the mechanical stimulation induced by the insect trying to escape is sensed by the tip of the tentacle. The sensitive tip then produces a series of action potentials, that is, pulse-like, propagating electrical disturbances that can communicate information (Fig. 1). In the case of the sundew, the action potentials induce the marginal tentacles to bend, pushing the insect toward leaf's center (Williams & Spanswick, 1976). Although action potentials are not transmitted to neighboring tentacles, a slower hormonal signal induces them to wrap around the insect and provide a secure trap (Williams & Pickard, 1972a, 1972b). Nearby secretory cells subsequently exude digestive enzymes "to the little stomach thus formed, and the plant makes a meal of its prey" (Pickard, 1973). The lobes of a Venus fly trap capture its prey by closing when an insect walking across it strikes two hairs or one hair twice. This "primitive memory" ensures that the trap closes only around live prey. The trap closes only after the stimulated sensory hairs communicate to the motor cells by means of an action potential (Benolken & Jacobson, 1970; Brown & Sharp, 1910; Burdon-Sanderson, 1873; Burdon-Sanderson & Page, 1876; Di Palma et al., 1961; Hodick & Sievers, 1989; Jacobson, 1965; Stuhlman & Darden, 1950; Williams & Bennett, 1982). John Burdon-Sanderson, an uncle of J. B. S. Haldane, first studied the movements and electrical properties of the Venus fly trap for Charles Darwin (Gillespie, 1970, 1972). Upon closure, the gland cells secrete enzymes that effect digestion of the insect and uptake of nutrients (Rea & Whatley, 1983; Rea et al., 1983; Robins, 1976; Robins & Juniper, 1980; Scala et al., 1968; Schwab et al., 1969).

The leaves of many sensitive plants, including Mimosa, fall and look dead and unappealing to a would-be herbivore once the grazing animal touches it (Aimi, 1963; Allen, 1969; Setty & Jaffe, 1972; Tinz-Fuchtmeier & Gradmann, 1991; Toriyama, 1954, 1955, 1957, 1967; Toriyama & Jaffe, 1972; Toriyama & Sato, 1968; Turnquist et al., 1993). Leaflet collapse may act as a defense mechanism since the collapse results in an increased exposure of sharp thorns (Eisner, 1981). Touching induces an action potential that propagates from the stimulated region to the rest of the plant (Sibaoka, 1962). This propagated "information" causes the rest of the plant to look unappealing also and to "deploy their thorns." It is also possible that mechanical stimulation by the wind induces an action potential that causes the leaflets to collapse. This reduces the exposed surface from which moisture may be lost (D. F. Grether, pers. comm.).

Plants that do not show obvious movements also elicit action potentials (Paszewski & Zawadzki, 1973; Scott, 1962). In Luffa, action potentials cause a transient inhibition of growth (Shiina & Tazawa, 1986a). Action potentials may be involved in phloem unloading and, consequently, the distribution of nutrients in plants (Eschrich et al., 1988; Fromm, 1991). Action potentials propagated through the phloem may also be involved in pathogen resistance (Wildon et al., 1992). In various flowers, pollen falling on the stigma generates an action potential that may be involved in subsequent pollination, incompatibility, or maturation processes (Goldsmith & Hafenrichter, 1932; Sinyukhin & Britikov, 1967). At the level of stimulus-response coupling, plants and animal cells undergo many similar processes, including the generation and propagation of action potentials and perhaps stimulation by neurotransmitters, including acetylcholine (Dettbarn, 1962; Fluck & Jaffe, 1974; Tretyn & Kendrick, 1991). Including studies on plant excitability with studies of animal excitability may help us understand the evolution of our own nervous system (Hille, 1984, 1992).

In order to understand the physiological basis of the complex behaviors of animals, neurobiologists took a reductionist approach and began studying the long nerve cells of squids which are so large they were originally thought to be blood vessels (Cole, 1968; Eckert et al., 1988; Hodgkin, 1964; Junge, 1981; Katz, 1966; Lakshminarayanaiah, 1969; Matthews, 1986; Stevens, 1966; Tasaki, 1968; Young, 1936, 1947). Studying simple systems allows the development of techniques and the formulation of theories necessary for understanding more complex systems. Likewise, in order to understand the complex behaviors of whole plants, some plant physiologists have turned to the giant algal cells, such as Chara and Nitella, where vegetative and reproductive growth and development, adaptive physiological mechanisms, and nutrient uptake and translocation can be readily studied (Amino & Tazawa, 1989; Andjus & Vucelic, 1990; Barber, 1911a, 1911b; Beilby et al., 1993; Bisson & Bartholomew, 1984; Bisson et al., 1991; Blatt & Kuo, 1976; M. Brooks, 1939; S. Brooks, 1939; Brooks & Brooks, 1941; Brown, 1938; Buchen et al., 1991, 1993; Coleman, 1986; Collander, 1949, 1954; Cote et al., 1987; Dainty, 1962, 1963a, 1963b; Dainty & Ginzburg, 1964a, 1964b, 1964c; Dainty & Hope, 1959; Diamond & Solomon, 1959; Ding et al., 1991, 1992; Dorn & Weisenseel, 1984; Forsberg, 1965; Gertel & Green, 1977; Green, 1954, 1958a, 1958b, 1959, 1960, 1962, 1963, 1964, 1968; Green & Chapman, 1955; Green & Chen, 1960; Gillet et al., 1989, 1992, 1994; Green et al., 1971; Hansen, 1990; Hejnowicz et al., 1985; Hoagland & Broyer, 1942; Hoagland & Davis, 1923a, 1923b; Hoagland et al., 1926; Hodge et al., 1956; Hogg et al., 1968a, 1968b; Homble & Foissner, 1993; Homble et al., 1989; Hotchkiss & Brown, 1987; Kamiya & Kuroda, 1956a; Kamiya & Tazawa, 1956; Katsuhara et al., 1990; Katsuhara & Tazawa, 1992; Kersey et al., 1976; Kishimoto, 1957; Kiss & Staehelin, 1993; Kitasato, 1968; Kiyosawa, 1993; Kwiatkowska, 1988, 1991; Kwiatkowska & Maszewski, 1985, 1986; Kwiatkowska et al., 1990; Levy, 1991; Lucas, 1975, 1976, 1977, 1979, 1982; Lucas & Alexander, 1981; Lucas & Dainty, 1977a, 1977b; Lucas & Shimmen, 1981; Lucas & Smith, 1973; Lucas et al., 1978, 1989; MacRobbie & Dainty, 1958; MacRobbie & Fensom, 1969; Maszewski & Kolodziejczyk, 1991; McConnaughey, 1991; McConnaughey & Falk, 1991; McCurdy & Harmon, 1992; Metraux, 1982; Metraux & Taiz, 1977, 1978, 1979; Metraux et al., 1980; Miller & Sanders, 1987; Mimura & Kirino, 1984; Moestrup, 1970; Morrison et al., 1993; Mullins, 1939; Nagai & Hayama, 1979; Nagai & Kishimoto, 1964; Nagai & Rebhun, 1966; Nagai & Tazawa, 1962; Nothnagel & Webb, 1979; Nothnagel et al., 1982; Ogata, 1983; Ogata & Kishimoto, 1976; Ohkawa & Kishimoto, 1977; Ohkawa & Tsutsui, 1988; Okazaki & Tazawa, 1990; Okazaki et al., 1987; Osterhaut, 1927, 1931, 1958; Osterhaut & Hill, 1930a, 1930b; Palevitz & Hepler, 1974, 1975; Pickard, 1969, 1972; Pickett-Heaps, 1967a, 1967b, 1968; Ping et al., 1990; Pottosin et al., 1993; Probine & Barber, 1966; Probine & Preston, 1961, 1962; Reid & Overall, 1992; Reid & Smith, 1988, 1993; Reid et al., 1989; Rethy, 1968; Richmond et al., 1980; Rudinger et al., 1992; Sakano & Tazawa, 1986; Shen, 1966, 1967; Shepherd & Goodwin, 1992a, 1992b; Shimmen & Mimura, 1993; Shimmen & Yoshida, 1993; Sievers & Volkmann, 1979; Spanswick, 1970; Staves et al., 1992; Steudle & Tyerman, 1983; Steudle & Zimmermann, 1974; Studener, 1947; Sun et al., 1988; Takamatsu et al., 1993; Takatori & Imahori, 1971; Taylor & Whitaker, 1927; Tazawa, 1957, 1964; Tazawa & Kishimoto, 1964; Tazawa et al., 1994; Thiel et al., 1990; Tolbert & Zill, 1954; Trontelj et al., 1994; Tsutsui & Ohkawa, 1993; Turner, 1968, 1970; Volkmann et al., 1991; Vorobiev, 1967; Walker & Sanders, 1991; Wasteneys & Williamson, 1992; Wasteneys et al., 1993; Wayne & Tazawa, 1988, 1990; Wayne et al., 1990, 1992, 1994; Weidmann, 1949a, 1949b; Weisenseel & Ruppert, 1977; Yao et al., 1992; Zanello & Barrantes, 1992, 1994; Zhang et al., 1989; Zhu & Boyer, 1992).

The characean algae, which include Chara and Nitella, are thought to be the ancestors of all higher plants (Chapman & Buchheim, 1991; Graham, 1993; Graham & Kaneko, 1991; Grambast, 1974; Groves & Bullock-Webster, 1920, 1924; Imahori, 1954; Manhart & Palmer, 1990; Pal et al., 1962; Pickett-Heaps & Marchant, 1972; Wilcox et al., 1993; Wood & Imahori, 1964, 1965). Indeed, Pliny the Younger considered the charophytes to be members of the genus Equisetum (Plinius Secundus, 1469).

The study of excitability in plant cells forms the foundation of the study of excitability in isolated cells. Although excitability in tissues and organs of whole plants and animals were well known since the early work of Luigi Galvani, the electrical phenomena were too complicated to allow much progress (Green, 1953). A giant breakthrough came when electrical measurements were made on single cells. Indeed, action potentials were observed in the isolated internodal cells of Nitella in 1898 by Georg Hormann, using extracellular electrodes, approximately 30 years before they were observed in isolated nerve cells by Adrian and Bronk (1928). In fact, action potentials (also known as negative variations, action currents, and death currents) were so well studied in characean cells by Blinks (1936), Osterhaut (1931), and Osterhaut's colleagues at the Rockefeller Institute, that Cole and his colleagues at the National Institutes of Health began studying excitability in characean cells. It may be surprising to know that Cole and Curtis wrote the following in their 1939 paper "Electrical impedance of the squid giant axon during activity":

Recently the transverse alternating current impedance of Nitella has been measured during the passage of an impulse which originated several centimeters away (Cole and Curtis, 1938b). These measurements showed that the membrane capacity decreased 15 per cent or less while the membrane conductance increased to about 200 times its resting value. Also this conductance increase and the membrane electromotive force decrease occurred at nearly the same time, which was late in the rising phase of the monophasic action potential. Similar measurements have now been made on Young's giant nerve fiber preparation from the squid (Young, 1936). These were undertaken first, to determine whether or not a functional nerve propagates an impulse in a manner similar to Nitella, and second, because the microscopic structure of the squid axon corresponds considerably better than that of Nitella to the postulates upon which the measurements are interpreted.

Characean action potentials can be induced by various stimuli, including suddenly lowered or raised temperature or pressure, UV irradiation, and odorants, as well as by a mechanical stimulation or a depolarizing current (Harvey, 1942a, 1942b; Hill, 1935; Kishimoto, 1968; Osterhaut & Hill, 1935; Staves & Wayne, 1993; Ueda et al., 1975a, 1975b; Zimmermann & Beckers, 1978). As in animal cells, the action potential is an all-or-none response and does not usually depend on the strength of the stimulus. In characean cells there is a refractory period following an action potential, during which a stimulus cannot cause a second action potential. Details of the characean action potential have been reviewed by Kishimoto (1972), Hope and Walker (1975), Beilby (1984), Tazawa et al. (1987), and Tazawa and Shimmen (1987).

The action potential is conducted in both directions away from the place at which the plasma membrane is first depolarized past the threshold. The conduction rate is 0.01-0.4 m [s.sup.-1] (Auger, 1933; Sibaoka, 1958; Umrath, 1933), depending on the conductivity of the medium (Sibaoka, 1958). This is faster than the conduction velocity in sponges (0.003 m[s.sup.-1]; Mackie et al., 1983) and slower than the conduction velocity of action potentials in nerves, which is between 0.4 and 42 m[s.sup.-1] (Eckert et al., 1988; Matthews, 1986).

The propagation velocity of an action potential along a cell depends on how rapidly the depolarization (i.e., the decrease in membrane potential) diminishes with distance. The membrane will become depolarized next to the initial site of depolarization, and the potential will increase (i.e., hyperpolarize) with distance away from the initial site of depolarization until the membrane potential is equal to the resting potential. This is known as electrotonic transmission. An action potential can be propagated only if sufficient current travels down the cell to depolarize the adjacent membrane below the threshold in membrane potential. A new action potential will begin only if the membrane potential of the adjacent membrane is depolarized past the threshold.

The ionic current responsible for depolarizing the membrane and propagating the action potential can travel through the cytoplasm or across the plasma membrane. The current moves along a potential difference in a manner described by Ohm's Law:

I = -E/R[prime] = -EG (1)


I is current density (in A [m.sup.-2])

E is potential (in V)

R[prime] is the specific resistance (in [Omega] [m.sup.2])

G is the specific conductance (in siemens per [m.sup.2] (S [m.sup.-2]) or [[Omega].sup.-1] [m.sup.-2]).

The magnitude of depolarization of the adjacent membrane depends on the amount of current traveling through the cytoplasm, which in turn depends on the relative resistances of the cytoplasm and the membrane. In order to select for the movement of the ionic current through the cell from one end to the other, instead of through the membrane and outside the cell (which would negate the depolarizing effect of the ionic current), the resistance of the cytoplasm must be low and the resistance of the plasma membrane must be high (like an insulated wire). Thus, fast action potentials propagate along nerve cells whose cytoplasmic resistances have been lowered by making their diameters large and whose plasma membrane resistance has been increased by surrounding the axon with a high-resistance myelin sheath. Thus, the difference in propagation velocity between various excitable cells depends on their structure. As in excitable cells in animals, the action potential in characean cells is transmitted from cell to cell (Sibaoka & Tabata, 1981; Spanswick 1974b; Spanswick & Costerton, 1967; Tabata, 1990).

Characean internodal cells exhibit a response to electrical stimulation that is similar to the contraction response skeletal muscles display following an electrical stimulation by nerve cells. In both cases, the response is nicknamed E-C coupling. In animal cells, it refers to excitation-contraction coupling, where electrical excitation causes muscle contraction (Ebashi, 1976). In characean cells, E-C coupling refers to the fact that electrical stimulation causes the cessation of protoplasmic streaming (Findlay, 1959; Hill, 1941; Hormann, 1898; Kishimoto & Akabori, 1959).

The protoplasm of characean cells constantly moves around the periphery of the cell like a rotating belt at a rate of [10.sup.-4] m [s.sup.-1], in a process known as protoplasmic streaming (Allen & Allen, 1978; Corti, 1774; Ewart, 1903; Goppert & Cohn, 1849; Kamiya, 1959, 1981; Kamiya & Kuroda, 1956b; Shimmen, 1988; Shimmen & Yokota, 1994). Protoplasmic streaming, which is driven by the same interactions between actin and myosin that cause contraction in muscles, allows the mixing and transport of essential molecules through the protoplasm of large cells where diffusion would be limiting.

The time it takes for the average particle to diffuse a given distance through a cell can be calculated using Einstein's random walk equation (Berg, 1993; Einstein, 1926; Perrin, 1923; Pickard, 1974):

t = [x.sup.2]/(2D) (2)


t is the time (in s)

x is the average distance the particles move (in m)

D is the diffusion coefficient (in [m.sup.2] [s.sup.-1]).

Note that equation 2 describes the simple case where diffusion is restricted to one dimension. Diffusion can also be described in two dimensions (x and y) where t = [r.sup.2]/(4D) and [r.sup.2] = [x.sup.2] + [y.sup.2]. In three dimensions (x, y, and z), t = [r.sup.2]/(6D) and [r.sup.2] = [x.sup.2] + [y.sup.2] + [z.sup.2] (Berg, 1993).

According to the above equation, the time it takes for a particle to diffuse a given distance is governed only by its diffusion coefficient. The diffusion coefficient of a spherical particle in solution depends on the thermal motion of the particle; consequently, the diffusion coefficient is proportional to temperature. Boltzmann's Constant (k, in J [K.sup.-1]) is the coefficient of proportionality that relates the energy of the particle to the temperature. The kinetic energy [(1/2)m[v.sup.2]] of a particle moving in three dimensions is a consequence of the thermal motion of the particle and is equal to (3/2)kT where T is the absolute temperature (in K). The velocity of a particle of mass [m.sub.j] (in kg) is equal to [(3kT/[m.sub.j]).sup.1/2]. If we consider that the particle is large compared with water, then we can use the equations of fluid mechanics to describe the movement of the particle through an aqueous environment. Thus, the movement of the particle depends on the hydrodynamic radius of the particle ([r.sub.H], in m) and the viscosity of the solution ([Eta], in Pa s). Formally, the diffusion coefficient D is given by the Stokes-Einstein equation:

D = kT/(6[Pi][r.sub.H][Eta]) (3)


D is the diffusion coefficient (in [m.sup.2] [s.sup.-1])

k is Boltzmann's Constant (1.38 x [10.sup.-23] J [K.sup.-1])

T is the absolute temperature (in K)

[r.sub.H] is the hydrodynamic radius (in m)

[Eta] is the viscosity of the solution (in Pa s).

If we assume that the viscosity of the fluid phase of the cytoplasm is 0.004 Pa s (Luby-Phelps et al., 1986) and that most small metabolites have a hydrodynamic radius between [10.sup.-10] and [10.sup.-9] m, then most diffusion coefficients will be between 5 x [10.sup.-11] and 5 x [10.sup.-10] [m.sup.2] [s.sup.-1] at 298 K. Thus, a "typical" metabolite will take between 25 and 250 ms to diffuse all the way across a 5 x [10.sup.-6] m cell, but it will take between [10.sup.3] and [10.sup.4] s (2.8 h) to diffuse across a [10.sup.-3] m diam. characean internodal cell and [10.sup.7] and [10.sup.8] s (4 months) to diffuse along the long axis of a 10 x [10.sup.-2] m long characean internodal cell. Diffusion is thus limiting in large cells (i.e., slower than the rates of enzymatic reactions), and mixing by protoplasmic streaming (i.e., convection) becomes necessary. In general, the larger the cell, the more organized the protoplasmic streaming.

In the natural world, cessation of streaming results not from electrical excitation but from the mechanical stimulation of internodal cells by a predator or other objects such as falling sticks. This mechanical stimulation generates a depolarization of the plasma membrane that is known as a receptor potential (Kishimoto, 1968). The receptor potential is an amplification mechanism whereby the minuscule mechanical energy of the tactile stimulus is transduced by the receptor of the stimulus (in this case a mechanoreceptor) into electrical energy that is amplified in proportion to the magnitude of the initial stimulus. (Energy is not created from this amplification process but is released in the form of ionic currents from the electrical energy already stored across the cell membrane in the form of a membrane potential.) The receptor potential usually lasts as long as the stimulus is present and can be considered an electrical replica of the stimulus. However, the stimulus must be given rapidly enough or the receptor shows a slow decrease in its sensitivity to the stimulus, known as accommodation (Kishimoto, 1968; Staves & Wayne, 1993). The actin- or tubulin-based cytoskeleton appears not to be involved in the function of this mechanoreceptor (Staves & Wayne, 1993); however, the involvement of a membrane skeleton (Faraday & Spanswick, 1993) has not been ruled out.

The receptor potential is not self-perpetuating, and thus the depolarization due to the receptor potential decreases with distance away from the activated receptor. [The theoretical description of how potentials and currents spread through cells, known as "cable theory," was originally worked out by Lord Kelvin (1855; Wheatstone, 1855) to describe the electrical properties of the transatlantic telegraph cable. He showed that the potential drops linearly along an insulated cable placed between a battery and ground just like the temperature drops across a substance placed between a heat source and a heat sink.] If the stimulus is great enough and fast enough to cause the membrane potential to depolarize below a certain threshold level, an action potential will be elicited. An action potential is a large transient depolarization of the membrane potential that is self-perpetuating (i.e., regenerative) and thus allows the rapid transmission of information over long distances without any loss of signal strength (information). Thus, receptor potentials are useful for signal transduction within a single small cell, and action potentials are necessary for signal transmission in a giant cell or between cells.

The action potential generated in one area of a characean cell is responsible for causing the cessation of protoplasmic streaming throughout the cell (Sibaoka & Oda, 1956). When streaming stops, the outer layer of the flowing protoplasm gels (i.e., forms cross-bridges with the actin cables) and prevents any leakage of protoplasm that may occur as a result of a small-animal attack (Kamitsubo et al., 1989; Kamitsubo & Kikuyama, 1992). Moreover, the stimulated cell may become isolated from the neighboring cells since the intercellular passage of substances through small tubes known as plasmodesmata is also inhibited. The cessation of streaming inhibits transport through the plasmodesmata indirectly since, in the absence of streaming, unstirred layers form around the openings of the plasmodesmata and arrival of substances at the pore becomes diffusion limited (Ding & Tazawa, 1989). The cessation of cytoplasmic streaming has no effect on plasmodesmatal transport in small cells where diffusion is not limiting (Tucker, 1987).

III. Recording the Voltage Changes During an Action Potential

The action potential in characean internodal cells can be observed using simple electrophysiological techniques (Fig. 4; Brooks & Gelfan, 1928; Umrath, 1930, 1932, 1934, 1940). According to Alan Hodgkin (1951),

The most satisfactory way of recording the electrical activity of a living cell membrane is to insert a small electrode into the interior of the cell and to measure the potential (i.e voltage) of this electrode with reference to a second electrode in the external medium. This method was first employed in plant cells (see Osterhaut, 1931) and has now been widely used in animal tissues.

When a glass microcapillary electrode is placed into the vacuole and the reference electrode is placed in the external medium, an action potential is observed following stimulation. The action potential appears to be composed of two components: a fast and a slow one (Fig. 5; Findlay, 1970; Findlay & Hope, 1964a; Kishimoto, 1959; Shimmen & Nishikawa, 1988). If we insert two microcapillary electrodes in the cell, we can resolve that these two components are the result of two action potentials; a fast one that occurs across the plasma membrane and a slow one that occurs across the vacuolar membrane (Findlay & Hope, 1964a). The average resting potentials across the plasma membrane and vacuolar membrane are -0.180 V and -0.010 V, respectively. [Note: In both cases the potential on the exoplasmic side of the membrane (E-space) is considered to be zero by convention and the protoplasmic side of the membrane (P-space), i.e. the side that is facing the cytosol, is negative.]

During an action potential, the plasma membrane depolarizes to approximately 0 V and the vacuolar membrane hyperpolarizes to approximately -0.050 V. The changes in the membrane potential, according to the Goldman-Hodgkin-Katz Equation, are due to the ionic currents that flow as a consequence of a change in the membrane permeability of each ion.

The change in membrane permeability that occurs during an action potential can be visualized by measuring the specific conductance of the membrane. The specific conductance is an electrical measure of the overall membrane permeability to all ions. The specific conductances of the plasma membrane and vacuolar membrane at rest are 0.83 siemens [m.sup.-2] (S[m.sup.-2]) and 9.1 S [m.sup.-2], respectively. The specific conductances change with time during an action potential (Fig. 6). The peak conductances during the action potential of the plasma membrane and vacuolar membrane are 30 S [m.sup.-2] and 15 S [m.sup.-2], respectively (Cole & Curtis, 1938; Findlay & Hope, 1964a; Oda, 1962). In the squid giant axon, the specific conductance of the plasma membrane increases from 10 S [m.sup.-2] to 400 S [m.sup.-2] during an action potential (Cole & Curtis, 1939). In both Nitella and squid, the specific conductance of the plasma membrane increases approximately 40 times during an action potential.

While the specific conductance is an important measure of membrane permeability, it does not tell us which ions are permeating the membrane and carrying the current that leads to the action potential. Next, we will determine which ions are responsible for carrying the currents that cause the membrane voltage changes that characterize the action potential.

IV. The Ionic Basis of the Resting Potential

Before we can understand the ionic basis of the action potential, we must first understand the ionic basis of the resting potential and ask, How do the ion concentrations in the cell and extracellular milieu affect membrane potential? The electrical potential across a membrane is determined to a large extent by the difference in ion concentrations across the membrane. Therefore, it is important to know the concentrations of the major ions on each side of a membrane. The concentrations of [Cl.sup.-], [Na.sup.+], [K.sup.+], and [Ca.sup.2+] in the external medium, protoplasm, and cell sap of characean cells as reported by Lunevsky et al. (1983) are given in Table I.

As a comparison, the concentrations of these ions in the protoplasm and the extracellular milieu of a squid axon are also given (Eckert et al., 1988). When we compare the characean internodal cell to the squid axon, we see first that the plant cell has three compartments that bathe two excitable membranes, whereas the animal cell has only two compartments that bathe one excitable membrane. This very fact makes the axon a much simpler system to study since it is geometrically similar to the transatlantic telegraph cable, thus making cable theory easily applied to the analysis of the results. This is the reason that Kenneth Cole and Howard Curtis (1939) began studying the giant squid axon rather than continue with characean intemodal cells. Secondly, we see that the [Na.sup.+] concentration in the external medium is drastically different in the two cell types.

The difference in the concentration of each ion across a differentially permeable membrane creates the driving force for diffusion across the membrane. As each permeant cation diffuses across the membrane, it leaves behind a negative charge (e.g., protein with ionized carboxyl groups) that will tend to attract the cation back to the original side. Thus, there is a chemical force that causes the cations to move from high concentrations to low concentrations and at the same time sets up an electrical force that tends to move the cations back. Because the membrane is permeable to some ions (e.g., [K.sup.+]) and impermeable to others (e.g., proteins), at equilibrium there is no net movement of charge and the chemical force equals the electrical force (see Appendix D). There is thus a stable electrical potential that results from the initial uneven distribution of ions, as was shown by Leonor Michaelis (1925) using dried collodion and apple skins as "the prototype of what we will call a semipermeable membrane." The unequal distribution of ions thus gives rise to a transmembrane potential difference that is electrically equivalent to a battery.

The unequal distribution of charge is only possible because the nonconducting lipid bilayer that separates two conducting aqueous solutions acts as a capacitor, that is, a component that has the capacity to separate charges (Appendix C). Otherwise, the membrane potential difference (i.e., the battery) would eventually run down. A capacitor is a component that resists changes in voltage when current flows through it (much like a pH buffer resists changes in pH). The specific membrane capacitance is a measure of how many charges (ions) must be transferred from one side of the membrane to the other side either to set up or to dissipate a given membrane potential. The specific membrane capacitance of all membranes is approximately 0.01 F [m.sup.-2] (Cole, 1970; Cole & Cole, 1936a, 1936b; Cole & Curtis, 1938; Curtis & Cole, 1937; Dean et al., 1940; Findlay, 1970; Fricke, 1925; Fricke & Morse, 1925; Williams et al., 1964). Using this value, it is possible to calculate the minimum number of ions that must diffuse across the membrane in order to establish or dissipate a membrane potential using the following relation:


[q.sub.j] = -([C.sub.m] [E.sub.m])/([z.sub.j]e) (4)


[q.sub.j] is the number of ions that diffuse across a membrane per unit area (in ions [m.sup.-2])

[C.sub.m] is the specific membrane capacitance (0.01 F [m.sup.-2] = 0.01 C [V.sup.-1][m.sup.-2])

[E.sub.m] is the membrane potential set up by the diffusion of ions (in V)

[z.sub.j] is the valence of the ion

e is the elementary charge (1.6 x [10.sup.-19] C [ion.sup.-1]) [q.sub.j][z.sub.j]e is equal to the charge density (in C [m.sup.-2]).

Using the equation for membrane capacitance (4) and the equilibrium potentials that we will calculate below, we will see that, at equilibrium, the initial concentrations change by less than 0.001% after the establishment of an equilibrium potential (Plonsey & Barr, 1991). This is important to ensure that there is no violation of the principle of electroneutrality, which states that in a volume greater than a given size (e.g., macroscopic dimensions) the number of positive charges must equal the number of negative charges. Electroneutrality is an outcome of the fact that any net charge sets up an electric field that tends to attract oppositely charged particles (as described by Coulomb's Law) that consequently restore the net charge of the volume to zero.

As a consequence of a membrane capacitance, and the diffusion of ions across a differentially permeable membrane, an equilibrium potential (or Nernst potential) is established (Nernst, 1888, 1889). The resultant equilibrium potential for each ion species is described by the Nernst Equation:

[E.sub.j] = (RT/[z.sub.j]F) ln ([n.sub.e]/[n.sub.p]) (5)


[E.sub.j] is the equilibrium potential for ion j (in V) on the protoplasmic side of the membrane, assuming the potential of the exoplasmic side is 0 V

R is the gas constant (8.3l J [mol.sup.-1] [K.sup.-1])

T is the absolute temperature (in K)

[z.sub.j] is the valence of ion j

F is the Faraday Constant (9.65 x [10.sup.4] coulombs [mol.sup.-1])

[n.sub.e] and [n.sub.p] are the concentrations of a given ion on the exoplasmic and protoplasmic sides of the membrane, respectively (in mol [m.sup.-3]). We are (simply but wrongly) assuming that the activity coefficients of the ions are identical and equal to 1 on both sides of the membrane. See Appendix D for the derivation of the Nernst Equation.
Table II
The equilibrium potential (in V) of each ion across the plasma membrane and
vacuolar membrane of a characean internodal cell and the plasma membrane of a
squid nerve.

 Characean internodal cell Squid nerve
 Plasma membrane Vacuolar membrane Plasma membrane

[Cl.sup.-] 0.103 -0.051 -0.026
[Na.sup.+] -0.100 0.049 0.075
[K.sup.+] -0.180 -0.002 -0.075
[Ca.sup.2+] 0.059 0.121 0.118

The equilibrium potentials for each ion across the plasma membrane and the vacuolar membrane calculated from the Nernst Equation (at 298 K) are given in Table II. The equilibrium potentials across the plasma membrane of a squid axon are given for comparison.

The equilibrium potentials of all the ions diffusing across a membrane contribute to the resting membrane potential. David Goldman (1943) and Hodgkin and Katz (1949) showed that at equilibrium the net flow of all ions through the membrane is zero and the equilibrium potential is determined by the permeability of the membrane to a given ion ([P.sub.j]) according to the following equation known as the Goldman-Hodgkin-Katz Equation:

[E.sub.d] = (RT/F) ln [P.sub.K] [[K.sub.e]] + [P.sub.Na] [[Na.sub.e]] + [P.sub.Cl] [[Cl.sub.p]]/[P.sub.K] [[K.sub.p]] + [P.sub.Na][[Na.sub.p]] + [P.sub.Cl][[Cl.sub.e]] (6)


[E.sub.d] is the diffusion potential (in V) on the protoplasmic side of the membrane, assuming the potential of the exoplasmic side is O V

R is the gas constant (8.31 J [mol.sup.-1] [K.sup.-1])

T is the absolute temperature (in K)

F is the Faraday Constant (9.65 x [10.sup.4] coulombs [mol.sup.-1])

[P.sub.K], [P.sub.Na], and [P.sub.Cl] are the permeability coefficients of [K.sup.+], [Na.sup.+], and [Cl.sup.-] ions, respectively (in m [s.sup.-1])

[K.sub.e], [Na.sub.e], and [Cl.sub.e] are the concentrations of [K.sup.+], [Na.sup.+], and [Cl.sup.-] on the exoplasmic side of the membrane (in mol [m.sup.-3])

[K.sub.p], [Na.sub.p], and [Cl.sub.p] are the concentrations of [K.sup.+], [Na.sup.+], and [Cl.sup.-] on the protoplasmic side of the membrane (in mol [m.sup.-3]). See Appendix E for the derivation of the Goldman-Hodgkin-Katz Equation.

The resting potential of the plasma membrane of characean internodal cells and squid axons is approximately -0.18 V and -0.075 V, respectively, indicating that for both cell types [P.sub.K] [is much greater than] [P.sub.Na] [is greater than] [P.sub.Cl] and the membrane potential is determined to a large extent by the passive diffusion of [K.sup.+] (MacRobbie, 1962; Spanswick et al., 1967). The greater the permeability to [K.sup.+], the more hyperpolarized the membrane will tend to be. As we will see later, a hyperpolarized membrane is a stable membrane, compared to a depolarized membrane. Thus increasing the [K.sup.+] permeability has a stabilizing effect on the membrane. Notice that when [P.sub.K] [is much greater than] [P.sub.Na] [is greater than] [P.sub.Cl], the Goldman-Hodgkin-Katz Equation reduces to the Nernst Equation for [K.sup.+] (equation 2).

If the plasma membrane potential was only a consequence of the diffusion of [K.sup.+] from the protoplasm ([approximately equal to]100 mol [m.sup.-3]) to the extracellular solution (0.1 tool [m.sup.-3]), the cell would have a membrane potential of -0.18 V. According to equation 4, 1.125 x [10.sup.16] [K.sup.+] [m.sup.-2] would have to diffuse across the plasma membrane in order to "charge the capacitance" of the membrane to -0.18 V. If we assume that the typical characean internodal cell is a cylinder 0.5 x [10.sup.-3] m in diameter (d) and 3 x [10.sup.-2] m long (l), it has a surface area ([Pi]dl) of 4.7 x [10.sup.-5] [m.sup.2]. Thus, 5.3 x [10.sup.11] [K.sup.+] ions must diffuse across the plasma membrane of one cell to make a membrane potential of -0.18 V. A cylindrical internodal cell with the above dimensions will have a volume ([Pi][r.sup.2]l) of 5.89 x [10.sup.-9] [m.sup.3]. Thus, there were initially 5.89 x [10.sup.-7] mol [K.sup.+] in the cell. Using Avogadro's Number, we see that there were initially 3.5 x [10.sup.17] [K.sup.+] in the cell. Thus, only [(5.3 x [10.sup.11])/(3.5 x [10.sup.17])] x 100% = 0.00015% of the initial [K.sup.+] ions must diffuse out of the cell in order to charge the capacitance of the membrane and create a membrane potential of -0.018 V.

A closer look at the Goldman-Hodgkin-Katz Equation shows that when [P.sub.Na] and [P.sub.Cl] are nonzero, the resting potential will be less than that predicted by the Nernst potential for [K.sup.+]. However, the plasma membranes of both cell types have electrogenic pumps that pump out cations at the expense of ATP to help generate a more negative membrane potential. Characean cells have a [H.sup.+]-ATPase (Spanswick, 1974a, 1980, 1981) and squid nerves have a [Na.sup.+]/[K.sup.+] ATPase (Eckert et al., 1988). The membrane potential of the characean plasma membrane is usually between -0.18 and -0.30 V. The characean plasma membrane has three stable states. The K-state, where the membrane potential (more positive than -0.18 V) is determined predominantly by the diffusion of [K.sup.+]; the pump state, where the electrogenic [H.sup.+]-pumping ATPase contributes to the resting potential of approximately between -0.18 and -0.30 V; and a third stable state which occurs at high pH where the permeability to [H.sup.+] or O[H.sup.-] becomes so large that the diffusion potential is determined by the permeability coefficients for [H.sup.+] or O[H.sup.-] ([P.sub.H] or [P.sub.OH]; Beilby & Bisson, 1992; Bisson & Walker, 1980, 1981, 1982). While the plasma membranes of characean cells in the pump state and high pH state are excitable, and cells in the [K.sup.+]-state are inexcitable, we will only talk about the action potential in cells that are just at the interface between the [K.sup.+]-state and the pump state (-0.18 V), since it has been shown that the action potential is mostly due to the changes in the conductance of the passive diffusion channels and not the electrogenic [H.sup.+]-pumping ATPase (Kishimoto et al., 1985).

The vacuolar membrane of characean cells also has an electrogenic [H.sup.+]-pumping ATPase as well as an electrogenic [H.sup.+]-pumping pyrophosphatase (Shimmen & MacRobbie, 1987; Takeshige et al., 1988; Takeshige & Tazawa, 1989) capable of hyperpolarizing the membrane potential to values greater than -0.25 V, yet the vacuolar membrane potential ([approximately equal to] -0.01 V) is similar to the equilibrium potential for [K.sup.+] and [Cl.sup.-], indicating that there is a large permeability to [K.sup.+] and [Cl.sup.-] that effectively short-circuits the pumps (Rea & Sanders, 1987; Tyerman, 1992).
Table III

The electrochemical potential (in V) of each ion across the plasma membrane
and vacuolar membrane of a characean internodal cell and the plasma membrane
of a squid nerve

 Characean internodal cell Squid nerve

 Plasma membrane Vacuolar membrane Plasma membrane

[Cl.sup.-] -0.283 0.041 -0.049
[Na.sup.+] -0.080 -0.059 -0.150
[K.sup.+] 0 -0.008 0
[Ca.sup.2+] -0.239 -0.131 -0.193

If we assume that an ion is moving from a P-space (initial state) to an
E-space (final state), we can tell whether the movement is spontaneous
(passive, or exergonic) in this direction by multiplying the electrochemical
potential with the product of the valence of the ion times the Faraday (zF).

When the product of the electrochemical potential and zF is negative, cations
and anions are accumulated passively (spontaneously) and efflux is active.

When the product of the electrochemical potential and zF is positive, cations
and anions are accumulated actively and efflux is passive (spontaneous).

In reality, active transport usually results from the energy available from
the electrochemical gradient of [H.sup.+] established by the primary
[H.sup.+]-pumping ATPase. Secondary transporters then move the actively
accumulated ions across the membrane.

The difference between the resting membrane potential ([E.sub.m]) and the equilibrium potential for an ion ([E.sub.j]) across that membrane, known as the electrochemical potential, is an indication of whether or not that ion is in passive equilibrium, actively taken up, or actively extruded. Assuming that the membrane potentials across the characean plasma membrane and vacuolar membrane are -0.18 V and -0.01 V, respectively, the electrochemical potentials ([E.sub.m] - [E.sub.j]) across each membrane can be calculated and are given in Table III. The electrochemical potentials across the plasma membrane of a squid axon are given for comparison (assuming [E.sub.m] [is approximately equal to] -0.075).

At the resting potentials of the characean and squid plasma membrane, [K.sup.+] is passively (spontaneously) distributed across the plasma membrane [zF([E.sub.m] - [E.sub.K]) = 0]; [Cl.sup.-] is actively (not spontaneously) accumulated against its electrochemical potential gradient [zF([E.sub.m] - [E.sub.Cl]) [is less than] 0] and moves passively out of the cell; [Na.sup.+] is actively extruded against its electrochemical potential gradient and moves passively into the cell [zF([E.sub.m] - [E.sub.Na]) [is less than] 0]; and [Ca.sup.2+] is also actively extruded against its electrochemical potential gradient [zF([E.sub.m] - [E.sub.Ca]) [is less than] 0] and moves passively into the cell. On the other hand, at the resting potential of the characean vacuolar membrane, [Cl.sup.-], [K.sup.+], [Na.sup.+], and [Ca.sup.2+] are actively extruded from the protoplasm to the vacuole across the vacuolar membrane. The active movement of ions requires energy and is thus an endergonic reaction. The passive movement of ions is an exergonic process which releases energy. This energy can be coupled to endergonic processes to do work, including the cotransport of substances.

In order to better understand the electrophysiology of excitable cells, it helps to draw an equivalent circuit that explains the electrical analogs in the membrane. First, let us assume that at the resting potential, the sum of all ionic currents ([Sigma][I.sub.j], in A [m.sup.-2]) is 0 A. The model put forth by Cole and Curtis (1938) includes the observations that the membrane potential is due to an electromotive force (the equilibrium potential due to the unequal distribution of ions) and is equivalent to a battery that is in series with a conductance (proteinaceous ion channels) and in parallel with a capacitor (as a result of the lipid bilayer). Their model is shown in Fig. 7A and a structural interpretation of the equivalent circuit is given in Fig. 7B.

In order to describe the resting and action potential in giant squid axons, Hodgkin (1964) partitioned the series conductance and electromotive force of the equivalent circuit into a number of conductances (one for [Na.sup.+], one for [K.sup.+], and one for the ions that do not contribute to the action potential--the leak) and a number of electromotive forces due to the equilibrium potentials of each ion.

The contribution of the electromotive force for each ion to the overall membrane potential depends on the ability of that ion to carry current. The fact that the electromotive force and the conductance for an ion are in series means that if the conductance is zero for a given ion, then the electromotive force for that ion will not contribute anything to the membrane potential, even if there is a large electromotive force. Since the conductance for all ions except [K.sup.+] is so small in the resting cell, the membrane potential is essentially equal to [E.sub.K] (the equilibrium potential for [K.sup.+]).

The current density ([I.sub.j], in A [m.sup.-2]) carried by each ion depends on both the specific conductance of the membrane for that ion ([g.sub.j], in S [m.sup.-2]) and the electrochemical potential for that ion ([E.sub.m] - [E.sub.j]). This relationship is just another form of Ohm's Law where the specific membrane conductance for an ion ([g.sub.j]) is equal to the reciprocal of the specific resistance of the membrane to that ion ([r.sub.j], in [Omega] [m.sup.2]).

[I.sub.j] = -[g.sub.j]([E.sub.m] - [E.sub.j]) = -([E.sub.m] - [E.sub.j])/[r.sub.j] (7)


[I.sub.j] is the current density (in A [m.sup.-2]) carried by ion j

[g.sub.j] is the partial specific conductance (in S [m.sup.-2]) of the membrane for ion j

[e.sub.m] is the membrane potential (in V)

[E.sub.j] is the Nernst potential or equilibrium potential (in V) for ion j

[r.sub.j] is the partial specific resistance of the membrane (in [Omega] [m.sup.2]) for ion j.

We use Benjamin Franklin' s convention that positive current is carried by positive charges (Cohen, 1941). So a current carried by [Cl.sup.-] is negative and a current carried by [Na.sup.+] or [K.sup.+] is positive. (Consequently, an inward current is carried by the influx of a cation and the efflux of an anion). At rest the sum of all currents equals zero. We can now use the equivalent circuit of the resting membrane to help us understand the action potential. We will see that there is a change in the membrane potential during an action potential because there is a change in the conductance (or the permeability) of the membrane to certain ions.

V. The Ionic Basis of the Action Potential

The basic principles involved in the generation of an action potential are the same in animal, plant, and fungal cells. The specifics of the action potentials are different and result from the fact that, in general, animal cells live in solutions that are isotonic and are full of ions, while plants and fungi live in dilute solutions that are very close to distilled water. The capability of cells to live in dilute solutions is a consequence of the presence of a rigid extracellular matrix (cell wall) that can support and prevent the lysis of the plasma membrane that otherwise would occur when the osmotic pressure on the two sides of the membrane differ by more than 100 Pa. (Plant and fungal cells can build up pressure differences 1000-10,000 times greater than this value.) Therefore, the "animal type of action potential" is not possible in plant cells (and vice versa), because the ion concentrations surrounding a plant cell are different from those found in the extracellular milieu of animal cells.

Hodgkin and Katz (1949) found that external [Na.sup.+] is required for the action potential of squid axons. Upon stimulation in normal seawater, the squid axon depolarizes from approximately -0.075 V to +0.04 V at the peak of the action potential. However, when the [Na.sup.+] is replaced by choline, both the rate of depolarization and the amplitude of the action potential decreases. Hodgkin and Katz (1949) then proposed the sodium hypothesis, which states that the massive depolarization and overshoot of the membrane potential to positive potentials results from an influx of [Na.sup.+]. Using the radioactive tracer(24)[Na.sup.+], Keynes (1951) then showed that electrical stimulation causes an 18-fold increase in [Na.sup.+] influx. Later it was found that tetrodotoxin (TTX), the deadly poison found in and (mostly) removed from the Japanese puffer fish eaten as sashimi, prevents the action potential by specifically blocking [Na.sup.+] currents in giant axons (Narahashi et al., 1964). Not all animal cells have [Na.sup.+]-based, TTX-inhibited action potentials. The [Na.sup.+]-based action potentials occur only in higher animals. Evolutionarily, they begin to appear with the Coelenterates. The more ancient and ubiquitous action potentials result from "[Ca.sup.2+] spikes" (Hille, 1984, 1992).

The equilibrium potential for [Na.sup.+] ([E.sub.Na]) is not large enough in characean cells to account for the large depolarization that occurs during an action potential (Williams & Bradley, 1968). Upon stimulation, the characean plasma membrane depolarizes to approximately 0 V. While the electrochemical potential of [Na.sup.+] will tend to drive [Na.sup.+] into the cell at the resting potential, it will cease to move passively into the cell once the potential depolarizes to -0.100 V and the electrochemical potential for [Na.sup.+] approaches 0 V. Thus [Cl.sup.-] and [Ca.sup.2+] ions have positive equilibrium potentials and are the only ions that are capable of depolarizing the membrane to 0 V. The cation [Ca.sup.2+] can depolarize the membrane by entering the cell, and the anion [Cl.sup.-] can depolarize the membrane by leaving the cell. Thus, while the action potentials of the squid and characean plasma membrane are similar in terms of the voltage changes, the ions that carry the depolarizing currents are different.

Characean cells have a vacuolar membrane in addition to the plasma membrane. The membrane potential of the vacuolar membrane hyperpolarizes from -0.01 V (protoplasmic side negative) to -0.05 V (protoplasmic side negative) during an action potential. Using similar logic, we see that [Cl.sup.-] is the only current carrier capable of bringing the vacuolar membrane membrane potential to the -0.05 V it attains at the peak of the action potential. In this case, [Cl.sup.-] will move from the vacuole to the protoplasm.

VI. Chloride Efflux Occurs in Response to Stimulation

Using a thermodynamic approach, we have determined that [Ca.sup.2+] and [Cl.sup.-] ions are capable of carrying the current that leads to the change in the plasma membrane potential that occurs during an action potential in characean cells. There are two ions that are candidates for the charge carrier during the action potential, and there were two schools of thought on which was the charge carrier: One thought that [Ca.sup.2+] was important and the other thought that [Cl.sup.-] was important. Hope (1961a, 1961b) and Findlay (1961, 1962), working in Australia, noticed that the magnitude of the depolarization that occurred during an action potential depended on the external [Ca.sup.2+] concentration, where the depolarization increased as the external [Ca.sup.2+] concentration increased, and, further, that external [Ca.sup.2+] was required for the action potential (Findlay & Hope, 1964b). They suggested that the action potential was due to an increase in the permeability to [Ca.sup.2+] and [Ca.sup.2+] was the current-carrying ion. However, using 45[Ca.sup.2+] as a tracer, they were unable to observe any change in 45[Ca.sup.2+] influx (probably due to the difficulty in separating wall-bound 45[Ca.sup.2+] from cytoplasmic 45[Ca.sup.2+]). Thus the role of [Ca.sup.2+] in the action potential remained enigmatic (Hope & Findlay, 1964). Fifteen years later, Hayama et al. (1979) detected a [Ca.sup.2+] influx, again bringing the action of a [Ca.sup.2+] influx into the picture.

On the other hand, Mullins (1962), working in the United States, proposed that the action of [Ca.sup.2+] was to activate the mechanism responsible for [Cl.sup.-] efflux. Gaffey and Mullins (1958), Mullins (1962), and Hope and Findlay (1964) loaded internodal cells with 36[Cl.sup.-] and measured its efflux in the resting cell and following stimulation. They found that there is an increase in [Cl.sup.-] efflux during an action potential. Mailman and Mullins (1966) measured the [Cl.sup.-] efflux using a Ag/AgCl electrode, confirming the data obtained using radioactive tracers and improving on the time resolution from hours using the tracer technique (Hope et al., 1966) to seconds using the electrode technique (Coster, 1966). Typical [Cl.sup.-] efflux values are given in Table IV.
Table IV
[Cl.sup.-] efflux in a characean internodal cell at rest and during an action

 Efflux (mol [m.sup.-2] [s.sup.-1])

Resting cell 1 x [10.sup.-8]
Excited cell 100 x [10.sup.-8]

Given a membrane depolarization of 0.18 V and a specific membrane capacitance of [10.sup.-2] F [m.sup.-2], an increase in the efflux to 1.125 x [10.sup.16] [Cl.sup.-] [m.sup.-2] (= 1.87 x [10.sup.-8] mol [m.sup.-2], using Avogadro's Number as a conversion factor) would be needed to discharge the membrane capacitance and depolarize the membrane to 0 V (equation 4). Assuming that the action potential lasted 1 s, this would be equivalent to an efflux of 1.86 x [10.sup.-8] mol [m.sup.-2] [s.sup.-1]. Thus, the increase in the efflux in response to stimulation is more than enough to overcome the membrane capacitance and account for the depolarization observed during the action potential.

We can estimate the change in membrane permeability to [Cl.sup.-] ([P.sub.Cl]) during excitation using the following formula (Dainty, 1962) based on the Goldman flux equation (Goldman, 1943):

[Mathematical Expression Omitted]


[J.sub.Cl] is the flux of [Cl.sup.-] in (mol [m.sup.-2] [s.sup.-1])

[E.sub.m] is the diffusion potential (in V) on the protoplasmic side of the membrane, assuming the potential of the exoplasmic side is 0 V.

R is the gas constant (8.31 J [mol.sup.-1] [K.sup.-1])

T is the absolute temperature (in K)

F is the Faraday Constant (9.65 x [10.sup.4] coulombs [mol.sup.-1])

[z.sub.Cl] is the valence of [Cl.sup.-] (-1)

[P.sub.Cl] is the permeability coefficient of the membrane to [Cl.sup.-] (in m [s.sup.-1])

[[n.sub.Cl].sup.o] is the concentration of [Cl.sup.-] on the exoplasmic side of the membrane (in mol [m.sup.-3])

[[n.sub.Cl].sup.i] is the concentration of [Cl.sup.-] on the protoplasmic side of the membrane (in mol [m.sup.-3]). See Appendix E for a derivation of the Goldman-Hodgkin-Katz Equation.

Given the observed fluxes of [Cl.sup.-] and assuming that the cytosolic and extracellular concentrations of [Cl.sup.-] remain constant at 22 and 0.4 mol [m.sup.-3], respectively, and the membrane potential is -0.18 V, we find that the average permeability coefficient of the membrane for [Cl.sup.-] rises approximately 100-fold from 4.5 x [10.sup.-10] m [s.sup.-1] to 4.5 x [10.sup.-8] m [s.sup.-1] during an action potential.

We can also relate the [Cl.sup.-] flux ([J.sub.Cl]) measured chemically to the conductance of the membrane ([g.sub.Cl]) for [Cl.sup.-] measured electrically using the following equation (Hodgkin, 1951; Hodgkin & Keynes, 1955; Hope & Walker, 1961; Keynes, 1951; Linderholm, 1952; Smith, 1987; Teorell, 1953; Ussing, 1949a, 1949b; Ussing & Zerahn, 1951):

[g.sub.Cl] = ([[z.sub.Cl].sup.2][F.sup.2]/RT)[J.sub.Cl] (9)


[g.sub.Cl] is the partial specific membrane conductance for [Cl.sup.-] (in S [m.sup.-2])

[z.sub.Cl] is the valence of [Cl.sup.-] (-1)

F is the Faraday Constant (9.65 x [10.sup.4] coulombs [mol.sup.-1])

R is the gas constant (8.31 J [mol.sup.-1] [K.sup.-1])

T is the absolute temperature (in K)

[J.sub.Cl] is the unidirectional flux of [Cl.sup.-] (in mol [m.sup.-2] [s.sup.-1]).

The result is only approximate since the equation only holds when the [Cl.sup.-] ions move across the membrane independently of each other and the membrane potential is at the equilibrium potential for [Cl.sup.-] (i.e., +0.103 V). Many ions probably move through long narrow pores and interact with each other, invalidating the use of this equation (MacRobbie, 1962). Moreover, the membrane potential never reaches the equilibrium potential for [Cl.sup.-]. However, using equation 9, we can approximate the partial specific conductance of the resting membrane ([g.sub.Cl] = 0.037 S [m.sup.-2]) and of the excited membrane ([g.sub.Cl] = 3.7 S [m.sup.-2]). Thus [g.sub.Cl] contributes approximately 4% to the overall conductance of the resting membrane and about 12% to the overall conductance of the excited membrane.

Following the massive depolarization, the membrane repolarizes again due to the efflux of [K.sup.+]. This is true for axons as well as for characean cells (Hodgkin & Huxley, 1953; Keynes, 1951). [K.sup.+] efflux has been determined by measuring 32[K.sup.+] fluxes or by using flame photomerry (Kikuyama et al., 1984; Oda, 1976; Spear et al., 1969; Spyropoulos et al., 1961). The [K.sup.+] efflux is equal to the [Cl.sup.-] efflux. They are both 1.8 x [10.sup.-5] mol [m.sup.-2] [impulse.sup.-1] (Oda, 1976). Therefore, during excitation, [P.sub.K] is approximately 2.3 x [10.sup.-5] m [s.sup.-1] (calculated using equation 8). This is 1000 times greater than the resting [P.sub.K] (Gaffey & Mullins, 1958; Smith, 1987; Smith & Kerr, 1987; Smith et al., 1987a, 1987b). The necessity of a [K.sup.+] efflux for the subsequent repolarization is supported by the observation that a [K.sup.+]-channel blocker, tetraethylammonium (TEA) causes a prolongation of the action potential in some but not all cells (Belton & Van Netten, 1971; Shimmen & Tazawa, 1983a; Staves and Wayne, 1993; Tester, 1988).

The massive efflux of [Cl.sup.-] and [K.sup.+] from the cell is accompanied by water loss and a transient decrease in turgor (Barry, 1970a, 1970b). The water loss results in a transient change in the volume of the cell that can be detected with a position transducer (Kishimoto & Ohkawa, 1966) and by laser interferometry (Sandlin et al., 1968).

Now we can begin to account for the membrane potential changes that occur during a characean action potential by the movement of [Cl.sup.-] and [K.sup.+]. We can make an equivalent circuit to help us visualize the changes in membrane potential that results from the changes in conductance.

Figure 10 shows an equivalent circuit of a characean cell. The resistors symbolize the channels that provide the conducting pathway for a given ion. The batteries represent the electomotive force for each ion due to the unequal distribution of ions (i.e., Nernst potential or equilibrium potential). The capacitor represents the ability of the lipid bilayer to separate charge. The plasma membrane has an electrogenic [H.sup.+]-pumping ATPase with an electromotive force of -0.46 V (due to the hydrolysis of ATP; Blatt et al., 1990). The potential difference across the plasma membrane (approximately -0.180 V, inside negative) is defined as the membrane potential of the protoplasmic side minus the membrane potential of the exoplasmic side (defined as 0 V).

The vacuolar membrane has a negative potential difference that is also defined as the membrane potential of the protoplasmic side (-0.010 V) minus the membrane potential of the exoplasmic side (defined as 0 V). The membrane potential of the vacuole is determined to a large extent by the [K.sup.+]-dependent electromotive force since the [K.sup.+] conductance is so high. This conductance effectively shunts the [H.sup.+]-pumping ATPase and pyrophosphatase on the vacuolar membrane so they do not contribute significantly to the vacuolar membrane potential. Note that the potential differences across the plasma membrane and the vacuolar membrane are oppositely directed.

VII. Application of a Voltage Clamp to Relate Ions to Specific Currents

Up until now we have been talking about experimental setups where the current is applied as a stimulus and we record the changes in membrane potential. This experiment can be done in reverse by using a voltage clamp, which was designed by K. S. Cole in 1949 to measure the current that flows when the membrane potential is "clamped" to a given voltage (Sherman-Gold, 1993; Standen et al., 1987). No net current flows when the membrane potential is clamped to the resting potential, whereas there is a current flow when the membrane potential is clamped to potentials less negative than the "threshold potential for excitation." When the membrane potential remains constant, the change in the amount of current that flows is a measure of the conductance. The voltage clamp is superior to the traditional current clamp in that it can rapidly clamp the membrane and allow one to distinguish the "instantaneous" currents that flow from the discharge of the membrane capacity (capacity currents) from the time-dependent ionic currents (Hodgkin et al., 1952; Kishimoto, 1964).

The pioneering work on voltage clamping the giant squid axons by Alan Hodgkin, Andrew Huxley, and Bernard Katz established the classical principles of membrane biophysics (Hille, 1984, 1992). When Hodgkin and his colleagues clamped the membrane potential at values less negative than the threshold potential (-0.056 V), they saw a time-dependent current. First there was an inward current and then this was replaced by an outward current. They noticed that when they removed the [Na.sup.+] from the external medium, the early inward current disappeared but the late outward current remained. By subtracting the current trace obtained in the absence of [Na.sup.+] from the one obtained in the presence of [Na.sup.+], they obtained a difference trace that represented the [Na.sup.+] current. They assumed that the current trace obtained in the absence of [Na.sup.+] represented the [K.sup.+] current. This was confirmed by removing the natural protoplasm by perfusion and substituting it with either [K.sup.+]-containing or [K.sup.+]-free fluid and observing that the late current disappeared when they used [K.sup.+]-free fluid. By dividing the magnitude of the [Na.sup.+] current or the [K.sup.+] current at a given time by the membrane potential which was held constant by the clamp, they could calculate the change in [Na.sup.+] and [K.sup.+] conductances with time that occurred during an action potential (Hodgkin, 1964).

Hodgkin and his colleagues found that the resting membrane potential results from the fact that [g.sub.K] [is greater than] [g.sub.Na] [is greater than] [g.sub.Cl]. The action potential occurs after a stimulus causes an increase in the conductance to [Na.sup.+] ([g.sub.Na]). Thus, upon stimulation, a substantial amount of [Na.sup.+] moves down its electrochemical potential gradient from the external medium into the axoplasm. This inward current causes a shift in the membrane potential toward the [Na.sup.+] equilibrium potential (i.e., depolarization). The membrane potential consequently shifts away from the [K.sup.+] equilibrium potential so that the electrochemical potential gradient now drives an increased efflux of [K.sup.+]. This is accompanied by an increase in the conductance to [K.sup.+] ([g.sub.K]). The increased conductance for [K.sup.+] will repolarize the membrane back to its resting level. The repolarization of the membrane to its resting level due to [K.sup.+] efflux is facilitated by the time-dependent decrease in [g.sub.Na] (i.e., inactivation). Since the [K.sup.+] efflux overlaps the [Na.sup.+] influx, the membrane never depolarizes all the way to [E.sub.Na]. The peak depolarization is somewhere between [E.sub.K] and [E.sub.Na] and can be predicted from the Goldman-Hodgkin-Katz Equation using the time-dependent relative permeabilities and concentrations of [K.sup.+] and [Na.sup.+] (see Eckert et al., 1988; Junge, 1981; Matthews, 1986).

Lunevsky et al. (1983), working in the former Soviet Union, used a voltage clamp to study the action potential across the plasma membrane of the characean alga Nitellopsis. They inserted one electrode in the protoplasm and one in the medium to measure the membrane potential. The membrane is clamped to the desired voltage by passing just enough current through the cell using Ag/AgCl wires.

Using a step-voltage clamp, where the membrane potential can be varied in a stepwise manner, Lunevsky et al. (1983) obtained a series of current traces that represented current movement through the plasma membrane at each membrane potential. They resolved their data into three currents: the quick transient, the slow transient, and the steady state current (in addition to the leakage current).

The first, quick transient component lasts for several hundred milliseconds. When the membrane is depolarized to -0.05 V it appears as an inward current. It changes from an inward current to an outward current as the membrane potential is clamped to more and more depolarized values. The reversal potential for this current--that is, the voltage where the current is neither inward nor outward ([I.sub.j] = 0 A [m.sup.-2])--is between -0.060 and -0.020 V in artificial pond water (APW). This rapid, transient current could be studied better if we could block the second current, so we'll talk about the second current and then come back to the first.

The second, slow transient current appears when the membrane is depolarized below a threshold between -0.09 and -0.12 V and the maximum peak inward current is seen at potentials 0.01 to 0.02 V more positive than the threshold. The slow transient current exhibits activation-inactivation kinetics that are similar to, although slower than, the [Na.sup.+] current in squid axons. The reversal potential of the slow transient current depends on the external [Cl.sup.-] concentration. When the external [Cl.sup.-] concentration is increased 3.25-fold, from 32 mM to 104 mM, the reversal potential changes from -0.010 V to -0.040 V in a manner completely accounted for by the Nernst Equation, as [Cl.sup.-] is the only ion carrying the current. Further evidence that the second slow transient current is carried by [Cl.sup.-] comes from the observation that this current is inhibited by the well-known Cl-channel blockers, ethacrynic acid and anthracene-9-carboxylic acid. The peak current carried by [Cl.sup.-] ions is between 4 and 7 A [m.sup.-2]. The net flux can be linked to the observed current using the following equation:

[J.sub.Cl] = [I.sub.Cl]/([z.sub.Cl]F) (10)
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Author:Wayne, Randy
Publication:The Botanical Review
Date:Jul 1, 1994
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