This paper develops a simple reaction-kinetic model to describe electrogenic pumping and co- (or counter-) transport of ions. It uses the standard steady-state approach for cyclic enzyme- or carrier-mediated transport, but does not assume rate-limitation by any particular reaction step. Voltage-dependence is introduced, after the suggestion of Läuger and Stark (Biochim. Biophys. Acta 211:458-466, 1970), via a symmetric Eyring barrier, in which the charge-transit reaction constants are written as k12 = ko12 exp(zF delta psi/2RT) and k21 = ko21 exp(-zF delta psi/2RT). For interpretation of current-voltage relationships, all voltage-independent reaction steps are lumped together, so the model in its simplest form can be described as a pseudo-2-state model. It is characterized by the two voltage-dependent reaction constants, two lumped voltage-independent reaction constants (k12, k21), and two reserve factors (ri, ro) which formally take account of carrier states that are indistinguishable in the current-voltage (I-V) analysis. The model generates a wide range of I-V relationships, depending on the relative magnitudes of the four reaction constants, sufficient to describe essentially all I-V datas now available on "active" ion-transport systems. Algebraic and numerical analysis of the reserve factors, by means of expanded pseudo-3-, 4-, and 5-state models, shows them to be bounded and not large for most combinations of reaction constants in the lumped pathway. The most important exception to this rule occurs when carrier decharging immediately follows charge transit of the membrane and is very fast relative to other constituent voltage-independent reactions. Such a circumstance generates kinetic equivalence of chemical and electrical gradients, thus providing a consistent definition of ion-motive forces (e.g., proton-motive force, PMF). With appropriate restrictions, it also yields both linear and log-linear relationships between net transport velocity and either membrane potential or PMF. The model thus accommodates many known properties of proton-transport systems, particularly as observed in "chemiosmotic" or energy-coupling membranes.

Summary. Sudden respiratory blockade has been used to study rapid changes of the resting membrane potential, of intracellular adenosine 5'-triphosphate (ATP) levels, and of pyridine nucleotide reduction in Neurospora crassa. Membrane depolarization occurs with a first-order rate constant of 0.167 sec -1, following a lag period of about 4 sec, at 24 ~ (ambient temperature). This depolarization is several-fold too slow to be directly linked to electron transfer, as judged from the rate of pyridine nucleotide reduction, but has essentially the same rate constant as the decay of ATP. The latter process, however, shows no lag period after the respiratory inhibitor is introduced. Plots of membrane potential versus the intracellular ATP concentration yield saturation curves which are readily fitted by a Michaelis equation, to which is added a constant term representing the diffusion component of membrane potential. Parameters obtained from such fits indicate the maximal voltage which the pump can develop at high ATP levels to be 300 to 350 mV, with an apparent 1(1/2 of 2.0 rr~. The data strongly suggest that an electrogenic ion pump in the plasma membrane of Neurospora is fueled by ATP; comparison of the measured membrane potentials with the energy available from hydrolysis of ATP indicates that two ions could be pumped for each molecule of ATP split.Although the existence of electrogenic ion pumps was postulated about 50 years ago from extracellular studies on plant tissues and on epithelial membranes, their acceptance as bona fide physiological entities did not occur until the past 10 years. During this period proof has been evolving from two quite separate lines of research. First, in certain nerve and muscle preparations, where membrane potential and resistance can be measured with micropipette electrodes, it has been possible to demonstrate a precise quantitative correspondence between the currents (and fluxes) generated by the sodium pump and the voltage and resistance characteristics of the particular membrane [2,18,23,33,51,52]. Related experiments on plant and fungal preparations have given less complete data, but have clearly demonstrated the existence of membrane potentials which are extremely difficult to account for in terms of conventional ion-diffusion processes 21 J. Membrane Biol, 14

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The vacuolar membrane of the yeast Saccharomyces cerevisiae, which is proposed as a system for functional expression of membrane proteins, was examined by patchclamp techniques. Its most conspicuous feature, in the absence of energizing substrates, is a cation channel with a characteristic conductance of -120 pS for symmetric 100 mM KCI solutions and with little selectivity between K+ and Na' (PNa+/PK+ 1) but strong selectivity for cations over anions (PCI-/PK+ < 0.1). Channel gating is voltage-dependent; open probability, P., reaches maximum (-0.7) at a transmembrane voltage of -80 mV (cytoplasmic surface negative) and declines at both more negative and more positive voltages (i.e., to 0 around +80 mV). The time-averaged current-voltage curve shows strong rectification, with negative currents (positive charges flowing from vacuolar side to cytoplasmic side) much larger than positive currents. The open probability also depends strongly on cytoplasmic Ca2+ concentration but, for ordinary recording conditions, is high only at unphysiologically high (21 mM) Ca2+. However, reducing agents such as dithiothreitol and 2-mercaptoethanol poise the channels so that they can be activated by micromolar cytoplasmic Ca2+. The channels are blocked irreversibly by chloramine T, which is known to oxidize exposed methionine and cysteine residues specifically.Invention of patch-clamp techniques in 1976 (1, 2) has opened up a whole new range of biological preparations to direct electrophysiological analysis. Isolated single channel molecules can be studied in micrometer-sized patches of cell membranes, and thylakoid membranes of individual chloroplasts (3), inner and outer membranes of mitochondria (4, 5), and small microbial cells (6) have become readily accessible. This circumstance, particularly when combined with new developments in molecular biology, greatly enhances the utility of electrophysiological studies on microorganisms, which had until recently been restricted to a few fungi (7-10), slime molds (11, 12), and one species of swollen bacteria (13).The yeast Saccharomyces cerevisiae seems particularly advantageous for investigation with patch electrodes, for two reasons: (i) the electrical properties of active transport systems in its plasma membrane can readily be compared with those already described (from measurements with penetrating electrodes) in another ascomycete fungus, Neurospora (14, 15), and (ii) Saccharomyces is becoming a major system for stable expression and manipulation of both animal and plant genes (e.g., see refs. 16-18).Previous patch-clamp studies on Saccharomyces have reported plasma membrane K+ channels that are voltagedependent (19) and generally fit into an emerging pattern of outward-rectifying channels in surface membranes of plants and plant-like cells (20,21). More recently, K+ channels have been described as voltage-gated, opening beyond + 100 mV in wild-type strains of yeast, but at lower voltages in a mutant, pmal-105 (22). Most intriguing, this mutant is defective in the structura...

SUMM1ARY1. Muscles with high intracellular sodium concentrations can extrude sodium into solutions which contain 10 m-equiv/l. of either potassium or rubidium. Potassium or rubidium replaces the extruded intracellular sodium. These cation movements take place equally well when the external anion is chloride or sulphate, though muscles deteriorate if left for long periods in sulphate solutions.2. Measurements of intracellular potentials during extrusion of sodium into solutions containing potassium show:(a) an internal potential more negative than the potassium equilibrium potential (EK); at 200 C the difference is nearly 20 mV.(b) that a difference between the membrane potential and ER is dependent on temperature and is abolished by 10-5 M ouabain.(c) an internal potential which becomes more negative in the presence of 0.1 % cocaine, a concentration of cocaine which substantially increases the membrane resistance to potassium movement.In the absence ofpotassium or rubidium no such hyperpolarization occurs. 3. When muscles extrude into solutions which contain rubidium they have internal potentials which are 10-20 mV more negative than when extruding sodium into corresponding solutions containing potassium.4. Measurements of electrical conductance in the potassium solution suggest that the electrochemical potential difference for potassium ions may be large enough to account for the measured inward potassium movements during sodium extrusion. The reliability of the measurements does not, however, exclude the possibility that some part of the inward potassium movement is chemically linked to outward movement.5. Measurements of membrane conductance in solutions containing rubidium, and of net movements of rubidium in the presence and absence of ouabain, lead to the conclusion that at least 90 % of the inward rubi-* Present address: