Interpretation of current-voltage relationships for “active” ion transport systems: I. Steady-state reaction-kinetic analysis of class-I mechanisms

SummaryThis 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. Acta211:458–466, 1970), via a symmetric Eyring barrier, in which the charge-transit reaction constants are written ask12=k120exp(zFΔΨ/2RT) andk21=k210exp(−zFΔΨ/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,r0) which formally take account of carrier states that are indistinguishable in the current-voltage (I–V) analysis. The model generates a wide range ofI–V relationships, depending on the relative magnitudes of the four reaction constants, sufficient to describe essentially allI–V data 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.

[1]  J. Dainty,et al.  Voltage—Current Characteristics of Chara australis During Changes of pH and Exchange of Ca-Mg in the External Medium , 1970 .

[2]  W. Wilbrandt,et al.  The concept of carrier transport and its corollaries in pharmacology. , 1961, Pharmacological reviews.

[3]  G. Stark,et al.  Kinetics of carrier-mediated ion transport across lipid bilayer membranes. , 1970, Biochimica et biophysica acta.

[4]  C. Slayman,et al.  Proton Pumping and Generalized Energetics of Transport: A Review , 1974 .

[5]  H. Britton.  The concept and use of flux measurements in enzyme studies. A theoretical analysis. , 1966, Archives of biochemistry and biophysics.

[6]  C. Mead,et al.  A barrier model for current flow in lipid bilayer membranes , 1973, The Journal of Membrane Biology.

[7]  Q. Al-Awqati,et al.  Urinary acidification in turtle bladder is due to a reversible proton-translocating ATPase. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[8]  W. Junge.  The critical electric potential difference for photophosphorylation. Its relation to the chemiosmotic hypothesis and to the triggering requirements of the ATPase system. , 1970, European journal of biochemistry.

[9]  P. Curran,et al.  Response of the Frog Skin to Steady-State Voltage Clamping , 1972, The Journal of general physiology.

[10]  I. Glynn,et al.  The sodium pump. , 1975, Annual review of physiology.

[11]  W. R. Lieb,et al.  Testing and characterizing the simple carrier. , 1974, Biochimica et Biophysica Acta.

[12]  C. Carter-Su,et al.  Membrane potentials and the energetics of intestinal Na+-dependent transport systems. , 1978, The American journal of physiology.

[13]  P. Geck,et al.  Coupling in secondary transport. Effect of electrical potentials on the kinetics of ion linked co-transport. , 1976, Biochimica et biophysica acta.

[14]  R. Moreton.  An investigation of the electrogenic sodium pump in snail neurones, using the constant-field theory. , 1969, The Journal of experimental biology.

[15]  V. Markin,et al.  Nigericin-induced charge transfer across membranes , 1975, The Journal of Membrane Biology.

[16]  R. Benz,et al.  The rate constants of valinomycin-mediated ion transport through thin lipid membranes. , 1971, Biophysical journal.

[17]  P. Läuger.  A channel mechanism for electrogenic ion pumps. , 1979, Biochimica et biophysica acta.

[18]  M. Saier.  Bacterial phosphoenolpyruvate: sugar phosphotransferase systems: structural, functional, and evolutionary interrelationships. , 1977, Bacteriological reviews.

[19]  S. Schultz,et al.  Coupled transport of sodium and organic solutes. , 1970, Physiological reviews.

[20]  L. Mullins,et al.  Calcium movement in nerve fibres , 1979, Quarterly Reviews of Biophysics.

[21]  J. Lanyi,et al.  Existence of electrogenic hydrogen ion/sodium ion antiport in Halobacterium halobium cell envelope vesicles. , 1976, Biochemistry.

[22]  D. Robertson,et al.  Active transport in membrane vesicles from Escherichia coli: the electrochemical proton gradient alters the distribution of the lac carrier between two different kinetic states. , 1980, Biochemistry.

[23]  B. Rosen,et al.  Cation/proton antiport systems in Escherichia coli. Properties of the calcium/proton antiporter. , 1980, The Journal of biological chemistry.

[24]  J. Lanyi,et al.  Gating effects in Halobacterium halobium membrane transport. , 1979, The Journal of biological chemistry.

[25]  WF Schmidt III,et al.  Ouabain-insensitive salt and water movements in duck red cells. I. Kinetics of cation transport under hypertonic conditions , 1977, The Journal of general physiology.

[26]  H. Morowitz.  Proton semiconductors and energy transduction in biological systems. , 1978, The American journal of physiology.

[27]  W. Junge.  Chapter 24 Electrogenic Reactions and Proton Pumping in Green Plant Photosynthesis , 1982 .

[28]  Kaback Hr.  Molecular biology and energetics of membrane transport. , 1976 .

[29]  D. Sanders,et al.  Mechanism of Cl− transport at the plasma membrane ofChara corallina: II. Transinhibition and the determination of H+/Cl− binding order from a reaction kinetic model , 1981, The Journal of Membrane Biology.

[30]  O. Andersen,et al.  Potential energy barriers to ion transport within lipid bilayers. Studies with tetraphenylborate. , 1975, Biophysical journal.

[31]  G. A. Kerkut,et al.  The electrogenic sodium pump and membrane potential of identified neurones in Helix aspersa. , 1974, Comparative biochemistry and physiology. A, Comparative physiology.

[32]  R. M. Spanswick.  Chapter 3 The Electrogenic Pump in the Plasma Membrane of Nitella , 1982 .

[33]  R. Benz,et al.  Transport kinetics of hydrophobic ions in lipid bilayer membranes. Charge-pulse relaxation studies. , 1976, Biochimica et biophysica acta.

[34]  B. Rosen,et al.  Cation/proton antiport systems in Escherichia coli. , 1978, Biochemical and biophysical research communications.

[35]  K. Krab,et al.  Proton-pumping cytochrome c oxidase. , 1979, Biochimica et biophysica acta.

[36]  Y. Kagawa,et al.  Purified proton conductor in proton translocating adenosine triphosphatase of a thermophilic bacterium. , 1977, The Journal of biological chemistry.

[37]  S. Feldberg,et al.  Charge pulse studies of transport phenomena in bilayer membranes , 1977, The Journal of Membrane Biology.

[38]  I. Glynn,et al.  Conformational transitions between Na+-bound and K+-bound forms of (Na+ + K+)-ATPase, studied with formycin nucleotides. , 1978, Biochimica et biophysica acta.

[39]  R. H. Fillingame,et al.  Energy-transducing H+-ATPase of Escherichia coli. Purification, reconstitution, and subunit composition. , 1979, The Journal of biological chemistry.

[40]  P. J. Garrahan,et al.  The Distinction between Sequential and Simultaneous Models for Sodium and Potassium Transport , 1976 .

[41]  S. Schultz.  Basic principles of membrane transport , 1980 .

[42]  W. R. Lieb,et al.  A Necessary Simplification of the Kinetics of Carrier Transport , 1973 .

[43]  D. Gradmann.  Analog circuit of theAcetabularia membrane , 1975, The Journal of Membrane Biology.

[44]  E. Komor,et al.  A possible mechanistic role of the membrane potential in proton—sugar cotransport of Chlorella , 1978, FEBS letters.

[45]  J. D. Robinson,et al.  The (Na+ + K+)-activated ATPase. Enzymatic and transport properties. , 1979, Biochimica et biophysica acta.

[46]  A. Finkelstein.  CARRIER MODEL FOR ACTIVE TRANSPORT OF IONS ACROSS A MOSAIC MEMBRANE. , 1964, Biophysical journal.

[47]  R. Kinne.  Properties of the Glucose Transport System in the Renal Brush Border Membrane , 1976 .

[48]  R. Benz,et al.  The transport of potassium through lipid bilayer membranes by the neutral carriers valinomycin and monactin , 1971, The Journal of Membrane Biology.

[49]  E. L. King,et al.  A Schematic Method of Deriving the Rate Laws for Enzyme-Catalyzed Reactions , 1956 .

[50]  F. Conti,et al.  The steady-state properties of an ion exchange membrane with mobile sites. , 1966, Biophysical journal.

[51]  P. C. Caldwell.  Possible mechanisms for the linkage of membrane potentials to metabolism by electrogenic transport processes with special reference toAscaris muscle , 1973, Journal of bioenergetics.

[52]  R. Thomas,et al.  The role of bicarbonate, chloride and sodium ions in the regulation of intracellular pH in snail neurones , 1977, The Journal of physiology.

[53]  A. Eddy.  Proton-Dependent Solute Transport in Microorganisms , 1978 .

[54]  R. Thomas,et al.  Membrane current and intracellular sodium changes in a snail neurone during extrusion of injected sodium , 1969, The Journal of physiology.

[55]  A. Goffeau,et al.  The proton-translocating ATPase of the fungal plasma membrane. , 1981, Biochimica et biophysica acta.

[56]  Kaback Hr.  Molecular biology and energetics of membrane transport , 1976, Journal of cellular physiology.

[57]  D. Robertson,et al.  MECHANISM OF LACTOSE TRANSLOCATION IN MEMBRANE VESICLES FROM ESCHERICHIA COLI , 1979, Biochemistry.

[58]  E. Racker.  Mechanisms of Ion Transport and ATP Formation , 1978 .

[59]  J. Kootsey,et al.  A kinetic model for determining the consequences of electrogenic active transport in cardiac muscle. , 1979, Journal of theoretical biology.

[60]  R. Thomas.  Ionic mechanism of the H+ pump in a snail neurone , 1976, Nature.

[61]  P. Mitchell,et al.  The Mechanism of Proton Translocation in Reversible Proton-Translocating Adenosine Triphosphatases , 1974 .

[62]  P. Maloney,et al.  Voltage sensitivity of the proton‐translocating adenosine 5′‐triphosphatase in Streptococcus lactis , 1980, FEBS letters.

[63]  U. Reichert,et al.  A possible mechanism of energy coupling in purine transport of Saccharomyces cerevisiae , 1975, FEBS letters.

[64]  R. M. Spanswick.  Evidence for an electrogenic ion pump in Nitella translucens. I. The effects of pH, K + , Na + , light and temperature on the membrane potential and resistance. , 1972, Biochimica et biophysica acta.

[65]  R. H. Adrian,et al.  Membrane potential and conductance during transport of sodium, potassium and rubidium in frog muscle , 1966, The Journal of physiology.

[66]  B. Hille.  Ionic selectivity, saturation, and block in sodium channels. A four- barrier model , 1975, The Journal of general physiology.

[67]  P. Geck,et al.  Electrically silent cotransport on Na+, K+ and Cl- in Ehrlich cells. , 1980, Biochimica et biophysica acta.

[68]  G. Kimmich.  Coupling between Na+ and sugar transport in small intestine. , 1973, Biochimica et biophysica acta.

[69]  J. Diamond.  Transport of Salt and Water in Rabbit and Guinea Pig Gall Bladder , 1964, The Journal of general physiology.

[70]  M. Marmor.  The independence of electrogenic sodium transport and membrane potential in a molluscan neurone , 1971, The Journal of physiology.

[71]  S. Ginsburg,,et al.  Use of current-voltage diagrams in locating peak energy barriers in cell membranes , 1976, The Journal of Membrane Biology.

[72]  E. Komor,et al.  The effect of intracellular pH on the rate of hexose uptake in Chlorella. , 1979, Biochimica et biophysica acta.

[73]  A S Frumento,et al.  The electrical effects of an ionic pump. , 1965, Journal of theoretical biology.

[74]  P. Geck,et al.  Coupling in secondary active transport. Activation of transport by co-transport and-or counter-transport with the fluxes of other solutes. , 1972, Biochimica et biophysica acta.

[75]  S. Hladky.  The energy barriers to ion transport by nonactin across thin lipid membranes. , 1974, Biochimica et biophysica acta.

[76]  B. Rosen,et al.  Cation/proton antiport systems in Escherichia coli. Properties of the potassium/proton antiporter. , 1980, The Journal of biological chemistry.

[77]  P. Mitchell.  CHEMIOSMOTIC COUPLING IN OXIDATIVE AND PHOTOSYNTHETIC PHOSPHORYLATION , 1966, Biological reviews of the Cambridge Philosophical Society.

[78]  S. Feldberg,et al.  Charge pulse studies of transport phenomena in bilayer membranes , 2005, The Journal of Membrane Biology.

[79]  S. Schuldiner,et al.  Sodium-proton antiport in isolated membrane vesicles of Escherichia coli. , 1978, Biochemistry.

[80]  W. Stoeckenius,et al.  Bacteriorhodopsin and the purple membrane of halobacteria. , 1979, Biochimica et biophysica acta.

[81]  F. Bentrup,et al.  Electrogenic membrane transport in plants a review , 1980, Biophysics of structure and mechanism.

[82]  B. Rosen,et al.  Cation/proton antiport systems in escherichia coli: properties of the sodium/proton antiporter. , 1979, Archives of biochemistry and biophysics.

[83]  R. H. Adrian,et al.  Rectification in muscle membrane. , 1969, Progress in biophysics and molecular biology.

[84]  G. Hammes,et al.  Structure of oxidative- and photo-phosphorylation coupling factor complexes. , 1979, Biochimica et biophysica acta.

[85]  B. Rosen,et al.  Cation/proton antiport systems in Escherichia coli. Absence of potassium/proton antiporter activity in a pH-sensitive mutant. , 1980, The Journal of biological chemistry.