Control processes in oxidative phosphorylation: kinetic constraints and stoichiometry

Control processes in oxidative phosphorylation have been studied in three experimental models. (1) In isolated yeast mitochondria, external ATP is a regulatory effector of cytochrome-c oxidase activity. In phosphorylating or uncoupling states, the relationships between respiratory rate and delta mu H+, and the respiratory rate and cytochrome-c oxidase reduction level are dependent on this kinetic regulation. (2) In rat liver mitochondria, the response of the respiratory rate to uncoupler addition is age-dependent: liver mitochondria isolated from young rats maintain a greater delta mu H+ than liver mitochondria isolated from adults, with the same respiratory rate obtained with the same concentration of uncoupler. This behaviour is linked to redox proton pump properties, i.e., to the degree of intrinsic uncoupling induced by uncoupler addition. (3) The effect of almitrine, a new kind of ATPase/ATPsynthase inhibitor, was studied in mammalian mitochondria. (i) Almitrine inhibits oligomycin-sensitive ATPase - it decreases the ATPase/O value without any change in delta mu H+; (ii) almitrine increased the mechanistic H+/ATP stoichiometry of ATPase/ATPsynthase; (iii) almitrine-induced changes in H+/ATPase stoichiometry depend on the flux magnitude through ATPase. These results are discussed in terms of the following interdependent parameters; flux value, force, pump efficiency and control coefficient.     

H+/ATP stoichiometry of proton pump of turtle urinary bladder

Urinary acidification in the turtle urinary bladder is due to a reversible proton-translocating ATPase. To estimate the H+/ATP stoichiometry of this pump, we measured the delta G'ATP in the epithelial cells and the maximum e.m.f. generated by the pump. The latter is the maximal transepithelial electrochemical gradient for protons placed across the epithelium that is needed to nullify the rate of transport and averaged 179 +/- 7 mV. The delta G'ATP averaged 50.1 kJ/mol. The H+/ATP stoichiometry of these bladders was 2.92 +/- 0.1. In other experiments, the bladders were poisoned by iodoacetate and cyanide and a variable transepithelial electrochemical gradient for protons was placed across them. It was noted that ATP synthesis occurred at a transepithelial electrochemical gradient for protons greater than 120 mV. The delta G'ATP in other bladders treated identically averaged 40.0 kJ/mol, giving a H+/ATP stoichiometry of 3.4 +/- 0.1. We conclude that the H+/ATP stoichiometry of the proton pump of turtle urinary bladder is approximately 3.     

Stoichiometry of the H+-ATPase of growing and resting, aerobic Escherichia coli

The H+/ATP stoichiometry of the proton-translocating ATPase was investigated in growing and nongrowing, respiring cells of Escherichia coli. The protonmotive force, delta p, was determined by measuring the transmembrane chemical gradient of protons, delta pH, from the cellular accumulation of benzoate anions, and the electrical gradient, delta psi, from the accumulation of the lipophilic cation tetraphenylphosphonium (TPP+). The accumulation of lactose was also used to calculate the delta p in this lactose operon constitutive beta-galactosidase negative mutant. The phosphorylation potential, delta GP', was determined by measuring the cellular concentration of ATP, ADP, and inorganic phosphate. According to chemiosmotic principles, at steady state the phosphorylation potential is in thermodynamic equilibrium with the protonmotive force, and thus the ratio delta p/delta GP' can be used to determine the H+/ATP ratio. Respiring E. coli cells, in mid-exponential phase of growth or incubated in buffer, at external pHs from 6.25 to 8.25 had a constant delta GP' of about 500 mV. The H+/ATP ratio was found to be 3 when the delta p value derived from lactose accumulation levels was used. However, when the delta p values derived from delta pH and delta psi were used in the calculations, the H+/ATP ratio varied from about 2.5 at external pH 6.25 to about 4 at pH 8.25. Arguments are presented for the hypothesis that the delta psi values obtained from the TPP+ measurements are likely to be inaccurate and that a value of 3 H+/ATP, independent of the external pH, is likely to be the valid stoichiometry.     

Modification of the Neurospora crassa plasma membrane [H+]-ATPase with N,N'-dicyclohexylcarbodiimide

The [H+]-ATPase of the Neurospora plasma membrane is composed of a single Mr = 104,000 polypeptide (B. J. Bowman, F. Blasco, and C. W. Slayman, J. Biol. Chem. (1981) 256, 12343-12349). The carboxyl-modifying reagent N,N'-dicyclohexylcarbodiimide (DCCD) inactivates the ATPase with pseudo-first order kinetics, suggesting that one site on the enzyme is involved. The rate constant for inactivation at pH 7.5 and 30 degrees C is approximately 1000 M-1 min-1, similar to values reported for the DCCD-binding proteolipid of F0-F1-type [H+]-ATPases and for the sarcoplasmic reticulum [Ca+2]-ATPase. Although hydrophobic carbodiimides are inhibitory at micromolar concentrations, a hydrophilic analogue, 1-ethyl-3-(dimethylaminopropyl)-carbodiimide, is completely inactive even at millimolar concentrations. This result implies that the DCCD-reactive site is located in a lipophilic environment. [14C]DCCD is incorporated into the Mr = 104,000 polypeptide at a rate similar to the rate of inactivation. There is no evidence for a separate low molecular weight DCCD-binding proteolipid. Using quantitative amino acid analysis, we established that complete inhibition occurs at a stoichiometry of 0.4 mol of DCCD/mol of polypeptide. Overall, the results are consistent with the idea that DCCD reacts with a single amino acid residue of the Neurospora [H+]-ATPase, thereby blocking ATP hydrolysis and proton translocation.     

Relationship between phosphorylation potential and electrochemical H+ gradient during glycolysis in Streptococcus lactis.

Assays of intracellular ATP, ADP, and inorganic phosphate allowed calculation of the phosphorylation potential (delta G'ATP/F) maintained during glycolysis by Streptococcus lactis. At the same time, the electrochemical H+ gradient (delta mu-H+/F) was evaluated by distribution methods, using radioactive tetraphenylphosphonium bromide as a probe for the membrane potential and salicylic acid as a probe for the pH gradient. Detailed comparisons were made at pH 5, when the reaction mediated by the proton-translocating ATPase (BF0F1) was likely to have been poised near equilibrium; for those conditions, the ratio delta G'ATP/delta mu-H+ was used to estimate stoichiometry for BF0F1 during ATP hydrolysis. At an external pH of 5, in the presence or absence of valinomycin, this ratio was close to 3, over a range of 370 to 510 mV (8.5 to 11.7 kcal/mol) for delta G'ATP/F and a range of 128 to 167 mV for delta mu-H+/F. Other work suggested that delta G'ATP/delta mu-H+ increased from its minimum value of 3 to 4.3 as the external pH changed from pH 5 to 7.     

Flux-dependent increase in the stoichiometry of charge translocation by mitochondrial ATPase/ATP synthase induced by almitrine

After studying the effects of almitrine, a new kind of ATPase/ATP synthase inhibitor, on two kinds of isolated mammalian mitochondrion, we have observed that: (1) Almitrine inhibits oligomycin-sensitive ATPase; it decreases the ATP/O value of oxidative phosphorylations without any change in the magnitude of delta mu H+. (2) Almitrine increases the mechanistic H+/ATP stoichiometry of ATPase as shown by measuring either (i) the extent of potassium acetate and of potassium phosphate accumulation sustained by ATP utilisation, or (ii) the electrical charge/ATP (K+/ATP) ratio at steady-state of ATPase activity. (3) Rat liver mitochondria are at least 10-times more sensitive to almitrine than beef heart mitochondria. (4) The change in H+/ATP stoichiometry induced by almitrine depends on the magnitude of the flux through ATPase. The inhibitory effect of almitrine on ATPase/ATP synthase complex, as a consequence of such an H+/ATP stoichiometry change, is discussed.     

Some peculiarities of functioning of H+-ATPase from the membranes of the anaerobic bacterium Lactobacillus casei

Radiation inactivation analysis gave the target sizes of 176 +/- 5 kDa and 275 +/- 33 kDa for ATPase from anaerobic Lactobacillus casei and aerobic Micrococcus luteus bacteria respectively. The values are close to the known molecular masses of the enzymes. Thus, to function the L. casei ATPase, like the F1-ATPases, requires a complete structure composed of all the enzyme subunits. L. casei ATPase is inhibited by 4-chloro-7-nitrobenzo-2-oxa-1,3-diazole owing to modification of an amino acid residue(s) with pK greater than 8.5. L. casei ATPase consists of six identical subunits and differs from alpha 3 beta 3 gamma delta epsilon-type F1-ATPases in a number of catalytic properties. Namely, ATP hydrolysis under the 'unisite' conditions proceeds at a relatively high rate suggesting the absence of cooperative interactions between the catalytic sites. Contrary to mitochondrial F1-ATPase. L. casei ATPase does not form an inactive complex with ADP. These findings imply essential differences in the operating mechanism for L. casei ATPase and F1 ATPase.     

Kinetic analysis of the protonation of a surface group of a macromolecule

High-field 31P-NMR studies of whole cells of Streptococcus faecalis have shown that delta pH can be formed by ATP hydrolysis and also by lactate transport. We have used 31P-NMR to measure the pH dependence of the variable stoichiometry of the proton/lactate carrier. At low external pH (pH approximately equal to 6.5) the influx stoichiometry was 1.1 H+/lactate, while at high pH (7.5) the ratio was almost 2; the apparent midpoint pH of this variable stoichiometry is 7. delta psi measurements support the electrogenic nature of lactate transport at high pH; the variable rate of membrane depolarization caused by lactate transport also had a midpoint near pH 7.0. The data is consistent with a symmetrical carrier operating with variable stoichiometry as proposed by Michels et al.     

H+ ATPase of chromaffin granules. Kinetics, regulation, and stoichiometry

The chromaffin granule ATPase mediates an inwardly directed transport of H+ against concentration gradients, thereby forming and maintaining an electrochemical transmembrane H+ gradient. The kinetics of this ATPase, its activity modulation by changes in electrochemical H+ gradients, and the stoichiometry between H+ transport and ATP hydrolysis were studied in intact bovine chromaffin granules, resealed chromaffin granule ghosts, and highly purified fragmented chromaffin granule membranes. In fragmented membranes the H+ ATPase has a KM for ATP of 69 microM, a maximum of activity at pH 7.3, and a Vmax of 111 nmol/min/mg of protein at 20 degrees C. Trimethyl tin inhibits the ATPase at much lower concentrations than dicyclohexylcarbodiimide, whereas oligomycin, reserpine, and other inhibitors were without effect. In intact chromaffin granules, the ATPase activity was stimulated up to 300% by collapsing the H+ transmembrane gradients. H+/ATP stoichiometry was measured in resealed chromaffin ghosts devoid of ATP and catecholamines under conditions where no net pH changes occur upon ATP hydrolysis. After addition of ATP, the rates of H+ accumulation in the ghosts and ATP hydrolysis were both linear for about 60-100 s, and the ratio of H+ to ATP was 1.71. These data indicate that the H+ ATPase of chromaffin granules has both kinetic similarities and dissimilarities with other known H+ ATPases. The regulation by changes in H+ gradients and the fixed H+/ATP ratio of this ATPase is further evidence of its primary role in establishing electrogenic H+ translocation and H+ gradients in chromaffin granules.     

Metabolic modulation of stoichiometry in a proton pump

The current-voltage characteristics of the ATP-dependent proton pump in the plasma membrane of Neurospora have been explored under varied metabolic conditions imposed by mutation and by differential respiratory inhibition. The reversal potential, or presumed equilibrium potential, for the pump was observed at about -400 mV under energy-replete conditions, and at about -200 mV during a stable metabolic downshift of 55 percent. Steady-state levels of adenine nucleotides and inorganic phosphate, however, were not affected by this partial energy restriction, so that under both normal and restricted conditions the apparent free energy of ATP hydrolysis remained near -500 mV. The results suggest that a normal pump stoichiometry of 1 H+ extruded/1 ATP split is modified to 2 H+/1 ATP, by chronic energy restriction.     

The gastric [H,K]ATPase:H+/ATP stoichiometry

An H+/ATP ratio of 2 for H+ transport was determined from initial rate measurements at pH 6.1 in a purified gastric microsomal fraction containing the [H,K]ATPase. This ratio was independent of external KCl, though the apparent K0.5 for ATP was increased from 10.78 +/- 0.51 (n = 3) to 64.6 +/- 11.9 (n = 3) microM ATP and from 5.13 +/- 0.64 (n = 3) to 65.2 +/- 0.64 (n = 3) microM ATP for H+ transport and the K+-stimulated ATPase, respectively, as K+external was increased from 12 to 150 mM. The H+/ATP ratio was also relatively independent of ATP concentration. Maximum initial rates obtained in KCl-equilibrated vesicles were independent of added valinomycin, though net H+ transport was increased 29.3 +/- 1.03% (n = 6) by the addition of ionophore. Maximum net H+ transport in this vesicle preparation was 185 +/- 2.1 (n = 14) nmol mg-1 of protein. Initial rate measurements of ATPase represent a burst of K+-dependent activity of approximately 10-15 s duration. The H+/ATP stoichiometry was calculated based on the K+-stimulated component of hydrolysis. Under most conditions, the Mg2+-dependent component of hydrolysis was less than 10% of the (Mg2+ + K+) component of hydrolysis.     

The F1-type ATPase in anaerobic Lactobacillus casei

An ATPase from anaerobic Lactobacillus casei has been isolated and 100-times purified. The 400 kDa enzyme molecule was found to have a hexagonal structure 10 nm in diameter composed of at least six protein masses. SDS-electrophoresis reveals four or, under certain conditions, five types of subunit, of apparent molecular masses 57 (alpha), 55 (beta), 40 (gamma), 22 (delta) and 14 (epsilon) kDa with stoichiometry of 3 alpha, 3 beta, gamma, delta, epsilon. The following features resembling F1-ATPases from other sources were found to be inherent in the solubilized L. casei ATPase. (i) Detachment from the membrane desensitizes ATPase to low DCCD concentrations and sensitizes it to water-soluble carbodiimide. (ii) Soluble ATPase is inhibited by Nbf chloride and azide, is resistant to SH-modifiers and is activated by sulfite and octyl glucoside, the activating effect being much stronger than in the case of the membrane-bound ATPase. Substrate specificity of the enzyme is also similar to that of other factors F1. Divalent cations strongly activate the soluble enzyme when added at a concentration equal to that of ATP. An excess of Mn2+, Mg2+ or Co2+ inhibits ATPase activity of F1, whereas that of Ca2+ induces its further activation. No other F1-like ATPases are found in L. casei. It is concluded that this anaerobic bacterium possesses a typical F1-ATPase similar to those in mitochondria, chloroplasts, aerobic and photosynthetic eubacteria.     

A homologous sequence between H+-ATPase (F0F1) and cation-transporting ATPases. Thr-285----Asp replacement in the beta subunit of Escherichia coli F1 changes its catalytic properties

A sequence of 10 amino acids (I-C-S-D-K-T-G-T-L-T) of ion motive ATPases such as Na+/K+-ATPase is similar to the sequence of the beta subunit of H+-ATPases, including that of Escherichia coli (I-T-S-T-K-T-G-S-I-T) (residues 282-291). The Asp (D) residue phosphorylated in ion motive ATPase corresponds to Thr (T) of the beta subunit. This substitution may be reasonable because there is no phosphoenzyme intermediate in the catalytic cycle of F1-ATPase. We replaced Thr-285 of the beta subunit by an Asp residue by in vitro mutagenesis and reconstituted the alpha beta gamma complex from the mutant (or wild-type) beta and wild-type alpha and gamma subunits. The uni- and multisite ATPase activities of the alpha beta gamma complex with mutant beta subunits were about 20 and 30% of those with the wild-type subunit. The rate of ATP binding (k1) of the mutant complex under uni-site conditions was about 10-fold less than that of the wild-type complex. These results suggest that Thr-285, or the region in its vicinity, is essential for normal catalysis of the H+-ATPase. The mutant complex could not form a phosphoenzyme under the conditions where the H+/K+-ATPase is phosphorylated, suggesting that another residue(s) may also be involved in formation of the intermediate in ion motive ATPase. The wild-type alpha beta gamma complex had slightly different kinetic properties from the wild-type F1, possibly because it did not contain the epsilon subunit.     

The sodium ion translocating adenosinetriphosphatase of Propionigenium modestum pumps protons at low sodium ion concentrations

The purified ATPase (F1F0) of Propionigenium modestum has its pH optimum at pH 7.0 or at pH 6.0 in the presence or absence of 5 mM NaCl, respectively. The activation by 5 mM NaCl was 12-fold at pH 7.0, 3.5-fold at pH 6.0, and 1.5-fold at pH 5.0. In addition to its function as a primary Na+ pump, the ATPase was capable of pumping protons. This activity was demonstrated with reconstituted proteoliposomes by the ATP-dependent quenching of the fluorescence of 9-amino-6-chloro-2-methoxyacridine. No delta pH was formed in the presence of the uncoupler carbonyl cyanide m-chlorophenylhydrazone or by blocking the ATPase with dicyclohexylcarbodiimide. In the presence of valinomycin and K+, the delta pH increased, in accord with the operation of an electrogenic proton pump. The proton pump was only operative at low Na+ concentrations (less than 1 mM), and its activity increased as the Na+ concentration decreased. Parallel to the decrease of H+ pumping, the velocity of the Na+ transport increased about 6-fold from 0.1 to 4 mM NaCl, indicating a switch from H+ to Na+ pumping, as the Na+ concentration increases. Due to proton leaks in the proteoliposomal membranes, fluorescence quenching was released after blocking the ATPase with dicyclohexylcarbodiimide, by trapping residual ATP with glucose and hexokinase, or by the Na+-induced conversion of the proton pump onto a Na+ pump. Amiloride, an inhibitor of various Na+-coupled transport systems, was without effect on the kinetics of Na+ transport by the P. modestum ATPase.     

The ionic composition of the hydrothermal vent tube worm Riftia pachyptila: evidence for the elimination of SO2-4SO and H+ and for a Cl-/HCO-3HCO shift

Riftia pachyptila is one of the most specialized invertebrate hosts of chemoautotrophic symbionts. Crucial to the functioning of this symbiosis is how these worms cope with fluctuating ion concentrations. Internal sulfate levels in R. pachyptila appear comparable with other benthic marine invertebrates, despite the production of sulfate internally by means of the bacterial oxidation of hydrogen sulfide, suggesting that these worms are able to eliminate sulfate effectively. Internal chloride levels appear comparable; however, coelomic fluid chloride levels decrease significantly as the amount of coelomic fluid bicarbonate increases, demonstrating a 1:1 stoichiometry. We believe this shift in chloride, out of the body fluids, is needed to compensate for changes in electrochemical balance caused by the large increase (up to and greater than 60 mmol L-1) in negatively charged bicarbonate. Riftia pachyptila fits the general pattern of monovalent ion concentrations that is seen in other benthic marine invertebrates, with a high [Na+] : [K+] ratio extracellularly and low [Na+] : [K+] ratio intracellularly. Extracellular pH values of 7.38+/-0.03 and 7.37+/-0. 04 for coelomic fluid and vascular blood, respectively, as well as intracellular pH values of 7.37+/-0.04 and 7.04+/-0.05 for plume and trophosome tissue, respectively, were measured. On the basis of significant decreases in extracellular pH and, in some cases, Na+ and K+, in worms exposed to carbonyl cyanide m-chlorophenylhydrazone, sodium vanadate, and N-ethylmaleimide, we suggest that high concentrations of H+-ATPases, perhaps Na+/H+- or K+/H+-ATPases, are involved in H+ elimination in these animals.     

Energy transformation coupled to formate oxidation during anaerobic fermentation

A correlation between the rate of ATP synthesis by F0F1 ATP-synthase and formate oxidation by formate hydrogen lyase (FHL) has been established in inverted membrane vesicles of Escherichia coli JW 136 mutant with double deletions (delta hya/ delta hyb) of hydrogenase 1 and 2 grown anaerobically on glucose in the absence of external electron acceptors (pH 6.5). ATP synthesis was suppressed by H+ -ATPase inhibitors N,N'-dicyclohexylcarbodiimide (DCCD) and sodium azide as well as by the protonophore carbonyl cyanide-m-chlorophenyhydrazone (CCCP). Copper ions inhibited formate-dependent hydrogenase and ATP-synthase activities but did not affect the ATPase activity of vesicles. The maximal rate of ATP synthesis (0.83 microM/min x mg protein) stimulated by K+ ions was determined when sodium formate, ADP and inorganic phosphate were applied simultaneously. The results confirm the assumption about the dual role of hydrogenase 3, formate hydrogen lyase subunit, which is able to couple the reduction of protons to H2 and their translocation through a membrane with chemiosmotic synthesis of ATP.     

Almitrine, a new kind of energy-transduction inhibitor acting on mitochondrial ATP synthase

At low concentrations, almitrine inhibits yeast cell multiplication by acting on oxidative metabolism. Studies on isolated mitochondria display the following features: (i) almitrine inhibits ATPase activity and decreases ATP/O ratio during oxidative phosphorylation; (ii) no direct effect on respiration can be evidenced; (iii) ATP/O value decreases without any change in the magnitude of delta p; (iv) the higher the ATP synthesis and respiratory fluxes, the larger is the decrease in ATP/O ratio induced by almitrine. These results indicate that almitrine does not act as a classical protonophoric uncoupler nor as previously studied non protonophoric uncouplers (e.g., general anesthetics). Our data show a direct inhibitory effect of almitrine on ATPase-ATP synthase complex. But, in contrast to the classical inhibitors of this complex, almitrine decreases the ATP/O ratio in a flux-dependent manner. Thus, almitrine could induce either an intrinsic uncoupling of H+/-ATPase (i.e., slip in this proton pump) or a change in the mechanistic H+/ATP stoichiometry at the ATPase level.     

Existence of an adenosine 5'-triphosphate dependent proton translocase in bovine neurosecretory granule membrane

The addition of ATP to bovine neurohypophysial secretory granules suspended in isotonic sucrose medium induces a positive polarization, delta psi, of their interior without affecting their internal pH. In KCl-containing media, ATP failed to generate large delta psi but induced a pH gradient (delta pH; interior acidic). These observations are consistent with the existence in the neurosecretory granule membrane of an ATP-dependent inward electrogenic H+ translocase (H+ pump), capable in KCl-containing media of acidifying the granule matrix by H+-Cl- cotransport. The delta psi and delta pH generated by the H+ pump, defined as the ATP-induced changes sensitive to the H+ ionophore carbonyl cyanide m-chlorophenylhydrazone (CCCP), were blocked by N,N'-dicyclohexylcarbodiimide, an inhibitor of all H+ pumps, and were insensitive to oligomycin, a mitochondrial ATPase inhibitor. In sucrose medium, measurements were complicated by a Donnan equilibrium reflecting the presence in the granule of peptide hormones and neurophysins which resulted in a CCCP-resistant resting delta pH. In KCl-containing media, the Donnan equilibrium was destroyed since the membrane is permeable to cations, but under these conditions a CCCP-resistant K+-diffusion potential was observed. The ATP-induced delta psi was also monitored by the extrinsic fluorescent probe bis(3-phenyl-5-oxoisoxazol-4-yl)pentamethine oxonol. The hypothesis of a granule H+ pump is further supported by the presence of an oligomycin-resistant ATPase in the preparation and the ultrastructural localization of such an activity on the granule membrane. The H+ pump has been found in both newly formed and aged neurosecretory granules. Its possible physiological function is discussed with reference to that of chromaffin granules, with which it has many similarities.     

Energy-spilling reactions of Streptococcus bovis and resistance of its membrane to proton conductance.

Glucose-excess cultures of Streptococcus bovis consumed glucose faster than the amount that could be explained by growth or maintenance, and nongrowing chloramphenicol-treated cells had a rate of glucose consumption that was 10-fold greater than the maintenance rate. Because N,N-dicyclohexylcarbodiimide, an inhibitor of the membrane-bound F1F0 ATPase, eliminated the nongrowth energy dissipation (energy spilling) without a decrease in ATP and the rate of energy spilling could be increased by the protonophore 3,3',4',5-tetrachlorosalicylanilide, it appeared that a futile cycle of protons through the cell membrane was responsible for most of the energy spilling. When the rate of energy spilling was decreased gradually with iodoacetate, there was only a small decrease in the phosphorylation potential (delta G'p) and the theoretical estimate of H+ per ATP decreased from 4.2 to 3.6. On the bases of this ratio of H+ to ATP and the rate of ATP production, the flux of protons (amperage) across the cell membrane was directly proportional to the rate of energy spilling. Amperage values estimated from delta G'p were, however, nearly twice as great as values which were estimated from the heat production (delta H) of the cells [amperage = (0.38 x wattage)/delta p]. The last comparison indicated that only a fraction of the delta G of ATP hydrolysis was harvested by the F1F0 ATPase to pump protons. Both estimates of amperage indicated that the resistance of the cell membrane to proton conductance was inversely proportional to the log of the energy-spilling rate.