Control of respiration in proteoliposomes containing cytochrome aa3. I. Stimulation by valinomycin and uncoupler

1. Both valinomycin and p-trifluoromethoxy carbonyl cyanide phenylhydrazone (FCCP) are required for full release of respiration by cytochrome c oxidase-containing proteoliposomes (prepared by sonicating beef heart cytochrome aa₃ in salt solution with 4 parts phosphatidylcholine, 4 parts phosphatidylethanolamine and 2 parts cardiolipin) in the presence of external ascorbate and cytochrome c. In the absence of valinomycin the response to FCCP is rather sluggish, as reported by Wrigglesworth et al. (1976) (Abstracts, 10th Int. Congr. Biochem., No. 06-6-230).2. The K_m for cytochrome c in 67 mM, pH 7.4, phosphate buffer with ascorbate as substrate, was 9 μM in both absence and presence of valinomycin and FCCP. Energization thus acts non-competitively towards cytochrome c oxidation.3. The apparent K_m for oxygen is greater in the energized than in the deenergized state; double reciprocal plots of respiration rate versus oxygen concentration are concave downward in the absence of uncouplers, as found with intact mitochondria. Energization thus acts “competitively” towards oxygen.4. Despite the lack of a functional ATPase system, all the kinetic features of energization found in intact mitochondria can be mimicked in the reconstituted liposomes. This supports the chemiosmotic idea that electrical and perhaps H⁺ gradients modify the oxidase activity in reconstituted vesicles.     

Control of respiration in proteoliposomes containing cytochrome aa3. I. Stimulation by valinomycin and uncoupler.

1. Both valinomycin and p-trifluoromethoxy carbonyl cyanide phenylhydrazone (FCCP) are required for full release of respiration by cytochrome c oxidase-containing proteoliposomes (prepared by sonicating beef heart cytochrome aa3 in salt solution with 4 parts phosphatidylcholine, 4 parts phosphatidylethanolamine and 2 parts cardiolipin) in the presence of external ascorbate and cytochrome c. In the absence of valinomycin the response to FCCP is rather sluggish, as reported by Wrigglesworth et al. (1976) (Abstracts, 10th Int. Congr. Biochem., No. 06-6-230). 2. The Km for cytochrome c in 67 mM, pH 7.4, phosphate buffer with ascorbate as substrate, was 9 micrometer in both absence and presence of valinomycin and FCCP. Energization thus acts non-competitively towards cytochrome c oxidation. 3. The apparent Km for oxygen is greater in the energized than in the deenergized state; double reciprocal plots of respiration rate versus oxygen concentration are concave downward in the absence of uncouplers, as found with intact mitochondria. Energization thus acts "competitively" towards oxygen. 4. Despite the lack of a functional ATPase system, all the kinetic features of energization found in intact mitochondria can be mimicked in the reconstituted liposomes. This supports the chemiosmotic idea that electrical and perhaps H+ gradients modify the oxidase activity in reconstituted vesicles.     

Effects of detergents and cytochrome c binding on scalar and vectorial proton ejection by proteoliposomes containing cytochrome oxidase.

The detergent lauryl maltoside abolishes respiratory control and proton ejection by cytochrome c oxidase-containing proteoliposomes over a narrow concentration range. Expression of cryptic activity (inward-facing oxidase) is released over the same concentration range. Catalytic functions (Vmax. and Km) of the enzyme are not changed by the detergent. Lipid micelles containing detergent bind approximately the same amount of cytochrome c as do vesicles containing an equivalent amount of lipid. Uncoupler-insensitive proton release is seen when proteoliposomes are pulsed with ferrocytochrome c at low ionic strength. Such uncoupler-insensitive acidification is not seen at higher ionic strength, nor with oxygen pulses of anaerobic solutions previously incubated with cytochrome c. Vesicles at low ionic strength catalyse cytochrome c autoxidation; this process can mimic proton re-equilibration in systems that have pumped protons from inside to the bulk phase. Proton re-equilibration following a pulse of cytochrome c or oxygen is multiphasic. The slowest phases are attributed to vesicle heterogeneity, some internal alkali being retained within vesicles of low intrinsic proton permeability. This can be overcome by the addition of either very low levels of carbonyl cyanide p-trifluoromethoxyphenyl-hydrazone or high levels of valinomycin.     

Protons,pumps, and potentials: Control of cytochrome oxidase

Cytochromec oxidase oxidizes cytochromec and reduces molecular oxygen to water. When the enzyme is embedded across a membrane, this process generates electrical and pH gradients, and these gradients inhibit enzyme turnover. This respiratory control process is seen both in intact mitochondria and in reconstituted proteoliposomes. Generation of pH gradients and their role in respiratory control are described. Both electron and proton movement seem to be implicated. A topochemical arrangement of redox centers, like that in the photosynthetic reaction center and the cytochromebc ₁ complex, ensures charge separation as a result of electron movement. Proton translocation does not require such a topology, although it does require alternating access to the two sides of the membrane by proton-donating and accepting groups. The sites of respiratory control within the enzyme are discussed and a model presented for electron transfer and proton pumping by the oxidase in the light of current knowledge of the transmembranous location of the redox centers involved.     

Control of proteoliposomal cytochrome c oxidase: the overall reaction

The control of cytochrome c oxidase incorporated into proteoliposomes has been investigated as a function of membrane potential (delta psi) and pH gradient (delta pH). The oxidase generates a pH gradient (alkaline inside) and a membrane potential (negative inside) when respiring on external cytochrome c. Low levels of valinomycin collapse delta psi and increase delta pH; the respiration rate decreases. High levels of valinomycin, however, decrease delta pH as valinomycin can also act as a protonophore. Nigericin (in the absence of valinomycin) increases delta psi and collapses delta pH; the respiration rate increases. On a millivolt equivalent basis delta pH is a more effective inhibitor of activity than is delta psi. In the absence of any ionophores the cytochrome oxidase proteoliposomes enter a steady state, in which there are both delta pH and delta psi components of control. Present and previous data suggest that the respiration rate responds in a linear way ("ohmically") to increasing delta pH but in a nonlinear way to delta psi ("non-ohmically"). High levels of both delta psi and delta pH do not completely inhibit turnover (maximal respiratory control values lie between 6 and 10). The controlled steady state involves the electrophoretic entry and electroneutral exit of K+ from the vesicles. A model is presented in which the enzyme responds to both delta pH and delta psi components of the proton-motive force, but is more sensitive to delta pH than to delta psi at an equivalent delta mu H+. The steady state of the proteoliposome system can be represented for any set of permeabilities and enzyme activity levels using the computer simulation programme Stella.     

Formation of pH and potential gradients by the reconstituted Azotobacter vinelandii cytochrome bd respiratory protection oxidase.

To directly characterize the bioenergetic properties of the cytochrome bd terminating branch of the Azotobacter vinelandii electron transport chain, the purified cytochrome bd oxidase was reconstituted into a phospholipid environment consisting of phosphatidylethanolamine and phosphatidylglycerol (3:1). The average diameter of the proteoliposomes after extrusion through a polycarbonate membrane was 94 +/- 4 nm. Initiation of respiration upon the addition of 20 microM ubiquinone-1 to proteoliposomes loaded with the pH-sensitive dye pyranine resulted in an immediate alkalization of the vesicle lumen by an average pH change of 0.11 unit. This pH gradient was readily collapsed upon the addition of nigericin, carbonyl cyanide p-(tri-fluoromethoxy) phenyl-hydrazone, gramicidin, Triton X-100, or 2-heptyl-4-hydroxyquinoline N-oxide (HQNO). Proteoliposomal respiration initiated in the presence of the potentiometric membrane dye rhodamine 123 caused the generation of a transmembrane potential; the potential was collapsed upon the addition of either valinomycin or HQNO. The formation of both pH and potential gradients during turnover demonstrates that the A. vinelandii cytochrome bd oxidase is coupled to energy conservation in vivo.     

Orientation and reactivity of cytochrome aa3 heme groups in proteoliposomes

Reduction of cytochrome aa₃ in proteoliposomes with ascorbate plus cytochrome c confirms that not more than 55% of the molecules are externally accessible and that the remainder are reduced only on the addition of membrane-permeable N,N,N′,N′tetramethyl-p-henylenediamine. Reduction in the presence of terminal inhibitors such as cyanide, azide, and carbon monoxide shows that likewise 50% of the cytochrome a is accessible and 50% inaccessible. Dithionite reduces part of the cytochrome a₃ in the presence of azide, and none in the presence of cyanide. Methyl viologen, which is somewhat membrane permeable, can reduce part of the cyanide-complexed cytochrome a₃ at low concentrations and all of it at high concentrations. Cytochrome a₃ is therefore also distributed randomly inside and outside the vesicles. Cytochrome c oxidase with externally facing cytochrome a is stimulated to high activity by its membrane association. Its turnover is dependent on the external pH and it is inhibited by external azide; trapping of azide cannot be used to demonstrate the orientation of the cytochrome a₃ hemes associated with externally facing cytochrome a. Cytochrome c oxidase with internally facing cytochrome a is rather sluggishly reactive. Its low activity accounts for the apparent failure of detergents to release extra activity on lysing proteoliposomes. Double reciprocal plots of the reaction of added cytochrome c with proteoliposomes indicate apparent biphasic binding in the energized state, which is abolished upon the addition of uncouplers and valinomycin. But no transmembraneous effect upon the oxidase reaction other than energization has been identified.     

Energized transport of potassium ions in the absence of valinomycin by cytochrome c oxidase-reconstituted vesicles

Valinomycin-independent energized uptake of K⁺ was observed in cytochrome c oxidase reconstituted proteoliposome. The rate of K⁺ influx was proportoinal to the magnitude of electron flux. The energized uptake of K⁺ was abolished by p-trifluoromethoxycarbonylcyanide phenylhydrazone or by nigericin. Using the safranine fluorescence technique, it was demonstrated that even in the absence of valinomycin, liposomes and proteoliposomes reconstituted with cytochrome c oxidase are able to discriminate between Na⁺ and K⁺ and show a preference for K⁺ in the presence of excess Na⁺.     

Functional reconstitution of the gamma-aminobutyric acid transporter from synaptic vesicles using artificial ion gradients.

The gamma-aminobutyric acid transporter of rat brain synaptic vesicles was reconstituted in proteoliposomes, and its activity was studied in response to artificially created membrane potentials or proton gradients. Changes of the membrane potential were monitored using the dyes oxonol VI and 3,3'-diisopropylthiodicarbocyanine iodide, and changes of the H+ gradient were followed using acridine orange. An inside positive membrane potential was generated by the creation of an inwardly directed K+ gradient and the subsequent addition of valinomycin. Under these conditions, valinomycin evoked uptake of [3H]GABA which was saturable. Similarly, [3H]glutamate uptake was stimulated by valinomycin, indicating that both transporters can be driven by the membrane potential. Proton gradients were generated by the incubation of K(+)-loaded proteoliposomes in a buffer free of K+ or Na+ ions and the subsequent addition of nigericin. Proton gradients were also generated via the endogenous H+ ATPase by incubation of K(+)-loaded proteoliposomes in equimolar K+ buffer in the presence of valinomycin. These proton gradients evoked nonspecific, nonsaturable uptake of GABA and beta-alanine but not of glycine in proteoliposomes as well as protein-free liposomes. Therefore, transporter activity was monitored using glycine as an alternative substrate. Proton gradients generated by both methods elicited saturable glycine uptake in proteoliposomes. Together, our data confirm that the vesicular GABA transporter can be energized by both the membrane potential and the pH gradient and show that transport can be achieved by artificial gradients independently of the endogenous proton ATPase.     

Valinomycin induced energy-dependent mitochondrial swelling,cytochrome <Emphasis Type="Italic">c</Emphasis> release,cytosolic NADH/cytochrome <Emphasis Type="Italic">c</Emphasis> oxidation and apoptosis

In valinomycin induced stimulation of mitochondrial energy dependent reversible swelling, supported by succinate oxidation, cytochrome c (cyto-c) and sulfite oxidase (Sox) [both present in the mitochondrial intermembrane space (MIS)] are released outside. This effect can be observed at a valinomycin concentration as low as 1 nM. The rate of cytosolic NADH/cyto-c electron transport pathway is also greatly stimulated. The test on the permeability of mitochondrial outer membrane to exogenous cyto-c rules out the possibility that the increased rate of exogenous NADH oxidation could be ascribed either to extensively damaged or broken mitochondria. Accumulation of potassium inside the mitochondria, mediated by the highly specific ionophore valinomycin, promotes an increase in the volume of matrix (evidenced by swelling) and the interaction points between the two mitochondrial membranes are expected to increase. The data reported and those previously published are consistent with the view that “respiratory contact sites” are involved in the transfer of reducing equivalents from cytosol to inside the mitochondria both in the absence and the presence of valinomycin. Magnesium ions prevent at least in part the valinomycin effects. Rather than to the dissipation of membrane potential, the pro-apoptotic property of valinomycin can be ascribed to both the release of cyto-c from mitochondria to cytosol and the increased rate of cytosolic NADH coupled with an increased availability of energy in the form of glycolytic ATP, useful for the correct execution of apoptotic program.     

Light-induced generation of a protonmotive force and Ca2+-transport in membrane vesicles of Streptococcus cremoris fused with bacteriorhodopsin proteoliposomes

The light-driven primary proton pump bacteriorhodopsin has been incorporated in the cytoplasmic membrane of Streptococcus cremoris, in order to generate a protonmotive force across these membranes. This has been achieved by fusion of S. cremoris membrane vesicles with bacteriorhodopsin proteoliposomes. This fusion occurred when both preparations were mixed at low pH (less than 6.0), as shown by sucrose density gradient centrifugation and by dilution of fluorescent phospholipids incorporated into the bacteriorhodopsin proteoliposomes. Fusion was strongly enhanced by the presence of negatively charged phospholipids in the liposomal bilayer. When proteoliposomes were used that showed light-dependent proton uptake, the orientation of bacteriorhodopsin in the fused membranes was inside-out with respect to the in vivo orientation in Halobacterium halobium. Consequently, in the light a ΔΨ, interior positive and a ΔpH, interior acid were generated. This protonmotive force could drive calcium uptake in the fused membranes. The uptake increased hyperbolically with increasing light intensity and was abolished by bleaching of bacteriorhodopsin. Addition of the ionophore valinomycin stimulated calcium uptake and led to an increase of the ΔpH. Calcium uptake was strongly decreased in the dark and in the light in the presence of uncouplers, nigericin or both valinomycin and nigericin.     

Phospholipid vesicles containing bovine heart mitochondrial cytochrome c oxidase exhibit proton translocating activity in the presence of gramicidin.

Phospholipid vesicles containing bovine heart mitochondrial cytochrome c oxidase (COV) were characterized for electron transfer and proton translocating activities in the presence of the mobile potassium ionophore, valinomycin, and the channel-forming ionophore, gramicidin, in order to determine if the ionophores modify the functional properties of the enzyme. In agreement with previous work, incubation of COV with valinomycin resulted in a perturbation of the absorbance spectrum of oxidized heme aa3 in the Soret region (430 nm); gramicidin had no effect on the heme aa3 absorbance spectrum. Different concentrations of the two ionophores were required for maximum respiratory control ratios in COV; 40- to 70-fold higher concentrations of valinomycin were required to completely uncouple electron transfer activity when compared to gramidicin. The proton translocating activity of COV incubated with each inophore gave a similar apparent proton translocated to electron transferred stoichiometry (H+/e- ratio) of 0.66 +/- 0.10. However, COV treated with low concentrations of gramicidin (0.14 mg/g phospholipid) exhibited 1.5- to 2.5-fold higher rates of alkalinization of the extravesicular media after the initial proton translocation reaction than did COV treated with valinomycin, suggesting that gramicidin allows more rapid equilibration of protons across the phospholipid bilayer during the proton translocation assay. Moreover, at higher concentrations of gramicidin (1.4 mg/g phospholipid), the observed H+/e- ratio decreased to 0.280 +/- 0.020, while the rate of alkalinization increased an additional 2-fold, suggesting that at higher concentrations, gramicidin acts as a proton ionophore. These results support the hypothesis that cytochrome c oxidase is a redox-linked proton pump that operates at similar efficiencies in the presence of either ionophore. Low concentrations of gramicidin dissipate the membrane potential in COV most likely by a channel mechanism that is different from the carrier mechanism of valinomycin, yet does not make the phospholipid bilayer freely permeable to protons.     

The effect of trypsin treatment on the incorporation and energy-transducing properties of bacteriorhodopsin in liposomes

Bacteriorhodopsin and trypsin-modified bacteriorhodopsin have been reconstituted into liposomes by means of a low pH-sonication procedure. The incorporation of bacteriorhodopsin in these proteoliposomes is predominantly in the same direction as in vivo and the direction of proton pumping is from inside to outside the liposomes. The direction of proton translocation and electrical potential generation was studied as a function of the reconstitution pH. Light-dependent proton extrusion and generation of a Δp, interior negative and alkaline was observed at a reconstitution pH below 3.0 using bacteriorhodopsin, and at a pH below 3.5 using trypsin-modified bacteriorhodopsin. The shift in inflection point is explained in terms of differences between bacteriorhodopsin and trypsin-modified bacteriorhodopsin in a specific protein-phospholipid interaction which depends on the surface charge density of the cytoplasmic side of bacteriorhodopsin. The magnitude of the protonmotive force (Δp) generated by trypsin-modified bacteriorhodopsin in liposomes was quantitated. Illumination of the proteoliposomes resulted in the generation of a high Δp (135 mV, inside negative and alkaline), with a major contribution of the pH gradient. The ionophores nigericin and valinomycin induced, respectively, a compensatory interconversion of ΔpH into Δψ and vice versa. If no endogenous proton permeability of the membrane would exist, a protonmotive force could be generated of − 143 mV as electrical potential alone or − 162 mV as pH gradient alone.     

Control of respiration in sonicated cytochrome oxidase proteoliposomes by gated and ungated ionophores

Respiration of cytochrome oxidase-containing sonicated proteoliposomes is partially stimulated by nigericin or by alamethicin. Valinomycin at low concentrations fully releases the nigericin-dependent respiration but inhibits the alamethicin-dependent respiration. Respiratory stimulation by the gated ionophore alamethicin must occur in the face of a continuing membrane potential; stimulation by nigericin is accompanied by an increase in the measured membrane potential. We conclude that delta pH rather than delta psi may be the main source of respiratory control in our type of proteoliposomes.     

The K+-ionophores nonactin and valinomycin interact differently with the protein of reconstituted cytochromec oxidase

The K⁺-ionophores valinomycin and nonactin induce a qualitatively identical change of the visible spectrum of isolated oxidized cytochromec oxidase (red shift), but the amplitude is half with nonactin. Valinomycin, in the presence or absence of a protonophore, stimulates the respiration of the reconstituted enzyme to a higher extent than nonactin and results in a higherK _m for cytochromec. In contrast, nonactin causes a fivefold rate of proton conductivity across a liposomal membrane, after induction of a K⁺-diffusion potential. The data indicate that respiratory control by these antibiotics is not only due to degradation of a membrane potential, but rather to specific interaction with and modification of cytochromec oxidase.     

ATP synthesis by ATPase proteoliposomes from the thermophilic cyanobacterium Synechococcus 6716 by ionophore-induced electric potentials and proton gradients

ATP synthesis driven by low pre-established electric potentials and pH gradients is studied in large ATPase proteoliposomes, prepared from the ATPase complex and native lipids from the thermophilic cyanobacterium Synechococcus 6716. Electric potentials and pH gradients were achieved by valinomycin and nigericin, respectively, in the presence of a K⁺ gradient across the membrane. External base-pulses were also applied. In this system ATP synthesis driven by valinomycin-induced K⁺ influx, nigericin-induced internal acidification and by external base-pulses is demonstrated. Electric potentials and pH gradients of equivalent size lead to roughly similar ATP synthesis activities. ATP synthesis is optimal at 80–100 nM valinomycin and at 0.75−1 μM nigericin at the proper pre-set ion gradients. Uncoupler and DCCD inhibit ATP synthesis. Prior activation of the complex by thiol agents or trypsin was not required for synthesis activity. The ATP synthesis rate increases with the size of electric potential or pH gradient. The threshold value of the electrochemical gradient for significant ATP synthesis is about 30 mV. ATP production proceeds for more than 60 min. The generation of ionophore-induced electric potentials and pH gradients have been followed by oxonol VI and intraliposomal Neutral red, respectively. The extent of the absorbance changes of both probes is proportional to the size of electric potential or pH gradient. Ionophore-induced oxonol VI and Neutral red responses are stable for at least 30 min. The results are discussed in terms of membrane permeability and vesicle size.     

β-Glucosidase of Aspergillus aculeatus

Two kinds of cytochrome c oxidase were partially purified from iron-grown T. ferrooxidans. The first type (cytochrome c oxidase I) was easily solubilized without a detergent and had a pH-optimum at 3.0. The other (cytochrome c oxidase II) which was bound tightly to the cell membrane and solubilized with sodium dodecyl sulfate had a pH-optimum at 5.2. Each type was heat-sensitive and inhibited by cyanide and azide. Since the pH level of the bacterial iron oxidizing activity corresponded closely with the pH of cytochrome c oxidase I but not cytochrome c oxidase II, it was proposed that the former may play an important role in the iron oxidizing system.     

Control of electron transfer by the electrochemical potential gradient in cytochrome-c oxidase reconstituted into phospholipid vesicles

The kinetics of electron transfer between cytochrome-c oxidase and ruthenium hexamine has been characterized using the native enzyme or its cyanide complex either solubilized by detergent (soluble cytochrome oxidase) or reconstituted into artificial phospholipid vesicles (cytochrome oxidase-containing vesicles). Ru(NH3)2+6 (Ru(II] reduces oxidized cytochrome a, following (by-and-large) bimolecular kinetics; the second order rate constant using the cyanide complex of the enzyme is 1.5 x 10(6) M-1 s-1, for the enzyme in detergent, and slightly higher for COV. In the case of COV the kinetics are not affected by the addition of ionophores. Upon mixing fully reduced cytochrome oxidase with oxygen (in the presence of excess reductants), the oxidation leading to the pulsed enzyme is followed by a steady state phase and (eventually) by complete re-reduction. When the concentrations of dioxygen and oxidase are sufficiently low (micromolar range), the time course of oxidation can be resolved by stopped flow at room temperature, yielding an apparent bimolecular rate constant of 5 x 10(7) M-1 s-1. After exhaustion of oxygen and end of steady state, re-reduction of the pulsed enzyme by the excess Ru(II) is observed; the concentration dependence shows that the rate of re-reduction is limited at 3 s-1 in detergent; this limiting value is assigned to the intramolecular electron transfer process from cytochrome a-Cua to the binuclear center. Using the reconstituted enzyme, the internal electron transfer step is sensitive to ionophores, increasing from 2-3 to 7-8 s-1 upon addition of valinomycin and carbonyl cyanide m-chlorophenylhydrazone. This finding indicates for the first time an effect of the electrochemical potential across the membrane on the internal electron transfer rate; the results are compared with expectations based on the hypothesis formulated by Brunori et al. (Brunori, M., Sarti, P., Colosimo, A., Antonini, G., Malatesta, F., Jones, M.G., and Wilson, M.T. (1985) EMBO J. 4, 2365-2368), and their bioenergetic relevance is discussed with reference to the proton pumping activity of the enzyme.     

Regulation of neuropeptide Y (NPY) binding by guanine nucleotides in the rat cerebral cortex

The Na+-motive NADH oxidase activity from Vibrio alginolyticus was extracted with octylglucoside and reconstituted into liposomes by dilution. On the addition of NADH, the reconstituted proteoliposomes generated delta psi (inside positive) and delta pH (inside alkaline) in the presence of a proton conductor CCCP, and accumulated Na+ in the presence of valinomycin. These results indicate that the NADH oxidase activity, reconstituted in opposite orientation, leads to the generation of an electrochemical potential of Na+ by the influx of Na+.     

The cytochrome c oxidase of Paracoccus denitrificans pumps protons in a reconstituted system

The purified two-subunit cytochrome c oxidase of Paracoccus denitrificans was reconstituted into phospholipid vesicles having a high internal buffering capacity and exhibiting a respiratory control index greater than 6.6. With these proteoliposomes, pH changes of the suspending medium were monitored in response to reductant pulses in the presence of valinomycin and potassium. When reduced cytochrome c was added to allow for a limited number of turnovers (2-12), a net acidification of the extravesicular space could be observed. This apparent proton ejection by the vesicles was abolished by inhibition of the oxidase with azide, by bypassing the oxidase with ferricyanide, or by preventing charge compensation by omitting valinomycin. Addition of uncoupler led to an alkalinization, rather than an acidification, of the extravesicular space in response to reduced cytochrome c. We thus conclude that cytochrome c oxidase of P. denitrificans is a proton pump. Under the conditions described here, an apparent stoichiometry of 0.6 proton ejected/electron was obtained by extrapolation to zero turnovers.