33

Biochimica et Biophysica Acta, 1054 (1990) 33-40

Elsevier BBAMCR 12740

The energy requirements of pH homoeostasis define the limits of pH regulation - a model Harald Kugel 1, Adalbert Mayer 1, Gunter O. Kirst 2 and Dieter Leibfritz 3 I Fachbereich 1-Physik, 2 Fachbereich 2-Biologie and 3 Fachbereich 2-Chemie, Universitiit Bremen, Bremen (F.R.G.)

(Received 4 January 1990)

Key words: NMR, 31p_;pH regulation; Proton/hydroxide transport; ATP; (Platymonas subcordiformis)

The regulation of intraceilular pH of Platymonas subcordiformis cells is investigated with 31p_NMR spectroscopy at various external pH values. The limits of pH homeostasis differ between respiring cells and cells solely glycolyzing. The former retain their normal cytoplasmic pH for external pH values from 5 to more than 12, while in the latter intracellular pH is less stable below external pH 6, and external pH of more than 11 causes hydrolysis of intracellular polyP. The power necessary to maintain a stable intracellular pH is calculated form the electrochemical potential and H ÷ / O H - flux rates across the cell membrane. H + / O H - transport across the membrane by diffusion as well as through hydrogen-bonded chains is considered. Comparison of the minimal power necessary to keep intracellular pH stable at various external pH values by ATP consuming processes with the estimated power available to aerobic and anaerobic cells in the dark shows that different energy turnover may explain the different behaviour of the cells when exposed to extreme pH values.

Introduction The regulation of cytoplasmic pH is fundamental to cell metabolism. Various metabolic pathways change their activity or even their direction (synthesis versus degradation) in relation to the pH. Cytoplasmic pH may therefore play a role as metabolic regulator, signalling specific states of the cell to pH sensitive cellular processes [1,2]. Especially in order to allow cytoplasmic pH to respond to processes within the cell, it is necessary to maintain stable cytoplasmic pH independent of varying conditions in the environment of the cell [3]. Phytoplancters living in tidal waters may be exposed to conditions of anaerobiosis as well as low or high pH along with different salinities. Mechanisms to stabilize internal pH against the impact of varying external pH working even under conditions of anaerobiosis are a prerequisite for survival. Internal pH values have been measured in several macro- and microalgae at varying external pH (4-7). The algae maintain a stable internal pH over a certain range of pH in the medium. However, NMR investiga-

Correspondence (present address): H. Kugel, Department of Diagnostic Radiology, University of Cologne School of Medicine, JosephStelzmann-Strasse 9, D-5000 Ktiln 41, F.R.G.

tions showed a decrease of cytoplasmic pH when switching from aerobic to anaerobic conditions in the dark of typically 0.5 units [6,8,9]. A smaller decrease as reported [10] in Dunaliella paroa is probably due to insufficient removal of oxygen from the samples.Platymonas subcordiformis is an euryhaline microalga living in tidal waters, tolerating a wide variety of salinities [11,12]. Deviations of the external pH from its normal value in seawater (pH 8) to higher values up to 11 - occurring at high cell densities in the light - are also tolerated (Kirst, unpublished data). A closer inspection of cytoplasmic pH of Platymonas at varying external pH revealed that the value typical for respiring cells in the dark as well as the value typical for solely glycolyzing cells remained nearly unaffected. Thus, the typical difference of pHeyt between respiring and anaerobic cells was not affected by external pH in the range 6 to 12 [9], while there are differences between the two metabolic states concerning the limits of pH stabilization. The mechanisms of pH homeostasis in microorganisms are still under investigation. While short-term homeostasis may be accomplished by buffering processes [13], long-term stabilisation calls for an active removal of excess H ÷ or O H - from the cell, for example by direct or indirect pumping processes [13,14]. There have been doubts about the role of proton pumps based on their (high) requirements for ATP [15].

0167-4889/90/$03.50 © 1990 Elsevier Science Publishers B.V. (Biomedical Division)

34 Here the estimated energy requirements of active p H regulations at various external p H will be related to energy available to Platymonas cells, giving a possible explanation for the behaviour of cellular metabolism at external pH.

Titrations of external p H were done in the N M R tube by addition of small amounts of HC1 or N a O H . The p H of the suspension was checked immediately before and after recording each spectrum.

Experimental results Materials and Methods Cultures of P. subcordiformis (Hazen) were obtained from the culture center at GiSttingen (F.R.G.) and grown in artificial seawater containing 410 m M NaC1 in a biostat under continuous light (10 W m -2) as described [16]. Cells assigned for measurement were transferred to culture flasks and kept in a 16 h light/8 h dark regime, for 3 d, bubbled with air. Algae were prepared for measurement by washing in an isotonic medium free of phosphate and free of paramagnetic ions as Mn 2 ÷ and centrifugation at 180 × g for 2 rain. The final pellet, 0.95-1 ml packed volume, determined by centrifugation of aliquots at 5000 × g for 1 min - was transferred to an N M R tube (15 m m OD) and resuspended in artificial seawater without phosphate and microelements to 5 ml suspension. Spectra were obtained on a Bruker WH360 at 145.78 M H z in the F T mode, unlocked and without decoupiing. Pulses with a flip angle of 80 o and a repetition time of 1 s were used. Spectra were accumulated within 10-20 min. To avoid sedimentation and to maintain either aerobic or anaerobic conditions, the cell sample was gassed with N 2 resp. air with a flow rate of 200 m l . min -1 between two successive pulses using an automatic valve synchronized to the spectrometer [8]. Due time was allowed for all gas bubbles to leave the sample before each pulse. Chemical shifts were determined with a spectral resolution of 0.03 ppm. They were referenced against a 1 M solution of methylene biphosphonic acid contained in a concentric capillary in the sample volume; each capillary used was referenced against 85% H a P O 4 yielding chemical shifts between +18.80 p p m and + 19.05 p p m for different reference capillaries. Cytoplasmic p H values were determined from the chemical shift of the signal of cytoplasmic inorganic phosphate. A p H calibration curve for the chemical shift of cytoplasmic Pi was obtained using a solution containing ions in concentrations resembling intracellular ion concentrations of Platymonas [9]. Relative p H determinations are possible with a precision of +__0.05 p H units in the region between p H 6.0 and p H 7.6 and + 0.07 p H units from p H 7.6 to p H 8.0. The absolute determination of p H e y t depends on the precise reproduction of the cytoplasmic milieu in vitro for calibration. The systematic error due to mismatch of the calibration medium can be estimated to be less than 0.2 p H units [9].

Aerated cells maintain a p H typical for respiring cells at external p H between 5.3 and 12.3. It increases with a slope of about 0.05 units p n i n t / p H e x t - from 7.5 at PHex t 5.3 to 7.8 at PHex t 12.3. Below pHex t 5.3 pHcy t decreases. At pHex t 3.8 it is as low as 6. (Cytoplasmic p H values below 6 are difficult to estimate from N M R spectra, because the signal of Pi approaches the signal of phosphomonoesters, so that due to the line width of both signals it is difficult to determine the chemical shift of Pi exactly. Moreover, below p H 5.5 the chemical shift of Pi is nearly insensitive to pH.) Anaerobic cells in the dark maintain a p H typical for cells with glycolysis as sole energy source only above PHex t 6. PHcyt increases from 7.0 at pHex t 6.5 to 7.3 at pHex t 12.1. Below pHex t 6 pHcy t is less stable. It decreases to about 6.4 at p H ~xt 4.1, corresponding to a slope of 0.29 units pHcy t per unit pHex t (Fig. 1). An advantage of 31P-NMR is the capability to follow the status of cellular energy metabolism and cytoplasmic p H at the same time. Aerated ceils show the typical features of well energized respiring ceils between pHex t 5.3 and 12.3, i.e., a low level of inorganic cytoplasmic pH, clearly visible signals of nucleotide phosphates with A T P exceeding ADP, and a signal assigned to the phosphagene phosphoarginine (PArg) (Fig. 2). The spectra at PHex t 4 and below are different: neither A T P nor A D P signals remain visible, indicating that the energy requirements to counteract acidification exceed the energy supply, so that no detectable level of nucleotides can be maintained. The breakdown of the nucleotide signal as well as the acidification of the cytoplasm 8

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Fig. 1. Cytoplasmic pH versus external pH in cell suspensions as determined with 31P-NMR in aerated (filled symbols) and anaerobic (open symbols) cell suspensions. Bars indicate accuracy of pH determination from measured chemical shift of pHcy t. Data partially reproduced from [9]. The marks (a)-(f) correspond to spectra shown in Fig. 2.

35

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SPECTRA OF ANAEROBICCELL SUSPENSIONS

Fig. 2. Spectra of aerated (a, c, e) and anaerobic (b, d, f) cell suspensions at selected pHext, corresponding to marked pH values in Fig. 1. Spectrum (f) shows disintegration of polyP at PHex t 11.0 in anaerobic cells (elevated level of terminal phosphate residue PP-1), while there is no PP-1 signal in aerated cells even at PHex t 12.3 (spectrum (e)).

is reversible upon raising pH~xt. In alkaline media up to PHext 12 no significant deviations from normal spectra are observed. The disappearance of the ADP peaks parallel to the ATP signal shows that hydrolyzed ATP does not necessarily show up as ADP. In 31p-NMR spectra of Chlorella fusca loss of ATP is not balanced by gain of ADP and Pi upon the transition from aerobic to anaerobic conditions [8]. The same applies to Tetrahymena upon heat shock [17]. There are two possible explanations: (a) ADP is immobilized by bonding to enzymes (or any other mechanism) so that it is not fully detectable with N M R [8]; or (b) ADP is further hydrolyzed to AMP or even unphosphorylated nucleosides [17]. Any signal of AMP will be masked by the broad sugar phosphate signal. The specta of anaerobic cells show their typical features as well: only a small ATP-y-signal is visible next to a fl-signal of ADP, there is no PArg, and Pi is increased. Below pHex t 6, nucleotide signals disappear.

At pHex t 3.9, spectra of aerated cells are indistinguishable from spectra of anaerobic cells. There is a difference between aerated and non-aerated cells at alkaline pH~xt with respect to polyP. Above PHext 11 in anaerobic suspensions when pHcyt reaches 7.3, polyP chains start to disintegrate, as can be seen from the increase of a signal at - 5 ppm, which originates from pyrophosphate (PPi) and terminal groups of polyp (PP-1). Growing intensity of terminal and penultimate signals of polyp relative to the core signal indicate a shortening of the average chain-length. Further alkalisation of the medium up to pHex t 13 enhances the disintegration of polyP. The disintegration is not reversible upon returning to a normal pHcx t of 8. The cells still retain their capability of oxidative phosphorylation, though. In aerated cells no effect on the polyP pool is observed, even though pHcy , in these cells eventually goes up to 7.8. Distintegration of polyP in P. subcordiformis cells

36 may be interpreted as a response to alkaline stress in the cytoplasm of non-respiring cells. This interpretation is supported by the effect of alkaline stress on the cytoplasm caused by addition of NHaC1 to media at normal pHex t [9]. Hydrolysis of polyP can act as an additional pH buffer. It may serve as an additional energy buffer as well, which is used to fuel some pH-stabilizing mechanism. In any case, the onset of irreversible disintegration of polyP marks the point where regulation of cytoplasmic pH is no longer efficient enough to prevent severe changes of phosphate metabolism. Considering both cytoplasmic pH and effects on the polyP pool, PHcyt is kept sufficiently stable in the range between pHex t 5 and 12 in respiring cells, while regulation in solely glycolyzing cells is efficient only between pHext 6 and about pHex t 11. Discussion

L Energetics of Platymonas The two metabolic states as represented by spectra typical for respiring cells in the dark and spectra typical for glycolyzing cells in the dark correspond to two different states of energy supply. Respiring cells in the dark gain energy available as phosphate-bonding energy in ATP by oxidizing glucose equivalents. Electron micrographs show large starch grains in Platymonas [18], so there is sufficient substrate for a considerable length of time (tricarboxylic acid cycle assumed). This is supported by the fact that starch is not degraded before about 14 d in cells kept under continuous dark conditions (Kirst, unpublished data). ATP turnover can be estimated from oxygen consumption during dark respiration. Per 6 mol 02, 1 mol glucose equivalent is mobilized from starch and oxidized to 6 mol CO 2 and 6 mol H20; 36 mol ATP are synthesized from ADP - including ATP production during the glycolysis preceding the tricarboxylic cycle and assuming that cytoplasmic NADP is converted to ATP as well [19]. The respiration rate of a typical sample of Platymonas under measurement conditions has been measured as 2 mg 02 1-1 sample volume s-1. Cellular volume amounts to 15% of total sample volume. Converted to cellular volume, the oxygen consumption is 13 mg 02 1-1 rain-1 equivalent to 6.8/~mol 02 1-1 s -1. Using this amount of oxygen, 41 /tmol ATP 1-1 s -1 will be produced, which upon hydrolysis to ADP releases an energy of 2.2 J s-1 1-1 (assuming an energy release of 55 KJ mo1-1 under in vivo conditions [20]). P. subcordiformis has a cell volume of typically 440.10 -is 1 (interpolated from [16]), so it is capable to provide the power of 9.7- 10 -13 W to fuel processes by hydrolyzing the ATP produced during respiration.

The accuracy of the values given here is limited by two factors: the determination of the cellular volume is done with an accuracy of +15%; the actual energy released upon the hydrolysis of ATP depends on several factors such as the degree of Mg 2÷ complexation and the actual local concentration of ATP, ADP and Pi in the compartment where hydrolysis takes place. These parameters are not known exactly, so the value of 55 KJ mo1-1 is only an approximative one. Especially when comparing different metabolic states as glycolysis and respiration resulting in different phosphorylation potentials, the specific energy release may vary by about 10%. Aquatic plants can survive anoxic conditions, so in general the glycolytic pathway will not be suppressed by switching off respiration and subsequent accumulation of metabolic intermediates. On the other hand, there is no indication of a large Pasteur effect ([21], Chpt. 6). So, we assume that the rate of consumption of carbohydrates is about the same during respiration as during glycolysis in the dark. Then 2.3/tmol ATP 1-1 cellular volume s -1 are produced during glycolysis, 1/18th of the amount in respiring cells. A single cell, therefore, can provide a power of 5.3 • 10 -14 W using ATP transported energy. Raven [20] gave an estimation of the minimal power a single cell needs for maintenance processes - repair processes etc. to keep the organism alive - together with an estimation of power requirements for growth. For a model freshwater cell with a volume of 524.10-15 1 slightly larger than Platymonas - he calculated 39. 10 -12 W for growth at a typical rate and 5.4.10 -14 W for maintenance processes, based on the calculation of energy output rates for maintenance respiration. If one assumes that these power requirements will be of the same order in a marine organism, comparison of the values shows t h a t Platymonas cells depending on glycolysis as their only energy source can provide the power required to keep the organism alive. Respiring Platymonas cells provide more power, but it does not meet power requirements for typical growth, which requires additional energy input by photophosphorylation.

II. Energy requirements of pH homeostasis The estimation given here for the energy required to maintain a stable cytoplasmic pH under varying external pH depends on two assumptions: (a) pH homoeostasis is accomplished by an active, energy-requiring process; and (b) H ÷ / O H - flux into or out of the cell depends superlinearly on the pH-difference, A pH, between cytoplasm and external medium (i.e., the second derivative of H + / O H - flux with respect to A pH is positive). (a) While short-time regulation of pHcyt may be accomplished by physico-chemical buffering and the translocation of H + / O H - to and from cellular com-

37 partments, pH regulation against longer lasting loads requests an active removal of H ÷ or O H - from the cell by plasma membrane pumps or metabolic adjustments [13]. Platymonas, living in tidal regions, depend on longer term stabilization, as pH stress will eventually last for periods in the order of the tidal cyclus. The lack of a large vacuole in these cells excludes regulation of cytoplasmic pH by depositing excess protons into a vacuole. While H+-ATPases have been proposed by a number of authors [22,23], other H +-transporting mechanisms such as N a + / H + antiporters are possible as well [24]. The knowledge of a special mechanism is not essential for the estimation of a minimal power requirement of pH homoeostasis, provided that excess H + / O H - is finally extruded from the cell and that the extrusion process is linked directly or indirectly to ATP hydrolysis. (b) The second assumption - a superlinear dependence of H + / O H - flux crossing the plasmalemma on ApH - needs a more detailed foundation. The supposition that H + / O H - fluxes through a phospholipid membrane can be calculated simply by integrating the electrodiffusion equation and using a constant permeability known by measurement or estimation has turned out to be too simple. Gutknecht [25] and Nichols and Deamer [26] demonstrated that H + / O H - flux through lipid bilayers does not change much with pH. This means that the flux is not the result of a simple electrodiffusion process as described by the Goldmann equation. Proposed alternative mechanisms are H + / O H - transport mediated by weak acids or bases in the membrane [27] and transport via hydrogen-bonded chains of water molecules [28]. Nagle points out that a special arrangement of hydrogen bonds, namely transient hydrogenbonded chains crossing only a single monolayer most of the time instead of going all the way across the membrane bilayer, will give a superlinear dependence of flux on the driving potentials as pH-gradient A pH or electric transmembrane potential A~/'. H + and O H - transport are equivalent as permeation of O H - equivalents through hydrogen-bonded chains can occur as translocation of proton defects. There are some indications that this model may apply to bilayers: Verkman [29] measured a superlinear dependence of proton flux on A pH in brush border membrane vesicles, and Deamer [30] investigating liposomes from egg phosphatidylcholine and phosphatidic acid found a flux J given by the equation: J ~ J0sinh(2.3 . A p H )

(1)

as predicted by Nagle [28] for transient hydrogenbonded chains. Considering biological membranes, consisting of mixtures of lipids and containing proteins, there might be additional processes contributing to H + / O H - flux,

which are describable as diffusion, especially in marine organisms. Though transmembrane transport proteins usually are highly specific, a diffusion-like proton leakage is not excluded. Additionally, non-electrogenic diffusion of undissociated acids may contribute to proton transport. Undissociated HC1 or HNO 3 have a high permeability through lipid bilayers [31,21]. Mainly CI-, but also HSO4, NO3 and other anions are present in seawater. In Platymonas, the limit of stable PHcy t is shifted towards a lower PHex t by about one unit if artificial seawater is substituted by an isotonic solution of sorbitol (data not shown). This supports the assumption that substances in seawater augment H + flux across the membrane. Consequently, H + / O H - flux can be described as exponential function of A pH across the plasmalemma, which is determined by PHex t as long as pHcy t remains unchanged. The dependence will retain its exponential character whether there is a diffusion like contribution or not. The dependence of flux on the electric transmembrane potential Ag, is less clear. There is a linear dependence in brush border membrane vesicles [29]. Nagle [28] predicts a superlinear dependence for the partial transient hydrogen-bonded chain model mentioned before. The influence of A~/,on flux is difficult to predict, if contributions of non-electrogenic flow of undissociated acids or bases have to be taken into account. The following calculations show that variations of Ag, within reasonable limits will result only in minor perturbations of the flux as a function of pHex t. To show the general characteristics of H + / O H - flux as a function of exp(PHext) the H + / O H - flux will be modelled as a pure diffusion process using the Goldman equation first. Deviations of the results if the flux is described by the partial transient hydrogen-bonded chain model without diffusion (using Eqn. 1) will be discussed afterwards. To maintain a given cytoplasmic pH, a permanent action must be taken to remove just as many ions - H + or O H - - as enter the cell following a driving potential ApH or A~/,. The minimal energy that is necessary to remove a single ion is equivalent to the loss of potential energy that the ion experiences by passing the membrane, given as the electrochemical potential difference across the plasmalemma. The minimal power Pstab nece s s a r y to stabilize pHcyt is therefore given by the number of ions entering the cell (resp. leaving the cell) per unit time: Pstab = JH+/OH -'A]'t

(2)

where A# is given by: A/t = 2.303RT(pHin t - p H e x t ) - FA~

(3)

38 Following the G o l d m a n n equation [32] at low external pH, the flux JH÷ of protons into a single cell is given as: - K'A~ JH ÷ = P H + ~

3

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Fig. 3. P o w e r r e q u i r e m e n t o f a s i n g l e cell for a c t i v e p u m p i n g of H + / O H - v e r s u s e x t e r n a l p H at m e m b r a n e p o t e n t i a l zY/, = - 1 0 0 m V (resp. - 4 0 m V a n d - 2 0 0 m V , b r o k e n lines) c a l c u l a t e d for d i f f u s i o n d e s c r i b e d b y t h e G o l d m a n n e q u a t i o n . (a) level o f p o w e r a v a i l a b l e to a r e s p i r i n g cell; (b) level o f p o w e r a v a i l a b l e to a s o l e l y g l y c o l y z i n g cell.

(5) Total H + / O H - flux is given as the sum J o n - + JH+Membrane potentials in algae have been measured to lie between - 4 0 mV and - 2 0 0 mV (inside negative). For the calculation here a value of - 1 0 0 mV is assumed. Maximal polarization will decrease A~/, not below - 2 0 0 mV and maximal depolarization will lead to A~/, not above - 4 0 mV. With A~/, in this range, the denominator 1 - e (K'a~') assumes values between 0.8 and 1. H + / O H - flux vanishes if pHex t reaches the value of 9.4. Measured values for PH+/OH- range from 1.4-10 - 6 to 10 -8 m s -1 [30], usually determined in purified bilayers. The value of 1.4- 10-6 m s-a was measured at physiological p H for plant phospholipids, which seems to be closest to an algal membrane. Permeabilities of H ÷ and O H - are assumed to be equal. The H + / O H - flux tending to decrease A p H across the plasmalemma is given as the sum of H+-flux (Eqn. 4) and O H - flux (Eqn. 5). Jri + depends mainly on pH~xt as this term determines the value of the difference in brackets, as soon as PHext lies below PHin t + K"A~/" (approx. 9.4). Jots- is determined mainly by Pnin t (as ( p H i , t - 14) is the larger exponent in the brackets) and therefore nearly constant at fixed PHin t. Above pHex t 6.4 H + / O H - flux is dominated by Jon , below pHex t 6.4 by J , + . At PHex t 6.2 H ÷, flux into the cell reaches the value of H ÷ production by glycolysis alone (7.6-10 -19 mol H ÷ s -1 per cell) calculated following Busa and Nuccitelli [21. Between pHex t 6 and 5, H ÷ flux reaches values above which the cytoplasm suffers from a rapid acidification ( A p H : 1 in the order of minutes), even if there is a cytoplasmic buffering capacity/3 of 5 0 . 1 0 -3 mol H ÷ 1-1 p H - 1 (which is a typical value according to Ref. 33). As A,/, appears in the smaller exponent, it has a negligible influence on the factor in brackets in Eqns. 4

and 5. H + flux therefore depends only linearly on A,/,, but exponentially on pHex t. Variations of A,/, thus can not efficiently counteract an acidification of the cytoplasm at low pHex tThese arguments apply for both aerobic and anaerobic cells, as small variations of pHin t have no effect on Jn+ either. Extreme alkaline media - pHex t > 9.6 - reverse the sign of flux. H ÷ flux is directed out of the cell, O H flux into the cell. Following a similar argument as before, now JOH- dominates H + / O H - flux, while JH+ depending on p H i , t remains small. Considering changes of sign as A p H driven O H flux is directed against its electric potential, JoB- is given as JoH_=_PoH_K,A~it. lO3(lo(PHext-14+K"a,t")_loPHi, L 14)

(6)

10 (pHext-14+K''aq') is the dominating term in the brackets, consequently J O H - n o w depends exponentially on the p l a s m a l e m m a potential. Inserting fluxes as given by Eqns. 4, 5 or 6, respectively, into Eqn. 2 gives minimal power requirements for active homoeostasis. With A~/, = --100 mV, the result is given as a function of pHex t in Fig. 3. To show the effect of variations in A,/, values for A,/, = -- 40 mV and - 2 0 0 mV are given as dashed lines. Intersections of power requirements with the lines representing estimated powers available to respiring respective anoxic cells in the dark mark the limits of the range of PHex t, inside which there is enough ATP to fuel p H homoeostasis. Outside these limits major deviations from normal cell metabolism will occur. The intersections lie 1 to 1.5 units shifted to lower resp. higher pHex t for respiring compared to those for anaerobic cells, thus allowing a broader range of pnex t for respiring cells to retain their normal metabolic state. This agrees with experimental results.

39 While depolarisation at acid pHex t has only little influence on the limits of stabilization, hyperpolarization in the alkaline can efficiently support p H regulation. But electrogenic H + / O H - p u m p s will rather increase polarization at acid pHex t and decrease polarization at alkaline PHext, while non-electrogenic cotransports require additional energy for active transport of the co-transported ion.

Conclusion Transport of H + / O H - by diffusion is characterized by a membrane permeability PH+/OH -. The fact that permeabilities of protons through lipid bilayers measured at fixed driving potentials (zapH resp. A~/,) are not independent of p H [27] caused the discussion of alternative transport mechanisms. Transport through transient hydrogen-bonded chains without contribution of diffusion processes gives a flux described by Eqn. 1. Here, the m e m b r a n e is characterized by a p H independent specific flux J0 instead of PH+/OH -. Given a fixed pHin t this equation gives an exponential dependence of JH+/OH - on PHex t as well. Values of J0 have not been published so far, but they can easily be calculated from a given PH+/OH measured at a fixed ApH. Using a value of J0 consistent with PH+/OH - and considering A p H as the only driving potential, the flux resulting from Eqn. 1 will differ from the flux given by the G o l d m a n equation by not more than a factor of 3 within the range of pHex t considered here. This is not more than another uncertainty that has to be taken into account, resulting from the fact that any mechanism works with an efficiency of less than one, thus requiring a larger power than the minimal power given here. The assumption of constant power available to respiring cells within the limits of stable pHcy t has to be questioned as well. A larger A T P demand may increase the respiration rate, but as measured rates after uncoupling do not exceed 260% of the control rate [34], variations in available energy will be less than one order of magnitude. Assuming transport through hydrogen-bonded chains alone or a mixture of this type of transport and diffusion will vary the exact position of the limits of active homoeostasis, but not change the overall features given using the G o l d m a n n equation, concerning the dependence of flux on pHex t. The dependence of flux on A~/, is more speculative. Nagle [28] predicts an exponential one for the partial transient hydrogen-bonded chain model. Verkman [29] measured a linear dependence in brush border m e m brane vesicles for A~p ranging from 20 mV to 90 mV. Contributions of non-electrogenic flow of undissociated acids or bases will decrease the influence of A~/, on total H + / O H - flux.

The effect of a linear dependence of J on A~/, on homeostasis power resembles the situation employing the G o l d m a n n equation at acid PHex t, while an exponential dependence is modelled at alkaline pHex t. The real influence of A~ on JH+/OH m a y be stronger than displayed in Fig. 3 at acid pH~x t and it m a y be less than displayed there at alkaline pH~xt. The limitations of the model discussed here do not change the fact that the power available to a cell imposes limits on factors like external pH, outside which p H stabilization by mechanisms drawing their energy directly or indirectly from A T P is not possible. Photosynthesizing cells produce A T P at a higher rate than respiring cells in the dark. The cell has a larger power to counteract stresses at its disposal. Illuminated Platymonas m a y resist even lower pH~x t than respiring cells - a smaller portion of photosynthetically produced energy can be used for growth processes at extreme pH~xt, so that longer endurance of extreme pHex t impairs growth. Probably this is a reason for the formation of cysts, that is observed with Platymonas sp., if the algae are subjected to pH~x t of 6.0 or less respective 9.5 or more for a longer time [35].

Acknowledgements We are grateful to the Deutsche Forschungsgemeinschaft for financial support.

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