Cytosolic acidification by weak lipophilic acids
To investigate short-term cytosolic pH regulation in the acidophilic unicellular green alga E. viridis, the cytosol was acidified by adding the lipophilic weak acids acetate or propionate to the perfusion solution (Fig. 1). To estimate the range where cytosolic acidification had a physiological effect, dark respiration was measured at different acetate concentrations. At an external pH of 5.6, the perfusion of 0.1, 1.0 or 10 mM acetate (0.012, 0.12 or 1.2 mM membrane-permeable acetic acid (AcH), respectively) had no significant effect on respiration in Eremosphaera. Instead of further increasing the acetate concentration in the perfusion medium, the external pH was lowered to pHout = 4.6 to increase the concentration of AcH, the protonated membrane-permeable form. At pH 4.6, the perfusion of 10 mM acetate (5.9 mM AcH) resulted in a doubling of the rate of respiration, from 1.4 to 2.8 mol O2 (mol Chl h)−1 (Supporting Information Fig. S1a). Propionate had an effect on respiration that was comparable to that of acetate. Photosynthetic oxygen evolution at pHout = 4.6 was more sensitive against perfusion of acetate. From a slight decrease at 2 mM acetate, oxygen evolution had completely vanished at 10 mM acetate (Fig. S1b). Millimolar concentrations of acetate at pHout= 4.6 resulted in a cytosolic acidification that affected both respiration and photosynthesis.
Control measurements showed that a decrease in the external pH from 5.6 to 4.6 did not affect the rate of photosynthesis (70 ± 5 mol O2 (mol Chl h)−1; n = 14) or the rate of respiration (approx. −2% of the photosynthesis rate; n = 16). Even a decrease of the external pH value to 3.0 had no effect on photosynthetic O2 evolution. A decrease of the external pH from 5.6 to 4.6 did result in a depolarization, ΔE = 11 mV, and a slight decrease in plasma membrane resistance, but no significant change in cytosolic pH and K+ concentration (Table S1). A decrease of the external pH from pH 5.6 to pH 3.6 resulted in a more pronounced depolarization (ΔE = 19 ± 2 mV, n = 14) of the plasma membrane and a small, but significant, cytosolic acidification (ΔpHcyt = −0.09 ± 0.01, n = 14). Being adapted to an acidic environment –Sphagnum bogs –Eremosphaera is obviously little affected by a moderate acidification of the perfusion medium.
Applying a constant dose of acetate over different time intervals
To allow a quantitative analysis of cytosolic pH changes, constant doses of the weak lipophilic acid acetate were applied to single algal cells over different periods of time, as follows: 1 mM acetate (AcH = 0.59 mM; pHout = 4.6) was perfused for 30 min, 2 mM acetate (AcH = 1.17 mM) was perfused for 15 min, 4 mM acetate (AcH = 2.34 mM) was perfused for 7.5 min, or 10 mM acetate (AcH = 5.9 mM) was perfused for 3 min. By doubling the external concentration of weak acid the driving force for uptake, and thus the influx rate, was doubled. Reducing the perfusion time to 50%, while doubling the influx rate, resulted in the same total amount (constant dose) of weak acid loaded into the cell. Using pH-selective microelectrodes the membrane potential and the cytosolic pH value were recorded during the four different acetate perfusion regimes (Fig. 2). Obviously, cytosolic acidification was not the same for the four different perfusion protocols. At 1 mM acetate, cytosolic acidification was rather small and was back regulated already during the 30-min perfusion interval. The membrane potential either showed a slight hyperpolarization or a depolarization as it was observed at higher acetate concentrations (Fig. 2). Increasing acetate concentrations resulted in increasing rates of acidification, increasing maximum acidifications at the end of acetate perfusion and increasing rates of recovery after acetate perfusion was stopped. Recovery of cytosolic pH was usually complete within 10 to 15 min (Fig. 2, Table 1). Control experiments with 2 and 10 mM propionate instead of acetate showed very similar results with slightly increased cytosolic acidification.
Figure 2. Effect of acetate on membrane potential, E, and cytosolic pH value, pHcyt. Acetate was applied at a constant dose by choosing the perfusion time inversely proportional to the acetate concentration (10 mM for 3 min, 4 mM for 7.5 min, 2 mM for 15 min and 1 mM for 30 min). During the perfusion of 2 mM acetate, the light was switched off for approx 3 min (illumination protocol indicated by black and white bar) to elicit characteristic light-induced cytosolic pH changes. Otherwise all experiments were performed under photosynthetically saturating white light.
Download figure to PowerPoint
Table 1. Effect of four different acetate concentrations on the cytosolic pH of Eremosphaera
|[Acetate]||Acidification ΔpHP||Recovery ΔpHR||Rate of acidification ΔpH min−1||Rate of recovery ΔpH min−1|
|1 mM||−0.13 ± 0.04 (n = 8)||0.17 ± 0.05 (n = 4)||−0.024 ± 0.07 (n = 8)||0.048 ± 0.01 (n = 4)|
|2 mM||−0.36 ± 0.06 (n = 11)||0.33 ± 0.05 (n = 7)||−0.077 ± 0.01 (n = 11)||0.15 ± 0.01 (n = 8)|
|4 mM||−0.76 ± 0.05 (n = 9)||0.69 ± 0.08 (n = 7)||−0.17 ± 0.01 (n = 9)||0.22 ± 0.01 (n = 9)|
|10 mM||−1.08 ± 0.02 (n = 15)||1.04 ± 0.08 (n = 8)||−0.49 ± 0.04 (n = 15)||0.36 ± 0.04 (n = 8)|
To quantify the acidification that is caused by the application of a weak lipophilic acid, one starts with the Henderson–Hasselbalch equation:
- (Eqn 1)
where Ac− and AcH are the concentration of the deprotonated and the protonated form, respectively. With Ac− + AcH = Actot, the Henderson–Hasselbalch equation can be rearranged into:
- (Eqn 2)
When lipophilic weak acids are applied, it is usually assumed that equilibrium (AcHcyt = AcHout; Fig. 1) is rapidly reached. Knowing the cytosolic pH and the concentration of AcH at equilibrium in the cytosol, the concentration of Ac− in the cytosol, , can be calculated (Eqn 1). This concentration corresponds to the amount of H+ loaded into the cell by the dissociation of AcH. Assuming that during the time of weak acid perfusion pH regulation can be neglected, the buffer capacity is calculated as β = /pH. Values calculated for β in this way (Table S2) range from β = 103 mM at 10 mM acetate (3 min) to β = 1185 mM at 1 mM acetate (30 min). These values are far too high and do depend on the duration of acetate perfusion. Apparently, this simple approach is not suitable for determining reliably the cytosolic buffer capacity. Probably one, or even both (see below), of the initial assumptions – equilibration and no significant pH regulation during the perfusion interval – are wrong.
To analyze further the relation between the perfusion protocol and cytosolic acidification, the amplitude of maximum cytosolic acidification, ΔpHP, was plotted against perfusion time, t (Fig. 3). The shorter the perfusion time – and the higher the external acetate concentration – the higher is ΔpHP, with an extrapolated maximum of −1.4 pH units at perfusion time t = 0. At the other extreme, if low acetate concentrations are perfused over correspondingly long periods of time, there is hardly any cytosolic acidification. This indicates that simple models, on how cytosolic acidification by weak acids works, do not hold. If the assumptions of rapid equilibration of AcH and no significant pH regulation during the acetate perfusion time did hold, one would expect the same acidification for all perfusion times because the total dose of H+ loaded into the cell is the same for all four perfusion regimes. To describe how cytosolic acidification by weak acids works, and to understand how pH homeostasis in a green plant cell reacts to this acidification, a quantitative model has to be developed.
Figure 3. Maximum cytosolic acidification, ΔpHP, as a function of perfusion time, t. Acetate was applied at a constant dose by choosing a perfusion time inversely proportional to the acetate concentration (10 mM for 3 min, 4 mM for 7.5 min, 2 mM for 15 min and 1 mM for 30 min). The data points were fitted by an exponential function ΔpHP = off + B·exp(−t/t0) with off = −0.01, B = −1.40 and t0= 11.7 min (R2= 0.997).
Download figure to PowerPoint
A mathematical model for cytosolic pH changes caused by weak acids
The total cytosolic concentration of weak acid, Actot, results from influx of the acid, AcH, driven by the concentration difference, AcHout–AcHcyt (Fig. 1). The permeability, P, of the plasma membrane for the weak acid, the cell-surface area, A, and the cytosolic volume, Vcyt, determine how rapidly Actot, increases. This can be summarized as:
- (Eqn 3)
The cytosolic pH change, dpHcyt/dt, is caused by deprotonation of acetic acid (Fig. 1), and is attenuated by the buffer capacity, β:
- (Eqn 4)
Deprotonation of acetic acid entering the cytosol via the plasma membrane is instantaneous (< 1 ns). Therefore, acidification is initially restricted to the cytosol, and only once AcHcyt significantly increases does a delayed acidification of cellular organelles occur (described later). The cytosolic buffer capacity, β, was assumed to be constant and not dependent on cytosolic pH, because titration experiments have indicated little pH dependency of β between pH 7.5 and 5.8 (Reid et al., 1989b; Takeshige & Tazawa, 1989).
Substituting AcHcyt in Eqn 3 according to Eqn 2 results in:
- (Eqn 5)
Substituting in Eqn 4 according to Eqn 2 followed by differentiation and rearranging (see Supporting Information Notes S1) results in:
- (Eqn 6)
Eqns 5 and 6 describe the cytosolic pH change caused by weak acids in the absence of any pH regulation (). There are only two unknown parameters, namely the buffer capacity of the cytosol, β, and the permeability, P, of the plasma membrane for weak acid.
To estimate these two unknown parameters, the initial rates of acidification – when acetate perfusion was started – and the initial rates of re-alkalinization – when acetate perfusion was stopped – were analyzed. The initial rate of acidification contains information about how quickly AcH can enter the cell (i.e. the permeability, P) and how well the cytosol is buffered (i.e. the buffer capacity, β). The rates of acidification given in Table 1 were measured over the first 2 min, which is about 10 times more than the time interval for complete exchange of the bath solution. However, Fig. 3 indicates that measuring after 2 min results in an underestimation of the acidification. Therefore, the exponential fit from Fig. 3 was used to correct acidification rates by multiplication with a factor of 1.185 (ΔpHP(t = 0 min)/ΔpHP(t = 2 min) = −1.41/−1.19 = 1.185). As seen in Fig. 4, the initial rate of acidification is linearly related to the external concentration of acetic acid, AcHout. This is expected from Eqn 6. At the moment when perfusion is started the total acetate concentration in the cytosol, Actot, is still zero. For Actot = 0, Eqn 6 becomes:
Figure 4. Initial rate of cytosolic acidification, ΔpHcyt/Δt, as a function of the external concentration of acetic acid, AcHout. Values for the acidification rate over the first 2 min (after starting the perfusion of acetate) from Table 1 were multiplied by a factor of 1.185 (according to Fig. 3) to calculate initial acidification rates (ΔpHcyt/Δt at t = 0). Data points were described by a linear trend line with a slope of −0.1048 min−1 mM−1 and an offset of 0.0353 min−1, R2 = 0.9994. The 95% CI for the y-axis intercept ranged from 0.0116 to 0.0606 min−1, and an F test gave a 2.4% probability for a straight line through the origin (i.e. the y-axis intercept is significantly different from zero).
Download figure to PowerPoint
- (Eqn 7)
With pK = 4.75 and pH = 7.2 the term 1 + 10pK−pH (= 1.0035) comes very close to one, and can thus be disregarded. Plotting the initial rate of acidification, ΔpHcyt/Δt, against AcHout in Fig. 4 results in a straight line with a slope of –P A/(βVcyt). With a slope of −0.1048 min−1 mM−1, one can calculate P A/Vcyt = 1.747 10−3 s−1 mM−1β, or with Vcyt/A = 6.3 µm, P = 11 10−9 m s−1 mM−1β. This reduces two unknown parameters to one.
The plot of ΔpHcyt/Δt against AcHout is linear – as expected (Fig. 4). However, the regression line does not go through the origin but has a significant, positive offset of +0.0353 min−1. Obviously, a constant offset in the absence of any cytosolic acidification (AcHout = 0) does not make sense because it would result in a constant alkalinization of the cytosol. This positive offset can be explained by a pH regulation mechanism, which is activated at small cytosolic acidifications (AcHout = 0.59 mM) and removes H+ from the cytosol at a constant rate (0.0353 min−1).
The initial rate of re-alkalinization – at the moment when acetate perfusion is stopped – contains information about cytosolic pH regulation, at maximum cytosolic acidification. As the question is how cytosolic pH regulation reacts to a certain pH deviation, the initial rate of re-alkalinization, ΔpHcyt/Δt, was plotted against the minimum pH, pHP, at the end of the acetate perfusion period (Fig. 5). This plot shows that the larger the acidification of the cytosol, the larger the rate of pH recovery, indicating a proportional pH regulation mechanism.
Figure 5. Initial rate of cytosolic pH recovery (ΔpHcyt/Δt in min−1) as a function of pH at the end of acetate perfusion, pHP. Data points (open circles; Table 1) resulted from pH recordings (Fig. 2). Calculated points (closed circles) were obtained with Eqns 5 and 8 for Vcyt/A = 6.3 µm, P = 3.3 10−7 m s−1, β = 30 mM, tR = 500 s, pHS = pHStart = 7.2 and eff = 0.0353 min−1. Open triangles indicate how calculated points change when β and tR are changed by 20%.
Download figure to PowerPoint
To account for the two different cytosolic pH regulation mechanisms indicated by Figs 4 and 5, two terms are added to Eqn 6:
- (Eqn 8)
The term eff reflects the pH regulatory mechanism that removes H+ from the cytosol at a constant rate – according to Fig. 4, eff = 0.0353 min−1. The term (pHS – pH(t))/tR describes the proportional pH regulation indicated by Fig. 5. Cytosolic pH recovery is proportional to the difference between the actual pH value, pH(t), and a ‘set point’ value, pHS. The rate of pH recovery is given by the proportional factor or time constant tR, with smaller values for higher rates of pH regulation.
The mathematical model given by Eqns 5 and 8 describes the cytosolic pH change caused by a weak lipophilic acid including two simple pH regulatory mechanisms. This model includes three parameters –β, P and tR– that need to be estimated. From Fig. 4, P = 11 10−9 m s−1 mM−1β was calculated, reducing it to two unknown parameters.
Reasonable values for β and tR were estimated by applying the mathematical model with different sets of values for β and tR. Eqns 5 and 8 were used to calculate pHP and Actot for the end point of the four different perfusion regimes (Fig. 2) with different values for β and tR. The resulting pHP and Actot values were used to calculate the corresponding ΔpHcyt/Δt values immediately after acetate perfusion was stopped (Eqn 8 with AcHout = 0). This was repeated with different values for β and tR, and the quadratic deviation between measured and calculated values (Fig. 5) for pHP and ΔpHcyt/Δt was calculated. The values for β and tR were systematically varied to minimize the quadratic deviation. For β = 30 mM and tR = 500 s the quadratic deviation had a minimum and the set of values calculated (closed circles) for both pHP and ΔpHcyt/Δt came very close to the experimentally determined values (open circles) at all four acetate concentrations (Fig. 5). With β = 30 mM the relation obtained from Fig. 4, P = 11 10−9 m s−1 mM−1β, resulted in P = 3.3 10−7 m s−1.
The mathematical model was validated by inserting the complete set of parameters (A = 0.071 mm2, Vcyt = 0.45 nl, P = 3.3 10−7 m s−1, β = 30 mM, tR = 500 s, and eff = 0.0353 min−1) into Eqns 5 and 8 to calculate the time course of acetate-induced cytosolic pH changes in Eremosphaera. These calculated pH traces (Fig. 6) display all the characteristic features of recorded pH traces (Fig. 2). The main difference seems to be a low pass filtering of the recorded pH traces, as a result of the time it takes to exchange the bath solution (10–15 s) and because of the response time of ion-sensitive microelectrodes (2–4 s). The re-alkalinization of the calculated traces approaches pH values of > 7.5, as a result of the pH regulation by constant H+ removal – represented by eff. In Fig. 6 the re-alkalinization phase is cut off as soon as pHcyt = pHStart = 7.2 is reached. It can be assumed that the constant H+ removal stops (eff = 0) as soon as a physiological pH or a certain set point in the cytosol is reached. This would explain the biphasic re-alkalinization frequently observed – at the moment the eff component is ‘switched off’ the slope of the re-alkalinization phase is decreased. The mathematical model (Eqns 5 and 8) qualitatively describes the time course of the acetate-induced cytosolic pH changes (Fig. 6) and quantitatively describes the amplitude of those changes as well as the initial acidification and re-alkalinization rates (Fig. 5).
Figure 6. The time course of cytosolic pH changes upon perfusion of different acetate concentrations was calculated using Eqns 5 and 8 for Vcyt/A = 6.3 µm, P = 3.3 10−7 m s−1, β = 30 mM, tR = 500 s, pHS = pHStart = 7.2 and eff = 0.0353 min−1.
Download figure to PowerPoint
Values for cytosolic acidification, pHP, the cytosolic concentration of deprotonated acetate, , and the cytosolic concentration of acetic acid, AcHcyt, at the end of acetate perfusion were calculated (Table 2). The values obtained showed that the original concept of constant acetate doses generally holds – the total concentration of H+ loaded into the cells () differed by < 1 mM (2%). Even with perfusion times of 30 min (1 mM acetate), equilibrium was not reached (Table 2). For all four perfusion regimes, the cytosolic AcH concentration was less than half of the external concentration. This demonstrates that reaching a stable or maximum cytosolic pH does not imply that equilibrium (AcHcyt = AcHout) has been reached. The mathematical model was also used to calculate to what extent different pH-regulatory mechanisms contribute to pH homeostasis during the different perfusion regimes. The higher the acetate concentration (and the shorter the corresponding perfusion time), the higher the proportion of H+ that are bound by cytosolic buffers and the smaller the proportion of H+ that are removed from the cytosol by pH-regulatory mechanisms – proportional regulation or constant efflux (Table 2). However, even at 3 min of perfusion with 10 mM acetate, approx. 25% of H+ are not bound by cytosolic buffers, but are removed by other pH-regulatory mechanisms.
Table 2. Calculated values for the cytosolic acidification, pHP, the cytosolic concentration of deprotonated acetate, , and the cytosolic concentration of acetic acid, AcHcyt
|[Acetate]||AcHout (mM)||pHP|| (mM)||AcHcyt (mM)||Percentage H+ buffered||Percentage H+ proportional regulation||Percentage H+ constant efflux|
|1 mM||0.59||7.12||44.89||0.19|| 5.0||23.4||70.8|
|10 mM||5.8||6.05||45.80||2.28||75.1||16.7|| 6.9|
The contribution of the vacuole to pH regulation
To determine what might be the contribution of the vacuole to short-term cytosolic pH regulation, vacuolar pH was measured during acetate perfusion. The acidification of the cytosol caused by acetate was accompanied by vacuolar acidification (Fig. 7). The maximum vacuolar acidification, up to 0.6 pH units, varied little (less than a factor of two) between the four different acetate perfusion regimes. The acidification of the vacuole continued for a few minutes after the perfusion of acetate was stopped (Fig. 7). The rate of pH recovery was generally low, and pH recovery was not complete during the time of the recording. The maximum rate of acidification was linearly related to the acetate concentration applied, being −0.020 ± 0.002 (n = 4), −0.041 (n = 1), −0.080 (n = 1) and −0.16 ± 0.03 min−1 (n = 4) at 1, 2, 4 and 10 mM acetate, respectively.
Figure 7. Effect of acetate on membrane potential, E, and on vacuolar pH value, pHvac. Starting from an external pH of 5.6, the external pH was decreased to pH 4.6 and then acetate (1 mM for 20 min, top, or 10 mM for 3 min, bottom) was added.
Download figure to PowerPoint
Two observations indicated that the recorded vacuolar pH changes are caused by pH regulation and do not simply result from passive distribution of AcH. (1) Acidification of the vacuole began almost immediately after starting acetate perfusion – parallel to the cytosolic acidification, at a time when the cytosolic AcH concentration was still very low. (2) The observed acidification is too large to be explained by passive AcH distribution between cytosol and vacuole (see Notes S2). Yet, a small part of vacuolar acidification is probably caused by passive AcH influx from the cytosol. This raises the question of whether active H+ uptake into the vacuole is part of the proportional pH regulation (term (pHS–pH(t))/tR in Eqn 8) or the constant H+ efflux (eff in Eqn 8), or both. Constant H+ efflux into the vacuole would result in the same rate of acidification at all four acetate concentrations, and an increasing maximum acidification with increasing perfusion times. This is clearly not the case for the vacuolar acidification observed here (Fig. 7). The linear increase in the rate of acidification with acetate concentration is expected for a proportional pH-regulatory mechanism (Table 2). It can therefore be concluded that the proportional pH-regulatory mechanism (term (pHS – pH(t))/tR in Eqn 8) reflects H+ pumping from the cytosol into the vacuole. A vacuolar acidification of up to 0.6 pH units (Fig. 7) at a vacuolar buffer capacity of βvac = 10 mM corresponds to the uptake of 6 mM H+. At a volume ratio of 1:3 between cytosol and vacuole, 6 mM vacuolar H+ are equivalent to 18 mM cytosolic H+. In relation to the concentration of Ac−(approx. 45 mM) that accumulates in the cytosol (Table 2), this means that up to 40% of the H+ load of the cytosol are pumped into the vacuole. This corresponds approximately to the maximum contribution estimated for the proportional pH regulation (Table 2).