A cohesion/tension model for the gating of aquaporins allows estimation of water channel pore volumes in Chara


Ernst Steudle. Fax: + 49 921 55 2564; e-mail: ernst.steudle@uni-bayreuth.de


The water permeability (hydraulic conductivity; Lp) of turgid, intact internodes of Chara corallina decreased exponentially as the concentration of osmolytes applied in the medium increased. Membranes were permeable to osmolytes and therefore they could be applied on both sides of the plasma membrane at concentrations of up to 2.0 m (5.0 MPa of osmotic pressure). Organic solutes of different molecular size (molecular weight, MW) and reflection coefficients (σs) were used [heavy water HDO, MW: 19, σs: 0.004; acetone, MW: 58, σs: 0.15; dimethyl formamide (DMF), MW: 73, σs: 0.76; ethylene glycol monomethyl ether (EGMME), MW: 76, σs: 0.59; diethylene glycol monomethyl ether (DEGMME), MW: 120, σs: 0.78 and triethylene glycol monoethyl ether (TEGMEE), MW: 178, σs: 0.80]. The larger the molecular size of the osmolyte, the more efficient it was in reducing cell Lp at a given concentration. The residual cell Lp decreased with increasing size of osmolytes. The findings are in agreement with a cohesion/tension model of the osmotic dehydration of water channels (aquaporins; AQPs), which predicts both reversible exponential dehydration curves and the dependence on the size of osmolytes which are more or less excluded from AQPs (Ye, Wiera & Steudle, Journal of Experimental Botany 55, 449–461, 2004). In the presence of big osmolytes, dehydration curves were best described by the sum of two exponentials (as predicted from the theory in the presence of two different types of AQPs with differing pore diameters and volumes). AQPs with big diameters could not be closed in the presence of osmolytes of small molecular size, even at very high concentrations. The cohesion/tension theory allowed pore volumes of AQPs to be evaluated, which was 2.3 ± 0.2 nm3 for the narrow pore and between 5.5 ± 0.8 and 6.1 ± 0.8 nm3 for the wider pores. The existence of different types of pores was also evident from differences in the residual Lp. Alternatively, pore volumes were estimated from ratios between osmotic (Pf) and diffusional (Pd) water flow, yielding the number of water molecules (N) in the pores. N-values ranged between 35 and 60, which referred to volumes of 0.51 and 0.88 nm3/pore. Values of pore volumes obtained by either method were bigger than those reported in the literature for other AQPs. Absolute values of pore volumes and differences obtained by the two methods are discussed in terms of an inclusion of mouth parts of AQPs during osmotic dehydration. It is concluded that the mouth part contributed to the absolute values of pore volumes depending on the size of osmolytes. However, this can not explain the finding of the existence of two different types or groups of AQPs in the plasma membrane of Chara.


There is accumulating evidence that water channels (aquaporins; AQPs) play an important role in plant water relations at all levels of organization (cell, tissue, organ and whole plant). AQPs facilitate the rapid, passive exchange of water across cell membranes. (For reviews see: Steudle & Henzler 1995; Maurel 1997; Kjellbom et al. 1999; Tyerman et al. 1999; Steudle 2000, 2001; Maurel & Chrispeels 2001; Javot & Maurel 2002; Tyerman, Niemietz & Bramley 2002). Most (75–95%) of the water permeability of plasma membranes is due to AQP activity (Henzler, Ye & Steudle 2004). Since the pioneering work of Agre and coworkers, there has been much effort expended in identifying the molecular structure of water channels (Jung et al. 1994; Murata et al. 2000; Ren et al. 2001). This has shown that AQPs are transport proteins with a molecular weight of about 30 kDa and that they span the membrane six times thereby forming a narrow, hydrophilic pore (Verkman & Mitra 2000). Work on the transport properties of AQPs demonstrated that, in accordance with their small diameter, AQPs are highly selective for water largely by excluding bigger molecules. AQPs just allow the passage of one water molecule after the other in a single file. However, some of the AQPs identified so far have proved to be permeable to small neutral solutes such as glycerol or urea as well (Agre, Bonhivers & Borgnia 1998; Biela et al. 1999; Borgnia et al. 1999; Dean et al. 1999; Gerbeau et al. 1999; Guenther & Roberts 2000).

In the turgid, intact internodes of the green alga Chara corallina, it has been demonstrated that small organic solutes such as ketones, amides or monohydric alcohols use water channels in addition to the bilayer to cross cell membranes (Henzler & Steudle 1995; Hertel & Steudle 1997; Henzler et al. 2004). Hence, AQPs of Chara are not ideally selective for water. Henzler & Steudle (2000) presented evidence that some of the Chara AQPs allow a rapid passage of hydrogen peroxide and may serve as ‘peroxoporins’ as well as ‘aquaporins’. The data of these authors indicated the existence of different AQPs with differing diameters and, thus, pore volumes.

Recently, Ye, Wiera & Steudle (2004) proposed a cohesion/tension (C/T) model for the gating of water channels. The model was based on the fact that osmotic solutes excluded from AQPs, should cause a tension (negative pressure) within the pores, leading to a reversible deformation or even collapse of channel protein as tensions increase (in response to increasing solute concentration). Tensions of 2.0 MPa (20 bars) or even higher have been induced by Ye et al. (2004). Deformation or collapse of AQPs was evident from a reversible decrease of hydraulic conductivity of the cell membrane (Lp). The larger the size (molecular weight) of the osmotic solute used, the more efficient was the reduction of Lp.

In the present paper, these experiments are continued. Further evidence for the validity of the C/T model of Ye et al. (2004) is presented. According to the model, different osmotic solutes should differ in their efficiency to close water channels, depending on their size in relation to the diameter of membrane pores. For example, a relatively small solute which could pass through an AQP should exert a smaller tension at a given concentration than a bigger one. According to the model, solutes have to be presented in the same concentration outside and inside the cell. So, they have to be sufficiently permeable on one hand while sufficiently large on the other. Different ethylene glycol ethers fulfil these requirements. They also vary in size. Acetone was used as a typical small organic solute which has been shown to pass across AQPs in addition to the bilayer (Henzler et al. 2004). The change in the activity of AQPs was measured by a pressure probe for concentration series using the different osmolytes of different degrees of exclusion from pores. Pore volumes were calculated from ‘dehydration curves’, which required the measurement of responses over large ranges of concentration. Using the extrapolation technique of Steudle & Henzler (1995), reflection coefficients of AQPs of solutes (σsa) were obtained as well. For the first time, the experiments provide estimates of the volumes of AQPs (Vc) of the plasma membrane of an intact plant cell. In alternative experiments, numbers of water molecules in water channels were estimated by comparing the osmotic (Pf) and diffusional (Pd) water permeability. According to Levitt's (1974) theory, ratios of Pf/Pd should directly yield the number of water molecules in an AQP, which is related to pore volume. Results indicate that the plasma membrane of Chara may contain a population of different AQPs rather than just one type, an idea previously suggested for different reasons (Henzler & Steudle 2000). Volumes of AQPs deduced from numbers of water molecules in AQPs (Pf/Pd ratios) were smaller than those calculated from dehydration curves. This suggested that either the channels are somewhat wider than just the diameter of a water molecule, or that the mouth parts of channels contributed to the overall Vc, or both.


Plant material

Internodes of Chara corallina used in the experiments were grown in artificial pond water (APW; composition in mole m−3: 1.0 NaCl, 0.1 KCl, 0.1 CaCl2 and 0.1 MgCl2) as described previously (Ye et al. 2004). Internodes (length: 50–150 mm; diameter: 0.8–1.0 mm) were isolated from adjacent internodes and whorl cells and fixed in a tube (inner diameter: 3 mm) to allow rapid circulation of APW around the cells and rapid exchange of media to minimize external unstirred layers.

Determination of Lp, Pf and Pd

The water permeability of the plasma membrane of Chara internodes (hydraulic conductivity, Lp) was calculated from half times of water exchange (inline image) as measured with the cell pressure probe


Here, V is the cell volume; A is the cell surface area; ɛ is the elastic coefficient of the cell (elastic modulus) and πi is the osmotic pressure of cell sap, which was calculated from cell turgor and external osmotic pressure. The osmotic permeability (Pf) in m s−1 is proportional to Lp in m s−1 MPa−1, and was calculated from the relation (Hertel & Steudle 1997)


(R is the gas constant; T is the absolute temperature; inline image is the molar volume of liquid water). The diffusional permeability of solutes (Ps) and of isotopic water (Pd) was estimated from half times of solute exchange as obtained from solute phases of biphasic pressure–time curves (Henzler et al. 2004)


Here, inline image is the half time of solute (HDO) exchange, and ks the corresponding rate constant. For a detailed description of these equations, see earlier publications by Steudle (1993) and Henzler & Steudle (1995). The cell pressure probe (completely filled with silicone oil) was introduced across the node into the fixed Chara internode (Henzler & Steudle 1995, Hertel & Steudle 1997; Henzler et al. 2004). Using the probe, the oil/cell sap meniscus forming in the tip of the capillary, was moved forward or backward and was kept stable after each move. From the half time of pressure relaxations, Lp and Pf were calculated as a control (Eqns 1 and 2).

Effects of high solute concentration on the transport of H2O and HDO

Heavy water (HDO; 3.8–4.8 m) was used for testing the diffusional water permeability (Pd) of the membrane. Control values of Pd were calculated from biphasic response curves (Steudle & Tyerman 1983; Steudle 1993; Eqn 3). To determine effects of concentration on Lp, Pf and Pd, solutes with different molecular weights were added to the medium. One solute was acetone which largely moves across the bilayer of the cell membrane. However, a limited transport of acetone across water channels is known to occur (Henzler & Steudle 1995; Hertel & Steudle 1997; Henzler et al. 2004). Other solutes were dimethylformamide (DMF); ethylene glycol monomethyl ether (EGMME); diethylene glycol monomethyl ether (DEGMME); and triethylene glycol monoethyl ether (TEGMEE), all of which were expected to be excluded from water channels because of their relatively large molecular sizes (Table 1). To avoid plasmolysis, concentrations were increased in steps of 0.2 m and proceeding to the next was delayed until full recovery of turgor. At each step, four hydrostatic pressure relaxations were induced to measure Lp at that concentration. Maximum concentrations were 2.0 m for acetone and 1.2 m for DMF and the three glycol ethers. HDO (the same concentration as in the control) was added to the medium in the presence of 1.2 m acetone or 1.2 m TEGMEE to measure changes of Pd in response to that treatment. Whether or not the effects of acetone and TEGMEE on aquaporins were additive was determined. To do this, cell Lp was first measured in the presence of 1.0 m acetone, later adding 0.2 m TEGMEE and measuring Lp again. Alternatively, Lp was first measured in the presence of 0.8 m TEGMEE, and again later after adding 0.4 m acetone. To remove solutes taken up by the internodes, the external concentration of the medium was reduced in steps of 0.2 m until the solution was APW again. Lp, Pf and Pd were re-examined to ensure that effects were completely reversible. For a given cell, the whole time course of experiments lasted for 4–12 h. During treatments, cells did not lose turgor pressure (0.6–0.7 MPa) within ± 0.05 MPa or ± 8%.

Table 1.  Pore volumes of water channels calculated from Lp/LpoCm dehydration curves of osmolytes of different molecular size and reflection coefficients (σs)
SoluteMolecular weights (g/mol)Overall reflection coefficient (σs)Values of E in Eqn 9 (maximum change of Lp/Lpoin percent)Values of decline constants, k (M−1) (Eqn 9)Overall reflection coefficients of water channel arrays (σsa)(Pore volumes (nm3) calculated assuming only one type of channel Eqn 9)(Pore volumes (nm3) calculated assuming two types of channels Eqn 12). Data for acetone refer to small channels and for the other solutes to big channels (Fig. 2b)
  1. Values of the decline constants, k, and of the residual Lp/Lpo, E, were obtained from Lp/LpoCm dehydration curves (Fig. 2a & b). Overall reflection coefficient of water channels (σsa) for different osmolytes were estimated from the intercept with σs axis by plotting the measured quantities σs against 1/Lp (Fig. 1; Eqn 6). Pore volumes of water channels in the column next to the last were calculated using Eqn 9, assuming a single type of channel and a reflection coefficient of unity for all solutes including acetone. In the last column, the model of two different types of channels has been employed, whereby the acetone data refer to the small and the other data to the big channels (Eqn 12; Fig. 2b). Values are means ± SD; n = 6–10 cells. cData from Ye et al. (2004),σs were measured at concentrations of 160 m m for acetone and 60, 40 and 25 m m for EGMME, DEGMME, TEGMEE, respectively. dData from Steudle & Tyerman (1983).

Acetone580.15 ± 0.03 c52 ± 0.81.41 ± 0.110.32 ± 0.072.3 ± 0.22.3 ± 0.2
DMF730.76 ± 0.06 d38 ± 1.81.25 ± 0.070.83 ± 0.13 d2.1 ± 0.1
EGMME760.59 ± 0.03 c46 ± 1.11.73 ± 0.080.78 ± 0.052.9 ± 0.15.6 ± 1.1
DEGMME1200.78 ± 0.05 c37 ± 2.41.99 ± 0.201.03 ± 0.103.3 ± 0.35.5 ± 0.8
TEGMEE1780.80 ± 0.07 c33 ± 2.52.31 ± 0.151.01 ± 0.063.8 ± 0.26.1 ± 0.8

The reflection coefficient of the water channel array (σsa)

It has been shown that the transport properties of the plasma membrane of Chara may be described in terms of a composite transport model (Henzler & Steudle 1995). According to the model, the overall reflection coefficient (σs) is expressed in terms of a weighted mean of two different arrays (water channel array, ‘a’, and the rest of the membrane, ‘b’). Transport properties of arrays are characterized by different sets of transport coefficients (Lpa, Psa, σsa and Lpb, Psb, σsb). According to basic irreversible thermodynamics (Kedem & Katchalsky 1963), the overall σs is given by


Here, γa and γb represent the fractional contributions in area of arrays ‘a’ and ‘b’, respectively (γa + γb = 1). Hence (γa · Lpa)/Lp and (γb · Lpb)/Lp represent the relative contributions of arrays ‘a’ and ‘b’ to the overall hydraulic conductivity of the membrane:


If we assume that the contribution of the lipid array to the overall water transport is constant (i.e. Lpb, σsb = constant) and that water channels just switch between an open and closed state, Eqns 4 and 5 can be used to evaluate the reflection coefficient of water channels (σsa). For a given solute, these equations yield (Henzler & Steudle 1995):


Thus, plotting the measured quantities σs and 1/Lp against each other should yield a straight line and the reflection coefficient of water channels (σsa) from the intercept with the σs axis. It should be noted that, when there are different types of water channels which exhibit a different dependence on concentration, σsa denotes a weighted mean of the reflection coefficients of these different channels (see Discussion). In any case, we may distinguish between an array with variable values (σsa and Lpa) and an array with constant values (σsb and Lpb; bilayer or ‘the rest of the membrane’).

Calculation of the pore volume of water channels

Zimmerberg & Parsegian (1986) presented a model of the gating of ion channels by the osmotic pressure of the medium on both sides of the membrane. According to the model, solutes excluded from channels cause a dehydration of membrane pores. This, in turn, results in a deformation or even collapse of channel protein as tensions (negative pressures) develop within pores. Ye et al. (2004) extended this idea to the aquaporins of Chara to explain the dependence of cell Lp on solute concentration. External osmotic pressure of solutes not accessible to the pores should have caused tensions in the water in channel pores to balance the water potential between pores and medium. As for ion channels, Ye et al. (2004) suggested that tensions cause a reversible collapse of the AQP protein and affect the ratio between the number of open and closed states of channels. The ratio between the number of open channels in untreated Chara (no) and the number of open channels during treatment with external permeating solutes (n) should be given by a Boltzmann distribution. This means that the ratio of n/no should depend on the difference in free energy between the two states (ΔG). The latter just refers to the pressure dependence of free energy (volume work: Vc · ΔPc), whereby ΔPc = hydrostatic pressure in the channel minus that in the surrounding medium, and Vc is the internal volume of the pores. In the presence of external solutes, ΔPc is negative. It is zero in its absence. We get (see Ye et al. 2004)


According to this equation, the Lp of treated cells should decline exponentially as the tension created within a channel in the presence of external solutes increases. In Eqn 7, kB = Boltzmann constant (kB = R/NL; R is the gas constant; NL is Avagadro's number =  6.023 × 1023 particles per mole); T is the absolute temperature. The tension created in the channels is related to external concentration (Cm) by van’t Hoff's law, that is


Hence, we predict an exponential decrease in Lp as the external concentration increases


As compared with Eqn 7, a term ‘E’ has been added in Eqn 9. It represents the residual Lp which is not affected by pore dehydration in the presence of external solutes. The parameter ‘F’ refers to the component of Lpo which is due to concentration dependent AQPs. Component ‘E’ may be caused by the permeability of the bilayer or by pores (AQPs or other transporters) that are not affected by concentration. Lp/LpoCm curves have been fitted exponentially with high correlation factors (see Results). Lpo is the original hydraulic conductivity, when Cm = 0. Hence, E + F = 1. According to Eqn 9, Lp/LpoCm curves should become horizontal lines when all channels responsive to external osmotic pressure are closed due to the cohesion/tension mechanism. The decline constant k is a measure of the intensity by which solutes of different sizes (molecular weights) affect Lp. According to the C/T model, one would expect that effects of solutes are less pronounced when molecules were not completely excluded from the pores, i.e. when reflection coefficients of pores (σsa) were smaller than unity. In this case, the pressures in the pores would be given by ΔPc = –σsa · RT · Cm, and Eqn 7 should read:


The factor of thousand arises from the fact that Cm should be given in mol m−3 rather than in the usual unit mole L−1 or m (as done here). Measurements of the concentration dependence of Lp should allow one to work out k values (in m−1) and channel volume Vc (in 10−27 m3 pore−1= nm3 pore−1= 1000 Å3 pore−1) provided that the reflection coefficient of the pore (σsa) is known for a given solute. From Eqns 9 and 10 we get:


In Eqn 9, only one type of channel of volume Vc has been assumed. However, the results of this paper suggest that there are two different types or groups of channels of different volumes Vc1 and Vc2 present, which may also differ in their reflection coefficients (σs 1a and σs 2a) for a given solute. In this case, Eqn 9 has to be extended to:


where k1 and k2 are defined according to Eqn 11. As in Eqn 9, the meaning of E is that of a residual water permeability, when all channels exhibiting a concentration dependence are closed. The terms F and G reflect the overall contributions of channels 1 and 2 to Lpo in the open state. Different from Eqn 9, the concentration dependence described by Eqn 12 should not be represented by a single exponential; rather, it should split into two superposed exponentials, which may be separated from each other provided that the differences in pore volumes are big enough (Fig. 2b). On the other hand, when there are channels for which the reflection coefficient of an osmolyte is virtually zero, these channels should not close in the presence of this solute, independent of its concentration as shown for acetone in this paper (see Results).

Figure 2.

(a) Effect of concentrations of five osmolytes (acetone, dimethylformamide and three glycol ethers) on bulk water permeability (Lp) of Chara internodes. As the concentration on both sides of the membrane increased from 0.2 to 2 m (acetone) or to 1.2 m (DMF and glycol ethers), Lp decreased for all osmolytes (n = 6 cells ± SD for each osmolyte). Points represent the mean values of relative Lp (compared with control at zero concentration, Lpo) (n = 6 cells for each concentration). Lp/Lpo curves were fitted exponentially (Eqn 9; r2 > 0.99). The bigger the molecular size of the solute used, the greater was its effect in reducing Lp. In (b), it is shown for TEGMEE that the fit in (a) contained two exponentials as expected in the presence of two different groups of AQPs with different pore volumes. Subtracting results of the dehydration curve for acetone (II, representing the small channels) from that for TEGMEE (I, representing all channels) resulted in the response curve for the wide channels (III, Eqn 12). From the different decline constants k1 and k2, channel volumes have been calculated (Eqn 11; Table 1). Error bars in (b) denote SD values (n = 6 cells), whereby the error bars in III represent the propagated errors from I and II. For each concentration and curve, mean values were significantly different from those of the other two (t-test; P < 0.05), except for curves II and III at concentrations of 0.2 and 0.4 m.


Reflection coefficients of water channels (σsa)

According to Eqn 6, plotting the measured overall reflection coefficients (σs) against the inverse of hydraulic conductivity (1/Lp) as measured for different concentrations yields the reflection coefficient of the water channel array (σsa) from the intercept with the σs axis. This is shown in Fig. 1a for acetone which goes through AQPs (overall σsa = 0.32 ± 0.07; n = 6 cells) and in Fig. 1b for TEGMEE, which does not (overall σsa = 1.01 ± 0.06; n = 6 cells). For other solutes, reflection coefficients are summarized in Table 1. They vary depending on the size and on the molecules’ polarity. Linear relationships between σsa and 1/Lp such as those shown in Fig. 1 have been verified before not only for Chara, but also for higher plant cells (Steudle & Henzler 1995). As pointed out in the Material and Methods section, σsa values would refer to a weighted mean in the presence of different AQPs (see Discussion).

Figure 1.

Plots of the overall reflection coefficients (σs) of Chara internodes versus the inverse of hydraulic conductivities (1/Lp) for six individual cells of Chara corallina as denoted by different symbols. Internodes were treated by two different permeating solutes with increasing concentrations (a: acetone; b: TEGMEE). As expected from Eqn 6, plots yielded a straight line. From the intercept of the lines with the σs axis, reflection coefficients of water channel arrays (σsa) were obtained for acetone (mean ± SD: σsa = 0.32 ± 0.07) and for TEGMEE (σsa = 1.01 ± 0.06).

Residual water permeability and decline constants of Lp/LpoCm curves

As the external osmolyte concentration increases, one would expect an exponential decrease of Lp given by a certain decline constant k and a residual water permeability E (Eqn 9). Figure 2a shows that Lp/Lpo decreased exponentially as the concentration of osmolyte increased. For all test osmolytes, single exponential fits of Lp/LpoCm curves (Eqn 9) resulted in high correlation factors of r2 > 0.99. It can be seen from Fig. 2a and b that there was significant difference among residual water permeabilities for osmolytes which differed substantially in size such as acetone and TEGMEE (t-test; P < 0.05). Residual water permeabilities (given as a percentage of the original Lpo) decreased as the size (molecular weight) of test solutes increased. For example, for acetone (the smallest solute used) E = 52%; for TEGMEE (the biggest) E = 33% (Fig. 2b; Table 1). This indicated that there were bigger and smaller channels present, and the bigger channels could not be closed in the presence of even considerable concentrations of the small solute acetone, presumably because of a rather low σsa of the big channels for acetone. A careful inspection of the dehydration curves for the big solutes EGMME, DEGMME, and TEGMEE showed that they would be better fitted as the sum of two exponentials according to Eqn 12 rather than by just one exponential (Eqn 9). The subtraction of the TEGMEE curve from the acetone curve of Fig. 2b showed that the TEGMEE curve contained two different components, one due to a big channel and one due to a small channel, as could be also verified from semilog plots (data not shown). Obviously, the different decline constants referred to different types of channels. Bigger channels responded to TEGMEE but not to acetone, whereas smaller channels responded to both acetone and TEGMEE. As for TEGMEE, there was also a splitting into two components for DEGMME and EGMME which resulted in two different k values and pore volumes (Table 1). However, a splitting of the DMF curve could not be done, presumable because the sizes of the acetone and DMF were too similar.

Pore volumes of water channels in Chara

When volumes of water channels were calculated using a single exponential (Eqn 9) and the σsa values of Fig. 1, volumes ranged between 2.5 ± 0.1 and 7.3 ± 0.2 × 10−27 m3 or 2.5 ± 0.1–7.3 ± 0.2 nm3 (data not shown), whereby the highest pore volume referred to the smallest osmolyte acetone, because of the low σsa for acetone. In view of the results of Fig. 2b, this can not be true. It is more likely that the small (‘acetone’) channels have a σsa ≈ 1 for acetone which did not affect the big channels, because they were too wide. The same should be true for the other solutes. Therefore, using the assumption of a σsa = 1 for all solutes, values of Vc ranged from 2.1 ± 0.1 to 3.8 ± 0.2 nm3 tending to increase with increasing size of the solute. However, when Eqn 12 was applied to split up effects in the presence of different channels, two different types of channels could be classified. When subtracting the contribution of the small ‘acetone’ channel (Vc = 2.3 nm3) from the dehydration curves in the presence of EGMME, DEGMME and TEGMEE, the volume of the bigger channel component was found to be 5.5 ± 0.8 to 6.1 ± 0.8 nm3 (last column of Table 1). For DMF, no separation of components was possible (see above). The data strongly indicate that channels of two different sizes are present (see Discussion).

Combined treatments with a small (acetone) and a large (TEGMEE) osmolyte

The striking difference in the residual Lp between acetone and the bigger osmolytes (Fig. 2) suggested that, for example, the more efficient TEGMEE closed more and, perhaps, a population of channels different from those which were affected by acetone. If true, the addition of TEGMEE should still have a substantial effect on Lp, even when the small-diameter channels had been already closed by fairly high concentrations of acetone. On the other hand, when all channels had been closed at a high concentration of TEGMEE, the addition of acetone should have no further effect. Figure 3 demonstrates that this was the case. An internode was treated with 0.2 m TEGMEE which reduced Lp to 77% of the control value (Lpo); 1.0 m of acetone decreased Lp to 59% of Lpo. When a mixture of both solutes was added to the same cell (i.e. adding 0.2 m TEGMEE in the presence of 1.0 m acetone), the relative reduction of Lp was 50%; the reduction was significantly greater than that of either single treatment (means ± SD, n = 6 cells, P < 0.05). Hence, in the presence of a rather high concentration of acetone, a relatively low concentration of TEGMEE did have an additional effect. However, when TEGMEE was present at rather high concentration, the addition of a substantial amount of acetone had no significant further effect (Fig. 3b). The results from Figs 2b and 3b suggest that there are different water channels in Chara which differ in their sensitivity depending on the size of solutes (see Discussion).

Figure 3.

(a) Treatment with either 0.2 m TEGMEE (big solute) or 1 m acetone (small solute) reduced cell Lp of Chara internodes down to 77 and 59% of the control, respectively. In the presence of 1 m acetone, the addition of 0.2 m TEGMEE resulted in a further significant reduction of Lp as compared with the treatment with 1 m acetone (n = 6 cells; P < 0.05). (b) When Chara internodes were treated first with 0.4 m acetone or 0.8 m TEGMEE, cell Lp was reduced to 77 and 47% as compared with control, respectively. In the presence of 0.8 m TEGMEE, the subsequent addition of 0.4 m acetone had no further significant effect on reducing Lp (n = 5 cells; P > 0.05). Dashed lines indicate the maximum residual value of Lp in the presence of high concentrations of acetone (52% of original Lpo).

Number of water molecules (N) within the pore

According to Levitt's (1974) theory, the number (N) of water molecules within a narrow pore where molecules move in a single file (i.e. one by one and without passing each other) is given by the ratio between the osmotic (Pf) and diffusional (Pd) water permeabilities. Pf is directly related to the hydraulic conductivity, Lp. The diffusional water permeability was determined in a separate experiment using isotopic water (HDO). We have:


This relation refers to the situation where all water passes across channels and there is no parallel passage across the bilayer (or rest of the membrane). This assumption is not met in the presence of a significant water flow across the bilayer (see Discussion). From the results shown in Fig. 4, we calculated that there were 47 water molecules aligned in a water channel when Pf and Pd were measured in control (APW). Treatments with 1.2 m acetone or 1.2 m TEGMEE reduced N to 34 and 23, respectively. Changes were significant (t-test; P < 0.05). For a non-porous pathway such as the bilayer, N = 1 should hold. Therefore, the results of Fig. 4 indicate a higher relative contribution of the bilayer passage as water channel activity decreased at high external concentration. The more effective solute TEGMEE had a stronger effect than the less effective acetone, as expected.

Figure 4.

The ratios between osmotic (Pf) and diffusional (Pd) water flow directly yield the number (N) of water molecules aligned in water channels. When Pf and Pd were measured in control (APW) with the aid of a cell pressure probe, N was 47 on average (n = 12 cells ± SD), suggesting that there are 47 water molecules aligned in a water channel of Chara. Treatments with 1.2 m acetone or 1.2 m TEGMEE reduced the value of N to 34 and 23 (n = 6 cells for each treatment), respectively. Please, note that six different cells have been treated with TEGMEE and acetone, respectively, because a treatment with both solutes would not have been possible for a single cell. Nevertheless, for each cell both Pf and Pd have been measured in control and treatment.


The results support the view of a cohesion/tension mechanism operating in water channels of the green alga Chara as reported earlier by Ye et al. (2004). The mechanism is thought to be the reason for the effect of high solute concentration around the membrane on its hydraulic conductivity. This effect has been known for a long time, but had not previously been explained satisfactorily (Dainty & Ginzburg 1964; Tazawa & Kamiya 1966; Steudle & Tyerman 1983). The problem is of general interest. An inhibition of cell Lp by high solute concentration or salinity is known not only for characean species. For example, growing maize in a solution of 100 m m NaCl (with an associated build up of osmotic active substances in the cells) reduced the Lp of root cortical cells by 68–83% (Azaizeh, Gunse & Steudle 1992). The fact that this osmotic stress was smaller by a factor of 6 to 10 than the stresses used in the present study suggests that AQPs of root cells may be more sensitive to mechanical stresses caused by the C/T mechanism than those of Chara (Wan, Steudle & Hartung 2004). Differences between species may be due to differences in the fine structure of AQPs (although the primary sequence of AQPs and the resulting structural fold should be largely conserved), or to differences in the interaction of AQPs with the bilayer into which AQPs are anchored. Because of experimental difficulties, quantitative studies of effects of osmotic stresses on water transport across plant membranes are still rare. In isolated cells of Chara, such effects can be studied rigorously, because both external and internal concentrations can be changed in a defined way over large ranges, provided that permeating osmolytes are used. Effects can be followed over hours on one individual cell. This is usually not possible for cells in a tissue.

We were limited in the use of osmolytes. On one hand, we wanted to cover a large range of reflection coefficients, that is, a large range of exclusion from pores and, hence, used compounds with a rather large range of molecular weights. On the other hand, to test the C/T model solutes had to permeate into the cell to act on both sides of the membrane. Therefore, we used only uncharged solutes. Because of their low permeabilities, salts such as KCl (present in the vacuole of a Chara cell in high concentration) could not be used. They would have required enormous time intervals for equilibration, if any. At the lower end, we used HDO and acetone as small, rapidly permeating substances. For larger molecules with high reflection coefficients, we employed glycol ethers and the bulky dimethyl formamide. These solutes are tolerated by the cells at high concentration and provide rather large overall reflection coefficients of up to σs = 0.80 in the presence of a reasonable solute permeability (Ye et al. 2004).

The data provide additional strong support for the C/T mechanism of a gating of water movement through AQPs in that: (1) the dehydration of membrane pores in the presence of osmotic solutes depended exponentially on the concentration of osmolytes as theoretically expected in the presence of a flip-flop between different conformational states of AQPs (Eqns 9 and 12). (2) There was a distinct effect of the size of osmolytes. It is known from other experiments that small osmolytes such as acetone and monohydric alcohols can slip through water channels whereas bigger ones do not (Henzler & Steudle 2000; Henzler et al. 2004). However, it had not yet been demonstrated that this may result in different residual water permeabilities as proposed by the model. The differences in the ‘osmotic efficiency’ between osmolytes as expected by the C/T theory was verified. (3) The model predicts that the switching between different conformations of AQPs should be reversible, and this was found, too. When osmotic stresses were withdrawn, cell Lp re-attained the original Lpo. Membrane integrity was not affected.

The absolute values of pore volumes presented in this paper are large. Depending on the solutes used they ranged between 2.1 ± 0.1 and 3.8 ± 0.2 nm3, when using the single-channel approach of Eqn 9 and values of σsa of unity. This procedure represents an oversimplification as curves should be fitted by two exponentials in the presence two types of channels (as indicated by the different values of residual Lp in Fig. 2). The results of Fig. 3 show that not all channels reacted to acetone even when it was present in high concentrations. They did react, however, to the bigger molecules of the glycol ethers. Hence, it is reasonable to assume that the overall value of σsa for acetone should be separated into a low value for the wider channels and into a rather high value for the smaller channels. A relation similar to that used in Eqn 6 should hold within the population of different AQPs, whereby different types of channels would contribute to σsa according to their water permeability. Hence, the reflection coefficient of the narrow channels may be close to unity for acetone.

When considering the fact that there were two different types of channels of differing size present, the values of channel volumes (diameters) have to be split up according to Eqn 12 (Fig. 2b; Table 1). This results in absolute values of the small and big channels of 2.3 ± 0.2 nm3 and 5.5 ± 0.8 to 6.1 ± 0.8 nm3/channel, respectively. These high values may contain a contribution of the vestibules of channels. A cylindrical AQP pore of a diameter of 0.4 nm (= 4 Å ≈ diameter of water molecule) and of a length of 5 nm (≈ about half of the thickness of a plasma membrane), has a volume of 0.63 nm3, which is smaller by a factor of 4–10 than those given above. The electron diffraction studies of Ren et al. (2001) indicated a length of the narrow part of the AQP-1 pore of red blood cells of only 1.8 nm, which would allow the single-file alignment of about 5 water molecules with a diameter of about 0.4 nm. This would result in a pore volume of only 0.23 nm3. The reason for the larger value obtained for Chara internodes could be that either the AQPs of these cells are rather big or that the osmotic dehydration technique used to measure them produces large values by incorporating mouth parts, or both.

When osmolytes are not only excluded from the narrow, single-file part of channels but also from their mouth parts, an overestimation of channel volume (narrow part) may result. For example, when we assume that the mouth parts at both sides of narrow part are shaped as truncated cones with a diameter at the entering part of the mouth of 0.8 nm (twice the diameter of the core part), and of a length of 2 nm (as the core part), we end up with an overall volume of 1.4 nm3, which is closer to that measured in this work. Dimensions such as those used here for mouth parts may be realistic (Zhu, Tajkhorshid & Schulten 2004), but more precise data would be required. They are not yet available for Chara. A narrow inner part of the channel (such as that of AQP1) and of two additional mouth parts acting as single-file pores would increase the number of water molecules from 5 to 15. However, in the mouth parts, channels may not strictly behave as no-pass pores for water, and the figure of 15 is, hence, a lower limit. The effects of mouth parts could account for some of the differences observed. They can not, however, account for the fact that the small osmolyte acetone could not affect the big channels even when applied at very high concentration. This is strong indication for the presence of different types of channels.

Zimmerberg & Parsegian (1986) found large pore volumes for ion channels. Their values range between 22 and 48 nm3 (including mouth regions). This is larger by a factor of 4–21 than our values obtained from osmotic dehydration. Zimmerberg & Parsegian (1986) subjected their membrane preparations (mitochondrial voltage-dependent anion channels from rat liver and from Neurospora, reconstituted into planar phospholipid bilayers) to big osmolytes which should have been completely excluded from the channel interior including mouth parts (polyethyleneglycol, MW: 20 000; polyvinylpyrolidone, MW: 40 000 and Dextran 1500, MW: 500 000). Membrane pores closed in the presence of osmotic pressures of only 3 bar (0.3 MPa equivalent to 120 m m), i.e. at tensions of as small as 3 bar. Channel closure was measured as a decrease in the electrical conductance of ion channels. Zimmerberg & Parsegian (1986) thought that the high sensitivity to tensions of their pores was due to the rather wide diameter of the channels. They speculate that there should also be channels of smaller diameters which should resist much higher tensions, as found here for the water channels of Chara. For Chara, we could use much smaller osmolytes than Zimmerberg & Parsegian (1986), just because of the smaller diameter of AQPs.

In the present study, the fairly large volumes of pores obtained from dehydration curves coincided with rather large values of the number of water molecules in the channels (N) obtained in an alternative experiment by comparison of the osmotic (Pf) and diffusional (isotopic, Pd) permeability to water. Values ranged between N = 35 and N = 60 for untreated cells (N = 47 on average). These data are bigger than those obtained earlier for Chara from Pf/Pd ratios (N = 27; Henzler & Steudle 1995; N = 31; Hertel & Steudle 1997). Literature data for other objects also indicated smaller N-values. For example, Finkelstein (1987) and Mathai et al. (1996) found N = 10–13 for red blood cells. In wheat root membrane vesicles, Niemietz & Tyerman (1997) reported an N = 3–7. Somewhat larger values were given for symbiosome membrane vesicles of soybean root nodules (N = 18; Rivers et al. 1997). Overall, values from different sources and for different objects range from N = 3–47 (including this paper). Using a van-der-Waals volume of water molecules of 1.46 × 10−2 nm3 (14.6 Å3), this would be equivalent to a range of 0.04 nm3−0.69 nm3 pore−1. Hence, our data for Chara are at the upper edge of values reported so far. The reason may be either that Chara does have such big pores (perhaps, less likely in view of the fact that AQPs are highly conserved; see above) or that our method of measurement incorporated mouth parts as discussed above. Wider mouth parts lacking a single-file transport of water may explain the differences between pore volumes obtained from dehydration curves and those from Pf/Pd ratios.

It has to be noted though that N-values from Pf/Pd ratios may represent overestimates because of problem with unstirred layers during the measurement of Pd. Extensive experience with the measurement of rapidly permeating solutes in Chara (such as HDO), however, shows that effects of internal unstirred layers are smaller than one might expect (see Discussions in Henzler & Steudle 1995, 2000; Hertel & Steudle 1997; Ye et al. 2004). It may be reasonable to assume that effects were probably not larger than 25%. Hence, the Pf/Pd ratio of 47 would have to be corrected to 35. However, even when corrected for unstirred layers, measured ratios do not straightforwardly represent Pf/Pd ratios of aquaporins. Rather, they are overall values for the entire membrane. When we denote the Pf(Pd) values of the AQP array(s) by PfAQP and PdAQP, respectively, and those of the rest of the membrane by Pfrm and Pdrm, we should get PfAQP/PdAQP from the relation (Finkelstein 1987)


Here, Pf and Pd denote the measured overall values. When water is only moving either across the bilayer or the water channel array, Pfrm and Pdrm would refer to the bilayer, where Pf = Pd could be assumed in the absence of pores. Bilayer values of the water permeability have been obtained for red blood cells (Pf = 3.0 × 10−5 m s−1; Mathai et al. 1996). They have been used to correct for the bilayer component assuming that Pfrm = Pdrm after blocking the porous passage (Finkelstein 1987; Mathai et al. 1996). Analogous data are difficult to obtain for Chara. During the most drastic closure of water channels in Chara in the presence of hydroxyl radicals, the residual Lp (Pf) was as small as 5–10% of the original (Henzler et al. 2004). In absolute terms, it was 2.2–8.6 × 10−5 m s−1 and is similar to that of the residual water permeability of red blood cells (see above). However, under these conditions Pf/Pd ratios were still as large as 11. This residual figure for Pf/Pd should contain: (1) effects of unstirred layers as well as (2) other ‘porous’ transporters for water which were not affected by the AQP inhibitor, and (3) remaining AQPs not affected by the harsh treatment. Anyhow, when using the residual values for Chara (as obtained after the treatment with hydroxyl radicals) in Eqn 13, Pf/Pd ratios for AQP arrays would increase from 47 to 62. We conclude that our measured values of N, even though rather large, may represent a lower limit of the true values, because we did not correct for the rest of the membrane (Eqn 13). They may be an upper limit, because we did not correct for internal unstirred layers. At least in part, the opposing effects may cancel.

The finding of differences in residual Lp values indicates the existence of different types of channels. The small osmolyte acetone may close only relatively narrow channels. It may largely pass through wider channels which could be only closed in the presence of bigger solutes. In this way, both the striking difference in the efficiency of osmolytes as well as the trend in the differences in pore volumes may be explained. The results of measurements with mixtures of small and big solutes support this view. Support also comes from the fact that, unlike the bigger solutes, the smaller acetone had reflection coefficients of the entire AQP array substantially smaller than unity (Table 1). The results are in agreement with earlier results of Henzler & Steudle (2000). These authors used hydrogen peroxide as an osmotic solute and concluded that it could rapidly pass through some but not all of the water channels. Hence, there are ‘real’ water channels and also some which could have been termed ‘peroxoporins’. Since H2O2 is an important metabolite and may act as a signal substance during pathogenic attacks, this view may be of some general importance.

In conclusion, the present results indicate a dehydration of aquaporins (water channels) in the plasma membrane of Chara by a cohesion/tension mechanism in the presence of high osmolyte concentrations. As expected from the C/T model, osmolytes of different size (in relation to the diameter of AQPs) differently affected cell Lp, that is, the efficiency of the osmotic dehydration of membrane pores at a given concentration of osmolyte. The results suggest that there are AQPs of bigger and smaller diameter (volume) that may select differently between osmolytes. The small solute acetone permeated across bigger but not across the smaller, whereas bigger solutes were completely excluded from all pores. Dehydration curves obtained in the presence of big osmolytes split into two exponentials which allowed evaluation of the volumes of bigger and smaller channels. Pore volumes estimated from exponential dehydration curves according to the C/T theory suggested pore volumes substantially larger than those reported for other membranes. We think that this is due to differences in channel volumes (diameters). The effect may also incorporate an exclusion of osmotic solutes from the mouth parts of AQPs, which should increase with increasing molecular size of osmolytes, but this can not completely explain the effect. The finding of relatively big pore volumes coincided with rather high numbers of water molecules in the pore as revealed from Pf/Pd ratios which ranged between 35 and 60 water molecules per pore. Compared with other AQPs, both the volumes of small (contributing to 48% of the overall water permeability) and big (contributing to 20% of the overall water permeability) water channels in the plasma membrane of Chara internodes were relatively large. This may be due to the fact that, to some extent, the measured volumes contained volumes of mouth parts. However, there may be also differences in the fine structure of channel protein due to interactions between AQPs and the bilayer. Channel volumes were small compared with those of ion channels. In comparison to AQPs of higher plants and ion channels, AQPs from Chara appeared to be fairly resistant to mechanical stress. Within the frame of the C/T model, high tensional forces of up to 5.0 MPa (50 bar) were required to close AQPs depending on the size of channels and that of the solute used.


We thank Professor Carol A. Peterson and Chris Meyer (University of Waterloo, Canada) for carefully reading the manuscript and making helpful suggestions. Thanks also go to Burkhard Stumpf (Department of Plant Ecology, University of Bayreuth) for his expert technical assistance.

Received 31 July 2004; received in revised form 1 November 2004; accepted for publication 3 November 2004