TY - JOUR
AU - Kataev, Anatolii, A.
AB - Abstract Determination of pore size of the cell wall of Chara corallina has been made by using the polyethylene glycol (PEG) series as the hydrophilic probing molecules. In these experiments, the polydispersity of commercial preparation of PEGs was allowed for. The mass share (γ p ) of polyethylene glycol preparation fractions penetrating through the pores was determined using a cellular ‘ghost’, i.e. fragments of internodal cell walls filled with a 25% solution of non‐penetrating PEG 6000 and tied up at the ends. In water, such a ‘ghost’ developed a hydrostatic pressure close to the cell turgor which persisted for several days. The determination of γ p , for polydisperse polyethylene glycols with different average molecular mass ( M −) was calculated from the degree of pressure restoration after water was replaced by a 5–10% polymer solution. Pressure was recorded using a dynamometer, which measures, in the quasi‐isometric mode, the force necessary for the partial compression of the ‘ghost’ in its small fragment. By utilizing the data on the distribution of PEG l000, 1450, 2000, and 3350 fractions over molecular mass ( M ), it was found that γ p , for these polyethylene glycols corresponded to the upper limit of ML =800–1100 D (hydrodynamic radius of molecules, rh =0.85–1.05 nm). Thus, the effective diameter of the pores in the cell wall of Chara did not exceed 2.1 nm. Chara, cell wall, pore size, polyethylene glycol, pressure relaxation. Introduction The plant cell wall, in addition to its mechanical function, also functions as a porous network determining the upper size limit for the molecules which the cell may exchange with its external medium. The limit is determined by the diameter of through pores in the cell wall. Despite the importance of the size of those pores, very little information is available concerning the pore diameters in the cell walls of plants. For higher plants, the upper limit of the average molecular mass ( M − L ) of the PEGs found by observing the transition, as the M − is increased in the hyper‐osmotic medium, from the phenomenon of plasmolysis occurring when the polymer passes through the cell wall, to collapse (cytorrhysis) of the whole cell, was 1450–4000 D (average hydrodynamic radius of the molecules is \(\overline{r}_{\mathrm{h}}\) =1.2–2.0 nm [The authors erroneously ascribe the radii \(\overline{r}_{\mathrm{h}}\) =1.9–2.25 nm to those M − values.]) depending on the plant species ( Carpita et al ., 1979 ). Based on the analysis of ion exchange kinetics, it has been suggested that there is a system of pores of less than 10 nm in diameter in the cell walls of Chara australis besides some pores with diameters of greater than 10 nm ( Dainty and Hope, 1959 ). However, using that technique through pores cannot be evaluated, because the entire network of capillaries and cavities in the three‐dimensional structure of the cell wall contributes to ionic exchange. More specific indications of maximum sizes of pores in Characeae, exemplified by Nitella syncarpa , have been presented previously ( Lyalin et al ., 1994 ). Using a portion of a cell wall tied at the ends (a cell ‘ghost’) of the internode filled with a solution of the non‐penetrating PEG 20 000 as an osmotic cell and measuring the change in the hydrostatic pressure, these authors established that only polyethylene glycols with M −<2000 D ( \(\overline{r}_{\mathrm{h}}{=}1.4\)  nm) may pass through the cell wall from the external medium. However, when commercially available polymer preparations are used, problems with M − L evaluation arise due to polymer polydispersity, i.e. due to the presence of fractions with molecular masses differing from the mean ( M −) in the preparation. Surprisingly, that property was not allowed for in most of the papers where aqueous pore diameters were measured using polymers, including measurements of ionic channel diameters in membranes ( Krasilnikov et al ., 1992 ; Ternovsky and Berestovsky, 1998 ; Merzliak et al ., 1999 ). In an earlier paper it has been demonstrated that failure to allow for polymer dispersity leads to an overestimation of ML and pore diameter ( Scherrer and Gerhardt, 1971 ). The authors demonstrated a fractionation of PEG preparations into quasi‐monodisperse fractions. According to their estimates, the limiting pore diameter in Bacillus megaterium cell wall is 2.2 nm ( ML =1200 D). This work aimed to develop a technique for determining through pore sizes in cell walls of Chara corallina using a series of polyethylene glycols with allowance for their polydispersity. Materials and methods Materials Internodal cells of Chara corallina 40–80 mm long were used that had been grown in tanks containing a layer of pond mud. Temperature was kept at 16–18 °C. Tanks were illuminated by 40 W luminescent lamps (day/night rhythm of 14/10 h); The solutes used to determine the pore size range were polyethylene glycols (PEGs) of molecular masses (D) of 300, 400, 600, 1450, 3350 (Sigma, USA), 6000 (Ferak, Germany), 1000 and 2000 (Merck, Germany), all purchased commercially. Solutions of PEGs were prepared in water containing 0.5 mM CaCl 2 , to prevent Ca 2+ desorption from the cell wall ( Taiz, 1984 ) resulting in damage of its porosity ( Lyalin et al ., 1994 ). Fabrication of polyethyleneglycol ‘ghosts’ of the cells Internodes of intact Chara with two nodes were placed on glass plates. A micropipette for cell perfusion with 25% PEG 6000 solution was inserted into one of the nodes. The other node was cut off. Then, cell contents were flushed out until the green colour vanished. After that the cut was rinsed with PEG solution through the micropipette, and the free end was tied up, with a polyester thread. The wall cut was slightly inflated with PEG solution until it acquired a cylindrical shape, the second end was tied up, and the remaining part of the cell was cut off. The cell ‘ghost’ was placed in water where it obtained a turgor close to that of the living cell (0.6–0.8 MPa). Turgor was preserved for several days. Unlike living cells, ‘ghosts’ were permeable to sucrose, which showed, along with the electron microscopy data ( Lyalin et al ., 1994 ) that the plasma membrane had been removed. ‘Ghosts’ used in experiments were exposed for more than 1 h in 0.5 mM CaCl 2 solution to remove low‐molecular weight components of the PEG 6000 solution. A simpler method of filling wall preparations with PEG solution as proposed earlier for Nitella syncarpa ( Lyalin et al ., 1994 ) was not suitable for the Chara ‘ghosts’ used in this study. Measurement of cell and ‘ghost’ pressure (P) To measure the pressure, a method was used based on measuring the force F necessary partially to compress the cylindrical cell or ‘ghost’ over a small region ( Tazawa, 1957 ) (Fig. 1A ). The force F applied to the squeezing plate is equalized by the sum of two forces: the force of the pressure P ( Fp ) on the plate, and the force F1 proportional to the normal components ( Tn ) of the special longitudinal tension, T , of the cell wall from both sides of the plate. Since all the involved forces ( Fp ,  T ) are proportional to the pressure P , the geometry of the deformed region depends only on the value of cell compression, δ. Therefore, when δ=constant (isometric mode) the measured force F will be proportional to P with negligible small allowance for extensibility of a cell wall (Δ D/DP∼ 10 −2  MPa −1 at P <1 MPa, Steudle et al ., 1982 ). The proportionality of F to P at δ=constant have been confirmed by experiments with Chara cells (data not shown) and investigations with Nitella flexilis ( Tazawa, 1957 ). In these osmotic experiments pressure P was varied using a sucrose solution of defined osmolarity. To measure the force continually, a dynamometer has been developed (Fig. 1B ). The vertical displacement of a squeezing plate ( b =2.5 mm) was transmitted with the help of a racking‐shaft (7) to a metal rod (8) of a mechanotron and further was transduced into an electrical signal ( Karpenko et al ., 1991 ). The racking‐shaft (the relation of arm lengths was 1 : 5) was intended for the desensitization of a dynamometer (Δδ/Δ F ) in contrast to the sensitivity of a mechanotron 6MX2 (12 μm cN −1 and 40 μA μm −1 , USSR), up to an indispensable level. The sensibility of the dynamometer was 2 μm cN −1 ensuring that the measurement mode was fairly close to isometric. When necessary, the sensor was calibrated in pressure units using the living cell and sucrose solutions of defined osmolarity. During measurements, cells or ‘ghosts’ were placed in a narrow long canal in plexiglas plate (Fig. 1A ) fixed to the micro‐manipulator table equipped with a micrometric screw for vertical adjustment of the table. The dynamometer itself was rigidly attached to the manipulator base. An automatic pipette was used to change and stir solutions in the canal. Fig. 1. Open in new tabDownload slide Geometry of a cylindrical cell (‘ghost’) at the place of its squeezing by the plate and the acting forces (A) and set‐up for measuring of squeezing force (B). F , squeezing force; Fp , force of hydrostatic pressure; T and Tn , specific longitudinal tension of the wall and its normal component. On the right: transverse section of a canal with a cell (‘ghost’) in it. D  − δ is a thickness of a compressed cell placed under the plate. (B) 1, Movable table of micromanipulator; 2, plexiglass chamber; 3, internode (‘ghost’) of Chara cell; 4, squeezing plate; 5, micrometre screw; 6, elastic diaphragm; 7, racking‐shaft; 8, movable metal rod of a mechanotron; 9, mechanotron 6MX2 (vacuum double diode with one movable anode); 10, steel casing. For further explanations see text. Fig. 1. Open in new tabDownload slide Geometry of a cylindrical cell (‘ghost’) at the place of its squeezing by the plate and the acting forces (A) and set‐up for measuring of squeezing force (B). F , squeezing force; Fp , force of hydrostatic pressure; T and Tn , specific longitudinal tension of the wall and its normal component. On the right: transverse section of a canal with a cell (‘ghost’) in it. D  − δ is a thickness of a compressed cell placed under the plate. (B) 1, Movable table of micromanipulator; 2, plexiglass chamber; 3, internode (‘ghost’) of Chara cell; 4, squeezing plate; 5, micrometre screw; 6, elastic diaphragm; 7, racking‐shaft; 8, movable metal rod of a mechanotron; 9, mechanotron 6MX2 (vacuum double diode with one movable anode); 10, steel casing. For further explanations see text. Determination of effective pore diameter (2r p ) The rp value for the cell wall was determined from the limiting size of the molecules capable of permeating the cell wall. The method was based on analysing the pressure relaxation curve, P ( t ), in response to the changes in the concentration of the tested substance in the external solution ( Steudle and Tyerman, 1983 ). For a penetrating solute, when its concentration was abruptly increased the pressure initially quickly fell to a certain Pmin value, and then returned to the original Po value as the solute entered the cell wall, thus, decreasing the concentration difference (Fig. 3 ). For non‐penetrating substances, the second phase was absent ( P∞ = Pmin ). For a mixture of both types of substances, the pressure P∞ at the end of the second phase had an intermediate value Pmin < P∞ < Po . If it is assumed, in the first approximation, that the pressure change Po−Pmin is proportional to the sum of mass shares of the penetrating and the non‐penetrating fractions of the substance, the value of the mass share of the molecules penetrating through the cell wall (γ p ) will be determined by the following expression: 1 The above supposition assumes that, in the molecular masses ( M ) of PEGs which interest the authors, the value Po − Pmin only slightly depends on M (Fig. 4A ). Commercially available PEG preparations are polydisperse. The mass share of the fractions with different molecular mass M in polydisperse preparations varies around the average molecular mass ( M −) according to the Poisson distribution (Fig. 2 ) ( Morawetz, 1967 ; Grosberg and Khokhlov, 1994 ). It is evident that the passage of a preparation with a definite M recorded in an osmotic experiment should only reflect the permeation of lighter fractions (hatched region under the w ( M ) curve in Fig. 2 ) with M ≤ ML , where ML is the upper limit of the mass of the molecules that freely permeate the cell wall. To evaluate the share of the permeating molecules, integral distribution curves S ( M ) were used for the PEGs tested. The value of ML was found from the S ( M ) curve (Fig. 2 ) for the particular PEG, from the condition SA = S ( ML )=γ p . To construct the S ( M ) curve, detailed chromatography analysis data were used for some PEG samples as reported previously ( Scherrer and Gerhardt, 1971 ). To evaluate aqueous pore diameter in the cell wall using PEGs, literature data were analysed for the average hydrodynamic radius of the molecules ( \(\overline{r}_{\mathrm{h}}\) ) for various PEGs ( Scherrer and Gerhardt, 1971 ; Kuga, 1981 ; Krasilnikov et al ., 1992 ). It was found that, in the PEG 200 to PEG 10 000 range, the dependence of \(\overline{r}_{\mathrm{h}}\) on the average molecular mass ( M −) is well approximated by the expression 2 where \(\overline{r}_{\mathrm{h}}\) and M − are expressed in nm and kDa, respectively. It is commonly assumed that this dependence of the average values is also observed in monodisperse PEG fractions. Fig. 2. Open in new tabDownload slide Characteristic molecular mass distribution, w ( M ), for polyethylene glycols (stroke line) and its integral function, S ( M ) (scale on the right). SA = \({{\sum}_{\mathrm{o}}^{\mathit{M}_{\mathrm{L}}}}\) w ( M )Δ M , overall mass share with M<ML . Fig. 2. Open in new tabDownload slide Characteristic molecular mass distribution, w ( M ), for polyethylene glycols (stroke line) and its integral function, S ( M ) (scale on the right). SA = \({{\sum}_{\mathrm{o}}^{\mathit{M}_{\mathrm{L}}}}\) w ( M )Δ M , overall mass share with M<ML . Fig. 3. Open in new tabDownload slide Kinetics of hydrostatic pressure (turgor) changing of the cell wall tied up from two ends (‘ghost’), filled with 25% solution of PEG 6000, to different osmotic solutes. For an impermeable solute (PEG 3350) the responses after the change from water to solution(↓)and back to water (↑) are monophasic, whereas for sucrose biphasic responses were obtained and the original turgor was re‐established. In the case of PEG 1000 the partial restoration of pressure ( P∞ < Po ) indicates that part of the fractions of polydisperse polymer does not penetrate through the wall. The solute concentrations: PEG 1000 and 3350, 5% (w/w); sucrose, 100 mM. Fig. 3. Open in new tabDownload slide Kinetics of hydrostatic pressure (turgor) changing of the cell wall tied up from two ends (‘ghost’), filled with 25% solution of PEG 6000, to different osmotic solutes. For an impermeable solute (PEG 3350) the responses after the change from water to solution(↓)and back to water (↑) are monophasic, whereas for sucrose biphasic responses were obtained and the original turgor was re‐established. In the case of PEG 1000 the partial restoration of pressure ( P∞ < Po ) indicates that part of the fractions of polydisperse polymer does not penetrate through the wall. The solute concentrations: PEG 1000 and 3350, 5% (w/w); sucrose, 100 mM. Fig. 4. Open in new tabDownload slide The relation of the relative share of the pressure's relaxing part (γ p =( P∞ − Pmin )/( Po − Pmin )), osmotic pressure, π s , and product σπ s , (= Po − Pmin , σ reflection coefficient) (A) to average hydrodynamic radius ( \(\overline{r}_{\mathrm{h}}\) ) of PEG molecules (PEG 300, 400, 600, 1000, 1450, 2000, and 3350, several ‘ghosts’) and overall mass shares (integral functions, S, B) for a few PEGs (on data of Scherrer and Gerhard, 1971 (. 1, PEG 1000; 2, PEG 1450; 3, PEG 2000 (interpolation); 4, PEG 3350. The relations of π s and σπ s to rh (dotted lines, scale on the right) were obtained from experiments on the living cell impermeable for PEGs (σ=1) and its ‘ghost’, correspondingly with the same concentration of PEGs (5%, w/w). The γ p values marked by dark circles are transferred to the corresponding curves of Fig. 4B. From the positions of dark circles on curves 1–4, it is seen that the upper limit of the polymer's molecular mass ( ML ) passing through the cell wall does not exceed 1100 D ( \(\overline{r}_{h}\) =1.05 nm). Fig. 4. Open in new tabDownload slide The relation of the relative share of the pressure's relaxing part (γ p =( P∞ − Pmin )/( Po − Pmin )), osmotic pressure, π s , and product σπ s , (= Po − Pmin , σ reflection coefficient) (A) to average hydrodynamic radius ( \(\overline{r}_{\mathrm{h}}\) ) of PEG molecules (PEG 300, 400, 600, 1000, 1450, 2000, and 3350, several ‘ghosts’) and overall mass shares (integral functions, S, B) for a few PEGs (on data of Scherrer and Gerhard, 1971 (. 1, PEG 1000; 2, PEG 1450; 3, PEG 2000 (interpolation); 4, PEG 3350. The relations of π s and σπ s to rh (dotted lines, scale on the right) were obtained from experiments on the living cell impermeable for PEGs (σ=1) and its ‘ghost’, correspondingly with the same concentration of PEGs (5%, w/w). The γ p values marked by dark circles are transferred to the corresponding curves of Fig. 4B. From the positions of dark circles on curves 1–4, it is seen that the upper limit of the polymer's molecular mass ( ML ) passing through the cell wall does not exceed 1100 D ( \(\overline{r}_{h}\) =1.05 nm). Results and discussion The characteristic shape of the curve P ( t ) for the ‘ghost’ when the external water was replaced with the PEG 1000 sample solution containing a certain share (γ p ) of the molecules penetrating through the cell wall is shown in Fig. 3 . The curve had a biphasic shape. The fast phase of the pressure decrease corresponded to the exit of water from the ‘ghost’. and the slow phase of pressure increase by penetration of PEG molecules into the ‘ghost’ ( Steudle and Tyerman, 1983 ). The pressure was not fully restored ( P∞ < Po ) suggesting that a non‐penetrating polymer fraction was present in the PEG sample. In Fig. 4A , data on the γ p values calculated according to equation (1) are shown for PEG samples with average molecular masses ranging from 300–3350 kDa. The curve had a sharp bend in the PEG 1000 region, and then quickly fell to zero as M − increased. The data for PEGs 1000, 1450, 2000, and 3350 transferred to the corresponding S ( M ) curves of Fig. 4B showed that the maximal molecular mass of the penetrating molecules was in the 800–1100 D range ( rh =0.85–1.05 nm). The deviation observed for PEG 1450 (curve 2) was probably related to the difference between fraction distributions between our PEG sample and that used earlier ( Scherrer and Gerhardt, 1971 ). The data of the latter authors were used to draw those curves. This is also suggested by the anomalous shape of curve 2 compared to curves 1 and 4. Note that, for another Characean species, Nitella , it was similarly shown that PEG 2000 only partially penetrates the ‘ghost’ while PEG 3000 does not penetrate at all ( Lyalin et al ., 1994 ). It is concluded that both subjects have approximately the same pore diameters in the cell walls. This conclusion, however, does not exclude the presence of a small pool of pores with larger diameters, with the transport of the tested polymer's molecules through those pores not causing any noticeable change of pressure in the ‘ghost’ during the experimental time (∼1 h). There is evidence for the existence of such pores, at least in the cell walls of higher plants ( Carpita et al ., 1979 ). The fact that the points of curves 1–4 (Fig. 4B ) lie in a single narrow range of the polymers’ molecular mass values supports the validity of equation (1) . On the other hand, that equation was obtained by assuming that the pressure change is independent of the polymer molecular mass. However, as M is increased, the ( Po − Pmin ) value (=σπ s ) decreases (Fig. 4A , dotted line). As visible from the matching of two dotted curves, this decrease occurred from the reduction of osmotic pressure of PEG solutions, π s , than of a reflection coefficient, σ, changing. To what extent can this effect influence the ML value in the above‐described manner? To answer that question, three solutions were used to perform measurements: two PEG solutions of identical concentrations but with different M − (mainly penetrating and non‐penetrating polymers), and a solution containing both PEGs with the same concentrations. If equation (1) is valid, then one can expect the value γ p ≈0.5. As the polymer pair, the easily penetrating PEG 600 and the poorly penetrating PEG 2000 (5% concentration) were used. Each series consisting of three measurements was performed on a single ‘ghost’. The obtained value γ p =0.47±0.03 was found to be close to the expected one. The theoretical analysis of a difference between the determined parameter γ p and the true value of a relative mass share of an permeating fraction, SA , had also shown that this difference did not exceed the natural dispersion of values of γ p in the experiment (see Appendix). Therefore, the above‐presented values of the extreme pore radius in the cell wall, 0.85–1.05 nm may be considered quite valid. Durability and permeability of the cell wall is largely determined by the presence of calcium bridges within it. When calcium is desorbed from the cell wall, it becomes looser ( Taiz, 1984 ). and the pore sizes in it increases. Thus, it was shown ( Lyalin at al ., 1994 ; Skobeleva et al ., 1996 ) on ‘ghosts’ from Nitella cells that, when EDTA (10 mM) is present, the turgor pressure of the ‘ghost’ filled with PEG 20 000, which normally does not penetrate through the cell wall, quickly falls. The same EDTA effect was observed in the experiments on ‘ghosts’ from Chara cells filled with PEG 6000 (data not shown). Penetration of PEG 20 000 ( \(\overline{r}_{\mathrm{h}}\) =5 nm) through the cell walls implies a massive increase of through pores with a diameter larger than 10 nm under the action of the chelator. It is important to note that the upper limit of pore diameters determined for Chara was similar to those estimated for walls of higher plants ( Carpita et al ., 1979 ) and of bacteria ( Scherrer and Gerhardt, 1971 ). Appendix Approximated estimation of the correctness of equation (1) The problem is to find a quantitative difference between the value of γ p , determined from the experiment, and the true value of a mass share of solution, SA (Fig. 2 ), permeating into a ‘ghost’. Let the values of pressure differences P∞ − Pmin and Po − Pmin with mean osmotic pressures ( \({{\pi}_{\mathrm{s}}^{\mathrm{p}}},\ {{\pi}_{\mathrm{s}}^{\mathrm{n}}}\) at concentrations C = Co ), both mass share of permeating and non‐permeating fractions of polydisperse polymer, respectively. Suppose, that (i) the concentration of solutions of polymer preparations, Co (%, w/w), is the same; (ii) the half‐time of the water flow equilibration (‘water phase’) is much less than the half‐time for the equilibration solute (‘solute phase’, Fig. 3 ); (iii) the osmotic pressure of the solution is proportional to the concentration of the solute (the last supposition is true up to the concentration of 10% (w/w) for PEGs in the range from 600–3350 D, studied here. Then the contribution of permeating and non‐permeating fractions of polydisperse polymer, taking into account the reflection coefficient, σ, will be equal to SA σ \({{\pi}_{\mathrm{s}}^{\mathrm{p}}}\) and (1− SA ) \({{\pi}_{\mathrm{s}}^{\mathrm{n}}}\) accordingly. Rewriting equation (1) with the above variables 1A whence 2A where As an example the value γ p − SA will be estimated using PEG 1000 (γ p =0.64, Fig. 4A ). According to a distribution curve for PEG 1000 (Fig. 4B ) it is reasonable to select for σ \({{\pi}_{\mathrm{s}}^{\mathrm{p}}}\ \mathrm{and}\ {\mathrm{{\pi}}_{\mathrm{s}}^{\mathrm{n}}}\) their mean values for M =600 and 1450 as σ \({{\pi}_{\mathrm{s}}^{\mathrm{p}}}\) =0.24 and \({\mathrm{{\pi}}_{\mathrm{s}}^{\mathrm{n}}}\) =0.19, respectively (Fig. 4A ). From equation (2A) γ p − SA = 0.053 is obtained. This value does not exceed the dispersion of γ p values in the experiment. 1 To whom correspondence should be addressed. Fax: +7 967 790509. E‐mail:  Gberest@mail.ru We are grateful to Professor E Steudle and Viktor Sivozhelezov for useful discussion of the manuscript. This work was supported by a grant from the Russian Foundation of Basic Research (grant No 99 04 48553). References Carpita N, Sabularse D, Montezinos D, Delmer DP. 1979 . Determination of the pore size of cell walls of living plant cells. Science 205, 1144 –1447. Dainty J, Hope AB. 1959 . Ionic relations of cell of Chara australis . I. Ion exchange in the cell wall. Journal of Biological Science 12, 395 –411. Grosberg AYu, Khokhlov AR. 1994 . Statistical physics of macromolecules . New York: AIP Press. Karpenko GN, Berlin GS, Barsukov II. 1991 . Application of mechanotronic techniques in medico‐biological research . Saratov: Saratov University Press (in Russian). Krasilnikov OV, Sabirov RZ, Ternovsky VI, Merzliak PG, Muratkhodjaev JN. 1992 . A simple method for the determination of the pore radius of ion channels in planar lipid bilayer membranes. FNEMS Microbiology and Immunology 105, 93 –100. Kuga S. 1981 . Pore size distribution analysis of gel substances by size exclusion chromatography. Journal of Chromatography 206, 449 –461. Lyalin OO, Ktitorova IN, Marichev GA. 1994 . Polyethylene glycol ‘ghosts’ of Nitella cells and their use in the study of cell wall properties. Russian Journal of Plant Physiology 41, 646 –650. Merzliak PG, Yuldasheva LN, Rodrigues CG, Carneiro CMM, Krasilnikov OV, Bezrukov SM. 1999 . Polymeric non‐electrolytes to probe pore geometry: application to the α‐toxin transmembrane channel. Biophysical Journal 77, 3023 –3033. Morawetz H. 1967 . Macromolecules in solution . New York: John Wiley and Sons. Scherrer R, Gerhardt P. 1971 . Molecular sieving by the Bacillus megatherium cell wall and protoplast. Journal of Bacteriology 107, 718 –735. Skobeleva OV, Ktitorova IN, Marichev GA, Lyalin OO. 1996 . Cell explosion as one of types of the plant cell's damage. 2. Cell explosion from the point of view of the membrane lysis. Fiziologiya rastenii 43, 511 –518 (in Russian). Steudle E, Ferrier JM, Dainty J. 1982 . Measurements of the volumetric and transverse elastic extensibilities of Chara corallina internodes by combining the external force and pressure probe techniques. Canadian Journal of Botany 60, 1503 –1511. Steudle E, Tyerman SD. 1983 . Determination of permeability coefficients, reflection coefficients and hydraulic conductivity of Chara corallina using the pressure probe: effects of solute concentration. Journal of Membrane Biology 75, 85 –96. Taiz L. 1984 . Plant cell expansion: regulation of cell wall mechanical properties. Annual Review of Plant Physiology 35, 585 –657. Tazawa M. 1957 . Neue Methode zure Messung des osmotischen Wertes einer Zelle. Protoplasma 48, 342 –359. Ternovsky VI, Berestovsky GN. 1998 . Effective diameter and structural organization of reconstituted calcium channels from the characeae alga Nitellopsis . Membrane and Cell Biology 12, 79 –88. © Society for Experimental Biology
TI -  Through pore diameter in the cell wall of Chara corallina
JF - Journal of Experimental Botany
DO - 10.1093/jxb/52.359.1173
DA - 2001-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/through-pore-diameter-in-the-cell-wall-of-chara-corallina-cLuloaB6gN
SP - 1173
VL - 52
IS - 359
DP - DeepDyve
ER -