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PLANT NUTRITION

Possible Influence of Cell Walls upon Ion Concentrations at Plasma Membrane Surfaces. Toward a Comprehensive View of Cell-Surface Electrical Effects upon Ion Uptake, Intoxication, and Amelioration¹

Appalachian Farming Systems Research Center, Agricultural Research Service, United States Department of Agriculture, Beaver, West Virginia 25813–9423

	ABSTRACT

TOP ABSTRACT COMPUTATION OF ION... APPLICATION OF THE MODELS... ALTERNATIVE METHODS OF ANALYSIS CONCLUSION LITERATURE CITED

 
Plant uptake of ions, intoxication by ions, and the alleviation of intoxication by other ions often correlate poorly with ion concentrations in the rooting medium. By contrast, uptake, intoxication, and alleviation correlate well with ion concentrations at the plasma membrane (PM) surface computed as though the PM were bathed directly in the rooting medium with no effect from the cell wall (CW). According to two separate lines of analysis, a close association of CWs and PMs results in a slight increase in cation concentrations and a slight decrease in anion concentrations at the PM surface compared with concentrations when the CW is separated or has no effect. Although slightly different, the ion concentrations at the PM surface computed with and without close association with the CW are highly correlated. Altogether, the CW would appear to have a small effect upon ion uptake by the PM or upon intoxication or alleviation of intoxication originating at the PM surface. These analyses have been enabled by the recent evaluation of parameters required for the electrostatic models (Gouy-Chapman-Stern and Donnan-plus-binding) used to compute electrical potentials and ion concentrations in CWs and at PM surfaces.

My interest is in the possible electrostatic interactions between CWs and PMs and whether such interactions affect ion concentrations at the PM surface and thereby affect nutrition, intoxication, and the alleviation of intoxication. A century-old electrostatic theory (Gouy-Chapman) has been used in the study of some membrane phenomena, especially photosynthesis (for review, see Barber, 1980), and is currently being used to interpret quantitatively the interactive effects of multiple ions (Kinraide, 1999, 2001, 2003a, 2003b; Zhang et al., 2001; Ahn et al., 2004). The quantitative nature of these studies has been enabled by the recent evaluation of parameter values needed in a Gouy-Chapman-Stern model for the determination of PM-surface electrical potentials (Yermiyahu et al., 1997; Kinraide et al., 1998; Vulkan et al., 2005; Table I). Knowledge of these potentials (illustrated in Fig. 1) then enables the computation of PM-surface ion activities (see below).

View larger version (51K): [in this window] [in a new window]   Figure 1. Possible electrostatic interactions between CWs and PMs. In the top portion of the figure, the PM is not influenced by the CW because of physical separation or some other reason. In the bottom portion, the PM is considered to be bathed by the Donnan-phase solution of the CW. Em (–105 mV) is the transmembrane electrical potential difference from rooting medium to cell interior. PM,medium (–41.8 mV) is the electrical potential of the PM surface when the PM is bathed directly by a rooting medium composed of 0.1 mM CaCl2, 1 mM NaCl, and 0.001 mM LaCl3 at pH 5.6 (solution no. 1 in Table II). CW,medium (–50.3 mV) is the electrical potential of the CW. PM,CW (5.1 mV) is the electrical potential of the PM surface relative to the CW. The PM surface-to-surface potential difference (indicated by the sloping lines) plays a role in ion transport (Kinraide, 2001) but is not considered in this study. Unlike the vertical dimensions (a voltage scale), the horizontal dimensions are not drawn to scale. Moreover, the depiction of the electrical profile is simplified as in the step change at the outer CW surface and in the straight lines through the CW and the PM.

View larger version (15K): [in this window] [in a new window]   Figure 2. Selenium uptake by roots in response to SeO42– activities in the rooting medium and at the PM surface. Atlas 66 wheat seedlings were cultured in media variously supplemented with CaCl2 and MgCl2, adjusted to several pH values. This figure is redrawn from Kinraide (2003a).

In this study, I shall present an analysis of possible CW effects upon ion concentrations at the PM surface. Specifically, I shall consider the differences in PM-surface ion concentrations when the PM is bathed directly in the rooting medium without effect from the CW and when the PM and the CW are intimately associated (Fig. 1).

	COMPUTATION OF ION CONCENTRATIONS AT PM SURFACES

TOP ABSTRACT COMPUTATION OF ION... APPLICATION OF THE MODELS... ALTERNATIVE METHODS OF ANALYSIS CONCLUSION LITERATURE CITED

 

Ion Concentrations at PM Surfaces Bathed Directly in the Rooting Medium

When plant-root PMs contact a solution, the Müller equation (expressing the Gouy-Chapman theory) describes the relationships among the PM-surface charge density (_PM), the ion concentrations in the solution ([I^Z]), and the electrical potential at the PM surface (_PM) (Barber, 1980; Tatulian, 1999). In the equation that follows, I use double subscripts to designate an interaction between the PM surface and the rooting medium; thus, _PM,medium designates the surface charge density when the PM is bathed in the medium, and _PM,medium designates the electrical potential when the PM is bathed in the medium (actually, _PM,medium is the potential difference _PM – _medium).

(1)

where 2_r0RT = 0.00345 at 25°C for concentrations expressed in M, and F/(RT) = 1/25.7 at 25°C for expressed in mV. _r is the dielectric constant for water; ₀ is the permittivity of a vacuum; and F, R, and T are the Faraday constant, the gas constant, and the temperature, respectively.

_PM,medium, expressed in Coul m^–2, is not constant. It is a function of the surface charges contributed by the usually negatively charged structural components of the PM itself (e.g. –COO^–, –OPO₃H^–, –NH₄⁺, etc.) and of the ions that bind to the PM surface (e.g. –COOAl²⁺, –OPO₃HCa⁺, –NH₄Cl⁰, etc.). Ordinarily, the PM surface is negative, but adequate concentrations of strongly binding cations (e.g. H⁺ and Al³⁺ in acidic soils) may convert the PM surface from negative to positive. To compute _PM,medium, one must know the density of charged structural components at the PM surface and the characteristics of ion binding to the PM surface (e.g. equilibrium constants for binding at both charged and neutral sites; Table I). Eventually, a surface charge density R^– (in mol unit charge m^–2) is obtained, which when multiplied by F (in Coul mol^–1) yields _PM,medium (in Coul m^–2).

Recent years have witnessed much progress in obtaining parameter values needed for the use of the Müller equation (Table I) to find _PM,medium by an iterative process described in Kinraide et al. (1998), and computer programs are available from the author. Thus, _PM,medium may be computed for many solutions. With the availability of _PM,medium, the concentration of ions at the PM surface may be computed from a Boltzmann equation.

(2)

[I^Z]_PM,medium signifies the concentration when the PM is in direct contact with the rooting medium. Equation 2 implies the assumption that the CW, if present, has no influence.

Many readers, and physiologists in particular, may be more accustomed to a variation of Equation 2 known as the Nernst equation, which incorporates chemical activities rather than concentrations (Nobel, 1991). If activity is the appropriate measure for the electrochemical equilibrium of an ion and if the electrical potential is accurately expressed as _PM,medium, then the following equation will define the activity of ions at the PM surface because ion activity in a bulk-phase medium can be computed accurately.

(3)

The problem is that the derivation of the Müller equation incorporates Equation 2, not 3. Consequently, Equations 2 and 3 are both correct only if the activity coefficients remain constant at all distances from the PM surface. This seems counterintuitive because the sum of free ion concentrations (and thus, presumably, the ionic strength from which activity coefficients are computed) can be much greater at the PM surface. In previous studies, I have assumed the constancy of activity coefficients and have related ion uptake and toxicities to {I^Z}_PM,medium rather than to [I^Z]_PM,medium, but the latter is usually a good indicator of physiological response, and for the remainder of this presentation I shall use concentrations principally.

[I^Z]_PM,medium appears to influence ion uptake and ion toxicity much more directly than [I^Z]_medium; that is, the former correlates with uptake and toxicity much more strongly than the latter (citations above). Nevertheless, these strong correlations are only weak evidence that [I^Z]_PM has been computed correctly. Implicit in the preceding treatment is the assumption that the PM is bathed in the rooting medium directly or that the CW has no influence on [I^Z]_PM. As an alternative, I shall assume an intimate interaction between CW and PM—namely, that the PM is bathed not by the rooting medium but by the solution in the CW Donnan phase.

Ion Concentration at PM Surfaces Bathed in the CW Donnan Phase

Measurements of the (nearly always negative) electrical potential of the CW Donnan phase (_CW,medium) are problematical. In several studies microelectrodes were pushed against cell surfaces and the potentials were recorded as the composition of the bathing solutions was changed (Nagai and Kishimoto, 1964; Saftner and Raschke, 1981; Shomer et al., 2003). These measurements corresponded substantially with expectation in that the depolarizing effectiveness of ions was related to size and charge (Shomer et al., 2003), corresponded to the strength of adsorption by CWs as determined by chemical assays (Franco et al., 2002), was in agreement with -potential responses of CW fragments (O'Shea et al., 1990), and corresponded roughly to the depolarizing effectiveness against PMs (Shomer et al., 2003).

A major difference between the PMs and the CWs is that the binding of ions to CWs appears to be much weaker than to PMs, especially with respect to apparent binding at neutral sites (Table I). In fact, all of the values in the "Donnan-Plus-Binding for CW" column in Table I appear to be small, except for the value for K_R,H. Chemical assays of isolated CW material indicate much greater values (references in Shomer et al., 2003), but the values presented in Table I were determined in vivo or at least in situ and pertain to sites that were accessible to measurements of electrical potential and available to reversible binding. If the reported values for R_Total = 1 M referred to sites available to reversible binding, then _CW,medium –200 mV in 0.1 mM NaCl. Such negative potentials have not been measured to my knowledge.

A Donnan-plus-binding model for the computation of _CW,medium was developed, and the success of this model for _CW,medium and the success of the Gouy-Chapman-Stern model for _PM,medium can be assessed from Figure 3. Assuming that _CW,medium can be computed, then ion concentrations in the CW Donnan phase can be computed from this equation, assuming once again that concentration is an adequate measure for electrochemical equilibrium.

(4)

View larger version (16K): [in this window] [in a new window]   Figure 3. A comparison of studies in which PM,medium and CW,medium were measured and computed. A, Parameters for a Gouy-Chapman-Stern model were evaluated for eight studies; B, parameters for a Donnan-plus-binding model were evaluated for five studies. Optimized values for total negative sites (RTotal) were computed for each study, but a single suite of binding constants was evaluated for the pooled PM data and for the pooled CW data (see Table I). The figure is redrawn from Shomer et al. (2003).

(5)

_PM,CW expresses the potential difference _PM – _CW, and _PM,CW is the surface charge density of PMs bathed in the CW Donnan phase. Finally, ion concentrations at the PM surface bathed in the CW Donnan phase may be computed from

(6)

Because [I^Z]_mediumexp[–Z_iF_CW,medium/(RT)] from Equation 4 may be substituted for [I^Z]_CW,medium in Equation 6, [I^Z]_PM,CW may be computed from

(7)

A Comparison of [I^Z]_PM,medium and [I^Z]_PM,CW

If the CW has had no effect upon [I^Z] at the PM surface, then [I^Z]_PM,CW = [I^Z]_PM,medium. That will be the case, of course, for neutral solutes (Z = 0) or for uncharged CWs. Although it is not readily apparent from the equations, if _CW,medium is negative and Z is positive, then [I^Z]_PM,CW > [I^Z]_PM,medium. That is, the model predicts that when the (nearly always negative) CW interacts with the PM, the effect is to cause (usually small) increases in cation concentrations and decreases in anion concentrations at the PM surface. Furthermore, [I^Z]_PM,CW is approximately proportional to [I^Z]_PM,medium. I shall illustrate these features by an analysis of some solutions presented in Table II.

In solution number 1, all solutes are at a minimum relative to the other solutions so that _CW,medium (–50.3 mV) is more negative than elsewhere. When the 1 mM NaCl was increased 10-fold, as in solution number 3, the negativity of _CW,medium declined to –21.6 mV. Consequently, [La³⁺]_CW,medium was driven down to 12.5 µM from 353 µM (Table III), and [Ca²⁺]_CW,medium and [H⁺]_CW,medium were driven down as well. These ions (La³⁺, Ca²⁺, and H⁺) depolarize the PM strongly (and depolarize the PM more strongly than the CW [see model parameters in Table I]), so the declines in their concentrations more than offset the increase in [Na⁺] (from 5,810 µM to 47,400 µM) because Na⁺ is a weakly depolarizing ion. The net effect is an increase in the negativity of _PM,CW from 5.1 mV to –18.4 mV. These opposing trends (declining negativity in _CW,medium and increasing negativity in _PM,CW) cause Equations 2 and 7 to compute approximately similar values because the change in _PM,medium (from –41.8 mV to –37.9 mV) is comparable to the change in _CW,medium + _PM,CW (from –45.2 mV to –40.0 mV). Thus, we see in Table III that the decline in [La³⁺]_PM,CW (45%) is not greatly different from the decline in [La³⁺]_PM,medium (37%).

View larger version (25K): [in this window] [in a new window]   Figure 4. Plots of Ca2+ concentrations in various phases for cells bathed in the rooting media presented in Table II.

What if the CW were more highly charged than the 0.0211 (moles negative charge)/(liter CW volume) found to be optimum for the computation of _CW,medium (Table I)? This is a possibility because glass microelectrodes and -potential measurements may not access directly the electrical potentials of the CW interior (see discussion in Shomer et al., 2003). The effect of this is illustrated in Figure 5 for La³⁺. If the charge is increased 10-fold to 0.211 M, the slope increases to 4.42 (top curve) from 1.46 for the standard run (middle curve)—a modest 3-fold increase. But if the microelectrodes and -potential measurements failed to access the CW interior, then the PM is unlikely to do so either. Consequently, the slope of the upper curve in Figure 5 is almost certainly too steep even if the CW charge were 10-fold higher. In any case, [La³⁺]_PM,CW and [La³⁺]_PM,medium are well correlated.

View larger version (23K): [in this window] [in a new window]   Figure 5. The effect of changing model parameters on the relationship of [La3+]PM,CW to [La3+]PM,medium.

The bottom curve in Figure 5 illustrates the effect of changing another parameter. If the constant for Ca²⁺ binding to CW negative sites is increased from 0 to 1,000 M^–1, then the slope is reduced to from 1.46 to 1.12. Shomer et al. (2003) found that reversible cation binding (except for H⁺) had trivial effects upon measured CW potentials in comparison to screening effects (which increase with ionic charge). I could find no reasonable adjustment of parameters that caused a reduction of slope to less than 1. Thus, the presence of a negatively charged CW always causes an increase in the concentration of cations at the PM surface if the PM is bathed in the CW Donnan phase rather than in the rooting medium directly. Is the CW ever positively charged in any medium that allows growth? Apparently not, as discussed at length by Shomer et al. (2003). This is in contrast to the PM, which is often positively charged in acidic soil solutions.

	APPLICATION OF THE MODELS TO SOME EXPERIMENTAL DATA

TOP ABSTRACT COMPUTATION OF ION... APPLICATION OF THE MODELS... ALTERNATIVE METHODS OF ANALYSIS CONCLUSION LITERATURE CITED

 
Figures 6 and 7 illustrate applications of the models to some published experimental data. In each case the generalities mentioned above are confirmed. Figure 6 is a continuation of Figure 2 and illustrates that selenium uptake corresponds to [SeO₄^2–]_PM,medium and [SeO₄^2–]_PM,CW about as well as to {SeO₄^2–}_PM,medium. Values for [SeO₄^2–]_PM,CW are smaller than values for [SeO₄^2–]_PM,medium, as expected for an anion. Figure 7 illustrates that uptake of Ca²⁺ correlates better with [Ca²⁺]_PM,medium and [Ca²⁺]_PM,CW than with [Ca²⁺]_medium. Values for [Ca²⁺]_PM,CW are larger than values for [Ca²⁺]_PM,medium, as expected for a cation. The data for Figure 7 were obtained with outside-out PM vesicles so that CWs were not present. Figure 7C presents the PM-surface concentration of Ca²⁺ as though a CW were present and as though the PMs were bathed in the Donnan phase of the CWs.

View larger version (16K): [in this window] [in a new window]   Figure 6. Selenium uptake by roots in response to [SeO42–]PM,CW and [SeO42–]PM,medium. Other details are presented in Figure 2.

View larger version (15K): [in this window] [in a new window]   Figure 7. Ca2+ uptake plotted against Ca2+ concentrations in various phases. [AlCl3] in the external bathing medium was 0, 2, or 5 µM. Data are from Huang et al. (1996), who measured Ca2+ uptake into outside-out PM vesicles from wheat roots. Em was clamped at –100 mV.

	ALTERNATIVE METHODS OF ANALYSIS

TOP ABSTRACT COMPUTATION OF ION... APPLICATION OF THE MODELS... ALTERNATIVE METHODS OF ANALYSIS CONCLUSION LITERATURE CITED

 
In the analyses above, I modeled CW-PM interaction as though the PM were bathed in the Donnan-phase solution of the CW. In reality, the PM may be pressed tightly against the CW so that the exterior PM surface may be substantially influenced by the Donnan phase but not bathed entirely in the Donnan-phase solution. Assume that the CW is a slab of permeable material with surface charges and binding sites. In this way we may treat the CW with a Gouy-Chapman-Stern model instead of the Donnan-plus-binding model. The model parameters are presented in Table I. Although Shomer et al. (2003) considered a Donnan-plus-binding model (negative charges and binding sites distributed throughout the CW) more appropriate than a Gouy-Chapman-Stern model (sites restricted to the CW surface), the latter model generated values that correlated with measured potentials slightly better than did the former model (Fig. 3B).

The potentials computed by the Gouy-Chapman-Stern model for the CW surface (Alternative _CW,medium) resemble closely the potentials computed by the Donnan-plus-binding model (_CW,medium; Fig. 8A). For the extreme case of interaction between the CW and PM, imagine that the negative binding sites at the PM surface (R^– under the heading "G-C-S for PM" in Table I), the neutral binding sites at the PM surface (P⁰ under the heading "G-C-S for PM" in Table I) and the negative binding sites at the CW surface (R^– under the heading "G-C-S for CW" in Table I) all lie in a plane—a plane in equilibrium with the rooting medium. A Gouy-Chapman-Stern model may be used to compute potentials at this CW-PM interface. Figure 8B indicates that those values (Alternative _PM,medium) correlate well with the potentials of the PM bathed directly in the rooting medium (_PM,medium). The effect is that the CW-PM interface attracts cations slightly more and anions slightly less than a naked PM (Fig. 8C).

View larger version (14K): [in this window] [in a new window]   Figure 8. Electrical potentials and La3+ concentrations computed by an alternative model. Alternative CW,medium refers to CW surface potential computed by a Gouy-Chapman-Stern model rather than a Donnan-plus-binding model. Alternative PM,medium refers to the potential at the CW-PM interface, and Alternative [La3+]PM,medium refers to concentrations at the CW-PM interface.

	CONCLUSION

TOP ABSTRACT COMPUTATION OF ION... APPLICATION OF THE MODELS... ALTERNATIVE METHODS OF ANALYSIS CONCLUSION LITERATURE CITED

Received March 19, 2004; returned for revision April 16, 2004; accepted April 16, 2004.

	FOOTNOTES

 
¹ This work was supported in part by the United States-Israel Binational Agricultural Research and Development Fund (BARD project no. IS–3120–99R).

Article, publication date, and citation information can be found at www.plantphysiol.org/cgi/doi/10.1104/pp.104.043174.

^* E-mail tom.kinraide{at}ars.usda.gov; fax 304–256–2921.

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This Article Abstract Full Text (PDF) All Versions of this Article: 136/3/3804    most recent pp.104.043174v1 Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via CrossRef Citing Articles via Web of Science (9) Citing Articles via Google Scholar Google Scholar Articles by Kinraide, T. B. Search for Related Content PubMed PubMed Citation Articles by Kinraide, T. B. Agricola Articles by Kinraide, T. B.