REGULAR ARTICLE

Aweb-accessible computer program for calculating electricalpotentials and ion activities at cell-membrane surfaces

Peter M. Kopittke & Peng Wang & Neal W. Menzies &

Ravi Naidu & Thomas B. Kinraide

Received: 9 May 2013 /Accepted: 14 October 2013 /Published online: 23 October 2013# Springer Science+Business Media Dordrecht 2013

AbstractAims Increasing evidence indicates that plant responsesto ions (uptake/transport, inhibition, and alleviation ofinhibition) are dependent upon ion activities at the outersurface of root-cell plasma membranes (PMs) ratherthan activities in the bulk-phase rooting medium.Methods A web-accessible computer program waswritten to calculate the electrical potential (ψ) at theouter surface of root-cell PMs (ψPM). From thesevalues of ψPM, activities of ion I with charge Z ({IZ})can be calculated for the outer surface of the PM({IZ}PM). In addition, ψ and {IZ} in the Donnan phaseof the cell walls (ψCW and {IZ}CW) can be calculated.Results By reanalysing published data, we illustratehow this computer program can assist in theinvestigation of plant-ion interactions. For example,

we demonstrate that in saline solutions, both Cadeficiency and Na uptake are more closely related to{Ca2+}PM and {Na+}PM than to {Ca2+}b and {Na+}b(activities in the bulk-phase media). Additionalexamples are given for Zn and P nutrition, Ni toxicity,and arsenate uptake.Conclusions The computer program presented hereshould assist others to develop an electrostatic viewof plant-ion interactions and to re-evaluate somecommonly-held views regarding mechanisms of iontransport, toxicity, competition among ions, and otherphenomena.

Keywords Electrical potential . Mineral nutrition .

Plant growth . Plant-ion interactions . Plasmamembrane . Toxicity

Plant Soil (2014) 375:35–46DOI 10.1007/s11104-013-1948-x

Responsible Editor: Ad C. Borstlap.

Electronic supplementary material The online version of thisarticle (doi:10.1007/s11104-013-1948-x) containssupplementary material, which is available to authorized users.

P. M. Kopittke : P. Wang :N. W. MenziesSchool of Agriculture and Food Sciences,The University of Queensland,St. Lucia, Queensland 4072, Australia

P. M. Kopittke (*) :N. W. Menzies : R. NaiduCooperative Research Centre for ContaminationAssessment and Remediation of the Environment(CRC-CARE),P.O. Box 486, Salisbury South,South Australia 5106, Australiae-mail: p.kopittke@uq.edu.au

R. NaiduCentre for Environmental Risk Assessmentand Remediation, University of South Australia,Mawson Lakes, South Australia 5095, Australia

T. B. KinraideAgricultural Research Service,U.S. Department of Agriculture,Washington, DC, USAe-mail: tom@kinraide.net

Introduction

When considering interactions between plants and ions,plant performance has been related predominantly to theconcentration or activity of the ions in the bulk-phaserooting medium. However, these relationships are oftenweak or inconsistent. For example, cations in the rootingmedium, especially Ca2+, Mg2+, and H+, may promoteor inhibit root elongation and may alleviate or enhancethe phytotoxicities of ionic species of trace metals andmetalloids such as Al (Brady et al. 1993; Kinraide2003b), Cu (Luo et al. 2008), Zn (Pedler et al. 2004),Se (Kinraide 2003a), and As (Wang et al. 2008). Ingeneral, the interpretation of ion effects is clarified bya consideration of ion activities at root-cell plasmamembrane (PM) surfaces in addition to ion activities inthe rooting media.

The PM surface carries negative charges, thus creatinga negative PM surface electrical potential (ψPM)(Kinraide andWang 2010). This negativeψPM influencesthe distribution of ions at the PM surface by attractingcations and repelling anions. Hereafter, the activity of anion I with charge Z in the bulk-phase rooting mediumwill be denoted {IZ}b whilst its activity at the outersurface of the PM will be denoted {IZ}PM. {I

Z}PM iscomputed from ψPM and {IZ}b as described later. Themagnitude of ψPM is not static, rather, it is influenced bythe composition of the rooting medium. Increases in theconcentration of cations reduce the negativity of ψPM dueto binding of the cations or by electrical screening (Wanget al. 2011); anions have relatively small effects uponψPM because of their usually low concentration atnegative PM surfaces and because of weak binding.

Whilst all cations reduce the negativity of ψPM, themagnitude of the reduction is a function of ion chargeand the strength of binding to the PM surface. For ionscommonly encountered in biological systems, theability to reduce the negativity of ψPM follows thisorder: Al3+ > H+ > Cu2+ > Ca2+ ≈ Mg2+ > Na+ ≈ K+

(Kinraide 2006). ψPM is different from thetransmembrane potential difference (Em) from the bulkphase of the rooting medium to the bulk phase of thecell interior as commonly measured bymicroelectrodes (see Nobel (2009), see also Fig. 1 ofKinraide (2001) or Fig. 1 of Wang et al. (2011)).

Increasing evidence indicates that plant responses toions (uptake/transport, inhibition, and alleviation ofinhibition) are dependent upon {IZ}PM rather than{IZ}b (for examples, see Kinraide (2006), Kopittke

et al. (2011a, c), Wang et al. (2008 or 2011)). Indeed,it has been known for almost 100 years that root tissuesare negatively charged (Devaux 1916), and it wasproposed at least 40 years ago that this negative chargecould possibly explain observed plant-ion interactions(for example, see van Hai and Laudelout (1971)).However, the absence of a readily available, fullyparameterized electrostatic model for the computationof ψPM (and, consequently, {IZ}PM) has hinderedefforts to examine these interactions. The recentdevelopment of such models (Kinraide and Wang2010; Yermiyahu et al. 1997b) provides an opportunityto investigate the role of ψPM in plant-ion interactions.

The above introduction omits any discussion of cellwall (CW) influences upon the electrical properties ofthe PM. However, the PMs of root cells are not exposeddirectly (or exclusively) to the rooting medium, rather,they are exposed, in part, to the Donnan phase of theCW, which is in turn exposed to the rooting medium.Hence, the composition of the rooting mediuminfluences both ψPM and the potential of the CWDonnan phase (ψCW) (see Kinraide (2004) for acomprehensive discussion). However, the presence ofthe CW has relatively small effect on {IZ}PM, and ionconcentrations at the PM surface modelled with andwithout the CW are highly correlated (Kinraide 2004).Thus, for simplicity, ion activities at the PM surface canbe computed as though the CW were absent, which isindeed the case for the cells of many organisms.

The aim of the present study is to present a WEB-accessible computer program that uses a fullyparameterized electrostatic model to calculate ψ forplant root cell PMs and CWs based upon thecomposition of the rooting medium. From this, valuesfor {IZ}PM and {IZ}CW can be determined. Inparticular, we hope to increase the ease with whichthese calculations can be conducted in order topromote their use amongst fellow scientists as well asindustrial and governmental technologists andregulators. In addition to electrostatic models, thecomputer program incorporates speciation capabilitiesso that preliminary speciation by dedicated speciationprograms is not required for many applications.

Using this computer program, we present examplesof how plant-ion interactions can be interpreted usingelectrostatic theory. We have chosen to focus on plantsin the present study, but the computer programdeveloped here can be applied to PMs of otherorganisms (Kinraide 2006; Wang et al. 2013).

36 Plant Soil (2014) 375:35–46

Materials and methods

A computer program (SGCS, Speciation GouyChapman Stern) was written to enable users to performreadily electrostatic calculations for plants growing incommonly encountered solutions. The values for ψPM,{IZ}PM, and other quantities may then be used examineplant-ion interactions. The program is available fromthe authors or from www.uq.edu.au/agriculture/sgcs/.Although the program has been substantially verifiedin terms of agreement between computed andmeasured values (Kinraide 2004; Kinraide and Wang2010), we intend to revise and upgrade the program asneeded. We invite users to make recommendations.

Microsoft Visual Basic, within Microsoft VisualStudio 2010, was used for programming. The SGCSprogram runs on both 32-bit and 64-bit operatingsystems with Microsoft Windows XP or later software.The code is written in three major sections; the firstsection performs the solution speciation, the secondperforms the electrostatic calculations, and the thirdprovides the linkages between the graphical userinterface (GUI) and the mathematical calculations forspeciation and electrostatics.

Speciation

This SGCS computer program does not providecomprehensive speciation capabilities (as doGEOCHEM or PhreeqcI), but rather it providesspeciation for the most commonly encountered ions

and some of their complexes. Cations in the speciationcalculations include Al3+, Ca2+, Cd2+, Cu2+, H+, K+,Mg2+, Mn2+, Na+, Ni2+, and Zn2+, while the anionsinclude AsO4

3−, Cl−, CO32−, NO3

−, OH−, PO43−, and

SO42−. A full list of included species/complexes can be

found within the computer program, but the listincludes the complexes Al-OH, Al-SO4, Al-PO4, Ca-CO3, Ca-SO4, Cd-Cl, Cd-CO3, Cd-SO4, Cu-CO3, Cu-OH, Cu-SO4, Mg-CO3, Mg-PO4, Mg-SO4, Mn-CO3,Mn-SO4, Ni-CO3, Ni-SO4, Zn-CO3, and Zn-SO4.Activity coefficients are calculated using theextended Debye-Hückle equation (equation 2.11 ofLindsay (1979)) with simplified values for theeffective size (108di) of hydrated ions: di=3 formonovalent ions, di=6 for divalent ions, and di=9for trivalent ions. When necessary, all speciationconstants are easily accessed and modified by theuser from within the GUI.

Electrostatic theory at the PM surface

The electrostatic theory used in the development of thecomputer program can be expressed in a few equations.Here we provide a brief synopsis of the theory aspresented in detail by Yermiyahu and Kinraide (2005)and Kinraide and Wang (2010). The PM is modelled asthough it were composed of negatively charged (R−)and neutral (P0) sites to which ions (IZ) may bind toform species RIZ−1 and PIZ. RT is the sum of all R siteswhether free or binding an ion (RT = R− + RIZ−1), andPT is the sum of all P sites whether free or binding an

Bulk Ca concentration (µM)

10-1 100 101 102 103 104 105

PM (

mV

)

-125

-100

-75

-50

-25

0

25

Bulk Ca concentration (µM)

10-1 100 101 102 103 104 105

{X+} P

M (

µM)

0

20

40

60

80

{Y- } P

M (

µM)

0.0

0.2

0.4

0.6

0.8

1.0X+

Y-

a b

Fig. 1 a Electrical potential at the outer surface of the root PM(ψPM) exposed to CaCl2 solutions at pH 5.6. b Activities of amonovalent cation (X+) and a monovalent anion (Y−) at the outersurface of the PM, when the concentrations of those ions in the

bulk solution are 1 μM. Note that, compared to the bulk solution,negative values for ψPM increase the activity X+ at the PMsurface ({X+}PM) but decrease the activity of Y− at the PMsurface ({Y−}PM)

Plant Soil (2014) 375:35–46 37

ion (PT = P0 + PIZ). Equations 1 and 2 express thebinding reactions.

R– þ IZ⇌RIZ–1 ð1Þ

P0 þ IZ⇌PIZ ð2ÞBinding constants may be expressed as

KR;I ¼ RIZ–1� �

= R–½ � IZ� �PM

� � ð3Þ

KP;I ¼ PIZ� �

= P0� �

IZ� �

PM

� � ð4Þ[R−], [P0], [RIZ−1], and [PIZ] denote membrane

surface densities expressed in units mol m−2. [IZ]PMdenotes the concentration of the free ion at the PMsurface expressed in M units. Its value is computedfrom ion concentration in the rooting medium ([IZ]b)by a Boltzman equation.

IZ� �

PM ¼ IZ� �

bexp –Z iFψPM= RTð Þ½ � ð5ÞF, R, and T are the Faraday constant, the gas

constant, and the temperature, respectively; RT/F=25.7 mV at 25 °C, so −ZiFψPM/(RT) = −ZiψPM/25.7 at25 °C for ψPM expressed in mV.

Equation 5 cannot be solved without a value forψPM which appears also in the Gouy-Chapmanequation for surface charge density (σ, in unitsColuombs per m2 (C m−2)).

s2 ¼ 2εrε0RTX

i IZ

� �bexp –Z iFψPM= RTð Þ½ �−1ð Þ ð6Þ

2εr ε0RT=0.00345 at 25 °C for concentrationsexpressed in M (ε r is the dielectric constant for waterand ε0 is the permittivity of a vacuum). σ is alsoequal to the sums of all PM surface species (in unitsmol m−2) times the charge of each species times F (inunits C mol−1).

σ ¼ – R–½ � þX

i Zi−1ð Þ RIZ–1� �þ

XiZi PI

Z� �n o

F

ð7ÞValues for ψPM are computed by incremental and

progressive assignment of trial values to it in Eqs. 5and 6 until values for σ in Eqs. 6 and 7 converge. σ isthe contingent surface charge density and is dependentupon the bathing medium and the ion bindingexpressed in Eqs. 1 and 2. The intrinsic surface charge

density (σ0) is the total charge density in the absence ofbinding (σ0=FRT). To compute the variables in Eq. 7,the constants σ0, KR,I, KP,I, RT, and PT must be known.Values for them for plants have been estimated inprevious studies (summarized in Kinraide and Wang(2010)). Finally, values for {IZ}PM is computed fromion activity in the rooting medium ({IZ}b) by theNernst variation of the Boltzman equation (Eq. 5).

IZ� �

PM ¼ IZ� �

bexp –Z iFψPM= RTð Þ½ � ð8Þ

Electrostatic theory in the Donnan phase

For plants, the program also permits calculation of ψ inthe Donnan space (also known as free space) of the CWs(ψCW). The CW was modelled initially as a Donnanphase composed of immobile negatively charged(RCW

−) and neutral (PCW0) sites to which ions can bind.

However, the experimental data indicate that H+ bindsto RCW

− strongly and that all other binding is relativelyvery weak andmakes no significant contribution toψCW

(Kinraide 2004; Shomer et al. 2003). Computed valuesfor ψCW correspond well to values obtained byimplantations of microelectrodes into CWs and ζ-potential measurements of CW fragments (Shomeret al. 2003). Ion activities in the Donnan space of CWsare calculated with a Nernst equation, {IZ}CW ={IZ}bexp[−ZiFψCW/(RT)] (Nobel 2009).

Results

Use of the computer program

The graphical user interface (GUI) allows for the inputand output of data as well as customization of some ofthe model parameters. All speciation constants andbinding constants (for ion binding to PM sites) are easilymodified from within the GUI. Similarly, values for RTand PT (μmol m−2) can be modified within the GUI.

Data can be inputted into the SGCS program by twogeneral methods, ‘manual input’ or ‘batch input’. Formanual input, data for each solution must be manuallyentered into the program and run individually, with theresults displayed within the program window. Forbatch input, data for multiple solutions can be enteredinto a CSV (comma-separated values) file which isthen imported into the program. Then, calculated

38 Plant Soil (2014) 375:35–46

values (e.g., bulk concentrations, bulk activities, andPM surface activities for free ions and the mostcommon species) are written to an output CSV filedesignated by the user. The CSV file must have adefined structure and layout (as expected by theprogram) and templates are provided.

For either of these input methods (manual or batch),the program can be run in two modes—‘speciation’ or‘manual speciation’. For ‘speciation’, the program runsboth the speciation and electrostatic components.Hence, in ‘speciation’ mode, the total elementalconcentrations are inputted and speciation calculationsare performed prior to the electrostatic calculationsbeing conducted. For ‘manual speciation’, thespeciation component of the program is by-passed,and the user must enter the concentrations of eachindividual ionic species manually (as determined inanother chemical speciation program such as PhreeqcIor GEOCHEM). These values are then used directlyfor electrostatic calculations.

The SGCS program conducts speciationcalculations for only certain elements (see above).However, in order to increase the versatility of theprogram, it is possible to input concentration valuesfor additional ions without speciation calculations forthose ions being performed by the SGCS program, butthese added ions are still used in the electrostaticcalculations. In particular, concentrations can beinputted for Ag+, Ba2+, Co2+, Cs+, Fe2+, Fe3+, Ga3+,Gd3+, Hg2+, In3+, La3+, Pb2+, Sc3+, Sr2+, and Tl+. Forexample, if the user wishes to add 10 μM Ag2SO4 to1 mM CaCl2 at pH 5.0, the concentration of free bulk-phase Ag+ inputted should be 9.8 μM (due to theformation of 0.2 μM AgSO4

−) as determined byindependent speciation. These free ion concentrations(e.g., 9.8 μM Ag+) are then used in electrostaticcalculations with their appropriate binding constantsavailable in Kinraide (2009).

If desired, the user can balance cation/anion chargein the solutions using Cl−. In these instances Cl−will beadded to, or removed from, the solution to ensure thesolution remains balanced (although charge cannot bebalanced if the total Cl− required is <0). If the user doesnot want the charge to be balanced using Cl−, theprogram will not run if the ‘charge error’ is > 30 %,where error = 100(positive – negative)/(positive+negative). The user is also able to equilibrate thesolutions with atmospheric CO2 (H2CO3) partialpressure if desired.

Accuracy of the computer program

Firstly, we checked the accuracy of the speciationcalculations by comparing to those using PhreeqcI2.17 and the MINTEQ database. The relevantconstants of the MINTEQ database were modified tobe the same as those in the SGCS database. Threesolutions were used to compare the two programs, withinput concentrations in μM units: Solution 1=5Al2(SO4)3, 1,000 CaSO4, 10 CuSO4, and sufficientH2SO4 to reduce the pH to 4.5; Solution 2=375 CaCl2,125 Ca(H2PO4)2, 500 CaSO4, 5 CdCl2, 10 ZnCl2, andsufficient HCl to reduce pH to 5.5; Solution 3=660CaCl2, 90 CaCO3, 250 CaSO4, 5 CdCl2, and 10 ZnCl2.Values calculated using the SGCS programcorresponded well to PhreeqcI values, although slightdifferences were observed with some CO3-species(such as CaHCO3

+, Table 1).Secondly, and importantly, values for ψPM

calculated using the electrostatic model outlined here(Eq. 1 to Eq. 8) have been shown to correspond well tosurface electrical potentials measured byelectrophoresis (to obtain zeta (ζ) potentials) or thesurface attraction of ionic dyes (Kinraide and Wang2010; Wang et al. 2013, 2008).

Discussion

The SGCS computer program allows the calculation ofion activities at the outer surface of the PM. ψPM istypically negative relative to the bulk medium. Ittherefore increases the PM-surface activity of cationsand reduces the PM-surface activity of anions. Theextent to which ions are attracted to or repelled fromthe PM surface depends also upon the charge of the ion(see the Eqs. 5 and 8). For example, when ψPM=−59.2 mV, monovalent cations will be concentrated10-fold relative to the bulk solution, divalent cationswill be concentrated 100-fold, and trivalent cations willbe concentrated 1,000-fold. In contrast, anions will bedepleted 10-, 100-, or 1,000-fold. Depolarization(decrease in negativity) of the PM caused by theaddition of salts to the bulk solution (Fig. 1a) willreduce the concentration of cations at the PM surfacebut will increase the concentration of anions (Fig. 1b).Thus, an increase in the cation concentration in thebulk solution typically decreases the uptake andtoxicity of other cations. This ‘competition’ among

Plant Soil (2014) 375:35–46 39

cations based upon global (whole surface) electrostaticinteractions is different in principle from competitionbased upon site-specific interactions among ions asdescribed by the biotic ligand model (BLM) (Kinraide2006). Furthermore, interactions between cations andanions (e.g., enhancement by cations of anion uptakeand toxicity) can be understood by electrostaticprinciples but not by site-specific competitions.

Here, using the SGCS computer program, wepresent examples of how activities of ions at the outerPM surface can be used to interpret plant-ioninteractions. Although we have focused on plant-ioninteractions, this electrostatic theory can be used toexamine interactions in other species, including

bacteria and animals (Kinraide 2006). The resultsbelow are presented in two parts, the first examiningthe uptake of essential nutrient ions in the deficient toadequate supply range, and the second examining thetoxicity (and alleviation of toxicity) of essential andnon-essential ions.

Mineral nutrition of essential cations and anions

Whilst plants are selective and active in their uptake ofnutrients (and different conditions influence theselectivity of this uptake), we suggest that the uptakeof nutrient ions is influenced by the activity of the ionat the outer surface of the root cell PM, which may

Table 1 Comparison of speciation calculations performed eitherwith the SGCS program or with PhreeqcI 2.17 using the Minteqdatabase modified so that the selected constants equalled those inthe default SGCS database. Data in the table are presented asionic activities (μM). Three solutions were examined, with inputconcentrations of (μM): Solution 1=5 Al2(SO4)3, 1,000 CaSO4,

10 CuSO4, and sufficient H2SO4 to reduce the pH to 4.5;Solution 2=375 CaCl2, 125 Ca(H2PO4)2, 500 CaSO4, 5 CdCl2,10 ZnCl2, and sufficient HCl to reduce pH to pH 5.5;Solution 3=660 CaCl2, 90 CaCO3, 250 CaSO4, 5 CdCl2,and 10 ZnCl2. Only selected ionic species are shown

Solution 1 Solution 2 Solution 3

SGCS PhreeqcI SGCS PhreeqcI SGCS PhreeqcI

Al3+ 2.9 2.9 0 0 0 0

AlOH2+ 0.9 0.9 0 0 0 0

Al(OH)2+ 0.2 0.2 0 0 0 0

AlSO4+ 3.2 3.2 0 0 0 0

Ca2+ 700 700 740 740 770 770

CaHCO3+ 0 0 0 0 1.8 1.4

CaHPO40 0 0 1.5 1.8 0 0

CaH2PO4+ 0 0 4.2 4.2 0 0

CaSO40 101 100 53 52 27 27

Cd2+ 0 0 3.4 3.4 3.4 3.3

CdCl+ 0 0 0.3 0.3 0.4 0.4

CdSO40 0 0 0.3 0.3 0.2 0.2

Cl− 0 0 770 780 1400 1400

Cu2+ 6.9 6.8 0 0 0 0

CuSO40 1.1 1.1 0 0 0 0

H+ 34 34 3.4 3.4 0.033 0.033

HPO42− 0 0 3.8 4.5 0 0

H2PO4− 0 0 220 220 0 0

SO42− 930 930 450 450 220 220

Zn2+ 0 0 7.4 7.4 7.2 7.0

ZnHCO3+ 0 0 0 0 0.2 0.1

ZnCO30 0 0 0 0 0.4 0.3

ZnSO40 0 0 0.6 0.5 0.3 0.3

40 Plant Soil (2014) 375:35–46

differ greatly from its activity in the bulk-phase rootingmedium.

Two cationic nutrients are examined here, the firstbeing Zn. Chaudhry and Loneragan (1972a, b)investigated the effect of Ca, Mg, Ba, Sr, and H onthe absorption of Zn by wheat roots at concentrationsrelevant for Zn nutrition (0.1 to 10 μM). The authorsobserved that at a constant bulk concentration of Zn,increases in Ca, Mg, Ba, Sr, or H reduced the uptake ofZn (Fig. 2a). For example, with 1 μM Zn in the bulksolution, a decrease in pH from 7 to 3, with 350 μMbasal Ca, reduced Zn uptake from 430 to 3.5 ng g−1 d−1.Given that the concentration of Zn in solution wasconstant, these changes in Zn uptake induced by Hcannot be explained by changes in {Zn2+}b (Fig. 2a).However, the increase in H+ from 0.1 to 1,000 μMactivity was computed to reduce the negativity of ψPM

from −51 to +33 mV thereby reducing {Zn2+}PM from45 to 0.06μM. Therefore, we suggest that these changesin Zn uptake resulted from changes in the negativity ofψPM which in turn influenced {Zn2+}PM. Indeed, acrossall cations, when Zn uptake was related to {Zn2+}PMrather than {Zn2+}b, the r

2 value improved from 0.604to 0.925 (Fig. 2).

Calcium was the second cationic nutrient examined.It is often reported that plant growth in salineconditions is reduced because cationic salts (typicallyNa or Mg) compete with Ca for uptake and induce Cadeficiency (Grattan and Grieve 1992, 1999). We

contend that the changes in Ca nutrition do not resultfrom site-specific competition, but rather, fromchanges in {Ca2+}PM resulting from variations inψPM. For example, Carter et al. (1979) examined theinfluence of cations (Mg, Na, and K) on Ca deficiencyfor the growth of barley (Hordeum vulgare L.) shootsand roots in nutrient solutions simulating saline soilsolutions of Canada. No significant relationship wasfound between dry mass and {Ca2+}b (r2=0.442,Fig. 3a). In contrast, the data demonstrate that changesin the solution composition influenced ψPM and that Caavailability was related to {Ca2+}PM (r2=0.910,Fig. 3b). Thus Ca deficiency in saline soils does notresult from direct competition between Ca and othercations, but rather, from a non-specific, cation-inducedreduction in {Ca2+}PM to deficiency levels (see alsoKopittke et al. (2011a)).

The SGCS model was also used to investigate therole of ψPM for anionic nutrients. In contrast to cationicnutrients, a reduction in the negativity of ψPM (causedby an increase in the concentration of cations) isexpected to increase the activity of the anionic nutrientat the PM surface and hence increase uptake (Fig. 1).However, our analyses here were hindered by a lack ofsuitable published data for nutrient anions (to besuitable, a study must examine uptake across anadequate range of solution compositions). In one study,Franklin (1969) studied uptake of P in excised roots ofbarley and found that the addition of various metals

{Zn2+}PM (µM)

0.01 0.1 1 10 100 1000

{Zn2+}b (µM)

0.01 0.1 1 10

Zn

upta

ke (

ng g-1

d-1

)

1

10

100

1000

10000R2 = 0.604 R2 = 0.925

a bCaMgBaSrH

Fig. 2 Effect of Ca, Mg, Ba, Sr, and H (pH) on the absorption ofZn by wheat seedlings related to the activity of Zn2+ in the bulksolution (a) or at the outer surface of the root PM (b). Data weretaken from Fig. 4 of Chaudhry and Loneragan (1972b) for H andfrom Table 1 and Fig. 2 of Chaudhry and Loneragan (1972a) for

the other cations (data are excluded from the highest Ca and Mgtreatments due to deleterious osmotic effects). Other than for theH+-treatments, a constant pH of 5.6 was assumed. The size of thesymbols is proportional to the concentration of the cation

Plant Soil (2014) 375:35–46 41

influenced the uptake of P (ranging from 5 to18 μg g−1). In solutions with a constant P concentrationof 20 μM, the order of effectiveness upon uptake (leastto greatest) was K ~ Li ~ Na < Ba ~ Sr ~ Mg ~ Ca <Fe(II) < Fe(III) ~ Al. Noticeably, this effect on uptakewas the opposite to that observed for cationic nutrients(Figs. 2 and 3), viz. an increase in the concentration of(depolarizing) cations increased P uptake butdecreased Zn and Ca uptake. However, the resultsof Franklin (1969) cannot be re-analysed precisely;solution pH was not stated and hence thedistribution among P-species (for example, HPO4

2−

and H2PO4−) cannot be calculated nor can ψPM be

calculated (for some of the cations, solution pHlikely varied widely among treatments). Regardless,given that the total P concentration remainedconstant in the bulk solution, it is unlikely that thesechanges in uptake can be explained by changes inbulk activities of P species.

Significantly, the sequence of metals enhancing Puptake (K to Al above) corresponds to the effectivenesswith which these metals depolarize the PM (Kinraide2009). P uptake increased with the strength of metalbinding to hard ligands such as the carboxylic acidgroups of the PM (Fig. 4). Thus P uptake was lowestin solutions containing cations that depolarize the PMthe least and highest in the solutions containing cationsthat depolarize the PM the most. These results holdsome significance for acidic soils that may be rich in Aland poor in available P.

Toxicity of essential and non-essential cationsand anions

We also used the SGCS model to investigate thephytotoxicity of essential and non-essential ions. Forcationic toxicants (such as Cu, Ni, or Cd), toxicity is

{Ca2+}PM (mM)

0 2 4 6

R2 = 0.910

{Ca2+}b (mM)

0 1 2 3 4

Rel

ativ

e dr

y m

ass

(%)

0

25

50

75

100

R2 = 0.443

a b

Fig. 3 The relative dry mass of shoots (●) and roots (○) of barley(Hordeum vulgare L.) grown in nutrient solutions for 3 to4 weeks as related to the activity of Ca2+ in the bulk solution(a), or at the outer surface of the root PM (b). The solutions were

at pH 5.5 and contained 0.5 to 10 mM Ca, 1.5 to 90 mM Na, 0.8to 6.0 mM K, and 0.25 to 15.5 mM Mg. Data were taken fromExperiments 1 to 4 of Carter et al. (1979)

HLScale

-2 -1 0 1 2

P u

ptak

e(µ

g g-1

roo

t)

0

4

8

12

16

20

R2 = 0.942

Fe2+

Al3+

Fe3+

Mg2+Ba2+

Sr2+

Ca2+

K+

Li+

Na+

Fig. 4 The uptake of P by excised roots of barley (Hordeumvulgare L.) related to the Hard Ligand Scale (HLScale) for tenmetals. The HLScale is a logarithmic scale of binding strengthbetween metals and hard ligands such as the carboxylic acidgroups of the PM. Thus the HLScale is a measure of theeffectiveness with which cations reduce the surface negativityof the PM (Kinraide 2009). Data for P uptake are taken fromFranklin (1969)

42 Plant Soil (2014) 375:35–46

commonly understood according to the biotic ligandmodel (BLM) which postulates that the adverse effectof a toxicant is determined by the degree of its bindingto a site (the ‘biotic ligand’) whose occupancy by thetoxicant leads to the toxicity (Paquin et al. 2002). Afurther postulate of the BLM is that the beneficialeffects of ameliorating cations (such as Ca, Mg, or H)arise from competition between the ameliorant and thetoxicant at the biotic ligand (Di Toro et al. 2001;Paquin et al. 2002; Slaveykova and Wilkinson 2005).In contrast, we postulate that the principle ameliorativeeffect of cations such as Ca, Mg, or H can be explained,usually, by this sequence: 1. Ameliorative cationsreduce the negativity of ψPM. 2. The reduced negativityof ψPM reduces the PM-surface activity of the cationictoxicant. 3. The reduced PM-surface activity of thetoxicant reduces its binding to the biotic ligand, ifindeed such a ligand plays a role. In some cases oneor more of the steps in the sequence may not besignificant. An ameliorative cation may be effectiveat such low concentrations that neither the PM-surface negativity nor the PM-surface activity of thetoxicant are significantly reduced (see below).

We reanalysed the data of Wu and Hendershot(2010) who examined the influence of H and Ca onthe toxicity of Ni to roots of pea (Pisum sativum L.).The authors reported that the addition of either H or Catypically decreased the toxicity of the Ni (Fig. 5a). Forexample, in solutions with 10 μM Ni and 2 mM Ca,relative root elongation improved from 51 % with1 μM H+ to 130 % with 100 μM H+ (Fig. 5a). Indeed,across all treatments, the toxicity of Ni was only poorly

correlated with {Ni2+}b (r2=0.580, Fig. 5a). Incontrast, the toxicity of Ni was more closely correlatedto {Ni2+}PM (r2=0.761, Fig. 5b), which decreased withthe addition of cations (Ca2+ or H+).

A second cationic toxicant was examined; in salinesystems, the excess salt may lead to specific-iontoxicities (Munns 2002). We reanalysed the data ofDavenport et al. (1997) who examined the effect ofCa (0.06 to 3.1 mM) on the uptake of Na from salinesolutions containing 5 to 150 mMNa. As expected, theauthors observed that the addition of Ca reduceduptake of Na. For example, in solutions containing110 mM {Na+}b, an increase in Ca from 0.06 to3.1 mM decreased Na uptake from 20 to 10 μmol g−1

root h−1 (Fig. 6b). Indeed, across all treatments, therelationship between Na uptake and {Na+}b wascomparatively poor (r2=0.686, Fig. 6a)—the authorsstating that this Ca-induced reduction in uptake waspossibly due to the binding of Ca to the cation channelsthrough which Na uptake was occurring. While Cablockade of Na-conducting channels may indeed be afactor in Na uptake and toxicity, the Ca-inducedreduction in {Na+}PM is surely important; r2=0.925(Fig. 6b) for {Na+}PM vs. Na uptake. Therefore, thisameliorative effect of Ca was in part non-specific, withthe addition of Ca decreasing the negativity of ψPM andhence decreasing uptake by lowering the activity of Naat the PM surface. Other examples regarding theimportance of electrostatic interactions in regulatingthe toxicity of cations (including Cu, Pb, and Mn) aregiven in Kinraide (2006), Kinraide and Wang (2010),and Kopittke et al. (2011b).

{Ni2+}PM (µM)

0 500 1000 1500 2000 2500 3000

R2 = 0.761

{Ni2+}b (µM)

0 10 20 30 40 50

Rel

ativ

e ro

ot e

long

atio

n

0.00

0.25

0.50

0.75

1.00

1.25

1.50R2 = 0.580

a b100 µM H+

10 µM H+

1 µM H+

Fig. 5 Growth of pea roots in solutions with toxic levels of Nirelated to the activity of Ni2+ in the bulk solution (a) or at theouter surface of the root PM (b). Solution pH values were 4, 5, or6 with Ca concentration at 0.04 mM (small symbols), 0.2 mM

(medium symbols), or 2 mM (large symbols). Data were takenfrom Table 1 of Wu and Hendershot (2010) with the pH 4treatments at 0.04 and 0.2 mM Ca excluded due to poor rootgrowth (> 80 % reduction when compared to other treatments)

Plant Soil (2014) 375:35–46 43

Finally, we examined the exacerbation of aniontoxicity and the enhancement of uptake caused by anincrease in the concentration of cations as reported forselenate, SeO4

2− (Kinraide 2003a). These observationscannot be explained by the usual hypotheses such aschannel blockade. As found for anionic nutrients (seeearlier), comparatively few data are available forexamining the effect of cations on the uptake of anionictoxicants. In a study with wheat, Wang et al. (2011)found that the addition of Ca, Mg, or H slightlyincreased both the toxicity and uptake of arsenate(AsO4

−) (data not presented). This is in contrast tothe effects upon cationic toxicants such as Ni and Na(see above) where an increase in the concentration ofcations decreased toxicity and uptake. However,relating As uptake to {H2AsO4

−}PM rather than{H2AsO4

−}b did not improve the r2 value (r2=0.803versus 0.839). This demonstrates that whilst ψPM-controlled PM-surface activities are important inregulating plant-ion interactions across a range ofconditions, other factors influenced by ψPM areimportant also. Kinraide (2001) and Wang et al.(2011) provide evidence that the surface-to-surfacetransmembrane potential difference (Em,surf) is alsoinfluential as it provides the ‘driving force’ for iontransport across the PM, but Em,surf becomes morenegative as ψPM becomes less negative. Indeed,inclusion of an additional term to account for Em,surf

in the regression analyses for arsenate uptake improvedthe r2 value to 0.922 (data not presented).

The preceding discussion, examining severalcationic and anionic nutrients and toxicants, highlightsthe importance of electrostatic properties of the PM in

determining the bioavailability of ions. We suggest thatthe electrostatic properties of the root PM have a non-specific effect on plant-ion interactions whereby anincrease in the concentration of cations decreases thenegativity of ψPM (Fig. 1a) thereby decreasing theactivity of cations at the PM surface but increasingthe activity of anions (Fig. 1b). We propose that manyof the ameliorative effects typically ascribed to‘competition’ can be explained by electrostatic effects.We do not, however, suggest that site-specificcompetition does not ever occur—certainly there areexamples where we would assert that competition doesindeed directly reduce toxicity of trace metals. Forexample, Zn toxicity was alleviated in wheat andradish (Raphanus sativus L.) by 1 to 5 μM Mg,concentrations too low to affect {Zn2+}b or {Zn

2+}PM(Zn2+ and Mg2+ have similar ionic radii) (Pedler et al.2004). Similarly, 50 μM Mg has been reported toalleviate Al toxicity in soybean, concentrations againtoo low to affect {Al3+}b or {Al

3+}PM (Silva et al. 2001).In a final example, 1 μM Cu (c. 5 μM {Cu2+}PM) atpH 5.6 strongly inhibits reproduction in free-livingrhizobia, but each 0.1 unit reduction in the pH of theculture medium causes a ten-fold increase in thereproduction (Kinraide and Sweeney 2003). Thesesmall reductions in pH cause the negativity of ψPM todecline by only 0.3 mVand the {Cu2+}PM to decline byonly 0.1 μM. In such cases the ameliorative cation mayact principally as a direct competitor with the toxicant ata biotic ligand, and global electrical effects may play noimportant role, but in our experience global electricaleffects appear to play the greater role, especially in thecase of cationic enhancement of anion toxicity where

{Na+}b (mM)

0 25 50 75 100 125

Na

influ

x (µ

mol

g-1 h

-1)

0

5

10

15

20

{Na+}PM (mM)

0 100 200 300

0.06 mM Ca0.77 mM Ca1.6 mM Ca3.1 mM Ca

R2 = 0.686

a b

R2 = 0.925

Fig. 6 Effect of Ca on the short-term influx of Na in roots of Triticum aestivum L. cv Kharchia, related to the activity of Na+ in the bulksolution (a) or at the outer surface of the root PM (b). Data were taken from Fig. 2 of Davenport et al. (1997), with all solutions at pH 6.5

44 Plant Soil (2014) 375:35–46

site-specific competition would appear to be unlikely.Finally, we have not considered here how different plantspecies respond to variations in {IZ}PM, althoughcertainly such differences exist (for a detaileddiscussion, see Kinraide and Wang (2010)). Forexample, in Fig. 3 it can be seen that Ca deficiencyreduces the growth of barley by 10 % when {Ca2+}PM< ca. 4 mM. However, other species have differentthresholds: growth of cowpea roots was decreased at≤1.6 mM (Kopittke et al. 2011a), wheat roots at≤0.76 mM (Kinraide 1999), pea (Pisum sativum L.)roots at ≤6 mM (Wang et al. 2010), and melon (Cucumismelo L.) roots at ≤15 mM (Yermiyahu et al. 1997a).Such variations need to be taken into account.

We hope that the WEB-accessible SGCS computerprogram described here will increase the ease withwhich electrostatic calculations can be performed,thereby allowing further investigation of the role ofelectrostatics in plant-ion interactions across a widerange of situations.

Acknowledgments Dr Kopittke is the recipient of an AustralianResearch Council (ARC) Future Fellowship (FT120100277). DrWang is a recipient of an ARC Discovery Early Career ResearcherAward (DE130100943).

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