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Heavy metal concentrations in plants and different harvestable parts:A soileplant equilibrium model

Sebastin D. Guala a, Flora A. Vega b, Emma F. Covelo b,*a Instituto de Ciencias, Universidad Nacional de General Sarmiento, Gutirrez 1150, Los Polvorines, Buenos Aires, Argentinab Departamento de Bioloxa Vexetal e Ciencia do Solo, Facultade de Bioloxia, Universidade de Vigo, Lagoas, Marcosende, 36310 Vigo, Pontevedra, Spain

The model proposed in this study makes possible to characterize the nonlinear behavior of the soileplant interaction with metal pollution.

a r t i c l e i n f o

Article history:

Received 8 February 2010Received in revised form27 April 2010Accepted 28 April 2010

Keywords:

Soil pollutionMetal uptakeInteraction modelPlant mortality

a b s t r a c t

A mathematical interaction model, validated by experimental results, was developed to modeling themetal uptake by plants and induced growth decrease, by knowing metal in soils. The model relates thedynamics of the uptake of metals from soil to plants. Also, two types of relationships are tested: total andavailable metal content. The model successfully tted the experimental data and made it possible topredict the threshold values of total mortality with a satisfactory approach. Data are taken from soilstreated with Cd and Ni for ryegrass (Lolium perenne, L.) and oats (Avena sativa L.), respectively.Concentrations are measured in the aboveground biomass of plants. In the latter case, the concentrationof metals in different parts of the plants (tillering, shooting and earing) is also modeled. At lowconcentrations, the effects of metals are moderate, and the dynamics appear to be linear. However,increasing concentrations show nonlinear behaviors.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

Increased attention has been focused on metals due to theirharmful negative effect on the environment. In trace amounts, theyare mostly necessary elements in living organisms; however, inhigher concentrations they are toxic. Soil pollution by metals can becaused by fertilizers and pesticides. The use of industrial efuentand sewage sludge on agricultural soil has become a commonpractice in developing countries, as a result of which these toxicmetals can be transferred and concentrated into plant tissues fromthe soil (Alloway, 1995). Industrial wastes are a major source of soilpollution from mining industries, chemical industries, metal pro-cessing industries, metallurgic operations, oil products and prod-ucts of fossil fuel combustion (Van Assche and Clijsters, 1990;

Kabata-Pendias, 2001).The mobility and bioavailability of these elements depend on

soil characteristics such as pH, organic matter, cation-exchangecapacity, and soil redox potential (Adriano,1986). Soil managementcan also change its physical, chemical, and biological characteris-tics; therefore, a different response of biological activity to metalstoxicity may be observed. The activities of microorganisms that

promote plant growth can be also altered as a result of high metalconcentrations (Wani et al., 2007).

At high concentrations, some metals have strong toxic effectsand are regarded as environmental pollutants (Nedelkoska andDoran, 2000; Chehregani et al., 2005). Heavy metals are poten-tially toxic for plants. Phytotoxicity results in chlorosis, weak plantgrowth and yield depression, and may even be accompanied byreduced nutrient uptake, and disorders in plant metabolism (Danet al., 2008).

In soils polluted by metals, plant growth can be inhibited bymetal absorption. However, some plant species are able to accu-mulate fairly large amounts of metals without showing stress,which represents a potential risk for animals and humans (Oliver,1997). Metal uptake by crops growing in contaminated soil is

a potential hazard to human health due to transmission in the foodchain (Brun et al., 2001; Gincchio et al., 2002; Friesl et al., 2006 ).There is also concern with regard to metal transmission throughnatural ecosystems (MacFarlane and Burchett, 2002;Walker et al.,2003). Parameters connected with metal uptake have been used assensitive indicators of metal toxicity (Wilke, 1991; Nannipieri et al.,1997). The toxicity of metals in soil varies signicantly according tothe characteristics of the soil and the time elapsed after contami-nation by metals (Doelman and Haanstra, 1984; Speir et al., 1995).Data from studies on the toxic effect of metals on soils have beenused to establish the concentrations at which metals affect soilbiological processes for regulatory purposes (Giller et al., 1998).

* Corresponding author.E-mail address:emmaf@uvigo.es(E.F. Covelo).

Contents lists available atScienceDirect

Environmental Pollution

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c om / l o c a t e / e n v p o l

0269-7491/$ e see front matter 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.envpol.2010.04.026

Environmental Pollution 158 (2010) 2659e2663

mailto:emmaf@uvigo.eshttp://www.sciencedirect.com/science/journal/02697491http://www.elsevier.com/locate/envpolhttp://www.elsevier.com/locate/envpolhttp://www.sciencedirect.com/science/journal/02697491mailto:emmaf@uvigo.es

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Although a large number of experimental studies have beencarried out to analyze the negative effects of the accumulation ofmetals in plants, little has been done to model mathematicalformulas that are capable of generally relating the concentration ofmetals in the liquid phase of a soil and the concentration of metalspresent in plants. In this study, we model the relationship betweenthe concentration of metals in soil and plants and in parts of plants(tillering, shooting and earing) with different concentration levels.Finally, we validate this relationship using recently publishedexperimental results.

2. Modeling

It is widely accepted that the effects of metals on forest oragrosystem soils are complex, due to the fact that soil chemistryand its liquid phase involve a large number of reactions (Lindsay,1979; Ulrich et al., 1980; Ulrich and Pankrath, 1983). We focus onthe toxic effects of ions of metals, many of which becomebioavailable in natural pH levels. De Leo et al. (1993)modeled theinteraction between soil acidity and forest dynamics whenaluminum is mobilized with acid deposition.Guala et al. (2009)simplied this model, in order to allow it to be validated experi-mentally. In this study we consider the model applicable to othermetals in soil, modifying it in order to make it independent of aciddeposition, assuming the mobility of other metals in natural pHlevels in soil. The dominant reaction may be represented as:

MOHnnH/Mn nH2O

In order to model the dynamic interaction, we have adapted thegeneral mathematical expression of the model that describes thedynamics of soil acidity with respect to aluminum mobility and thecharacteristics of trees, according to the model proposed byDe Leoet al. (1993),and modied byGuala et al. (2009). As a result, thenew system gives us:

dB

dt BhB mS;dSdt aA hBS;

dAdt fH bA aAB=p;

dHdt fH=m n bH W=p

(1)

whereBis the biomass of trees (kg m2),nis the oxidative numberof the metal,Sis the metal concentration in trees (mg kg1), andAandHare the available concentrations of metal Mn (mg L1) andproton H (mg L1) in the soil solution, respectively.tis time,Wisthe proton ux to the soil during rainfall (mgm2 yr1), p is theavailable water for roots (mm) and a,band4are the coefcients ofabsorption (Lkg1 yr1), leaching (yr1) and reaction (yr1),respectively. m is the atomic weight of the metal M. h(B) is the

function of biomass net-growth andm(S) is the function of mortalityor metabolic inefciency of trees due to the concentration of Mn

they contain. While De Leo et al. (1993) used B to refer to thebiomass of trees,Guala et al. (2009)showed that B may also indi-cate some other physiological characteristics, and that Equation(1)may also be applied to plants in general.

Although Equation(1) was originally proposed to specicallymodel the soileplant interaction under the condition of aluminummobility by acidity, we can reformulate the conditions of the lasttwo equations for any deposited metal Mn. In this case, we are notfocusing directly on the mobility of aluminum due to the concen-tration of protons H as a result of acid deposition W, but on theavailability of any deposited metal Mn plus soil acidity conditions.As a result, under equilibrium conditions, the reformulated Equa-

tion(1)could be rewritten as:

0 BhB mS;0 aA hBS;0 fH bA aAB=p;0 fH=m n bH W=p

(2)

As signicant amounts of metals may be available under naturalacidity conditions in the liquid phase of soil and absorbed by plantsinstead of being xed by the soil matrix, we may neglect the twolast expressions of Equation(2)by focusing on the concentration ofavailable metalsAin the second equation of Equation(2).

As a result, the system in equilibrium is expressed as:

0 BhB mS;0 aA hBS:

(3)

Using Equation(3), it is possible to calculate the relationshipbetween the concentration of available metals in soil A and theconcentration of metals in plants S. The expression yields:aA mSS

The net-growth function was assumed byDe Leo et al. (1993)tobe of the form h(B) a/(1 bB), where coefcients a, b > 0 areconstant; and the logistic form to be h(B) r(1B/k) as proposed byGuala et al. (2009). Although it does not appear explicitly afterEquation (3), in Equation (1) the denition of h(B) mutuallydetermines the functional form ofm(S). Therefore, the functionalform of growth h(B) should be considered. It is difcult to specifyhow metals in soils determine the metabolic inefciency. Despitethe fact that the quantitative relationship between the concentra-tion of metals in soils and biomass production has already beendocumented for some years, metals do not seem to cause a signif-icant risk far belowa certain survival threshold, although the effectson different organs of the plant are detected.

In particular, the functional form of the metabolic inefciencyand eventual mortalitym(S) is assumed byDe Leo et al. (1993)as:

mS cfS

e S

where in c;f; e>0; S0; e, S e is the critical survival value. Itdoes not mean that plants can resist until S e; this would be only

possible ifm(S) was 0 untilS e, which would mean that plants arecompletely insensitive to any concentration below e. Obviously, it iscrucial to choose the values of the parameters correctly.

Table 1

Ni concentration in the dry matter (mg kg1) of several parts of oats (Avena sativa L.)(Poulik, 1997).

Ni total content(mg kg1)

Ni in til lering Ni in shooting Ni in earing

0 0 0 0.7514 11.81 12.76 9.8828 20.26 17.47 15.81

56 27.26 27.96 25.6084 35.73 31.47 28.81168 e e e

Table 2

Cd concentration in the dry matter (mg kg1) of ryegrass (Lolium perenne, L.) incultivated and uncultivated soil after 60 days (Moreno et al., 2006).

Cd total content(mg kg1)

Cd in uncultivatedsoil

Cd inplant

Cd in cultivatedsoil

Cd in plant

0 0.1 5.8 0.1 25.650 25.3 63.0 24.3 53.8600 201 87.4 125 1741000 329 130 242 1982000 778 228 468 3865000 1209 e 1030 721

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According to the denition ofm(S) given above, the concentra-tion of available metal in soil Aas a function of the concentration ofmetals in plants S is explicitly written as:

A 1a

cf S

e S

S

c=a f=aS

e S

S (4)

Signs of Equation(4)were inverted for simplifying the ttingpropose, but mathematically is perfectly equivalent. As we can see,the process of determining coefcients is difcult, and the knownempirical methods yield widely varying results (De Leo et al., 1993;Guala et al., 2009). Therefore, the model needs to be written ina way whereby the relationship A-Smay be inferred from ttingEquation(4). However, the coefcientsc/a, f/aandecan be tted by

experimental results in order to establish the relationship betweenAandS. It should be noted that the relationshipAeSis independent ofthe growth functionh(B), which makes it possible to generalize themodel to a wide range of plants. We can now test the model in orderto verify whetherEquation (4) provides us withreliableresults whenwe introduce realistic values, in this case testing the model whenreferring particularly to different parts of plants. This is possible bywriting Equation(4)in a general mathematical form, where theconstant terms are put together in aggregate coefcients to be tted,giving us:

A C2S C1S

2

C3 S (5)

whereC1,C2,C3>0.

However, many studies do not compare the metal uptake to theavailable metal concentration in soilA, but instead to the total metalcontentof soilT(Poulik,1997;Athar and Ahmad, 2002;Moreno et al.,2006; Ryser and Sauder, 2006). In this case, we can dene Tasa proportional sumof theplaceswherethe metal is located: themetaluptake S, the available metalcontent in soilA and the metal adsorbedin the soil matrix (assuming a Freundlich linear relationship for thepurpose of simplicity). In equilibrium this is T k1SA k2A, wherek1,k2are the corresponding proportional coefcients for uptake andFreundlich adsorption, respectively. A simple algebraic calculationshows thatTcan be written in terms of Equation(5):

T k1SC2S C1S

2

C3 S k2

C2S C1S2

C3 S

C3k1 C21 k2S k1 C11 k2S2

C3 S

Now, as with Equation (5), we can aggregate terms toredene T:

T E2S E1S

2

E3 S (6)

where E1,E2,E3> 0. As a result, we can validate the model ttingresults that are shown either in terms of the available metal Aor interms of the total metal content T. For the sake of simplicityand dueto the mathematical equivalence of Equation(5)and Equation(6),wewill only use the coefcient C1, C2, C3 to refer to the tted resultsfor bothA and T.

3. Results

In order to validate the model, we used two studies thatmeasured the dynamic interaction between metal levels in soil andthe production of biomass and other physiological characteristics ofplants (Poulik, 1997;Moreno et al., 2006).

Table 1andTable 2show the results published byPoulik (1997)andMoreno et al. (2006),respectively. The corresponding coef-cients of Equation(5)are shown inTable 3andTable 4.

Poulik (1997) suggests a linear relationship for dose-S. However,although the behavior can be linearly approached far below thethreshold parametere (equivalently, coefcientsC3ofTable 3andTable 4), linearity vanishes in the tted function for all of theexperimental results when metal levels increase. Equation(5)and

Equation (6) suggest a more complex interaction as the concen-tration of metals in plants S moves closer to e, the linear ttingbecomes ineffective, and nonlinear terms become relevant. Theseterms are important in order to reliably predict the parameter e.Please note we do not assume that plants survive up to S e . Asmentioned, the threshold is not the death point of the plants.Metabolic problems and eventual mortality actually appear beforethis point. That is a referential value and indicates the limit afterwhich no plant of the given species under given conditions isstatistically expected to be found (De Leo et al., 1993; Guala et al.,2009).

Some results inTables 3 and 4seem to indicate that the rele-vance of coefcientC1is numerically negligible and should not betaken into account. This additional result would suggest that

further revisions should be made to the model, when metal dose isconsidered, from the perspective of the economy of parameters. Inthis case, Guala et al. (2009) andDe Leo et al. (1993) proposeddifferent expressions form(S) which vary slightly in mathematicalterms, but reect a conceptually different approach towards thegrowth of plants h(B). Although h(B) does notexplicitly appear afterEquation(3), expressions ofh(B) andm(S) are mutually dependentfrom the denition of Equation(1). Therefore, further denitions ofh(B) andm(S) should be considered.

Similar results appear to be provided by the comparative valuesof the thresholdeestimated from metals in soil and metal dose forthe same plant species, shown inTable 4. This would conrm theassumptions in the model, which encourages us to carry out moreexhaustive analyses.

Fig. 1shows the results of the experimental tting according tothe proposed model. As can be seen, the gure shows the thresholdconcentrations of metals e in plants and in parts of plants, whichspecies the effects for different plant organs. These thresholds arerepresented by the coefcientsC3of Equation(5)and Equation(6).

Table1 shows that under experimental conditions(Poulik,1997),the last registered concentrations of Ni (in mg kg 1) in tillering,

Table 3

Value of the 3 aggregate coefcients corresponding to the simplied polynomialformula (C1S

2eC2S)/(SeC3) for the Ni experiment (Poulik, 1997).

Coefcients Ni in tillering Ni in shooting Ni in earing

C1 2.61 1011 0.9094 1.302

C2 72.9 44.74 49.2C3 66.31 37.52 32.82R2 0.9896 0.9960 0.9978

Table 4

Value of the 5 aggregate coefcients corresponding to the simplied polynomial formulas (C1S2

eC2S)/(SeC3) for Cd experiments (Moreno et al., 2006).

Coefcients Cd in uncultivated soil Cd in cultivated soil Cd in uncultivated soil (total content) Cd in cultivated soil (total content)

C1 3.259 1013 2.859 1013 3.388 1014 6.718 107

C2 675.9 2074 2672 6302C3 425.1 2169 529.7 1629R2 0.9742 0.9920 0.9555 0.9956

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0 50 100 150 200 2500

100

200

300

400

500

600

700

800

900

1000

Cd in plant (mg/kg)

Cdinuncultivatedsoil(mg/kg)

a0 100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

Cd in plant (mg/kg)

Cdincultivated

soil(mg/kg)

b

0 50 100 150 200 2500

500

1000

1500

2000

2500

Cd in plant (mg/kg)

Cdtotalcontentinuncultiv.soil(mg/kg)

c0 100 200 300 400 500 600 700 800

0

1000

2000

3000

4000

5000

6000

7000

Cd in plant (mg/kg)

Cdtotalcontentincultiv.soil(mg/kg)

d

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Ni in tillering (mg/kg)

Nitotalcontentinsoil(mg/kg)

e0 5 10 15 20 25 30 35

0

20

40

60

80

100

120

140

160

180

Ni in shooting (mg/kg)

Nitotalcontentinsoil(mg/kg)

f

0 5 10 15 20 25 300

20

40

60

80

100

120

Ni in earing (mg/kg)

Nitotalcontentinsoil(mg/kg)

g

Fig. 1. Curves tted according to Equation(5) (equivalently Equation(6)) for experimental results. a), b), c) and d) by Moreno et al. (2006). e), f) and g) byPoulik (1997).

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shooting and earing of living oats (Avena sativa L.) are 35.73, 31.47,28.81 respectively, corresponding to a dose of 84 mg kg1 of Ni insoil. In this case, inTable 3the model predicts plant death before66.31, 37.52, and 32.82 respectively.

Table 2shows the Cd thresholds in ryegrass (Lolium perenne,L.)(Morenoetal.,2006)bothforthetotalandavailableCdcontentinsoil.In the case of uncultivated soil, the last value for Cd concentration ina living plant is 228 mg kg1 corresponding to a total Cd content of2000 mg kg1 and available Cd of 778 mg kg1. In the case of culti-vated soil, the last value for a living plant is 721 mg kg1 corre-spondingtoatotalCdcontentof5000mgkg1 andavailableCdinsoilof 1030 mg kg1, which is the highest concentration recorded.

A test for the accuracy of the different approaches of the modelcould be computed by the relative difference between C3 ttedfrom Equation(5)and from Equation(6). According to Table 4, themodel predicts plant death in uncultivated soil beforereaching a Cdconcentration in the living plant of 425.1 mg kg1 and529.7 mg kg1 for Cd dose and Cd in soil, respectively, with anaccuracy of more than 80%. Similarly, the model predicts plantdeath in cultivated soil before reaching a Cd concentration in theliving plant of 2169 mg kg1 and 1629 mg kg1 for Cd dose and Cdin soil, respectively, with an accuracy of more than 75%.

4. Discussion

The concentration of metals in plants, and in parts of plants, canbe predicted by a simple kinetic model based on theconcentration ofmetals in the soil. This fact can be linked to physiological absorptionmechanisms in plants. Hamon et al. (1999) found out a plateau in theaccumulation of metals by plants attributed to physiological reasons.The pattern of accumulation by plants is quite similar to saturableuptake of metals described for root membrane transporters of Cd, Znor Hg (Lombi et al., 2009; Esteban et al., 2008).

The model proposed in this study makes possible to characterizethe nonlinear behavior of the soileplant interaction with metalpollution, in order to contributetowards establishingthresholdvalues

for the toxic effects of metals on plants and eventual plant mortality.The model can be applied to different plants or crops in order to

understand how the different concentrations of metals that can befound in the soil can inuence their growth. Also knowing thethreshold values for toxic effects on plants and knowing theconcentrations of metals that are in the soil will help to choose themost suitable crop for each eld in order to remediate the soilcontamination by means of biouptake.

The effects of metals on plant development vary according to thedifferent soil characteristics, the type of plant and the type of metal.As a result, the model makes it possible to directly compare therelative fragility of different environments to the same pollutant.

Finally, the effects of metals on both plants and crops must betaken into account in order to establish the risk of these contami-

nants being transferred to the food chain.

Acknowledgements

This study was supported by the Xunta de Galicia in partnershipwith the University of Vigo through ngeles Alvarioand PargaPondal research contracts awarded to F.A. Vega and E.F. Covelo,respectively.

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