Journal of Hazardous Materials 423 (2022) 127008

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Journal of Hazardous Materials
journal homepage: www.elsevier.com/locate/jhazmat

Research Paper

A novel multiscale biophysical model to predict the fate of ionizable
compounds in the soil-plant continuum
Giuseppe Brunetti a, *, Radka Kodešová b, Helena Švecová c, Miroslav Fér b, Antonín Nikodem b,
Aleš Klement b, Roman Grabic c, Jiří Šimůnek daUniversity of Natural Resources and Life Sciences, Vienna (BOKU), Institute for Soil Physics and Rural Water Management, Muthgasse 18, 1180 Vienna, Austria
Czech University of Life Sciences Prague, Faculty of Agrobiology, Food and Natural Resources, Dept. of Soil Science and Soil Protection, Kamýcká 129, CZ-16500
Prague 6, Czech Republicc
University of South Bohemia in České Budějovice, Faculty of Fisheries and Protection of Waters, South Bohemian Research Center of Aquaculture and Biodiversity ofHydrocenoses, Zátiší 728/II, CZ-38925 Vodňany, Czech RepublicdUniversity of California, Riverside, Department of Environmental Sciences, CA 92521, USAb

A R T I C L E I N F O

A B S T R A C T

Editor: Dr. G. Echevarria

Soil pollution from emerging contaminants poses a significant threat to water resources management and foodproduction. The development of numerical models to describe the reactive transport of chemicals in both soil andplant is of paramount importance to elaborate mitigation strategies. To this aim, in the present study, a multi­
scale biophysical model is developed to predict the fate of ionizable compound in the soil-plant continuum. The
modeling framework connects a multi-organelles model to describe processes at the cell level with a semimechanistic soil-plant model, which includes the widely used Richards-based solver, HYDRUS. A Bayesian
probabilistic framework is used to calibrate and assess the capability of the model in reproducing the observa­
tions from an experiment on the translocation of five pharmaceuticals in green pea plants. Results show satis­
factory fitting performance and limited predictive uncertainty. The subsequent validation with the cell model
indicates that the estimated soil-plant parameters preserve a physically realistic meaning, and their calibrated
values are comparable with the existing literature values, thus confirming the overall reliability of the analysis.
Model results further suggest that pH conditions in both soil and xylem play a crucial role in the uptake andtranslocation of ionizable compounds.

Keywords:
Modeling
Ionizable compounds
Pharmaceuticals
Green pea
Bayesian analysis
Soil-plant continuum

1. Introduction
The latest data indicate that soil pollution represents an alarming
environmental issue (Das and Horton, 2018; Eugenio et al., 2018; The
Lancet Planetary Health, 2017). The European Environmental Agency
identified approximately 3 million potentially polluted sites in Europe(Van Liedekerke et al., 2014), while more than 19% of Chinese soils are
categorized as contaminated (CCICED, 2015). Worrying numbers arealso reported in the United States and Australia (DECA, 2010), and thelack of data from developing countries suggests an underestimation of
the problem.
Of growing interest is soil contamination by pharmaceuticals andpersonal care products (PPCPs) due to point (e.g., industrial effluents) or
diffuse pollution (e.g., agricultural and urban runoff) sources of pollu­
tion (Biel-Maeso et al., 2018; Lapworth et al., 2012; Li et al., 2014).

Sustainable practices, such as the use of reclaimed wastewater andbiosolids for irrigation and fertilization, respectively, constitute prefer­ential pathways for the introduction of PPCPs in the environment, as
conventional wastewater treatment processes are only moderately
effective at removing these chemicals from wastewater (Berendonk
et al., 2015; Christou et al., 2017a, 2017b; Reichel et al., 2014). Anti­
biotics (e.g., sulfonamides and macrolides) (Aznar et al., 2014;
Conde-Cid et al., 2018), analgesics (e.g., non-steroidal anti-in­
flammatory drugs) (Mejías et al., 2021; Qu et al., 2021), and antide­pressants (e.g., serotonin reuptake inhibitors) (Malvar et al., 2021; Wu
et al., 2010) are frequently detected in soils, where they can be degraded
into active metabolites (Koba et al., 2016; Kodešová et al., 2016),
migrate towards groundwater (Zhang et al., 2021), or be taken up by
plants (Chuang et al., 2019; González García et al., 2019; Klement et al.,2020; Sabourin et al., 2012). A better understanding of the* Corresponding author.
E-mail address: giuseppe.brunetti@boku.ac.at (G. Brunetti).
https://doi.org/10.1016/j.jhazmat.2021.127008
Received 2 June 2021; Received in revised form 6 August 2021; Accepted 20 August 2021
Available online 21 August 2021
0304-3894/© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

G. Brunetti et al.

Journal of Hazardous Materials 423 (2022) 127008

physicochemical processes driving the fate of pharmaceuticals in thesoil-plant continuum is of paramount importance to assess environ­mental risks and develop reliable mitigation strategies.
Numerical models play a crucial role in conceptualizing and trans­
ferring to a broad audience of decision-makers the key findings ofexperimental campaigns. A well-calibrated soil-plant model can be used
to perform long-term scenarios to quantify multiple environmental risk
factors (e.g., groundwater contamination, human risk exposure), anddevelop and test mitigation strategies (e.g., phytoremediation).
Recently, Brunetti et al. (2019) coupled the widely-used Richards-based
solver, HYDRUS (Šimůnek et al., 2016), with a modified version of themulti-compartment dynamic plant uptake model developed by Trapp(2007) to simulate the reactive transport of neutral compounds in thesoil-plant continuum. The model was successfully used to predict thefate of carbamazepine in green peas under transient conditions (Brunetti
et al., 2021). However, being limited to neutral compounds, the modelcannot be used to analyze the fate and transport of a broad spectrum ofpharmaceuticals, which exist in ionic form in the environment (Polesel
et al., 2015b; Prosser et al., 2014). These compounds pose serious
environmental risks. Arp et al. (2017) presented a procedure to screen
and rank neutral, ionizable, and ionic organic compounds according tobeing sufficiently persistent and mobile (PMOCs) to survive treatment
processes and enter drinking water sources. Only 9% of neutral sub­stances received the highest PMOC ranking, compared to 30% of
ionizable compounds and 44% of ionic compounds. This further un­derlines the importance of developing numerical tools able to simulate
the fate of electrolytes in the environment.
To fill this scientific gap, the model proposed by Brunetti et al.
(2019) is modified in this study to take into account processes such as
chemical dissociation, electrical interaction with plant biomembranes,and phloem transport. The modeling framework connects a
multi-organelles model to describe processes at the cell level with ageneral soil-plant model to simulate the reactive transport of electrolytes
in the soil and plant. The model is calibrated using a probabilistic
approach against extensive measurements from an experiment on the
uptake and translocation of five pharmaceuticals (i.e., citalopram,clindamycin, fexofenadine, irbesartan, and sulfamethoxazole) in green
pea plants. Selected pharmaceuticals include cations, anions, zwitter­ions, and ampholytes, thus being representative of a broad range ofcompounds frequently encountered in environmental problems (Baiet al., 2021; Hawker et al., 2013; Osorio et al., 2016; Schaffer and Licha,
2015). Furthermore, this physicochemical diversity guarantees
comprehensive testing of the proposed modeling approach. The pre­dictive performance of the model that for the first time couples amechanistic vadose zone model with a multi-compartment plant uptake
model to simulate the fate of electrolytes in the soil-plant continuum, thephysical meaning of its estimated parameters, as well as the strengths
and limitations of the prosed approach are discussed.

triangular spacing. Initially, all columns were irrigated with fresh water.
After 16 days, irrigation in 16 columns was changed from freshwater to asolution with 5 ionizable pharmaceuticals (citalopram, clindamycin,
fexofenadine, irbesartan, and sulfamethoxazole, Table S4). The
remaining columns were further irrigated with fresh water.
The choice of using spiked freshwater is not uncommon in plant
uptake studies (e.g., Goldstein et al., 2014; Gredelj et al., 2020b, 2020a;
Hurtado et al., 2016; Wu et al., 2010), and it aims to limit uncertainties
stemming from other components (e.g., DOC, nutrients), which could
undermine the model validation. Measured irrigation doses and con­centrations are listed in Table S5. Solutions for irrigation were preparedwhen needed and stored at 4 ◦ C. The intended concentration of eachcompound in solution was 100 ng cm− 3. Actual measured concentra­
tions (Table S5) were fifty to one hundred times over environmentally
relevant concentrations, e.g., in wastewater presented by Golovko et al.
(2014a, 2014b). Such concentrations were used to enhance the detec­tion and quantification of all compounds and their metabolites in all
matrices. Similar or even higher concentrations were also used in pre­vious studies (e.g., Chung et al., 2017; Klement et al., 2020; Kodešová
et al., 2019a; Montemurro et al., 2017).
Irrigation rates were adjusted to ensure optimal moisture conditions
for plant growth and avoid the solute leaching from the soil columns.
Pressure heads, h (at depths of 5 and 15 cm), and soil water contents, θ(at depths of 2.5 and 15 cm), were measured in four columns during theentire experiment using microtensiometers Tensior 5 (METER Group
Inc. USA, 2018a) and the ECH20 EC-5 sensors (METER Group Inc. USA,2018b), respectively. The columns were also weighed before and after
irrigation to record the water balance and estimate evapotranspiration.
An evaporation pan was used to estimate the evapotranspiration de­mand in the greenhouse. No outflow at the bottom was observed.
Selected columns were sequentially analyzed on the 16th (one col­umn), 23rd (four columns), 30th (4), 41st (4), and 48th day (4) of theexperiment. The above-ground plant parts were divided into stems,
leaves, and fruits. The columns (i.e., soil and roots) were cut into 4 equal
layers. All plant samples were weighted to characterize plant growth (i.
e., the fresh and dry masses of stems, leaves, fruits, and roots in 4 column
layers, Fig. S1 and Fig. S2). In addition, plant leaves were scanned, andtheir area (Fig. S3) was evaluated using the ImageJ software, version
1.47 (Schneider et al., 2012). Concentrations of all compounds and their
metabolites in all plant samples and all four soil layers were measured
using the method described below. One column irrigated with fresh
water was always similarly analyzed as a control. The remaining col­umns were used to measure soil hydraulic properties. However, pa­
rameters of the soil hydraulic functions (see Section 2.4.2) wereadditionally optimized using water flow data (irrigation, evapotranspi­
ration, soil water contents, and pressure heads) and numerical inversion,
which was in detail described by Brunetti et al. (2021).
2.2. Analytical methods

2. Materials and methods

The methods to analyze concentrations of studied compounds andtheir metabolites (clindamycin sulfoxide, N-desmethylcitalopram, N1acetylsulfamethoxazole, N4-acetylsulfamethoxazole) in plant tissues
and soils were described and validated in our previous studies (Golovko
et al., 2016; Klement et al., 2020; Koba et al., 2016; Kodešová et al.,2020, 2019a, 2019b). The analysis was directed towards metabolites
that are commonly measured in wastewater or sewage sludge and havebeen measured in soils and plants (e.g., Koba et al., 2017; Kodešová
et al., 2019b, 2019a). Details about the extraction procedure and vali­
dation of the analytical method for carbamazepine and its metabolites
were also presented by Brunetti et al. (2021). Methods are also briefly
introduced in the Supplementary Material. Plant tissues and soil samples
were freeze-dried and grounded. Compounds accumulated in 0.05 g ofplant tissue samples were extracted with a 1 mL extraction mixture(acetonitrile/water, 1/1, 0.1% of formic acid) by shaking at 1800 min− 1
for 5 min (TissueLyser II, Quiagen, Germany). Compounds remaining in

2.1. Case study description
The experimental setup was described before by Brunetti et al.
(2021). Briefly, the soil material was collected from the topsoil (0–25cm) of a Haplic Chernozem developed on loess. The soil was air-dried (afinal soil water content was around 0.15 g g− 1) and disintegrated (adiameter of aggregates was smaller than 5 mm). The soil was thenpacked into 24 plastic columns with an inner diameter of 15.4 cm, andequipped at the bottom with a thin non-woven textile with a 1 cm steel
mesh. The final height of the soil columns was 20 cm, and a bulk density
was 1.1 g cm− 3. The soil columns were then wetted to a soil watercontent of approximately 0.24 cm3 cm− 3. The experiment took place in agreenhouse (natural light, air humidity of 30–40%, and air temperatureof 20–24 ◦ C) between May 15 and July 2, 2018. Three seeds of green pea
plants (Pisum sativum L.) were sown directly into the columns in a2

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Journal of Hazardous Materials 423 (2022) 127008

2 g of soil samples were extracted with 4 mL of extraction mixture 1(acetonitrile/water 1/1, v/v acidified with 0.1% of formic acid) fol­
lowed with 4 mL of mixture 2 (acetonitrile/2-propanol/H2O, 3/3/4,
v/v/v, acidified with 0.1% of formic acid) in an ultrasonic bath (DT 255,
Bandelin Electronic, Sonorex Digitec, Berlin, Germany) for 15 min.
Concentrations of compounds in irrigation water were analyzed using a
triple-stage quadrupole mass spectrometer, Quantiva (Thermo Fisher
Scientific, San Jose, CA, USA), coupled with an Accela 1250 LC pump
(Thermo Fisher Scientific) and HTS XT-CTC autosampler (CTC Analytics
AG, Zwingen, Switzerland). Concentrations of compounds in plant andsoil extracts were measured using a hybrid quadrupole - orbital trap
mass spectrometer, Q Exactive™ HF Hybrid Quadrupole-Orbitrap™
Mass Spectrometer (Thermo Fisher Scientific, USA), operated inhigh-resolution product scan mode (HRPS). A Hypersil Gold aQ column(50 mm × 2.1 mm i.d., 5 µm particle size, from Thermo Fisher Scientific
San Jose, CA, USA) was used for the chromatographic separation ofthese target compounds. More detailed information about the instru­
ment settings was presented by Grabicova et al. (2018). Information
about conditions of analysis, including gradient elution conditions, m/zvalues, and retention time, is provided in Table S1. Recovery and Limitsof Quantification (LOQs) of compounds in different matrices are pre­sented in Table S2 and Table S3, respectively.

organelles is numerically described by the Nernst-Planck equation. The
total unit net flux of neutral and dissociated molecules J [MsL− 2T− 1] isdefined in terms of activity a [MsL− 3] as:
r
(
) ∑
)
Nj (
J = Pn an,o − an,i +Pdj Njadj,o − adj,i eNj
e
−
1
j=1

(1)

where the subscripts i and o indicate the flux from inside and outside,
respectively; r is the number of dissociation processes; Pn and Pdj aremembrane permeabilities [LT− 1] for the neutral and jth dissociatedform, respectively; an and adj are the activities of the neutral and jth
dissociated form [MsL− 3], respectively, which are calculated with theHenderson-Hasselbach equation. The subscripts used with units are as
follows: s represents a solute, l stands for liquid, p for protein, and fw for
fresh weight. Nj is defined as follows:
Nj =zj ⋅E⋅F
R⋅T(2)

where zj is the valence of the jth dissociated form [-] (+1 cationic, − 1anionic), E is the biomembrane potential [mL2T− 3I− 1], F is the Faraday
constant (96,484.56 C mol− 1), R is the universal gas constant(8314 J mol− 1 K− 1), and T is the absolute temperature [K].
The biomembrane permeability for the neutral molecules Pn iscalculated from the compound lipophilicity (Trapp, 2009). From diffu­
sion velocities and membrane thickness, the following equation wasderived:2.3. Modeling theory
The problem of predicting the transport of pharmaceuticals in thesoil-plant domain is tackled at two different scales and based on the useof two models. The first one, originally developed by Trapp (2000) andthen further refined (Trapp, 2009, 2004), provides a mechanistic
description of the uptake and redistribution of dissociating electrolytes
in plant cells’ organelles, and is used to estimate solute uptake factors
and plant-water partition coefficients. These parameters are then used ina soil-plant model (Brunetti et al., 2019), simulating the reactive
transport of chemicals in the soil and their translocation in the soil-plantcontinuum. In the following sections, we first describe the theoreticalbackgrounds of the two models, the differences with their original
implementations, and finally their joint use in the present researchstudy.

Pn = 10log KOW − 6.7(3)

where KOW is the octanol-water partition coefficient [-]. The same
equation is used for the permeability of dissociated molecules Pd, forwhich log KOW is 3.5 log units lowered.
While the activity a is the driving force in the diffusive exchange
across biomembranes, experiments often measure the total compoundconcentration, which includes neutral and dissociated molecules thatcan be dissolved or adsorbed. In particular, sorption to lipids and pro­teins is considered (González García et al., 2019), leading to thefollowing expression for the sorption coefficient K [L3Ms− 1]:)b(
K = αL 10log KOW + PKhsa(4)

2.3.1. Cell model
To predict the uptake of ionizable compounds in plants, Trapp(2000) developed a numerical model that simulates the redistribution ofchemicals among different cell’s organelles. The model, which was
successfully applied in other studies (e.g., Buchholz and Trapp, 2016;
González García et al., 2019; Trapp et al., 2008; Trapp and Horobin,2005), divides the plant cells into four compartments: cytoplasm, vac­uoles, phloem, and xylem. To enter cells, chemicals in soil pore water
have to cross a negatively charged biomembrane called plasmalemma(− 120 mV). Inside, the cytoplasm (neutral pH) surrounds vacuoles,
which occupy the largest fraction of the cell volume. Vacuoles are acidic
and enveloped in a positively charged biomembrane called tonoplast(+20 mV). After crossing the multiple cells and the Casparian strip,
water and nutrients are redistributed to different plant tissues byspecialized cells, phloem and xylem, which constitute the vascular sys­
tem of the plant. Phloem is highly alkaline (pH≈8.0), while xylem isgenerally acidic (pH≈5.5), though its pH can vary substantially due tomultiple environmental stressors (e.g., Bahrun et al., 2002; Dodd et al.,
2003; Wilkinson and Davies, 1997). Conceptually, the soil pore water isan outside compartment for the cytoplasm, which, in turn, is the outsidecompartment for vacuoles, xylem, and phloem.
Neutral compounds in the liquid phase, which are not affected by pH
conditions and electrical interactions with biomembranes, can easily
reach phloem and xylem and redistribute to different plant tissues.
Conversely, electrolytes can dissociate into ionic forms, which interact
with cell membranes. To account for these processes, the transport ofelectrolytes across multiple biomembranes and their accumulation inwhere α is a coefficient [L3Ml− 1] usually assumed to be 0.00122 m3kgl− 1(Trapp, 2007), L is the lipid fraction [MlMfw− 1], b is an empirical
exponent ranging from 0.77 to 0.96, P is the protein fraction [MpMfw− 1],
and Khsa is the binding constant to human serum albumin [L3Mp− 1],which is used to approximate the sorption of molecules to plant proteins.
The flux J can be expressed in terms of fractions f [-], which relate theactivity to the dissolved concentration (Trapp et al., 2008):
r
(
) ∑
)
Nj (
J = Pn fn,o Co − fn,i Ci +Pdj Njfdj,o Co − fdj,i eNj Ci
e
−
1
j=1

(5)

where fractions f are calculated by considering that the activity a islower than the liquid concentration C [MsL− 3] due to the molecularinteractions in non-dilute solutions, which reduce the chemical poten­
tial. The Setchenov and Debye-Hückel equations are used to calculate theactivity coefficients that relate the ion concentration in the liquid phase
to its activity (Trapp, 2009). The same formalism is applied to ampho­
lytes and zwitterions (Trapp and Horobin, 2005). Finally, the massbalance equations for different cell organelles can be written as:

3

G. Brunetti et al.

Journal of Hazardous Materials 423 (2022) 127008⎧
dCCyt ACyt
AVac
AXyl
APhl
⎪
⎪
JCyt +JVac +JXyl +
JPhl
=
⎪
⎪
dt
VCyt
VCyt
VCyt
VCyt
⎪
⎪
⎪
⎪
⎪
⎪
dCVac AVac⎪⎪⎪
⎨ dt = V JVacVac
⎪ dCXyl AXyl
⎪
⎪
JXyl
=
⎪
⎪
⎪
dt
VXyl
⎪
⎪
⎪
⎪
⎪
dC
A
⎪
⎪
⎩ Phl = Phl JPhl
dt
VPhl

where. F is a positive dimensionless solute uptake correction factor [-]that mimics the effects of the interaction between electrolytes and theroot membrane, as well as reduced potential uptake due to slow
permeability for polar compounds. These processes influence root solute
uptake and, consequently, solute transport in the soil. Therefore, the
HYDRUS source code has been modified to include the solute uptake
correction factor F [Eq. (9))]. The concentration at the outflow of thexylem is in flux equilibrium to roots. Since root cells are composed ofcytosol and vacuoles with density ρcell [MfwL− 3] equal to 1000 kg/m3,
the root-water partition coefficient can be calculated from Eq. (7):(6)

where C is the concentration of the compound in the organelle [MsL− 3], t
is the time [T], A is the surface area [L2], V is the volume [L3], and J is
the total net flux of the chemical across the biomembrane [MsL− 2T− 1].
By assuming equilibrium, it is possible to calculate the partition co­efficients between organelles K [-] and soil pore water:
⎧
CCyt
⎪
⎪
⎪
KCytS =
⎪
⎪
CW
⎪
⎪
⎪
⎪
⎪
C
⎪
Cyt
⎪
⎪
⎨ KVacS = C
W
(7)
⎪
C
Xyl
⎪
⎪ KXylS =
⎪
⎪
⎪
CW
⎪
⎪
⎪
⎪
⎪
C
Phl
⎪
⎪
⎩ KPhlS =CWCCyt VCyt + CVac VVac 1)⋅
KRXyl = (VCyt + VVac ρcell CXyl
as:where PR,water is the root permeability towards water [LT− 1]. In thepresent study, the actual transpiration rate reached approximately apeak of 0.005 m3/day m2 at day 38 (Fig. S4), with a corresponding root
mass of 308 g (Table S18). Meier et al. (2013) report an average root
specific area of 0.086 m2/g for green pea plants. Therefore, the esti­
mated roots permeability to water is approximately 2.2e-09 m/s.
Nevertheless, it must be emphasized that PR,water varies significantly as it
is influenced by environmental (e.g., transpiration demand) and plant
specific factors (Aston and Lawlor, 1979). PR,chem is the root permeability
towards chemical:r∑PR,chem = fn Pn +fdj Pdj(14)

j=1

where fn and fdj are the fractions of neutral and dissociated molecules [-],
respectively; Pn and Pdj are the permeabilities to neutral and dissociatedmolecules, respectively [LT− 1], which can be calculated with thefollowing equation:
Pn =

(8)

1
1
1
+ Pwall10log KOW − 6.7(15)

where Pwall is the permeability of the cell wall towards water, which isapproximately 0.25 mm/s (Trapp, 2000). The same equation is used forthe permeability of dissociated molecules Pd, for which log KOW is
3.5 log units lower (Trapp and Horobin, 2005). Recent studies haveshown that the liposome-water partition coefficient (KlipW) can be abetter predictor than log KOW to estimate sorption of ionizable chemicals(Bittermann et al., 2014; Tanoue et al., 2017). However, its use in plant
uptake modeling studies has been limited. Therefore, the present
modeling framework follows the original approach proposed by Trapp(2009).
Before proceeding with the analysis, the cell model has been vali­
dated against the original implementation of Trapp (2009). Details
about the model validation are reported in the Supplementary Material.

where CR is the chemical concentration in roots [MsMfw− 1], t is the time[T], QXyl is actual transpiration calculated by HYDRUS (i.e., xylem flow)[L3T− 1], MR is the roots mass [Mfw], QHYD is actual root solute uptake
calculated by HYDRUS [MsT− 1], KRXyl is the root-xylem partition coef­
ficient [L3Mfw− 1], and τR is the first-order metabolization coefficient[T− 1].
The root-soil equilibrium assumption does not hold for electrolytes,
which can dissociate into neutral and ionic forms depending on the pHof the surrounding environment and interact with the electricallycharged root cell biomembranes. As a consequence, the inflow concen­
tration in roots xylem can be different from soil pore water concentra­tion, and actual solute uptake must be corrected:(9)2.3.3. Phloem transport
Electrolytes in roots’ xylem are translocated upward with the tran­
spiration stream QXyl first to the stem, and then to leaves and fruits ac­
cording to their surface areas (Brunetti et al., 2019). Conversely, phloem
transports photosynthesized nutrients and chemicals downward fromthus leading to:dCR Qcorr
QXylCR + τ R CR
= HYD −dt
MR
MR KRXyl(12)

where KXylS is a partition coefficient between soil solution and xylem [-][Eq. (7)]. λ is another correction factor [-] that accounts for the slow
permeability of polar compounds, which is described by the following
equation:()
PR,chem
λ = min 1,(13)
PR,water

2.3.2. Soil-plant model
The numerical model developed by Brunetti et al. (2019) for neutralcompounds was further modified to simulate the translocation andtransformation of electrolytes in the soil-plant continuum. The model
combines the widely-used hydrological model, HYDRUS (Šimůnek et al.,2016), with a multi-compartment model of dynamic plant uptake(Trapp, 2007). HYDRUS numerically solves the Richards and theadvection-dispersion-reaction equations to describe water flow andreactive solute transport in variably saturated porous media, respec­tively. For a thorough description of the model structure, please refer toBrunetti et al. (2019). In the present study, for conciseness, we report
only the key equations necessary to interpret results.
The model was originally developed for neutral compounds with theassumption of phase equilibrium between root tips and soil, which im­plies that the inflow concentration in roots’ is equal to the concentrationin the soil pore water, thus leading to the following general mass balance
equation for the roots compartment:

Qcorr
HYD = QHYD × F

Mechanistically, the solute uptake correction factor F can be defined

F = KXylS λwhere CW is the chemical concentration in soil pore water [MsL− 3].

dCR QHYDQXyl−CR + τ R CR=
dt
MR
MR KRXyl

(11)

(10)

4

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Journal of Hazardous Materials 423 (2022) 127008

leaves to the stem, and then primarily to fruits. A smaller fraction canalso reach roots (González García et al., 2019). Since phloem transport isof particular importance for weak acids due to the ion trap effect (Trapp,2009), the soil-plant model of Brunetti et al. (2019) was further modi­
fied to include this process. The phloem flux QPhl from leaves is pro­portional to the change in the dry fruit mass MF and can be written as:
Roots
QPhl = QFruits
Phl + QPhl = −dMF
× TC,Ph − φ × QXyl
dt

⎧
⎪
⎪
⎨ − τ11βj = Γj ⋅Cj =
:
⎪
⎪
⎩ +τ′

N1

(16)

.

(20)

NN

2.4. Model calibration and uncertainty assessment
Five inverse modeling scenarios were used to assess the performanceof the model in reproducing experimental data involving uptake andtranslocation of five pharmaceuticals [i.e., citalopram (CIT), clindamy­cin (CLI), fexofenadine (FEX), irbesartan (IRB), and sulfamethoxazole(SUL)]. Clindamycin sulfoxide (CLIS), a metabolite of clindamycin, wasalso quantified in the soil and plant samples. Therefore, this metabolite
was included in the inverse modeling scenario CLI. Concentrations ofmetabolites of other pharmaceuticals were mostly below the limits ofquantification. Therefore, they are not considered in this study, and theanalysis is restricted to the parent compound. In the following sections,details about the calibration strategy, model setup, and algorithms areprovided.

(17)

where CS is the chemical concentration in the stem [MsMfw− 1], and KStPhl
is the stem-phloem partition coefficient [L3Mfw− 1], which can becalculated with the following equation:
CCyt VCyt + CVac VVac 1)⋅
KStPhl = (VCyt + VVac ρcell CPhl

⋅

⎫
′
⎫
⎧
⎪
+τ1N ⎪⎬ ⎨ C1j ⎬
:
⋅
:
⎭
⎪
⎪⎩
− τ ⎭ CNj

If only the parent compound is modeled, then Γj reduces to a single
degradation coefficients, which describes the transformation of theparent compound into unknown metabolites or its mineralization.

where QXyl is actual transpiration [L3T− 1], φ is the fraction of actual
transpiration that constitutes the phloem transport into roots [-], and TC,
3− 1
Ph is the phloem flux per the fruit dry mass [L Mdw ], which is assumed
to be 10 L/kg (Trapp, 2007). Eq. (10) can be rewritten as:
dCR Qcorr
QXylQXylCR + φCS + τ R CR
= HYD −dt
MR
MR KRXyl
MR KStPhl.

(18)

A similar formalism can be applied to describe the mass balance
equations for other compartments by taking into account that no furthertranslocation with xylem is assumed in leaves and fruits, while thephloem flux is negative for the leaves compartment and positive for thestem compartment [Eq. (16)]. The stem flux is further divided into two
components leaving the stem and entering roots and fruits. Eventually,
volatilization, gaseous uptake, and particle deposition processes can beembedded in the modeling framework, as described in Brunetti et al.
(2019). HYDRUS can simulate intraday transpiration fluctuations if
high-resolution climatic data are provided. This is generally done bypartitioning the evapotranspiration demand calculated with thePenman-Monteith equation. However, the plant model assumes that thephloem transport depends on the fruit mass and is always a fraction of
actual transpiration [Eq. (16)]. This ratio remains constant, even if
HYDRUS is able to simulate intraday fluctuations. Other more precise
numerical approaches are available to simulate an increase in thephloem flux at night (e.g., Hölttä et al., 2006), but they increase theoverall model complexity. A potential solution is to adopt differentiatedxylem/phloem ratios between day and night in Eq. (16). However, hightemporal resolution data are needed to test this approach.

2.4.1. Calibration strategy
Theoretically, the previously described cell and soil-plant models canbe solved sequentially. The former model is used first to calculate theuptake correction factor F and the partition coefficients between plantcompartments and xylem (KPXyl) and phloem (KPPhl). This information isthen passed to the latter model to estimate translocation and redistri­bution of electrolytes in different plant compartments. However, thisapproach would formally require calibrating multiple parameters in thecell model, thus significantly increasing the dimensionality of the in­verse problem.
To circumvent this problem, we first calibrate the solute uptake
correction factor and the partition coefficients in the soil-plant model for
multiple pharmaceuticals. Then, we validate and discuss the meaning
and implications of these partition coefficients using the cell model. In
this way, we reduce the dimensionality of the calibration problem andthe associated computational burden while still retaining the mecha­
nistic traits of the cell model in a validation step.
2.4.2. Model description and setup
The soil domain discretization in HYDRUS, as well as the boundary
and initial conditions, for the same experimental setup are described in
Brunetti et al. (2021) and not repeated here for conciseness. As in Bru­
netti et al. (2021), soil hydraulic properties are described by the unim­
odal van Genuchten–Mualem (VGM) function (van Genuchten, 1980)(parameters: θr [L3L− 3], θs [L3L− 3], α [L− 1], n [-], Ks [LT− 1]). The
piecewise linear Feddes function parameterizes the root water stress(Feddes et al., 1978) and regulates actual transpiration (parameters: P0,
POpt, P2H, P2L, P3). Simultaneously, a root density function modulates
actual root water uptake depending on the root growth, which isassumed to be logistic. A time series of Leaf Area Indices (LAI) is ob­
tained by fitting a logistic function to the measured one-sided leaves
area (Fig. S3). LAIs are then used to partition evapotranspiration into
potential evaporation and transpiration. The difference between total
evapotranspiration, measured by weighing the columns, and transpira­tion is used to estimate evaporation from the soil surface (Fig. S4).
The batch experiment data of Kodešová et al. (2020) and Schmidtová
et al. (2020) indicate that the Freundlich isotherm (parameters: (Kf [L3βM1-β M− 1], βCBZ [-]) well interprets the sorption of pharmaceuticals tothe solid phase, and thus this parameterization is used in the model.
Sorption of particular compounds can decrease due to their competition
for the same sorption sites or increase due to their cooperation. Thisbehavior was observed by Schmidtová et al. (2020) for the five

2.3.4. Metabolization
The soil-plant model considers compound degradation in both soil
and plants compartments. A comprehensive description is provided in
Brunetti et al. (2019). Here, we provide only key equations. HYDRUS
can simulate sequential degradation chains from parent to daughter
species using first-order rate coefficients µ [T− 1] in the liquid and solid
phases. The plant metabolization is modeled using one metabolization
matrix Γj for each compartment, which consist of multiple first-order
rate coefficients providing connections between parent and daughter
species. The matrix Γj is a square matrix of a dimension N (i.e., a numberof metabolites considered):
⎫
⎧
′
⎪
⎪
⎪
N
⎬
⎨ − τ11 . +τ1N ⎪
∑
Γj =
with
Γ ij ≤ 0
(19)
:
⋅
:
⎪
⎪
⎪
⎪
i=1
⎩ +τ′
. − τNN ⎭N1

where τ are first-order rate constants for the compound [T− 1], while τ’are similar first-order rate constants providing connections between
individual chain species [T− 1]. The metabolization rate vector for the jthcompartment, βj [MsMfw− 1T− 1], is thus defined as the dot product of themetabolization and concentration matrices:5

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Journal of Hazardous Materials 423 (2022) 127008

compounds analyzed in the present study. Due to an ambiguous impactof a compound mixture on sorption behavior, sorption parameters were
calibrated. The compound degradation in the soil is described by the
first-order degradation coefficient, µS [T− 1]. The only detected metab­
olite in the soil during the experiment was CLIS. The transformationfrom parent to child compound and its subsequent transport anddegradation is thus considered only for CLI.
Each plant compartment is assumed to have a logistic growth (pa­rameters: W [L3M− 1], Mmax [Mfw], M0 [Mfw], Kgr [T− 1], SA [L2Mfw− 1]).
The specific areas of fruits and leaves are used to partition transpiration
fluxes. All pharmaceuticals considered in the present study have very
low air-water partition coefficients, and thus volatilization, as well asgaseous uptake and particle deposition, are neglected. As for the soil, themetabolization chain in plants is considered only for CLI, whose main
metabolite (CLIS) can be taken up from the soil, generated in plants’tissues, and transported in xylem and phloem.

fruits are terminal compartments for the phloem transport and roots
exudation is neglected, their phloem partition coefficients do not in­fluence the transport of pharmaceuticals in the plant. Consequently, thenumber of parameters to be calibrated is 12 for scenarios CIT, FEX, IRB,
and SUL without metabolites. It is 18 for CLI, which includes an addi­
tional uptake correction factor and five additional reaction parameters
for its metabolite CLIS. Due to only minor changes in the molecular
structure of CLI and CLIS, their sorption coefficients are assumed to be
the same.
Uniform prior distributions are used in the Bayesian analysis. The
bounds of prior distributions (Table 1) for plant uptake and sorption
parameters (i.e., F, KPXyl, KPPhl) were set using the previously describedcell model, whose parameters are detailed in Table S19. On the other
hand, a literature survey was used to set the bounds of degradation
coefficients and soil sorption parameters (Brunetti et al., 2021; Huynh
and Reinhold, 2019; Kodešová et al., 2020; Schmidtová et al., 2020).

2.4.3. Bayesian analysis
A probabilistic approach based on the Bayesian inference is used tocalibrate the soil-plant model and assess the parameters’ uncertainty. A
nested sampling algorithm (Feroz et al., 2009) is combined with themodel and observations to estimate the parameters’ posterior distribu­
tions. A thorough description of the algorithm, which was successfully
applied in multiple studies (e.g., Brunetti et al., 2020b, 2020a; Elsheikh
et al., 2013; Liu et al., 2016), is provided in Skilling (2006) and Feroz
et al. (2009). As in Brunetti et al. (2020b) and Liu et al. (2016), a
convergence analysis is used to assess the stability and accuracy of thenested sampling estimator.
We assume that measurement errors are normally distributed withan average constant variance, σ2, and thus the log-likelihood functionℓ(Ω) for the jth set of measurements can be written as

3. Results and discussionℓj (Ω) = −kkk ( 2)1 ∑
ln(2π ) −ln σ −(Hi (Ω) − ̃yi )22
2
2σ 2 i=1

3.1. Bioaccumulation of pharmaceuticals
Before discussing the outcome of the numerical analysis, which is themain aim of this study, we briefly explain the differences in the observed
bioaccumulation of pharmaceuticals in the soil-plant continuum. The
role of different mechanisms on the uptake and translocation processes
is further investigated in the next section about modeling results, where
we combine experimental and numerical findings.
Experimental data used in the numerical analysis are shown in Fig. 1(gray circles) and reported in the Supplementary Material (Tables S6S17). Further, Fig. S6 in the Supplementary Material also shows
measured average fractions of the applied solute mass in the soil anddifferent plant compartments. Pharmaceuticals show important bio­
accumulation differences. CIT has the highest occurrence in the soil andis efficiently translocated into plants, where it is detected at meaningful
levels in leaves. This agrees with observations of Kodešová et al. (2019),
who reported an appreciable translocation of CIT in shoots. Thisbehavior can be explained by CIT’s largest persistency in soil, andmoderate lipophilicity (log KOW = 3.5), and poor affinity to proteins (Linet al., 2014), which facilitate its translocation with the transpiration
stream. A similar trend was observed in other studies for other selective
serotonin reuptake inhibitors (Redshaw et al., 2008; Reichl et al., 2018).
In contrast, FEX and IRB were not detected in shoots, only in soil androots. In comparison, IRB concentrations in the roots were more than
twice those of other compounds and lower than CIT and FEX in soil,
suggesting a strong affinity to roots’ components and poor sorption to
the soil matrix. Its high lipophilicity (log KOW = 6) and protein affinity(Yang et al., 2012) can partially explain its occurrence in roots and poor
mobility in plants (Dettenmaier et al., 2009). Nevertheless, the presenceof untracked metabolites generated by in-plant enzymatic biodegrada­tion cannot be excluded a priori by comparing observations (Villetteet al., 2019). The combined effect of cation-bridging (Polesel et al.,2015a), surface complexation (Klement et al., 2018), and hydropho­
bicity (log KOW = 5.6) also explain sorption of the zwitterion FEX toroots and its reduced translocation in shoots, which was observed in
Kodešová et al. (2019a) and reported for similar antihistamine in otherstudies (e.g., Wu et al., 2012).
The macrolide CLI and its main metabolite CLIS, which was alreadydetected in irrigation water (Table S5), exhibit the lowest accumulationin roots, while they both persist in soil. Their concentration in shoots ishigher than FEX and IRB, but lower than CIT and SUL, thus suggesting a
potential role of in-plant metabolism, a process that was observed forother antibiotics and macrolides in vegetables (e.g., Tian et al., 2019).
Conversely, SUL displays the highest and lowest concentrations in leaves
and soil, respectively. Its translocation towards shoots was already re­ported by other studies (Chitescu et al., 2013; Herklotz et al., 2010;
Klement et al., 2020; Kodešová et al., 2019b; Tanoue et al., 2012), and(21)

where Hi(Ω) and ỹi are the ith model realization and its corresponding
observation, respectively, and k is the number of observations in the jth
set of measurements. The measured data used in the Bayesian analysis
include the compound concentration in the soil at four different depths
and in four plant compartments (roots, stem, leaves, and fruits).
Therefore, the log-likelihood function L(Ω) is the aggregated sum of
single likelihoods. The mean and variance of each measurement set usedin the model calibration are calculated from the column replicates (seethe Supplementary Material):
12∑

L(Ω) =ℓj (Ω)(22)

j=1

The dimensionality of the inverse problem is reduced by fixing spe­cific model parameters (Table S18). In particular, Brunetti et al. (2021)
calibrated VGM parameters for the same experimental setup. Therefore,
these parameters are set to their median values reported in Brunetti et al.
(2021) and excluded from the model calibration. The plant growth pa­
rameters are obtained by fitting a logistic function to measured masses(Fig. S1), while water contents of plants’ tissues are assumed to beconstant and calculated from the average measured fresh and dryweights during the experiment (Fig. S1). The longitudinal dispersivity
and Feddes’ parameters are fixed according to Brunetti et al. (2021).
Consequently, only solute uptake correction factors, and sorption andreaction parameters in the soil-plant domain, are inversely estimated.
The number of calibrated parameters is further reduced by making
additional theoretical considerations. In particular, since volatilizationis neglected, and no further translocation with xylem is assumed inleaves and fruits, their partition coefficients do not affect the accumu­
lation of electrolytes in these compartments and can be set to any
realistic value in their parameter space. Similarly, since the roots and6

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Journal of Hazardous Materials 423 (2022) 127008

Table 1
Calibrated model parameters, their bounds, and 5%, 50%, and 95% quantiles of the parameters’ posterior distributions calculated from the Bayesian analysis. CIT, CLI,
FEX, IRB, and SUL refer to columns with five pharmaceuticals, i.e., citalopram, clindamycin, fexofenadine, irbesartan, and sulfamethoxazole.
Parameter

Posterior parameters quantiles (50%+45%− 45% )
CIT

CLI

FEX

IRB

SUL

CLISa

Prior Bounds
Posterior quantiles(10, 100).

Prior Bounds
Posterior quantiles(0.8, 1.5)
1.33+0.13− 0.29(0.8, 1.5)
0.92+0.16− 0.11(0.8, 1.5)
1.38+0.11− 0.24(0, 100)
66.7+24.7− 27.1

Prior Bounds
Posterior quantiles(0.8, 1.5)
1.42+0.07− 0.14(0, 5)
0.98+1.0− 0.5

Degradation rate in soil µS [day-1](0.8, 1.5)
1.27+0.2− 0.2(0, 50)35.4+13.6− 13.6(0, 10).

Freundlich exponent β [-](0, 100)
66.7+24.7− 27.1(0.8, 1.5)
1.42+0.07− 0.14

Solute uptake correction factor F [-]Prior Bounds
Posterior quantiles(0.01, 400)
4.3+2.4− 2.0(0.01, 50)
1.09+0.52− 0.47(0.01, 10)
2.81+1.75− 1.86(0.01, 1)
0.34+0.38− 0.17(0.01, 5)
3.64+1.18− 1.77(0.01, 50)
0.49+0.48− 0.38

Prior Bounds
Posterior quantiles(20, 10,000)
122+79− 35(1, 2,000)
68+27
− 19

(1, 500)(400, 8,000)(1, 200)
141+52− 64(1, 2,000)
68+27
− 19

Soil
Soil-water partition coefficient Kf [cm3β µg1-β g¡1]

Roots
Roots-Xylem partition coefficient KRXyl [cm3gfw-1]
Degradation rate in roots τR [day-1]
Stem
Stem-Xylem partition coefficient KStXyl [cm3gfw-1](0, 1)
0.02+0.01− 0.01(0, 1)
0.06+0.01− 0.01(0, 1)
0.06+0.02− 0.01

398+1,500− 353(0, 1)
0.05+0.01− 0.015, 459+2,050− 1,786(0, 1.5)
0.89+0.05− 0.04(0, 1)
0.21+0.04− 0.03

Prior Bounds
Posterior quantiles(0, 1)
0.87+0.11− 0.16(0, 1)
0.43+0.12− 0.12(0, 1)
0.72+0.24− 0.31(0, 1)
0.81+0.17− 0.26(0, 1)
0.18+0.18− 0.10(0, 1)
0.86+0.11− 0.20Prior Bounds
Posterior quantiles(0, 10,000)
27+10
− 6

(1, 2,000)
3.2+1.6− 1.1(1, 500)
540+2200− 480(400, 8,000)(1, 200)
12+8− 6(1, 2,000)
3.2+1.6− 1.1

4, 104+3,098− 3,030

Stem-Phloem partition coefficient KStPhl [cm3gfw-1]

Prior Bounds
Posterior quantiles(200, 10,000)

Degradation rate in stem τS [day-1]

Prior Bounds
Posterior quantiles(0, 1)
0.78+0.18− 0.34(0, 1)
0.27+0.34− 0.24(0, 1)
0.4+0.5− 0.31(0, 1)
0.77+0.20− 0.24(0, 1)
0.22+0.41− 0.19(0, 1)
0.5+0.36− 0.39Prior Bounds
Posterior quantiles(200, 10,000)(0, 1)
0.02+0.02− 0.02(0, 1)
0.09+0.07− 0.05(1, 500)
268+208− 238(200, 8,000)

Prior Bounds
Posterior quantiles(1,500, 3,000)
2, 254+568− 503(0, 1)
0.56+0.36− 0.41(0, 1)
0.47+0.44− 0.41(1, 20)
10+8− 7(0, 1)
0.06+0.09− 0.05(1,500, 3,000)
2, 254+568− 503(0, 1)
0.1+0.09− 0.08

Prior Bounds
Posterior quantiles(0, 1)
0.48+0.41− 0.40(0, 1)
0.51+0.41− 0.40(0, 1)
0.49+0.41− 0.41(0, 1)
0.51+0.42− 0.40(0, 1)
0.43+0.51− 0.37(0, 1)
0.63+0.33− 0.42

LeavesLeaves-Phloem partition coefficient KLPhl [cm3gfw-1]
Degradation rate in leaves τL [day-1]
FruitsDegradation rate in fruits τF [day-1]
a5, 514+3,671− 4,060

4, 500+4,271− 3,764(1,500, 3,000)
2, 098+737− 537(1, 500)
209+252− 183(200, 8,000)
4, 161+3,048− 3,6114, 728+2,791− 3,842(1, 20)
12+6− 8(1,500, 3,000)
2, 098+737− 537

CLI and CLIS are assumed to have the same sorption parameters in soil and plants but different metabolization rates.

can be mainly due to its low lipophilicity (log KOW = 0.89), while its
negligible occurrence in soil can be a combination of efficient root up­
take and degradation processes (Koba et al., 2017; Liu et al., 2010).
Concentrations of other metabolites were mostly below the limits ofquantification, which can be explained by very high transformation(formation and dissipation) rates (N1-acetylsulfamethoxazole,N4-acetylsulfamethoxazole) or slow transformation rates of CIT. In somecases, it could be due to larger values of the limits of quantification(Table S3).

predictive uncertainty in the stem compartment for FEX, thus simulta­
neously suggesting that the information content of measurements is not
sufficient to constrain model predictions and that the FEX concentra­
tions in the stem are overly sensitive to small variations in roots and soil.
A comparable but less evident behavior is observed for SUL in fruits, forwhich the model tends to predict slight compound bioaccumulation notdetected in measurements. Simplifications in the definition of thephloem transport, and inaccuracies in non-calibrated model parameters(Table S18) and observations can partially explain these deviations. In
particular, the quantification limit for SUL in fruits (0.19–0.63 ng g− 1,
Table S3) was one order of magnitude higher than for other compounds.
In addition, LOQs for SUL metabolites are also relatively high (N1 0.63–2 ng g− 1, N4 - 0.2–0.69 ng g− 1). It can be hypothesized that if
LOQs for SUL and its metabolites were lower, their concentrations infruits could be, in some cases, quantified. However, despite these
problems and considering the complexity of predicting the fate of mul­
tiple electrolytes, the model exhibits satisfactory performance andguarantees a comprehensive description of reactive transport processes
in both soil and plant tissues (Fig. 1 and Fig. S5).

3.2. Model predictive performanceFig. 1 shows a comparison between the measured (gray circles) andmodeled average concentrations of pharmaceuticals in soil (orange
lines) and in different plant compartments (green lines) obtained byrandom sampling of 100 solutions from the posterior parameter distri­butions. Results demonstrate that the model is able, except in few cases,
to reproduce with limited uncertainty and acceptable accuracy thereactive transport of multiple pharmaceuticals in the soil-plant domain.
Generally, model predictive checks don’t indicate systematic discrep­
ancies between model predictions and observations (Gelman et al.,2004), suggesting that the model should not be rejected and is well
suited for the numerical analysis.
Root water and solute uptake occurs mainly in the upper part of thesoil profile, where the root density is higher, and compounds are morebioavailable due to the non-linear sorption process (Fig. S5). The
chemicals accumulation of all pharmaceuticals in soil and roots, as wellas the transformation of CLI into CLIS and its subsequent translocation,
are well predicted. Similar good predictive performance is observed inleaves, and partially in the stem and fruits. The model shows a high3.3. Parameters assessment
The calculated 5%, 50%, and 95% quantiles of the parameters’posterior distributions for all pharmaceuticals are reported in Table 1.
Posterior distributions show a mixed behavior, with some parameters
precisely inferred and others exhibiting an appreciable uncertainty. In
the following sections, we compare estimated parameters with theliterature values, discuss their physical meaning and consequences for
multiple processes, and attempt to provide a mechanistic explanation byusing the Cell model.
7

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Journal of Hazardous Materials 423 (2022) 127008

Fig. 1. A comparison between the measured (gray circles) and modeled average concentrations of electrolytes in soil (orange lines) and plant’s compartments (green
lines) obtained by random sampling of 100 solutions from the posterior parameter distributions. The line color intensity reflects the posterior probability of the model
realization. The error bars indicate the standard deviations of the measurements (Tables S6-S17). The y-axis scale is intentionally kept the same, when possible, formultiple compounds to emphasize their different accumulation in plant tissues. (For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

3.3.1. Root solute uptake
The low uncertainty of the estimated solute uptake correction factors
F indicates that the interaction between electrolytes and roots mem­brane plays a fundamental role in the chemical uptake and transport(Haynes, 1980; Trapp, 2009). As previously described [Eqs. (12), (7),(5)], the electrolytes fluxes across the root biomembrane are strongly
influenced by soil and xylem pH, which govern the chemicals’ speciation
inside and outside roots, and thus their ability to permeate the root
membrane. Recently, Delli Compagni et al. (2020) used a combinationof Monte Carlo and Sensitivity analyses to identify factors influencing
bioaccumulation of multiple compounds in plants. The analysis revealed
that xylem and phloem pH had a large impact on the simulated con­centrations in plants’ tissues, thus confirming the findings of our present
study.
Fig. 2 shows the color maps obtained using the Cell model, illus­
trating the mutual influence of soil and root xylem pH on the uptake
correction factor, F, for each pharmaceutical under consideration. The
white bands correspond to the estimated 5% and 95% quantiles of thesolute uptake correction factor reported in Table 1 and identify theplausible range of soil and root xylem pH values.

The narrow bands for CLI and SUL suggest that the estimated solute
uptake factors can only be explained by similar pH conditions in soil androot xylem, whereas the existence domain is broader for other com­pounds. While commonly assumed acidic (Trapp, 2009), root xylem pH
can vary considerably due to multiple environmental stressors. In
particular, under drought conditions, xylem pH can significantly in­crease (Bahrun et al., 2002; Dodd et al., 2003; Gloser et al., 2016; Wil­kinson and Davies, 1997), activating the guard cell abscisic acidreceptors in the leaf epidermis and leading to stomatal closure to enable
the plant to retain water (Wilkinson, 1999). However, as shown inBrunetti et al. (2021), the soil water content during the experimentoscillated between 0.20 and 0.30, and the plant growth was sustained.
Therefore, root water stress was not present during the experiment andcannot be the cause of alkaline xylem conditions. Consequently, theestimated solute uptake factors in Fig. 2 can only be justified by slightly
acidic conditions in both xylem and soil. Unfortunately, no soil pH
measurements were performed during the experiment to confirm thisconclusion. However, variations of soil conditions due to multiple
stressors are not uncommon during experiments (Carter et al., 2016).
Therefore, a shift from original alkaline soil conditions (i.e., soil pH ≈8

G. Brunetti et al.

Journal of Hazardous Materials 423 (2022) 127008

Fig. 2. Color maps showing the mutual influence of soil and root xylem pH on the uptake correction factor, F, for each pharmaceutical. The white bands correspondto the estimated 5% and 95% quantiles reported in Table 1.

8.0) to acidic ones during the experiment is plausible and suggested bymodel calibration results for multiple compounds.

Bayesian analysis identifies a plausible range of xylem pH during theexperiment.
Interestingly, the overlapping between curves and uncertainty bands
in Fig. 3 for all pharmaceuticals exclude alkaline conditions in thexylem, and deductively in soil, thus confirming earlier discussion. In
particular, while for FEX, IRB, and CIT, the plausible ranges of xylem pH
are broad and extend from acid to slightly alkaline conditions, the do­mains of existence for CLI, SUL, and CLIS are restricted to acidic pH. Thisis mainly due to the molecules’ fluxes between cytosol and xylem. In
acidic xylem conditions, SUL is partially present in its neutral form,
which can diffuse back in the alkaline cytosol, where it dissociates into
anionic molecules. These molecules cannot permeate the membrane
again and thus remain trapped in the cytosol. Prevalent cationic3.3.2. Sorption and translocation in plant
Xylem pH affects not only root solute uptake but also electrolytes
sorption and translocation in the plant [Eq. (11)]. Fig. 3 shows the in­fluence of xylem pH on the root-xylem partition coefficient KRXyl (in alogarithmic scale) for each pharmaceutical. Curves (black lines in Fig. 3)
are obtained using the cell model and by varying the xylem pH in theinterval [4, 8], while red bands correspond to the estimated 5% and 95%
quantiles reported in Table 1, which indicate that partition coefficientsin roots and stem are generally affected by limited uncertainty. The
overlapping between curves and uncertainty bands inferred from theFig. 3. Influence of xylem pH on the root-xylem partition coefficient KPXyl (in a logarithmic scale) for each pharmaceutical. The red bands correspond to theestimated 5% and 95% quantiles reported in Table 1. The y-scale is intentionally kept the same for multiple compounds to emphasize sorption differences.
9

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Journal of Hazardous Materials 423 (2022) 127008

electrolytes, such as CLI and CIT, exhibit the opposite behavior. FEX(zwitterion) and IRB (ampholyte) sorption is characterized by a com­bination of cation-bridging (Polesel et al., 2015a), surface complexation(Klement et al., 2018), and hydrophobicity effects, and therefore, oncein the cell, they are readily sorbed to lipids (and other components) in
the vacuole. Theoretically zwitterions can form layer onto surface due totheir interconnections and thus largely increase sorption (Carrasquillo
et al., 2008; Vasudevan et al., 2009). Table 1 further indicates a sorption
decrease in the stem, and this can be explained by a lower lipid andprotein content in this compartment [Eq. (4)]. Finally, the phloem
partition coefficients exhibit high uncertainty for all pharmaceuticals.
There are different potential explanations for this behavior. On the one
hand, the high uncertainty suggests that phloem transport played aminor role in the chemicals’ translocation in plants. On the other hand,results can also indicate that observations are not informative of thisprocess and that measurements should be enriched.
It must be emphasized that the present model, and other existing soilplant uptake models, do not explicitly account for effects such ascompetitive (or cooperative) sorption, which may occur when multiple
compounds are simultaneously present. The main reason is that themodel complexity significantly increases when a mechanistic descrip­tion of such processes is considered, which may undermine the model
predictive capabilities (e.g., Brunetti et al., 2020b, 2020a) if extensive
observations are unavailable. However, the estimated posterior distri­butions of sorption coefficients (Table 1), inferred from observations
implicitly account for these processes, and calibrated parameters should
be formally regarded as effective. This is frequent in calibration
modeling studies, where the appropriate trade-off between model
complexity and generalizability is difficult to identify.

in fruits. IRB and FEX do not translocate to shoots due to their highlipophilicity, and thus no data are available to infer model parameters.
Conversely, degradation rates in leaves for CIT, CLI, SUL, and CLIS were
well identified and generally low. This can be partially explained by low
substrate levels, which cannot stimulate the enzymatic (e.g., MichaelisMenten) biodegradation (Hurtado et al., 2016).
3.3.4. Soil sorption
The divergence between priors and posteriors for all compounds(Table 1) indicates that the measurements are informative for soil
sorption parameters (i.e., Kf and β), which consequently played an
important role in the electrolytes transport and uptake during theexperiment (e.g., Brunetti et al., 2021). Estimated Kf and β values
indicate that CIT, CLI, FEX, and CLIS strongly sorb to the soil, while IRB
and SUL are mostly present in the liquid phase. This difference is mainly
due to the dissociation of electrolytes (Table S4) in the soil during theexperiment, which the previous discussion on plant uptake and sorption
suggests is slightly acidic. In these conditions, CIT and CLI are present
mainly in the cationic forms, which are attracted to the soil matrix due toits negative charge and the hydrophobicity of the compound (Schaffer
et al., 2012b, 2012a). This behavior was already discussed by Kodešová
et al. (2020) and Schmidtová et al. (2020) for the same soil under lab­
oratory conditions. The difference between the values estimated in these
two studies and those reported here can be explained by the different
operating conditions, pH shifts, and the influence of roots on the com­pound bioavailability. Conversely, SUL is present partially in anionicand neutral forms, which can explain its moderate affinity to the solid
phase (Kodešová et al., 2020; Schmidtová et al., 2020; Schübl et al.,2021). This was already observed in Archundia et al. (2019), who re­ported an increase in SUL sorption in acidic soil conditions due to spe­cific hydrophobic interactions with soil organic carbon (Boxall et al.,
2002; Kurwadkar et al., 2011; Srinivasan and Sarmah, 2014;
Thiele-Bruhn and Aust, 2004). Finally, estimated IRB and FEX sorption
parameters agree with what was reported in Klement et al. (2018), who
indicated that the molecular structure of these two compounds plays a
key role in their sorption capabilities. In particular, Polesel et al. (2015a)
suggests cation-bridging effect as the driving factor in zwitterion andampholytes sorption.

3.3.3. Degradation in plant
The posterior distributions of degradation parameters in plant tissues
show a mixed behavior (Table 1). Confidence intervals in roots are
narrow for all pharmaceuticals, thus indicating their influence on theelectrolytes translocation in plants. In particular, CIT and CLIS exhibit
the highest degradation rates, followed by IRB, FEX, CLI, and SUL.
Reichl et al. (2018) suggested that hydroxylation, demethylation, andconjugation with amino acids, were responsible for the in-plant
metabolization of sertraline, a pharmaceutical belonging to the samefamily of serotonin reuptake inhibitors as CIT. Similarly, efficientmetabolization of CLI was reported in Tadić et al. (2019). In anotherstudy, the macrolide clarithromycin, whose molecular characteristics
are comparable to CLI and CLIS, was efficiently metabolized in lettuce(Tian et al., 2019). To our knowledge, there have been no studies about
the metabolization of FEX and IRB in plants. However, the IRB metab­olization pathway in human cells is driven by the cytochrome P450
enzymes (Stearns et al., 1995), which have also been identified in plants(Carter et al., 2018). This supports its biotransformation in plants.
Conversely, FEX undergoes minimal metabolism in human cells, andtherefore, its transformation in roots is not completely enzymatic. It canbe speculated that the synergistic effect of roots endophytic bacteriaenhanced the degradation process (e.g., Nguyen et al., 2019). In supportof this, Kodešová et al. (2020) showed that the dissipation of FEX washighly correlated with the bacterial population in the soil. However,more data are needed to confirm these results. The model indicates that
SUL had the lowest, but still significant, degradation in roots. This agrees
with what was reported in other studies (e.g., Huynh and Reinhold,2019; Tanoue et al., 2012; Tian et al., 2019). Li et al. (2018) showed an
intensive SUL metabolism in radish tissue enzyme extracts (the SUL
recoveries in root and leaf enzyme extracts after 96 h were 34% and72%, respectively). Similarly, Wu et al. (2016) documented an evenfaster metabolism of SUL in carrot cell cultures.
Similar degradation rates were estimated for the stem compartment,
except for FEX and CLIS, for which the confidence intervals are large,
thus hindering any meaningful conclusion. In the same way, high un­
certainties were calculated for IRB and FEX in leaves and all compounds

3.3.5. Degradation in soil
The analysis precisely infers the first-order degradation coefficientsin the soil. These coefficients generally have low values, except for SUL
and the metabolite CLIS, with the former exhibiting a strong dissipation,a process that was already observed in other studies (e.g., Andriamalala
et al., 2018; Liu et al., 2010). Results generally agree with what
Kodešová et al. (2020) reported for the same soil, with CIT exhibiting thelowest degradation followed by IRB, FEX, and CLI. Simultaneously, themodel predicts that the metabolite CLIS is rapidly degraded, which
contradicts what Koba et al. (2017) found in laboratory conditions. The
presence of roots (Jin et al., 2019) and the different experimental con­ditions can partially explain this difference.
4. Conclusions
The main aim of this study was to develop and assess the predictive
performance of a soil-plant model for the analysis of the fate andtransport of electrolytes in the soil-plant continuum. The modelingframework connects a multi-organelles model describing processes atthe cell level with a general soil-plant model simulating the reactive
transport of electrolytes in the soil and plant. To circumvent the problemof high-dimensional model calibration, the soil-plant model was cali­brated independently, and estimated parameters were then validated
using the cell model.
Results are encouraging and show that the soil-plant model can
predict the fate of multiple pharmaceuticals in the soil-plant system withsatisfactory accuracy and acceptable uncertainty. The subsequent
10

Journal of Hazardous Materials 423 (2022) 127008

G. Brunetti et al.

validation with the cell model indicates that the soil-plant parameterspreserve a physically realistic meaning, and their estimated values arecomparable with the existing literature values, thus confirming theoverall reliability of the analysis. Model results further indicate that pH
conditions in both soil and xylem play a crucial role in the uptake andtranslocation of ionizable pharmaceuticals. Therefore, accurate moni­
toring of at least soil pH is recommended for experiments focused onelectrolytes transport in the soil-plant continuum to understand how
dissociation processes can affect chemicals’ sorption, uptake, andtranslocation.
The model can be further improved by refining the description ofcertain processes, such as plant hydraulics, changes in soil pH, sorption
kinetics, etc. Experiments with spiked wastewater (or groundwater) canbe used to assess the influence of other components (e.g., nutrients,
DOC) on the uptake process and improve the modeling framework.
However, this additional theoretical complexity must be accompanied
by more comprehensive measurements (e.g., leaf water potential,
metabolite tracking, etc.) to avoid degradation of the model’s predictive
performance. Conversely, ad hoc laboratory experiments are desirable
to better characterize physicochemical processes and improve theirdescription in the model for explanatory purposes. Nevertheless, thedeveloped modeling framework represents a step forward in this di­rection and promises to be a valuable tool for practitioners and scientists
assessing environmental risks.

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CRediT authorship contribution statement
Giuseppe Brunetti: Methodology, Writing – Original Draft, Formal
Analysis, Software. Radka Kodešová: Conceptualization, Supervision,
Funding acquisition. Helena Švecová: Validation, Resources. Miroslav
Fér: Data Curation, Investigation Antonín Nikodem: Data Curation,
Investigation, Aleš Klement: Data Curation, Investigation Roman
Grabic: Conceptualization, Funding acquisition, Jiři Šimůnek: Soft­ware, Writing – Review & Editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgments
The authors acknowledge the Czech Science Foundation financial
support, project Behavior of pharmaceuticals in the soil-water-plantsystem (No. 17-08937S). The work was also supported by the Euro­pean Structural and Investment Funds, projects NutRisk (No.
CZ.02.1.01/0.0/0.0/16_019/0000845), and partly also by the Ministryof Agriculture of the Czech Republic (No. QK21020080).
Appendix A. Supporting information
Supplementary data associated with this article can be found in the
online version at doi:10.1016/j.jhazmat.2021.127008.
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