GEOCHEMICAL SPECIATION MODELING OF TETRACYCLINE
SORPTION AND BIOAVAILABILITY IN THE ENVIRONMENT
By
Mohammed Ahmed Alsanad

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Crop and Soil Sciences - Master of Science
2015

ABSTRACT
GEOCHEMICAL SPECIATION MODELING OF TETRACYCLINE
SORPTION AND BIOAVAILABILITY IN THE ENVIRONMENT
By
Mohammed Ahmed Alsanad
The broad-spectrum antibiotic tetracycline is used extensively for human and animal
health, but as usual, causes unintended environmental consequences. Since large fractions
of tetracycline are not metabolized in animals, massive amounts of tetracycline are excreted
with animal manures and pollute soil, surface water, and groundwater. Among other risks,
tetracycline induces antibiotic resistance in environmental bacteria. In order to understand
and quantify this risk, the objective of this study was to model bacterial uptake of tetracycline in complex media. The speciation of tetracycline is complicated by several ionic species
that form complexes with aqueous cations and also with mineral surfaces, so computational
tools are needed. This study used many experimental data sets to create thermodynamic
parameters for use in the chemical speciation model Phreeqc. Experimental work has shown
that the neutral species of tetracycline dominates the uptake by bacteria, so a new method
for modeling the distribution of organic chemicals using Phreeqc was employed to successfully
model bacterial uptake in complex solutions of Ca2+ , M g 2+ , and five organic acids. Since
clay minerals are important sorbents, cation exchange parameters were developed for tetracycline and its K- and Ca-complexes. While experimental data for K- or Ca-systems could
be successfully fit separately, no parameter set could be found that fit both together over
a range of four ionic strengths. This calls into question the literature values for Ca2+ /K +
exchange itself, which provides a path forward for future research.

ACKNOWLEDGMENTS

I would like to take this opportunity to express my sincere appreciation to my advisor
Dr. Brian J. Teppen for his continuous support, help, patience, motivation, and guidance
throughout my Master study. I would like to thank my committee members: Dr. Stephen
A. Boyd and Dr. Hui Li from the Department of Plant, Soil and Microbial Sciences for their
assistances they provided. Also, I would like to thank my family: my parents and my wife
for supporting me spiritually throughout my life. Finally, I would like to thank King Faisal
University and Saudi Cultural Mission for the financial support during my Master’s degree.

iii

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

Chapter 1 Modeling the Bioaccumulation of Tetracycline into E.coli
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Modeling Tetracycline Uptake by Bacteria in Phreeqc . . . . . .
1.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
4
6
9
12

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Chapter 2 Geochemical Speciation Modeling of Tetracycline Sorption to
K- and Ca-Smectites . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Treatment of Cation-Exchange in Phreeqc . . . . . . . . . . . . . . .
2.2.2 Experimental Data on Tetracycline Exchange with K + or Ca2+ on
Clay Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Possible Impurities in the Clay or Deionized (DI) Water . . . . . . .
2.3.2 Other Parameters that Could Fit Data . . . . . . . . . . . . . . . . .
2.4 Reconciling for Tetracycline Exchange with Both K- and Ca-Clay Minerals .
2.5 Path Forward for Future Research . . . . . . . . . . . . . . . . . . . . . . . .
BIBLIOGRAPHY

. . . . . . . . . . . . .

iv

. . . . . . . . . . . . . . . . .

16
16
18
19
21
23
23
30
34
34
41

LIST OF TABLES

Table 1.1

Compilation of all chemical equations and equilibrium constants used
in the present study. All equations are written as they appear in the
Phreeqc database. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v

12

LIST OF FIGURES

Tetracycline chemical structure [1]. Where R1 = H, R2 = CH3 , R3 =
OH, and R4 = H [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

Tetracycline species distribution in pure water as a function of solution pH calculated using the Phreeqc parameters from Table 1.1. . .

6

Dominant species of tetracycline as a function of pH and Ca2+ concentration in aqueous solution [3]. L=tetracycline. . . . . . . . . . .

7

Approximate relationship of tetracycline neutral species (zwitterionic
species) concentration in solution with the intracellular (E.coli ) tetracycline concentration. These data cover a wide range of Ca2+ or
M g 2+ concentrations from 0 to 5.0 mmol/L and pH from 6 to 8 [4].
Solution-phase concentrations have not been corrected for bacterial
uptake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

Results of modeling the relationship between tetracycline neutral
species (zwitterionic species) concentration in solution and intracellular (E.Coli ) tetracycline concentration using Phreeqc. These data
cover a wide range of Ca2+ and M g 2+ concentrations from 0 to 5.0
mmol/L and pH from 6 to 8 [4], and include solutions containing
five different organic acids at pH 7 [5]. Solution-phase concentrations
have been corrected for bacterial uptake. The dark line is both the
linear regression of the data and the Phreeqc prediction for bacterial
uptake of tetracycline in each of the 130 systems. . . . . . . . . . .

11

Calculated equilibria for K- Ca-exchange using Phreeqc and the cation
exchange coefficients of Appelo and Postma [6] and Table 1.1 at three
different ionic strengths. IS= ionic strength, and CEC= cation exchange capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

Comparison of modeled and experimental [7] pH values of initial
tetracycline solution. . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Figure 2.3

Sorption of tetracycline to K-smectite at zero ionic strength. . . . .

28

Figure 2.4

Sorption of tetracycline to K-smectite at 0.01 mol/L ionic strength.

29

Figure 2.5

Sorption of tetracycline to K-smectite at 0.1 mol/L ionic strength.

30

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 2.1

Figure 2.2

vi

Figure 2.6

Sorption of tetracycline to K-smectite at 0.8 mol/L ionic strength. .

31

Figure 2.7

Sorption of tetracycline to Ca-smectite at zero ionic strength.

. . .

31

Figure 2.8

Sorption of tetracycline to Ca-smectite at 0.01 mol/L ionic strength.

32

Figure 2.9

Sorption of tetracycline to Ca-smectite at 0.1 mol/L ionic strength.

33

Figure 2.10

Sorption of tetracycline to Ca-smectite at 0.8 mol/L ionic strength.

33

Figure 2.11

Modeled versus experimental [7] Ca2+ /H4 (T ec)+ exchange when log k
= 5.5 for Eq. (2.16) and log k = 3.0 for Eq. (2.15) at zero ionic
strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

Modeled versus experimental [7] Ca2+ /H4 (T ec)+ exchange when log k
= 5.5 for Eq. (2.16) and log k = 3.0 for Eq. (2.15) at 0.1 mol/L ionic
strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Modeled versus experimental [7] Ca2+ /H4 (T ec)+ exchange when log k
= 5.5 for Eq. (2.16) and log k = 3.0 for Eq. (2.15) at 0.1 mol/L ionic
strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

Free energy diagram for a subset of cation exchange reactions in
Phreeqc. Current Phreeqc parameters (a) are shown on the left, while
a hypothetical future parameters set (b) is shown on the right. . . .

39

Free energy diagram for a subset of cation exchange reactions in
Phreeqc. Current Phreeqc parameters (a) are shown on the left, while
a hypothetical future parameters set (b) is shown on the right. . . .

40

Figure 2.12

Figure 2.13

Figure 2.14

Figure 2.15

vii

Chapter 1
Modeling the Bioaccumulation of
Tetracycline into E.coli

1.1

Introduction

In the 20th century, antibiotics were major new discoveries in terms of human and animal
medicine. In the world, including the United States, antibiotics protect the lives of millions
of humans and animals every year [8]. In 2010, the usage of antimicrobials in animal foods
was around 13.5 million kg [9].
Tetracycline is a broad-spectrum antibiotic that was discovered in early of 1950s [10]. The
chemical formula of tetracycline consists of four fused cyclic rings with attached functional
groups, including dimethylammonium, tricarbonylmethane, and diketone (Figure1.1). In the
aqueous phase, these functional groups often become ionized and cause tetracycline to form
cation, zwitterion (neutral), or anion species, depending on solution pH (Figure 1.2).
Tetracycline has extensive uses for human and animal health by protecting them from a
variety of infectious diseases. Tetracycline usage comprised 42% of the total antimicrobials
used in food animal production, 5, 602, 281 kg of tetracycline in 2010 [9]. Since large fractions
of tetracycline are not metabolized in the animals, massive amounts of tetracycline are
excreted with animal manures, either as the original compound or as its bioactive metabolites

1

[11, 12]. Thus, tetracycline and its derivatives are transferred to soil [13, 14], surface water
[15–18], and groundwater [14, 19, 20].
In the environment, tetracycline speciation in aqueous solutions can be very complex.
In the simplest case, tetracycline in pure water already contains four species, depending on
pH (Figure 1.2). Typically, aqueous solutions will also contain a variety of metal cations,
including Ca2+ , M g 2+ , and K + . These cations may form complexes with tetracycline, thus
reducing the activity of uncomplexed tetracycline and forming additional species that must
be considered (Figure 1.3). The activities of metal ions may be altered by the presence of
organic ligands that can complex the metals, or by sorption of the metals to solid phases such
as clay minerals or organic matter. Such competitive complexation or sorption of metals will
generally increase the activity of aqueous uncomplexed tetracycline. Finally, tetracycline
itself may sorb to a variety of soil minerals (e.g., smectite clays, goethite, or magnetite) and
to soil organic matter, thus decreasing tetracycline activity in solution.
Among the different species of tetracycline present in aqueous solution, including cationic
species of tetracycline and neutral or zwitterionic species, Zhang et al. [4] hypothesized that
the neutral species was the dominant form taken up by bacterial (Escherichia coli ) cells.The
neutral, zwitterionic species of tetracycline would thus acquire great importance in attempts
to understand the development of antibiotic resistance in bacteria. It would also mean that
geochemical components like pH and cations have an enormous influence on the induction
of bacterial resistance [4].
Though tetracycline levels discovered in many environmental media are lower than the
levels required to show minimum inhibitory concentration (MIC) for medicinal interests, observed environmental tetracycline levels probably do discriminate among bacteria by stressing populations [19, 21–24]. The result is that bacteria containing the genes for antibiotic
2

resistance will be more likely to survive, which will enhance the antibiotic resistance of bacterial inhabitants in our environment [19, 21–24]. This is a serious global problem. Early
in 2014, the World Health Organization published a cautionary report that the people are
in danger of finding themselves in a post-antibiotic era [25]. Also, the report has said that
doctors are unable to fight infections like drug-resistant gonorrhea, and we need modern
treatments to substitute for the drugs which bacterial resistance has made ineffective [25].
The usages of antibiotics are increasing but still imperfect to hold up with the resistance of
bacteria [26].
The resistance of bacteria is complicated and involves several aspects which can cause
many human and animal diseases [25]. In the United States itself, around 2 million diseases
and 23 thousand deaths happened due to the bacterial resistance [8]. If we lose the benefits
of antibiotics, we will be incapable to treat the infections of bacteria [8]. Therefore, in 2014,
the U.S. government has created a national strategy and an action plan to face and treat
this serious problem by several different steps [8].
In order to understand this complexity of tetracycline speciation in environmental waters,
computational tools are needed to iteratively and quantitatively estimate the distribution
of tetracycline among its many possible species. Phreeqc is a tool that was developed over
35 years and continues to be improved [27] for thermodynamic modeling of aqueous environmental systems. Phreeqc is a public-domain tool that has already been integrated with
saturated- and unsaturated-flow water transport modules [28], so it provides a framework
for future reactive-transport modeling.
Thermodynamic modeling, as in Phreeqc, is very useful because even the most sophisticated analytical procedures such as liquid chromatography coupled to tandem mass spectrometry (LC-MS-MS), [29] simply measure the total tetracycline concentration rather than
3

the component tetracycline species. Thermodynamic approaches allow a more powerful interpretation of these analytical LC-MS-MS data by estimating the distribution of tetracycline
among its possible species. Therefore, Phreeqc modeling is a method for extracting the most
value from data in order to better understand the complexation, sorption, and bioavailability
of antibiotics in the environment.
The objective of the current study was to develop a quantitative model for tetracycline
speciation in complex systems. A main goal was to be able to predict bacterial uptake
of tetracycline as a function of realistic geochemical variables, because bacterial uptake is
correlated very strongly with the induction of antibiotic resistance [4]. While many of the
relevant chemical equilibria have already been described, a new method was applied and fit
to the available data in order to describe bacterial uptake of tetracycline. This appears to
be the first implementation of a method to describe linear distribution reactions in Phreeqc,
and should be very broadly applicable to modeling the fate of organic solutes in complex
geochemical systems.

1.2

Methods

For developing the equations necessary to model the chemical speciation of tetracycline, the
recent datasets of Zhang et al. [4, 5] are robust in that they recorded tetracycline, metal
(Ca2+ and M g 2+ ), and organic ligand (acetate, oxalate, succinate, malonate, and citrate)
concentrations as well as pH and measurements of tetracycline uptake by E.coli bacteria.
The results of Zhang et al. [4] gave rise to the hypothesis that a single species of tetracycline

4

!
Figure 1.1 Tetracycline chemical structure [1]. Where
R4 = H [2].

R1 =

H,

R2 =

CH3 ,

R3 =

OH, and

(the neutral, zwitterionic species H3 T ec0 ) dominates the bacteria uptake. That is, the
significant positive correlation (Figure 1.4) between intracellular tetracycline concentration
and H3 T ec0 indicated that zwitterionic tetracycline was clearly the most favorable species
for uptake by the E.coli according to bioreporter technique [4, 5]. The uptake of all other
tetracycline species seemed to be either inconsequential or even negatively correlated with
bacterial uptake.
The present study adjusted the reported [4, 5] initial concentrations of tetracycline for
the reported bacterial uptake of tetracycline to yield uptake-adjusted estimates for the final equilibrium aqueous concentrations of tetracycline. For each final, equilibrium aqueous
concentration of tetracycline, Phreeqc was then used to estimate the fractional distribution
of tetracycline species in the LB medium. All chemical equilibria used for Phreeqc in the
present study are listed in Table 1.1.
The relationship of bacterial uptake to aqueous H3 T ec0 activity found by Zhang et al. [4]
was, at a first approximation, linear (Figure 1.4). Therefore, the present study tentatively
modeled bacterial uptake using the simple expression:

5

Speciation*Fraction*(mol/L)*

1.20E"04!
1.00E"04!
8.00E"05!
6.00E"05!
4.00E"05!
2.00E"05!
0.00E+00!
0.0!

2.0!

4.0!

6.0!

"2.00E"05!

H4(Tec)+!mol/l!

8.0!

10.0!

12.0!

pH*
H3(Tec)0!mol/l!

H2(Tec)"!mol/l!

H(Tec)2"!mol/l!

!
Figure 1.2 Tetracycline species distribution in pure water as a function of solution pH calculated using the Phreeqc parameters from Table 1.1.

(BacteriaTetracycline) ∼
= Kd (H3 T ec0aq )

(1.1)

(BacteriaTetracycline)
Kd ∼
=
0 )
(H3 T eCaq

(1.2)

so that

where Kd is the distribution coefficient. This simple approach seems appropriate because
Equations 1.1 and 1.2 were developed for the distribution of neutral organic compounds
into soil organic matter. In the present case, we used the neutral species of tetracycline
distribution into bacteria cells, which are reasonable analogues of soil organic matter.

1.2.1

Modeling Tetracycline Uptake by Bacteria in Phreeqc

Again, bacterial uptake of tetracycline limited to be controlled by just one tetracycline
species [4]. The functional relation between uptake and zwiterionic tetracycline seemed to

6

!
Figure 1.3 Dominant species of tetracycline as a function of pH and Ca2+ concentration in
aqueous solution [3]. L=tetracycline.
be approximately linear (Figure 1.4), so that it could be approximated with Eq. 1.1 and Eq.
1.2. Therefore, the study adopted an approach for modeling linear adsorption in Phreeqc
that has been presented by Appelo and Postma [6], but has apparently never been reported
in subsequent literature. This approach could be used to describe any linear distribution
reaction, and the present study applies it to describe the uptake of tetracycline by bacteria.
If a tetracycline molecule in a bacterial cell is designated “BacteriaTetracycline”, then the
distribution of tetracycline into bacteria can be expresses as the following process:

H3 T ec0aq + Bacteria = BacteriaTetracycline

(1.3)

Then,

Keq =

(BacteriaTetracycline)
(H3 T ec0 )(Bacteria)

But for distribution,
7

(1.4)

Kd =

(BacteriaTetracycline)
(H3 T ec0aq )

(1.5)

That is, Keq = Kd as long as (Bacteria) = 1.00 in Eq. 1.4.
In the “Sorption” model of Phreeqc, the present study created a “Surface” (a phase
that can sorb molecules) called “Bacteria”. This phase is assigned a certain number (call it
“TotalSites”) of possible sorption sites. Following the standard conventions for defining the
activities of sites in solid solutions [30], the activity of a certain type of site i like this in the
solid phase is approximated as its fractional occupancy [30].

# sites of type i
Activity of site i ∼
=
TotalSites

(1.6)

If the present study considers only the sorption of tetracycline, then the only two types
of sites in bacteria will be the occupied “BacteriaTetracycline” sites and the unoccupied
“Bacteria” sites, so

TotalSites = # BacteriaTetracycline + # Bacteria

(1.7)

Thus, the activity or fraction of the site-type “Bacteria” is:

(Bacteria) =

# Bacteria
# BacteriaTetracycline + # Bacteria

(1.8)

However, if # BacteriaTetracycline ≪ # Bacteria, then

(# Bacteria) ∼
= # BacteriaTetracycline + # Bacteria

8

(1.9)

And this means that:

(Bacteria) =

# Bacteria
# Bacteria
∼
= 1.00
=
# BacteriaTetracycline + # Bacteria
# Bacteria

(1.10)

If this is true, then Keq = Kd in Equations 1.4 and 1.5, and the Phreeqc speciation model
possesses a chemical equilibrium model for distribution. Thus, the distribution of tetracycline
into bacterial cells is treated as if the bacteria contained a large number of individual sites,
of which just a few are occupied by tetracycline. Note that if the aqueous concentration of
tetracycline is about 100 µg/L, then there are only 2.3e−7 mole/L of tetracycline. In the
real systems studied by Zhang et al. [4, 5], there were about 200 mg (dry weight) bacteria
per L of solution (Zhang, personal communication), so if one assumed the bacterial biomass
to be half carbon, then there were about 0.0085 moles bacterial carbon per liter of solution.
The bacterial cells thus comprised on the order of 40,000 moles of carbon for each mole of
tetracycline in the total system. Thus, it is plausible that # BacteriaT etracycline <<<
# Bacteria. For the present study, the relevant Phreeqc parameter assigned the bacteria to
have 10 moles of sites per L solution, which is huge compared to the amount of tetracycline,
in order to guarantee that:
# BacteriaT etracycline <<< # Bacteria is always true and (Bacteria) = 1.0000.

1.3

Results and Discussion

Figure 1.5 shows the measured bacterial uptake of tetracycline as a function of the uptakeadjusted, Phreeqc-modeled equilibrium H3 T ec0 activity. The 130 experimentally derived
points in Figure 1.5 correspond to initial tetracycline concentrations ranging from 25 to 125

9

Intracellular Bacterial
Tetracycline (µg/g)

60.00!

50.00!

40.00!

30.00!

20.00!

10.00!

●!100!ug/L!Tetracycline!
◊!Other!Concentra?ons!

0.00!
0.0!

20.0!

40.0!

60.0!

80.0!

100.0!

120.0!

140.0!

Neutral Species [H3(Tec)] in Solution (µg/L)
!

Figure 1.4 Approximate relationship of tetracycline neutral species (zwitterionic species)
concentration in solution with the intracellular (E.coli ) tetracycline concentration. These
data cover a wide range of Ca2+ or M g 2+ concentrations from 0 to 5.0 mmol/L and pH
from 6 to 8 [4]. Solution-phase concentrations have not been corrected for bacterial uptake.
µg/kg (ppb), pH values from 6 to 8, Ca2+ and M g 2+ concentrations from 0.1 to 5.3 mmol/L,
and concentrations of acetate, oxalate, succinate, malonate, and citrate varying from 0 to 20
mmol/L [14, 29]. The best linear fit to the data had an intercept of 1.9 ± 3.6 µg/g (ppm).
Thus, the 95% confidence interval for the intercept was larger than the intercept itself. Since
the intercept is not significantly different from zero, the origin of the line at zero. In this case,
Eq. 1.1 and Eq. 1.2 applied; a linear regression of the data in Figure 1.5, forced through the
origin, yielded a slope and 95% confidence interval of Kd = 524 ± 35 L/kg.
The Phreeqc method used in this study accurately modeled the bacterial uptake of the
tetracycline neutral species H3 T ec0 in solution and bacterial uptake (Figure 1.5). After adjusting the data (Figure 1.4), the data continued to mirror the linear relationship obtained
by Zhang et al. (Figure 1.5). The distribution relationship developed for Phreeqc is represented by the line in Figure 1.5. Furthermore, to our knowledge, no other researchers have
10

used this approach for distribution of organics into bacteria or organic matter using Phreeqc.

"Therefore, the approach of this study will help interested researchers in the fields of emerging

Intracellular Bacterial
Tetracycline (µg/g)

contaminants and remediation of soil and water pollution.

80"
70"
60"
50"
40"
30"
20"
10"
0"
0"

20"

40"

60"

80"

100"

120"

Estimated Neutral Species [H3(Tec)] in Solution (µg/L)
Figure 1.5 Results of modeling the relationship between tetracycline neutral species (zwitterionic species) concentration in solution and intracellular (E.Coli ) tetracycline concentration
using Phreeqc. These data cover a wide range of Ca2+ and M g 2+ concentrations from 0 to
5.0 mmol/L and pH from 6 to 8 [4], and include solutions containing five different organic
acids at pH 7 [5]. Solution-phase concentrations have been corrected for bacterial uptake.
The dark line is both the linear regression of the data and the Phreeqc prediction for bacterial
uptake of tetracycline in each of the 130 systems.
The key assumption made in the sorption module of Phreeqc to model the distribution of
tetracycline into bacteria is that the number of sorption sites is much larger than the number
of molecules of tetracycline sorbed. This assumption should be valid because distribution
is similar to a process of dissolution [31]. That is, the capacity of the bacterial phase for
tetracycline grows even larger as tetracycline becomes sorbed. As discussed above, there were
perhaps 40,000 moles of bacterial carbon per mole of tetracycline sorbed, so it seems the
assumption should be valid. Distribution is a very important geochemical process, yet the
literature seems to contain no previous examples of using Phreeqc to model distribution. This
11

work shows that this Phreegc model can be successfully applied to hydrophobic distribution.

1.4

Conclusions

A novel method was adapted to model the distribution of the neutral (zwitterionic) species
of tetracycline into bacterial cells. The method was applied to a range of pH values (6 − 8), a
range of concentrations of Ca2+ and M g 2+ , and varying five organic acids that can complex
the metals in competition with tetracycline. This study demonstrated that the method of
Appelo and Postma [6] can be effectively used to model distribution using Phreeqc. Given
that sorption of many hydrophobic organic compounds is dominated by distribution, this
functionality in Phreeqc may have widespread application. Furthermore, using Phreeqc we
successfully modeled the hypothesis of Zhang et al. [4, 5] that the uptake of tetracycline
by E.coli can be approximated as a process of distribution of a single tetracycline species,
namely the neutral, zwitterionic form.
Table 1.1 Compilation of all chemical equations and equilibrium constants used in the present
study. All equations are written as they appear in the Phreeqc database.
Section in Phreeqc
Reactions

log k

Database
SOLUTION MASTER
Tec

H4 (T ec)+

—

SPECIES
H4 (T ec)+ = H4 (T ec)+

0.000

H4 (T ec)+ = H3 (T ec)+ H +

−3.45a

H4 (T ec)+ = H2 (T ec)− + 2H +

−11.45a

12

Table 1.1 (cont’d)
Section in Phreeqc
Reactions

log k

H4 (T ec)+ = H(T ec)2− + 3H +

−21.23a

H4 (T ec)+ = T ec3− + 4H +

−33.64a

Ca2+ + H2 (T ec)− = CaH2 (T ec)+

3.4b

M g 2+ + H2 (T ec)− = M gH2 (T ec)+

3.9b

Ca2+ + H(Tec)2− = CaH(Tec)

5.8b

Mg2+ + H(Tec)2− = MgH(Tec)

4.1b

Ca2+ + H3 (Tec) = CaH3 (Tec)2+

3.0d

K + + H2 (T ec)− = KH2 (T ec)

1.04e

K+ + H3 (Tec) = KH3 (Tec)+

1.04e

Oxalate2− + H + = HOxalate−

4.27g

HOxalate− + H + = H2 Oxalate

1.25c

Ca2+ + Oxalate2− = Ca(Oxalate)

3.0g

M g 2+ + Oxalate2− = M g(Oxalate)

3.43g

M alonate2− + H + = HM alonate−

5.70c

HM alonate− + H + = H2 M alonate

2.85c

Ca2+ + M alonate2− = Ca(M alonate)

2.35c

M g 2+ + M alonate2− = M g(M alonate)

2.85c

Succinate2− + H + = HSuccinate

5.64c

HSuccinate− + H + = H2 Succinate

4.21c

Ca2+ + Succinate2− = Ca(Succinate)

2.0c

Database

SOLUTION SPECIES

13

Table 1.1 (cont’d)
Section in Phreeqc
Reactions

log k

M g 2+ + Succinate2− = M g(Succinate)

2.0c

H + + Acetate− = H(Acetate)

4.757f

M g 2+ + Acetate− = M g(Acetate)+

1.27g

Ca2+ + Acetate− = Ca(Acetate)+

1.18g

H + + Citrate3− = H(Citrate)2−

6.396f

2H + + Citrate3− = H2 (Citrate)−

11.157f

3H + + Citrate3− = H3 (Citrate)

14.258f

Ca2+ + Citrate3− = Ca(Citrate)−

4.87f

Ca2+ + Citrate3− + H + = CaH(Citrate)

9.26f

Ca2+ + Citrate3− + 2H + = CaH2 (Citrate)+

12.257f

M g 2+ + Citrate3− = M g(Citrate)−

4.89f

M g 2+ + Citrate3− + H + = M gH(Citrate)

8.91f

M g 2+ + Citrate3− + 2H + = M gH2 (Citrate)+

12.2f

Database

SOLUTION SPECIES

Fix H +
PHASES

0.000
H+

=

H+

# Bacteria is to allow distribution of
SURFACE MASTER
antibiotic into bacterial cells

—

SPECIES
Bacteria
SURFACE SPECIES

Bacteria

Bacteria = Bacteria

14

0

Table 1.1 (cont’d)
Section in Phreeqc
Reactions

log k

Bacteria + H3 (Tec) = BacteriaH3 (Tec)

−1.2805d

Database

EXCHANGE MASTER
X

X−

—

SPECIES
X−

EXCHANGE SPECIES

X−

0.0f

H4 (Tec)+ + X− = H4 (Tec)X

3.8d

CaH2 (Tec)+ + X− = CaH2 (Tec)X

7.0d

#CaH3 (Tec)2+ + 2X− = CaH3 (Tec)X2

#4.2d

MgH2 (Tec)+ + X− = MgH2 (Tec)X

2.0d

KH3 (Tec)+ + X− = KH3 (Tec)X

3.6d

N a+ + X − = N aX

0.0f

K + + X − = KX

0.7f

Ca2+ + 2X − = CaX2

0.8f

M g 2+ + 2X − = M gX2

0.6f

a data from Werner et al. 2006 were used, but equations were added to arrive at these values;
b data from Gu and Karthikeyan, 2005; c data from MINEQL+ database (Version 4.5, 2002);
d equation and value from this study; e data from Coibion and Laszio, 1979; f data from
Phreeqc database (Version 2.13.2-1727, 2007); g data from Werner et al. 2006.

15

Chapter 2
Geochemical Speciation Modeling of
Tetracycline Sorption to K- and
Ca-Smectites

2.1

Introduction

Antibiotics were major discoveries the 20th century that were enormously used in human and
veterinary medicine. These medicines protect the lives of millions of humans and animals
every year [8]. Later, antibiotics began to be used as feed supplements at subtherapeutic
levels to enhance productively and profitability in the livestock industry. In 2010, the usage
of antimicrobials in animal foods reached approximately 13.5 million kg [9].
Tetracycline is a broad-spectrum antibiotic that was discovered in early of 1950s [10]. The
chemical structure of tetracycline consists of four fused cyclic rings substituted with functional groups, including dimethylammonium, tricarbonylmethane, and diketone (Figure1.1).
In the aqueous phase, these functional groups gain or lose protons and causing tetracycline
to form cations, anions, and zwitterions (neutral) depending on solution pH (Figure 1.2).
Tetracycline is used extensively in human and veterinary medicine since the effectively
treat a variety of common infectious diseases. Tetracycline usage comprised 42% of the total

16

antimicrobials used in food animal production , 5, 602, 281 kg, in 2010 [9]. Since large fractions of tetracycline are not metabolized in the animals, massive amounts of tetracycline are
excreted with animal manures, either as the original compound or as its bioactive metabolites [11, 12]. Thus, tetracycline and its derivatives are transferred to soil [13, 14], surface
water [15–18], and groundwater [14, 19, 20].
In the environment, tetracycline speciation in aqueous solutions can be very complex.
In the simplest case, tetracycline in pure water already contains four species, depending on
pH (Figure 1.2). Typically, aqueous solutions will also contain a variety of metal cations,
including Ca2+ , M g 2+ , and K + . These cations may form complexes with tetracycline, thus
reducing the activity of uncomplexed tetracycline and forming additional species that must
be considered (Figure 1.3). The activities of metal ions may be altered by the presence of
organic ligands that can complex the metals, or by sorption of the metals to solid phases such
as clay minerals or organic matter. Such competitive complexation or sorption of metals will
generally increase the activity of aqueous uncomplexed tetracycline. Finally, tetracycline
itself may sorb to a variety of soil minerals (e.g., smectite clays, goethite, or magnetite) and
to soil organic matter, thus decreasing tetracycline activity in solution.
In order to understand this complexity of tetracycline speciation in environmental waters,
computational tools are needed to iteratively and quantitatively estimate the distribution of
tetracycline among its many possible species. Phreeqc is a tool that was developed over 35
years ago and continues to be improved [27] for thermodynamic modeling of aqueous environmental systems. Phreeqc is a public-domain model that has already been integrated with
saturated- and unsaturated-flow water transport modules [28], so it provides a framework
for future reactive-transport modeling.
Thermodynamic modeling, as in Phreeqc, is very useful because even the most sophis17

ticated analytical procedures such as liquid chromatography coupled to tandem mass spectrometry (LC-MS-MS), [29] only measures the total tetracycline concentration in solution
rather than the concentrations of the component, (e.g. changed) tetracycline species, which
may manifest different chemistries. Thermodynamic approaches allow a more powerful interpretation of already sophisticated analytical LC-MS-MS data by estimating the distribution
of tetracycline among its possible species. Therefore, Phreeqc modeling is a method for extracting the most value from analytical data sets in order to better understand complexation,
sorption, and bioavailability of antibiotics in the environment.
The objective of the current study was to develop a quantitative model for tetracycline
speciation in complex systems. A central goal is to be able to predict tetracycline sorption
to K- and Ca-clay minerals as a function of realistic geochemical variables. While many of
the relevant chemical equilibria have already been described, several new thermodynamic
relationships were fit to the available data in order to describe the competitive adsorption
of tetracycline to K- and Ca-clay minerals. Finally, the fit of the parameters to several
independent datasets was tested.

2.2

Methods

The thermodynamic parameters used in this study are listed in Table 1.1. Equations and
parameters that were newly developed for this study are highlighted in bold. Werner et al. [3]
measured tetracycline speciation and complexation by Ca2+ , and M g 2+ as functions of pH.
Their parameters were selected for the present study because they form a self-consistent set.

18

2.2.1

Treatment of Cation-Exchange in Phreeqc

For modeling cation exchange on clay minerals, the study followed the general method of
Appelo and Postma [6]. In this method, all cation exchange equilibria are referenced to
exchange with N a+ . That is, a Na-saturated clay is chosen as the thermodynamic “zero”,
and the energetic state of all other cations in the exchange complex are relative to this
“zero”. Thus, the cation exchange parameters in Table 1.1 for cation I i+ are referenced to
this equation:

N a+ + 1/i . I − Xi ⇐⇒ N a − X + 1/i . I i+

(2.1)

The Phreeqc database compiles all such reactions as half-reactions of the form:

N a+ + X − = N aX

logk = 0

(2.2)

where X − is a site of cation exchange on the clay mineral. The logk parameter in Phreeqc
is the logarithm (base 10) of the equilibrium constant (Kexch ) for this cation-exchange halfreaction. Since logk = 0, Kexch must equal 1, and so if any other cation-exchange halfreaction is added to that of N a+ , the Kexch and the logk for the overall reaction will simply
be the Kexch and the logk for the non-N a+ ion. Therefore, all cation exchange equilibria
are referenced to exchange with N a+ .
To illustrate how parameters in the database work, considered the exchange of K + for
Ca2+ on a clay mineral. The K + half-reaction (Table 1.1) is:

K + + X − = KX

19

logk = 0.7

(2.3)

If we multiply the previous reaction by 2, we will obtain the following equation:

2K + + 2X − = 2KX

logk = 1.4

(2.4)

Also, the Ca- exchange reaction in Phreeqc (Table 1.1) is:

Ca2+ + 2X − = CaX2

logk = +0.8

(2.5)

logk = −0.8

(2.6)

Reversing the previous reaction:

CaX2 = Ca2+ + 2X −

If we combine reactions 2.4 and 2.6, we will get the following equation:

2K + + Ca − X2 −→ 2KX + Ca2+

logk = +0.6

(2.7)

Therefore, since [ G = −RT lnk = −RT (2.3)logk] and R = 8.3145 J/K.mol, T = 298K
hence RT = 2.48 kJ/mol. Thus,

G = −(2.48)(2.3)(0.6) = −3.4 kJ/mol.

For the cation exchange half reaction that involves only one exchange site:

K + + 1/2Ca − X2 −→KX + 1/2Ca2+
So,

logk = +0.3

(2.8)

G = −(2.48)(2.3)(0.3) = −1.7 kJ/mol.

To check the K + and Ca2+ parameters in Table 1.1, the competitive cation exchange
between K + and Ca2+ was calculated at three different ionic strengths (Figure 2.1). The
results were as expected, and these parameters have been used in many modeling studies of

20

cation exchange involving K + and Ca2+ [32–34].
1.20E+00!

1.00E+00!

K+ on CEC

8.00E'01!

IS=$0.8$mol/L$$
6.00E'01!

IS=$0.1$mol/L$$

4.00E'01!

IS=$0.01$mol/L$$

2.00E'01!

0.00E+00!
0.00E+00!

2.00E'01!

4.00E'01!

6.00E'01!

K+

8.00E'01!

1.00E+00!

1.20E+00!

in Solution

Figure 2.1 Calculated equilibria for K- Ca-exchange using Phreeqc and the cation !exchange
coefficients of Appelo and Postma [6] and Table 1.1 at three different ionic strengths. IS=
ionic strength, and CEC= cation exchange capacity.

2.2.2

Experimental Data on Tetracycline Exchange with K + or
Ca2+ on Clay Minerals

Yunjie Ding [7] measured the cation exchange equilibria of tetracycline with K- and Casmectites. This is a robust data set that provides sorption data for K + , Ca2+ , and tetracycline as well as pH, the change in pH during experiment, and metal release from the
clays.
Ding [7] measured metal release by K + -clays and Ca2+ -clays during exchange reactions

21

with tetracycline. Such measurements were only possible for systems with no added background electrolyte (labelled ‘no ionic strength’ below), and could be useful for determining
whether tetracycline adsorbs to clays in forms other than the H4 T ec+ cation (Figure1.2).
For example, when tetracycline sorbs to calcium smectite, there are at least three possible
reaction stoichiometries. First, if two tetracycline molecules sorb to the clay and one Ca2+
ion appears in solution, then a reaction similar to

2H4 (T ec)+
+ CaX2 = 2H4 (T ec)X + Ca2+
(aq)

(2.9)

is inferred. Second, if tetracycline sorbs to the clay but the amount of Ca2+ ions in
solution remains constant, then a reaction like

H3 (T ec)0(aq) + CaX2 = [CaH3 (T ec)X2 ]

(2.10)

could be inferred. Third, note that Figure1.3 shows that the CaH2 (T ec)+ complex should
be an important tetracycline species in calcium systems [3]. Sorption of that complex should
result in one Ca2+ consumed from solution along with each two tetracycline sorbed, by the
reaction:

2CaH2 (T ec)+
+ CaX2 = 2[CaH2 (T ec)X] + Ca2+
(aq)
(aq)

(2.11)

Thus, the stoichiometry of changes in the inorganic cation concentration in solution as a
function of tetracycline sorption can be used to constrain interpretations of the operant sorption mechanisms. Indeed, it may be feasible to use cation-release data and apply Equations
2.9 – 2.11 to estimate the speciation of tetracycline and calcium on the exchange complex.

22

In each initial tetracycline solution, the following equilibrium was established at the initial
pH:

+
+
H4 (T ec)+
⇐⇒ H3 (T ec)o(aq) + H(aq)
⇐⇒ H2 (T ec)−
+ 2H(aq)
(aq)
(aq)

(2.12)

If the cationic species H4 (T ec)+ sorbs to the clay and is removed from solution, and if
we assume constant pH, then the above equilibrium will be re-established. If the amount of
H4 (T ec)+ removed from solution was Ci , then an amount of H + approximately equal to Ci
will need to be removed from solution in order to re-establish the above equilibrium. Thus,
proton consumption is an approximation of the amount of H4 (T ec)+ sorption under a given
condition, and should be reflected as a loss of protons from solution and an increase in the
solution pH after tetracycline sorption by the clay.

2.3
2.3.1

Results and Discussion
Possible Impurities in the Clay or Deionized (DI) Water

To test the performance of the tetracycline parameters, the pH values for all initial solutions
were calculated using Phreeqc. To do so, each initial concentration of tetracycline that
was used by Ding [7] was equilibrated and the pH was calculated. The calculated pH was
significantly lower than the observed pH, especially when the tetracycline concentrations
were low. Ding used tetracycline HCl to make his initial solutions, so the following equations
apply:

H4 T ecCl−→H4 T ec+ + Cl−

23

(2.13)

H4 T ec+ −→H + + H3 T ec0

(2.14)

Equation 2.14 shows that the solution pH should certainly be below 7 for all concentrations of tetracycline HCl in pure water. However, Ding observed many pH values above 8. A
hypothesis that is consistent with Ding’s data is that a basic impurity was present in all his
systems. One possibility is carbonate impurities in the SWy-2 clay he used [35], and another
possibility is impurities in the water. The deviations between observed and expected pH
values were systematic and a good fit to all data was obtained by adding 0.08 mmol/kgw
of N aHCO3 and 0.02 mmol/kgw of N a2 CO3 . The calculated and observed pH values as a
function of initial tetracycline concentrations are plotted in Figure 2.2. There is no evidence
for the nature of the high pH contaminant in the clay or water used by Ding [7], but in order
to fit pH properly, this buffer was used in all subsequent calculations.
Many complexation constants have been determined for tetracycline interactions with
cationic metals, but the main focus of this study was to develop some new thermodynamic
parameters for cation exchange reactions involving tetracycline. A provisional set of these
parameters are listed and highlighted in Table 1.1.
One important parameter for clay minerals is the cation exchange capacity (CEC), the
total quantity of cationic charge that can be reversibly sorbed per unit mass of clay. For
the clay mineral SWy-2 used by Ding [7], the CEC is known to be 78 cmol/kg. However,
sorption of tetracycline to both K-SWy-2 and Ca-SWy-2 with no other salt in the system
showed sorption plateaus at 42 − 43 cmol of tetracycline per kg clay p.79 of [7]. A plausible
reason for this discrepancy is explained by Ding p.88 of [7]:
“The basal spacing of smectites were 14.7 ˚
A with tetracycline loadings < 135 µmol/g ...

24

10!

9!

Initial pH

8!

7!

Ding's data for Ca
Phreeqc Ca

6!

Ding's data for K
Phreeqc K

5!

4!

3!
0!

100!

200!

300!

400!

500!

Initial tetracycline concentration µmol/L
!

Figure 2.2 Comparison of modeled and experimental [7] pH values of initial tetracycline
solution.
the distance between two adjacent clay sheets was 5.1 ˚
A ... molecular dynamics simulation
results indicate that at low loading rate (< 135 µmol/g), tetracycline lays parallel to clay
surfaces, .... When sorption approaches to 420 µmol/g, which is the sorption plateau in
Figure III-2, the clay sheets expands to 7.5 ˚
A. At this distance tetracycline adapts a tilted
position in clay interlayers. Molecular dynamic simulation results for sorption at 420 µmol/g
indicate that tetracycline molecules adapt vertically tilted position.”
The present study also adopts the hypothesis that the clay interlayer “fills up” at 42 − 43
cmol(+)/kg at which point the interlayer is plausibly “full” and causes a sorption plateau.
Further sorption of tetracycline is possible but requires the interlayer to rearrange so that
tetracycline can adopt a tilted configuration. Realistically, loading of clay minerals in nature
by tetracycline should be less than 42−43 cmol(+)/kg, so confining our fitting efforts to this
lower- tetracycline region of the sorption curve seems appropriate from an environmental,
25

practical standpoint. Ding [7] showed that tetracycline concentrations greater than 100
µmol/L (44 mg tetracycline/L) were required to achieve the sorption plateau even in the
absence of competing salts. For comparison, observed concentrations of tetracycline in liquid
manures may approach 40 mg tetracycline/L [36], but concentrations will generally be much
more dilute in environmental waters or soil solutions.
One benefit of this approach is that such a model might fit all smectite clays and thus be
widely applicable: All smectites have CEC > 42 − 43 cmol(+)/kg but all possess roughly
the same interlayer surface area (about 750 m2 /g) [30], and so many smectites should display plateaus or inflections in their tetracycline sorption near 42 − 43 cmol(+)/kg. For
example, Figueroa et al. [37] studied sorption of oxytetracycline and tetracycline to N amontmorillonite. Their oxytetracycline sorption isotherm at pH 5.5 and 10 mmol N aCl
showed a plateau at about 440 − 480 cmol(+)/kg—their Fig. 7a labels that plateau as 44
cmol(+)/kg, but this seems to be in conflict with the reported Kd of 5500 L/mol(+) (see
their Fig. 3 at 10 mmol N aCl and pH 5.5). At 0.1 mmol/L tetracycline and with a clay
of CEC = 80 cmol(+)/kg, the Kd predicts sorption of 440 mmol tetracycline per kg clay,
exactly 10x the plateau pictured in their Fig. 7a. Another paper (Li et al., [38]) also commented that the sorption results of Figueroa et al. [37] seem low by a factor of about 10.
Furthermore, the same authors (Li et al., [38]) observed an anomalous result that up to 42
cmol(+)/kg of tetracycline could sorb to SWy-2 smectite without any significant change in
the desorbed inorganic cations in solution. Again, this phenomenon and the high pH they
observed, are indirect evidence of carbonate impurities in the SWy-2 smectite clay itself.
Therefore, the present study fixed the quantity of cation exchange sites in the “exchange”
module of Phreeqc at 0.42 moles of exchange sites per kg clay, and the study hypothesizes
that this value should work for most smectite clays in the environment.
26

Aristilde et al. [39] observed maximum sorption of oxytetracycline (OT C + ) by smectite
to be 44 cmol(+)/kg even at OTC solution concentrations approaching 1 mmol/L at pH 4
and in a background of 0.01 mol/L N aN O3 . On the basis of X-ray diffraction analysis and
molecular simulations, they argued that OT C + was segregated into only half the smectite
interlayers, with the other half of the interlayers filled with N a+ , a phenomenon known as
demixing.
This study calculated tetracycline/K + exchange in 4 different ionic strength situations
that also included several tetracycline concentrations and different pH values. A first situation was without ionic strength (no salt other than tetracycline HCl and sodium carbonate),
while the remaining three cases added an additional 0.01 mol/L, 0.1 mol/L, and 0.8 mol/L
as KCl.
The study adjusted the new thermodynamic parameters to fit Ding’s results [7]. To
do so, this study systematically examined several values of the tetracycline/K + exchange
parameters before acceptable results were reached. Then, after a number of attempts, the
research achieved a good fit for tetracycline/K + exchange.
Figure 2.3 shows the comparison between the Phreeqc predictions and Ding’s data [7] at
zero ionic strength for tetracycline sorption by K-smectite, and the result was fit very well.
Note that Essington et al. [40] modeled the sorption of chlortetracycline (CT C) sorption by
Na-smectite. They concluded that cation-exchange of CT C + for N a+ was the dominant
sorption process below pH 5, but that sorption above pH 5 was only slightly smaller in
magnitude and needed to invoke strong sorption of the zwitterionic (neutral CT C 0 ) form
of CTC. The present study suggests that interlayer sorption of the N a+ -CT C 0 complex is
a species they could have considered.
Figure 2.4 compares the Phreeqc predictions with Ding’s data [7] at 0.01 mol/L as KCl
27

for tetracycline sorption by K-smectite. The result was good, but the prediction of Phreeqc
was slightly higher than Ding’s data. Figure 2.5 shows the comparison between the Phreeqc
predictions and Ding’s data [7] at 0.1 mol/L as KCl ionic strength. In this case, tetracycline
sorption by K-smectite was predicted very well. Figure 2.6 shows the comparison between
Phreeqc prediction and Ding’s data [7] at 0.8 mol/L as KCl ionic strength for tetracycline
sorption by K-smectite. Again, the result was good, but the prediction of Phreeqc was
slightly lower than Ding’s data.
500
450
400

Cs (µmol/g)

350
300
250
200
150
100
50
0
0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

Cw (mmol/L)

Figure 2.3 Sorption of tetracycline to K-smectite at zero ionic strength.
Next, the study attempted to create tetracycline/Ca2+ exchange parameters that were
consistent with the well-fitting tetracycline/K + parameters. For example, this study fixed
the H4 T ec+ /K + and H4 T ec+ /Ca2+ parameters at the same values that were effective in
K-clay systems and only varied the exchange parameters for Ca2+ /tetracycline complexes
such as CaH2 T ec+ /Ca2+ .
Figure 2.7 shows the comparison between the Phreeqc predictions and Ding’s data [7]
at zero ionic strength for tetracycline sorption by Ca-smectite, and the model results fit
28

350
300

Cs (µmol/g)

250
200
150
100
50
0
0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

Cw (mmol/L)

Figure 2.4 Sorption of tetracycline to K-smectite at 0.01 mol/L ionic strength.
experimental data very well. Figure 2.8 compares the Phreeqc predictions with Ding’s data
[7] at 0.01 mol/L as CaCl2 for tetracycline sorption by Ca-smectite. Also, the agreement
between model and experiment was very good. While Figures 2.7 and 2.8 make it tempting
to believe that a good overall fit had been found using the modeling parameters compiled in
Table 1.1, the results at higher ionic strength show this to be an illusion. Thus, great care
must be advised when using goodness-of-fit as the main criterion for selecting thermodynamic
modeling parameters. Figure 2.9 shows the comparison between the Phreeqc predictions and
Ding’s data [7] at 0.1 mol/L as CaCl2 ionic strength, and this time, the Phreeqc prediction
of tetracycline sorption was considerably higher than Ding had observed. Figure 2.10 shows
the comparison between the Phreeqc prediction and Ding’s data [7] at 0.8 mol/L as CaCl2
ionic strength for tetracycline sorption by Ca-smectite. Again, the result did not fit because
the prediction of Phreeqc was considerably higher than Ding’s data.

29

250

Cs (µmol/g)

200

150

100

50

0
0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

Cw (mmol/L)

Figure 2.5 Sorption of tetracycline to K-smectite at 0.1 mol/L ionic strength.

2.3.2

Other Parameters that Could Fit Data

The good fits to the data in Figures 2.7 and 2.8 above seem to be for the “wrong reasons”,
namely that a too-large log k (7.0, Table 1.1) for the following reaction:

CaH2 (T ec)+ + X − = CaH2 (T ec)X

(2.15)

is compensating for a too-small log k (3.8, Table 1.1) for this reaction:

H4 (T ec)+ + X − = H4 (T ec)X

(2.16)

relative to Ca2+ . The very poor fits shown in Figures 2.9 and 2.10 make it clear that
the log k for Eq. 2.15 was far too large, because the model predicted sorption that was far
too strong (compared to experimental data) at high ionic strength.
Two questions then present themselves:
1) If log k = 7.0 is much too large for Eq. 2.15, then what is a better value for modeling
the data?
30

90
80

Cs (µmol/g)

70
60
50
40
30

○ Phreeqc

20

◊ Ding's

data

10
0
0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

3.50E-01

Cw (mmol/L)

Figure 2.6 Sorption of tetracycline to K-smectite at 0.8 mol/L ionic strength.
500
450
400

Cs (µmol/g)

350
300
250
200
150
100
50
0
0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

1.80E-01

Cw (mmol/L)

Figure 2.7 Sorption of tetracycline to Ca-smectite at zero ionic strength.
2) If log k = 3.8 is too small for Eq. 2.16, relative to Ca2+ , then what is a better value
for modeling the data?
At this point, it becomes very clear that Ding [7] showed excellent foresight in measuring
tetracycline sorption across broad ranges of pH (Figure 2.2) and ionic strength. Figure 1.3
shows that the dominant cationic form of tetracycline in the pH region 6 − 8 is CaH2 (T ec)+ ,
and Ding performed dozens of experiments at various ionic strengths in that pH range. These
data at relatively high pH, and especially when ionic strength is also high, should be where
31

450
400

Cs (µmol/g)

350
300
250
200
150
100
50
0
0.00E+002.00E-024.00E-026.00E-028.00E-021.00E-011.20E-011.40E-011.60E-011.80E-012.00E-01
Cw (mmol/L)

Figure 2.8 Sorption of tetracycline to Ca-smectite at 0.01 mol/L ionic strength.
Eq. 2.15 would be expected to be the dominant competitor in cation-exchange reactions
with Ca2+ .
Conversely, Ding [7] also gathered dozens of datapoints at pH values below 5, often
when the ionic strength was very low. These are the conditions under which H4 (T ec)+ and
therefore Eq. 2.16 ought to be the dominant competitor in cation-exchange reactions with
Ca2+ . Thus, Ding’s datasets provide optimism that parameters for Equations 2.15 and 2.16
can both be refined and also be consistent with the K-clay results.
Following this logic, the study searched for a log k value that allows Eq. 2.16 to reproduce
the tetracycline-calcium competition for exchange sites fairly well at low ionic strength and
low pH. The data point at farthest right in Figure 2.11 was predicted with log k = 5.5 and
corresponds (experimentally) to pH 4 to 5 and very low ionic strength. Thus, a log k of
perhaps 6 might be a better estimate for the thermodynamics of Eq. 2.16. However, recall
that in the case of K + /H4 (T ec)+ exchange, a log k = 3.8 for Eq. 2.16 worked very well.
To find an approximate value for the thermodynamics of Eq. 2.15, we searched for good
fits to data at high pH and high ionic strength. One example below with log k = 3.0 for Eq.

32

450
400

Cs (µmol/g)

350
300
250
200
150
100
50
0
0.00E+00

5.00E-02

1.00E-01
1.50E-01
Cw (mmol/L)

2.00E-01

2.50E-01

Figure 2.9 Sorption of tetracycline to Ca-smectite at 0.1 mol/L ionic strength.
450
400

Phreeqc

Cs (µmol/g)

350
300
250
200
150

Ding's data

100
50
0
0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

Cw (mmol/L)

Figure 2.10 Sorption of tetracycline to Ca-smectite at 0.8 mol/L ionic strength.
2.15 shows good fits (especially for the higher-pH points at lower tetracycline concentrations)
when ionic strength was either 0.1 mol/L (Figure 2.12) or 0.8 mol/L (Figure 2.13).

33

500
450
400

Cs (µmol/g)

350
300
250
200
150
100
50
0
0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

1.80E-01

Cw (mmol/L)

Figure 2.11 Modeled versus experimental [7] Ca2+ /H4 (T ec)+ exchange when log k = 5.5 for
Eq. (2.16) and log k = 3.0 for Eq. (2.15) at zero ionic strength.

2.4

Reconciling for Tetracycline Exchange with Both
K- and Ca-Clay Minerals

The Phreeqc approach was able to model K + /H4 (T ec)+ exchange fairly well when logk =
3.8 for Eq. 2.16, while the Ca2+ /H4 (T ec)+ exchange appeared to demand logk = 6.0 for
the same equation in order to achieve a good fit. This is a significant problem that needs to
be reconciled. If that could be done, then it seems plausible that the cation-exchange terms
for K- and Ca-complexes could also be fit, and an overall set of self-consistent parameters
could be achieved for general K-Ca-tetracycline-clay systems.

2.5

Path Forward for Future Research

The current research problem is that it seems impossible to simultaneously fit the cation
exchange of tetracycline with both K + and Ca2+ . In particular, if tetracycline exchange
with K + was modeled well, then tetracycline exchange against Ca2+ was too weak, espe-

34

300

250

Cs (µmol/g)

200

150

100

50

0
0

0.05

0.1

0.15

0.2

0.25

0.3

Cw (mmol/L)

Figure 2.12 Modeled versus experimental [7] Ca2+ /H4 (T ec)+ exchange when log k = 5.5 for
Eq. (2.16) and log k = 3.0 for Eq. (2.15) at 0.1 mol/L ionic strength.
cially at high ionic strengths. In terms of Gibbs free energy [31], it seems that

G for

tetracycline/Ca2+ exchange needs to be more negative. Until now, the study has assumed
that the literature values for K + /Ca2+ exchange that are embodied in Phreeqc [6] were
adequate. Indeed, they do seem plausible (Figure 2.1) . Equation 2.8 shows that

G of

K- Ca-exchange is about -1.6 kJ/mol. Figure 2.14a shows this relationship graphically. Reviews of the literature [32], show that the previously estimated values for K- Ca-exchange
range from +2 to -14 kJ/mol. The “best” value from this range should be the subject of a
thorough literature review, but the “best” value seems likely to be more negative than -1.6
kJ/mol.
Suppose this “best” value is -4.6 kJ/mol. Then, K + /Ca2+ exchange would look like
Figure 2.14b. Suppose also that one had created a perfect parameter for K/tetracycline
exchange of

G for H4 (T ec)+ /K + that was -17.7 kJ/mol (Figure 2.14). Note that if the

study desires to simultaneously:
a) Increase the magnitude of

G for K + /Ca2+ exchange from -1.6 kJ/mol (Figure

35

160
140

Cs (µmol/g)

120
100
80
60
40
20
0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Cw (mmol/L)

Figure 2.13 Modeled versus experimental [7] Ca2+ /H4 (T ec)+ exchange when log k = 5.5 for
Eq. (2.16) and log k = 3.0 for Eq. (2.15) at 0.1 mol/L ionic strength.
2.14a) to -4.6 kJ/mol (Figure 2.14b) to reflect the “best” value from the literature [32].
b) Maintain the same value of

G for H4 (T ec)+ /K + , which is -17.7 kJ/mol [Both

Figures 2.14a and 2.14b].
Then, observe that the value of

G for H4(T ec)+/Ca2+ has increased from -19.3 kJ/mol

(Figure2.14a) to -22.3 kJ/mol (Figure 2.14b). Therefore, making the
exchange more negative and more favorable, for a given value of
has the effect of also making the value of
favorable. This change in the value of

G for K + /Ca2+

G for H4 (T ec)+ /K + ,

G for H4 (T ec)+ /Ca2+ more negative and more
G for H4 (T ec)+ /Ca2+ is in the right direction to

enable tetracycline to compete more effectively against Ca2+ . The study hypothesizes that
such a change will allow the cation exchange of tetracycline with both K + and Ca2+ to be
fit simultaneously.
An alternative strategy to looking through the literature for a “best” value of
K + /Ca2+ exchange would be to ask what value of

G for

G for H4 (T ec)+ /Ca2+ might be re-

quired to fit the data. In this case, a tentative answer is provided above, when the study
suggested that logk near 6 might be required to make Eq. 2.16 work for Ca-systems. This
36

logk = 6 corresponds to

G = -34.5 kJ/mol for Eq. 2.16 in order to enable accurate

modeling of H4 (T ec)+ /Ca+2
In terms of Figure 2.14b, if

G for H4 (T ec)+ (Eq. 2.11) were -34.5 kJ/mol and

G

for H4 (T ec)+ /K + were still fixed at -17.7 kJ/mol (Figure 2.14a and b), then the overall
energy-level diagram would be constrained to look like Figure 2.15.
Essington et al. [40] measured and attempted to model chlortetracycline (CT C) sorption
by N a-smectite. They concluded that cation-exchange was the dominant process below pH
5 and their fits to experiment resulted in the following reactions:

+ + X − = XH
H(aq)

logk = −2.2

+ + XN a = XH + N a+
H(aq)
(aq)

logk = −4.6

+ = XCT C + H +
XH + CT C(aq)
(aq)

logk = +8.75

(2.17)

(2.18)

(2.19)

Adding Equations 2.17 and 2.19 yields

+ = XCT C
X − + CT C(aq)

logk = +6.55

(2.20)

and both the form of Eq. 2.20 and the log k of 6.55 correspond very well to the present
study’s suggestion of log k = 6 for Eq. 2.16 above.
Alternatively, adding Equations 2.18 and 2.19 yields

+ = XCT C + N a+
XN a + CT C(aq)
(aq)

37

logk = +4.15

(2.21)

which relates the exchange of CT C + to that of N a+ , and provides an estimate for log
K following the convention of Appelo and Postma [6].
For future work, this study hypothesizes that the tetracycline/K + /Ca2+ exchange parameters shown in Figure 2.15b, with some refinement, should allow the approximately selfconsistent modeling of tetracycline cation exchange reactions with a single set of parameters.
This would enable complete speciation of tetracycline in complex mixtures of multiple inorganic cations and clay minerals. Furthermore, adding in the bacterial distribution method
from Chapter 1 would allow modeling of bacterial uptake and the induction of antibiotic
resistance in these complex mixtures.

38

Figure 2.14 Free energy diagram for a subset of cation exchange reactions in Phreeqc. Current!
Phreeqc parameters (a) are shown on the left, while a hypothetical future parameters set
(b) is shown on the right.

39

!

Figure 2.15 Free energy diagram for a subset of cation exchange reactions in Phreeqc. Current
Phreeqc parameters (a) are shown on the left, while a hypothetical future parameters set
(b) is shown on the right.

40

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41

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