Models of partitioning, uptake, and toxicity of neutral organic

chemicals in fish

A Thesis Submitted to the Committee on Graduate Studies in Partial Fulfillment of the Requirements for the Degree of Master of Science in the Faculty of Arts and Science

TRENT UNIVERSITY

Peterborough, Ontario, Canada

(c) Copyright by Alena Kathryn Davidson Celsie 2014

Environmental & Life Sciences M. Sc. Graduate Program

January 2015

ii

Abstract

Models of partitioning, uptake, and toxicity of neutral organic chemicals in fish

Alena Kathryn Davidson Celsie

A novel dynamic fugacity model is developed that simulates the uptake of chemicals in fish by

respiration as applies in aquatic toxicity tests. A physiologically based toxicokinetic model was

developed which calculates the time-course of chemical distribution in four tissue

compartments in fish, including metabolic biotransformation in the liver. Toxic endpoints are

defined by fugacity reaching a 50% mortality value. The model is tested against empirical data

for the uptake of pentachloroethane in rainbow trout and from naphthalene and

trichlorobenzene in fathead minnows. The model was able to predict bioconcentration and

toxicity within a factor of 2 of empirical data. The sensitivity to partition coefficients of

computed whole-body concentration was also investigated. In addition to this model

development three methods for predicting partition coefficients were evaluated: lipid-fraction,

COSMOtherm estimation, and using Abraham parameters. The lipid fraction method produced

accurate tissue-water partitioning values consistently for all tissues tested and is recommended

for estimating these values. Results also suggest that quantum chemical methods hold promise

for predicting the aquatic toxicity of chemicals based only on molecular structure.

Keywords: Partition coefficient, Octanol-water, lipid-water, tissue-water, COSMO-RS,

COSMOtherm, fish tissue, fugacity, fish model, toxicokinetics, Physiology-based toxicokinetic

(PBTK) model

iii

Acknowledgements

I would like to acknowledge my supervisors Don Mackay and Mark Parnis for guiding me in this

project for the past two years. You have both helped me from start to finish and taught me a

great deal along the way, from environmental chemistry to quantum chemistry. I am lucky to

have been able to work within such a broad spectrum of the subject of chemistry. Both Don and

Mark are highly knowledgeable experts in their respective fields and I could not have asked for

anyone more qualified to have guided me through this project. Thank you both for your time,

patience, and continued support over the last couple of years.

iv

Table of Contents

Abstract ........................................................................................................................................... ii

Acknowledgements ........................................................................................................................ iii

List of Figures ................................................................................................................................. vi

List of Tables .................................................................................................................................. vii

List of Abbreviations and Symbols ................................................................................................ viii

Glossary ...........................................................................................................................................ix

1.0 Introduction ............................................................................................................................... 1

2.0 Literature Review ...................................................................................................................... 4

2.1 Toxicokinetic Models ............................................................................................................ 4

2.2 Recent advances in toxicokinetic models ............................................................................. 5

2.3 Approaches for predicting environmental constants such as partition coefficients ............ 7

2.3.1 Partition coefficients: History of their development ..................................................... 7

2.3.2 Estimating partition coefficients using predictive methods .......................................... 9

2.3.3 Partition coefficient applications, advantages, and limitations .................................. 11

2.3.4 Lipid fraction method for predicting KTW ..................................................................... 14

2.3.5 Abraham’s Linear Free Energy Relationship (LFER) method ....................................... 16

2.3.6 COSMO-RS (COSMOtherm)........................................................................................... 19

3.0 Model development in this study ........................................................................................... 31

3.1 General Model Structure .................................................................................................... 32

3.2 Onset of toxicity ................................................................................................................... 36

3.3 Toxic endpoints .................................................................................................................. 37

3.4 Mathematical formulation of the model ............................................................................ 40

3.4.1 Mass balance equations and input parameters .......................................................... 40

3.4.2 Blood-tissue transport rates. ....................................................................................... 44

3.4.3 Compartment residence and characteristic times. ...................................................... 44

3.4.4 Steady-State Conditions................................................................................................ 45

3.5 Sensitivity Analysis ............................................................................................................... 46

4.0 Predicting partition constants in this study ........................................................................... 47

4.1 Lipid fraction theory method ............................................................................................... 47

4.2 Abraham parameters LFER method .................................................................................... 48

4.3 COSMO-RS method ............................................................................................................. 49

v

4.3.1 Predicting Abraham parameters using COSMOtherm ................................................. 50

4.4 Error Estimates ................................................................................................................... 52

5.0 Fish model simulation ............................................................................................................ 53

5.1 Results of fish model ........................................................................................................... 54

5.1.1 Model simulation sequence ......................................................................................... 54

5.1.2 Simulation of aquatic toxicity tests applied to a Fathead Minnow ............................ 59

5.1.3 Simulation of an aquatic bioconcentration test for PCE applied to a Trout ................. 68

5.2 Discussion of performance .................................................................................................. 73

5.3 Sensitivity of partition coefficients to model results ........................................................... 79

6.0 Tissue-water partition coefficient prediction method comparison ...................................... 83

6.1 KOW as a predictor ................................................................................................................ 84

6.2 Results of Lipid fraction method .......................................................................................... 84

6.3 Results of Goss 2013 modified Abraham approach ............................................................. 86

6.4 Results of COSMOtherm ‘solvent-surrogate’ approach ...................................................... 87

6.5 Discussion and error analysis .............................................................................................. 90

6.5.1 Values within a factor of 2 of experimental data ......................................................... 91

6.4.2 Discussion of KTW predictive methods ......................................................................... 93

7.0 Summary and Conclusion ........................................................................................................ 97

References .................................................................................................................................... 99

Appendix 1: Predicted vs. experimental KTW graphs .................................................................... A1

Appendix 2: Graphs for each tissue showing lowest COSMOtherm RMSE ................................. A2

vi

List of Figures:

Figure Page #

Figure 1: Chemical space diagram showing relationship between solubilities and partition coefficients in the octanol, air, and water phases

12

Figure 2: Molecular surface divided into segments during COSMOtherm calculation 24

Figure 3: σ-profile of methanol (left) generated from segmented molecule (right) 25

Figure 4: A visual description of the contact area parameter, aeff 26

Figure 5a: A visual representation of the theoretical fish divided into compartments representing different biotissue where the arrows represent the pathways in the organism that a narcotic agent could take, as assumed in this model. Figure 5b shows these pathways in a mathematical sense, where each compartment has a given fugacity (fx) and transport coefficient (Dx)

33

Figure 6: Concentration and corresponding probability of death graphical output from model. For each toxic endpoint described above one set of graphs are produced.

57

Figure 7: Summary sheet of input parameters and important fugacity-related values, shown as displayed in the model

58

Figure 8: Graphs taken from de Maagd et al. (1997) that have been regressed by these authors to determine the approximate time at which LBB occurred. A) NAPH regressed at LBB=8.1; t is approximately 3 hours. B) TCBz regressed at LBB= 14.0; t is approximately 17 hours

62

Figure 9: Graphs produced from CEFIC model output using NAPH as a chemical and a fathead minnow as a test fish. Model predicts that LBB is 8 mol/m3, and occurs after 6.4 hours

64-65

Figure 10: Graphs produced from CEFIC model output using trichlorobenzene as a chemical and a fathead minnow as a test fish. Model predicts that LBB is 14 mol/ m3 which occurs after 6.5 hours.

66-67

Figure 11: A 48 hour time-course for pentachloroethane concentration in 1000 g trout in this graph originally reported by Nichols et al. (1990). Black dots represent values reported from the toxicological study, whereas the smooth line represents Nichols predictive model for the toxicokinetics in a trout.

70

Figure: 12: A 48 hour time-course for pentachloroethane concentration in the blood of a 1000 g trout. Results from Nichols (1990) empirical study are overlaid on top of model results from this study for comparison

71

Figure 13: This is a plot of the whole body concentration vs. time for the 3 cases. During the first 3 hours the change in KOW (represented in this graph as ‘Z’) has little effect. After 5 hours the Z/2 line begins to deviate and becomes significantly lower. At 10 h the lines are well separated with the 3 cases being 7.9, 11.0 and 13.4 mol/ m3 for Z/2, Z and Z*2 respectively.

80

Figure 14: Graphical display of sensitivity of predicted concentrations over time when KOW has been doubled

82

vii

List of Tables:

Table Page #

Table 1: Predictive methods used for estimating environmental constants 10

Table 2: Parameters used by COSMOtherm 22

Table 3: Fugacity-based properties employed in this model 35

Table 4: Input parameters and symbols used in the model to describe test conditions 54

Table 5: Input parameters and symbols used in the model to describe organism properties 54

Table 6: Input parameters and symbols used in the model to describe chemical properties 55

Table 7: Input parameters relating to chemical properties used in model for FHM trial 59

Table 8: Lipid content fractions reported for compartments in a fathead minnow from Krishnan & Peyret (2009)

60

Table 9: Input parameters relating to organism properties used in model for FHM trial 61

Table 10: Results for fathead minnow from De Maagd and from the model using naphthalene as a test chemical

62

Table 11: Results for fathead minnow from the model using trichlorobenzene as a test chemical

62

Table 12: Input parameters relating to organism properties used in this model for trout trial. 69

Table 13: Input parameters relating to chemical properties used in model for trout trial

70

Table 14: Chemical concentration in blood reported by Nichols et al.10 and model predicted values at various times

72

Table 15: Average concentration ratios reported by Nichols et al.10 and concentration ratios predicted by this model.

72

Table 16: Predicted concentrations of NAPH at 50% lethality when KOW changes by a factor of

2

79

Table 17: Comparison of equilibrium concentrations for each of 3 cases (KOW, KOW/2, KOW*2) 81

Table 18: Experimental KTW values used in this study 83

Table 19: Root mean square error (RMSE) of experimental KOW values in comparison to

experimental KTW values. Partition coefficients for six chemicals were used to calculate each

RMSE value. These chemicals included 1,2-dichloroethane, 1,1,2-trichloroethane, 1,1,2,2-tetrachloroethane, pentachloroethane, and hexachloroethane.

84

Table 20: Bertelsen et al. (1998) partitioning data for different chemicals and fish tissues, with tissue lipid content and calculated tissue content reported

85

Table 21: RMSE values of predicted and experimental KTW values for various tissues in Trout.

These were calculated using the Lipid Fraction method

86

Table 22: RMSE values for predicted KTW values using Goss-Abraham method 86

Table 23: RMSE values for predicted vs experimental KTW values, where octanol-phase has been replaced (the water phase is pure water, the system has 2 phases)

87-88

Table 24: RMSE values for predicted vs experimental KTW values, where water-phase has been replaced (the octanol phase is pure octanol, the system has 2 phases)

88-89

Table 25: Adipose Tissue – RMSE values less than 0.3 log units 90

Table 26: Liver Tissue – RMSE values less than 0.3 log units 91

Table 27: Muscle Tissue – RMSE values less than 0.3 log units 91

Table 28: Blood Tissue – RMSE values less than 0.3 log units 91

Table 28: Kidney Tissue – RMSE values less than 0.3 log units 91

Table 29: Skin Tissue – RMSE values less than 0.3 log units 92

Table 30 RMSE results of each KTW predictive method including KOW, lipid fraction KTW, lipid

fraction KTW' Goss-Abraham predicted KTW, Goss-Abraham with COSMO predicted Abraham

parameters, and the closest predicted COSMOtherm mixture KTW value for each tissue.

93

viii

List of Abbreviations and Symbols:

LBB: Lethal Body Burden (mol •m3)

CBR: Critical Body Residue (mol •m3)

f: Fugacity (Pa)

Z: Z-value (mol•m-3•Pa-1)

γ: activity coefficient:

R: Molar gas constant (8.3145101 J•K-1 mol-1)

k: Boltzmann constant (1.380 658 x 10-23 J•K-1)

Å: Angstrom (1 Å = 10-10 m)

Greek alphabet letters used in this theses:

Alpha α Pi π

Beta β Sigma σ

Gamma γ Tau τ

Delta Δ Phi φ

Lambda λ Psi Ψ

Mu µ Omega ω

Nu ν

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Glossary:

Fugacity: A unit of pressure (Pa) which is analogous to partial pressure for ideal gases

Z-Value: A fugacity capacity (mol/m3∙Pa)

D-value: A rate constant which when multiplied by a fugacity value is equal to the rate

Bioaccumulation: The uptake of a chemical into an organism

Bioconcentration: The uptake of a chemical from respired phases, such as in water

Partitioning: The distribution of a chemical between two distinct phases

Partition coefficient: The equilibrium distribution of a chemical between two distinct phases,

represented by a constant value and quantified by the ratio of concentrations in each phase

Biomagnification: The ratio of the chemical concentration in a predator to that of its prey/diet

Solvent: The phase system in which the solute resides

Solubility: The extent to which a chemical may dissolve in a solvent. May be expressed as mass-

per-volume, such as g/m3 or mg/L

Chemical activity: The ratio of a chemical’s concentration to its solubility in a given phase

Phase: Any specified media

Gibbs energy: Represents the ability of a system to do work

Probability density: The likelihood that a particle will occupy a particular position or have a

particular momentum.

Quantized: Coming in discrete values

1

1.0 Introduction

The distribution and fate of chemicals in the environment is of importance due to their potential

and that of their decomposition products to bioaccumulate in organisms1. Bioaccumulation and

biomagnification of a given chemical can cause toxic effects to an organism or to an organism

further up the food chain. Environmental distribution, exposure, fate, and ultimately adverse

effects are governed largely by the chemical’s partitioning properties, which looks at the

distribution of a solute between phases. A considerable amount of research has been done to

investigate partition coefficients over a range of temperatures for a wide range of media such as

water, air, soil, sediments, and biotissue for a variety of different organisms. These partition

coefficients have been used to predict the fate of chemicals in both environmental and

toxicokinetic contexts. One partition coefficient is of particular importance because it has been

correlated to bioaccumulation in organisms, namely the octanol-water partition coefficient

(KOW). Predictions can be made using computational models which can be applied to specific

environments in order to estimate the concentration of chemicals in lakes, soil, organisms, or

other specified media. Physiologically-based toxicokinetic (PBTK) modeling is an example of such

a predictive model used to predict the biouptake and toxicity of a chemical within an organism2.

Fish are often used in simple PBTK-type models because they exist in the water, where

pollutants are likely to end up, they are an important organism to consider in biomagnification

and bioaccumulation factors, they are simple, and because the underlying theory of a simple

model may eventually be applied to a PBTK-type model for modeling the fate of chemicals in

humans.

Physiologically-based toxicokinetic models may treat the organism as a set of 'compartments' to

which chemicals will enter and exit. The concentration of a chemical that bioaccumulates in the

organism can be correlated to the chemical's KOW value, but alternatively it may be correlated to

2

other partitioning values, such as the more tissue-specific lipid-water partition coefficients

which have been derived in other studies3,4. Different tissue types in fish have displayed

different partitioning behaviour5,6 which implies that the partitioning behaviour within the fish

can be modeled more accurately if these tissue types are assigned their own specific properties,

such as lipid content, partitioning constants, volume, and blood flow. By assigning these

properties we introduce multiple compartments into a model. Multiple compartments each

mimicking different tissue types and their partitioning behaviour could be incorporated into a

PBTK-type model and this multicompartmental model may predict biological partitioning more

accurately than a model that treats the entire organism as one compartment. This will allow the

prediction of the distribution of a chemical within an organism, which is an especially important

application in the pharmaceutical industry and has also been shown to increase predictive

accuracy in whole-body concentration results13.

Multicompartmental PBTK-type models are not a new idea; there have been several

publications on this area of research2,7,8. However there has not been a multicompartmental

PBTK-type model developed for fish based on the fugacity concept; although fugacity-based

models have been developed2,9. Fugacity (f) is a unit of pressure (Pa) which is analogous to

partial pressure for ideal gases1. It has been referred to as an 'escaping tendency'.

The concentration-fugacity relationship is:

𝑓𝑖 =𝐶𝑖

𝑍𝑖 (1)

Where C is concentration (mol/m3) and Z is a fugacity capacity (mol/m3∙Pa). This relationship

demonstrates that fugacity can be converted into a concentration and vice versa. It is also useful

to use fugacity because at equilibrium the fugacity of two phases in contact with each other will

be equal. It should therefore be possible to develop a PBTK-type model containing multiple

3

compartments where the concentration of a chemical in each compartment is governed by both

the partitioning constants and fugacity7. The concentrations can be calculated over time by

integrating a differential equation which calculates the change in fugacity in each

compartment1. The fugacities will migrate towards a steady-state, and death occurs when a

whole-body ‘critical concentration’ or ‘critical fugacity’ is reached inside the fish. Fugacity is

present in all compartments, therefore a model could be developed in which fugacity is the

driving force for all advective and diffusive transport, and for all degradation reactions. Using a

fugacity approach to develop an environmental fate model will also be beneficial for testing

consistency with any other newly emerging similar models.

Having multiple tissue types represented implies that KOW alone might not accurately describe

partitioning behaviour for each compartment. Tissue-water partition coefficients (KTW) have

been investigated for various tissue types in fish5,6,10. The findings of the fugacity-based PBTK

multicompartmental model may be improved by using tissue-specific partition coefficients as

opposed to using KOW alone. There are various published methods of calculating tissue-water

partition coefficient (KTW) values such as by using lipid fractions5 or using linear free energy

relationships (LFERs) such as the method presented by Goss et al.6 and others. In this work a

novel approach for predicting partitioning using the computational software COSMOtherm was

investigated. The objective here was to search for possible mixtures (“solvent surrogates”)

which behave more like a given tissue than the traditional octanol-water system does. This

approach was compared to a lipid fraction approach and also to the LFER approach using

Abraham parameters developed from experimental data by Goss et al.6.

4

2.0 Literature Review

2.1 Toxicokinetic Models

The large and increasing number of organic chemicals of commerce require that effort be

devoted to assessing their toxicity to a range of organisms from algae to humans. Often the

preferred test organisms are fish and invertebrates because exposures are most accurately and

economically achieved by respiration from a water phase. It is relatively straightforward to

determine the concentration in the water that causes mortality expressed as a LC50 using

standard test methods such as OECD 20311, however interpretation of toxic effects and chemical

potency may be quite difficult when measurement is based on external chemical concentrations

alone. While it is generally accepted that the concentration internal to the organisms is strongly

influenced by water-to-organism partitioning from the external concentration, it is likely that

the internal concentration at a vulnerable target site within the organism best expresses the

toxic potency. The whole body concentration or Critical Body Residue (CBR) may or may not be

a reliable indicator of the concentration at the target site. Accordingly, increasing effort is being

devoted to developing toxicokinetic models that describe the uptake and disposition of the

chemical in the organism being used in the test. Indeed, in drug design and mammalian

toxicology such models are standard tools for deducing Administration, Distribution,

Metabolism and Excretion (ADME). Krishnan and Peyret12 have reviewed the literature on

Physiologically Based ToxicoKinetic (PBTK) models applied in ecotoxicology to several types of

organisms, including fish. Some of their suggested values have been used as a basis for input

values in this study (see Table 8). Stadnicka et al.13 have shown convincingly that PBTK models

outperform simple single compartment or whole body models. Additionally, such models

provide a plausible basis for species to species and chemical to chemical extrapolation since

5

they include descriptions of the fundamental transport, partitioning and reaction processes that

comprise toxicokinetic processes.

2.2 Recent advances in toxicokinetic models

The complex task of simulating toxicity can be treated as two sequential events. First is the

toxicokinetics that quantifies the time dependence of where and in what quantities the chemical

becomes distributed throughout the organism. Second is an assessment of the toxicodynamics,

i.e. the interaction of the chemical with tissues resulting in the onset of adverse effects14. These

types of models have been applied to fish and other organisms. Some example of PBTK models

have been developed in studies by Nichols and colleagues10,15,16,17, Escher18,19, Hermens and

colleagues20 Landrum and colleagues21, and Hendricks and colleagues22,23.

Recent advances in predicting biotissue partitioning constants

Wania & Breivik24 have modified a level III fugacity-based multimedia fate model to input more

accurate partition coefficients using a polyparameter linear free energy (PP-LFER) approach. In

their model partitioning was characterized by five linear solvation energy parameters and

results were compared to a single parameter linear free energy (SP-LFER) approach. Each

method describes partition coefficients differently and the results were quite varied depending

on the partition coefficient value used. Studies have investigated methods for calculating tissue-

plasma partition coefficients including Schmitt25, Rodgers & Rowland26, and Poulin & Theil27. On

average these methods have been able to predict KTissue-Plasma values within a factor of 3 of

experimental values. Goss et al.6 have modified an Abraham parameter approach as a method

of calculated KTW values for various tissues within organisms and successfully applied this

method to bovine tissue.

6

Models which have utilized the fugacity approach

Fugacity is a very good descriptor of advective and diffusive processes and it can serve as an

equilibrium criterion, all which makes fugacity a good approach for predicting fate of chemicals

in the environment2,28. Fugacity-based environmental fate models have been extensively

reviewed by Wania in a 1998 publication28 . Although published quite some time ago the

fugacity concept has been utilized since before this time1 and Wania’s paper is a good resource

for finding published fugacity models that have been applied in various environmental contexts.

Some examples include Mackay & Paterson1, Clark et al.29, Gobas30, Wania & Mackay31, and

Gobas et al.32.Wania & Mclachlan9 have developed a multicompartment environmental fate

model using the fugacity approach and applied this model to predict the deposition and uptake

of semivolatile organic compounds in forests.

First objective and hypothesis of this study

The first objective of this study is to develop a PBTK-type toxicokinetic fugacity-based

multicompartment model and successfully apply it to model the bioconcentration and toxicity in

a fish. This will be done using fugacity-based relationships and simulations will be done by using

optimized input parameters from relevant literature and results will be compared to empirical

data. It is hypothesized that the model will be able to successfully model the empirical data

within a factor of two using reasonable input parameters.

7

2.3 Approaches for predicting environmental constants such as partition coefficients

2.3.1 Partition coefficients: History of their development

The earliest documented partition coefficient can be regarded as Henry's Law constant,

developed in 1802 by William Henry in order to describe the relative concentrations of gases

(both organic and inorganic) between water and air1. He formulated the relationship:

𝑃𝑖 = 𝐻 ∙ 𝐶𝑤 (1)

Where Pi is the partial pressure of the gas in air (Pa), H is Henry's Law constant (Pa·m3/mol), and

Cw is the concentration of the gas in the water phase (mol/m3).

Later, the ideal gas law was developed to define the properties of gases, and it states:

𝑃𝑖𝑉 = 𝑛𝑅𝑇 (2)

Where Pi is the partial pressure of the gas (Pa), V is it volume (m3), n represents number of

moles, R is the ideal gas constant (8.314 Pa∙m3/mol∙K), and T is the temperature (K). This

equation can be rearranged in order to predict the concentration in air:

𝑛

𝑉= 𝐶𝐴 =

𝑃𝑖

𝑅𝑇 (3)

Combining the Ideal Gas Law and Henry's law, the air-water partition coefficient can be

calculated for any solute:

𝐾𝑎𝑤 =𝐶𝐴

𝐶𝑤=

(𝑃𝑖/𝑅𝑇)

(𝑃𝑖/𝐻)= 𝐻/𝑅𝑇 (4)

Later partitioning was measured between different solvents. In 1891 Walther Nernst

investigated the partitioning of benzoic acid between water and benzene. He proposed the

‘distribution law’ which states that when a non-dissociating species partitions between two

immiscible solvents at high dilution the ratio of the concentrations in each solvent will be

constant. Nernst termed this constant the 'distribution coefficient', and it is now referred to as a

'partition coefficient'.

8

Partition coefficients have become widely used to describe the concentration ratio between

several different media including air, water, sediment, soil, sludge, biotissue, and others. Once it

had been established that solutes will partition predictably between solid, liquid, and gaseous

phases this established a link between partitioning values and predicting relative concentrations

of chemicals in each of the two phases that it is exposed to. Partition coefficients are therefore

specific to a solute and the two-phase solvent mixture.

Overton33 and Meyer34 researched anaesthetics and established mechanisms of what is termed

'baseline reversible narcosis'. Narcosis occurs when a narcotic agent builds up in an organism to

the point that it loses consciousness. In their studies Overton and Meyer showed that narcosis

occurs at a fairly constant chemical concentration inside an organism and this provided a

foundation for correlating partition coefficients to toxicity within organisms. In their studies, it

was observed that relative narcotic activities of drugs often paralleled oil/water partition

coefficient values. Independently these studies both discovered a strong correlation between

the polarity of a compound and its potency as an anaesthetic. This polarity was expressed as a

value called the oil/gas partition coefficient, since all experiments were performed using olive

oil. A higher value corresponds to a higher concentration of the anaesthetic remaining in the

olive oil, which in turn corresponds to occurrence of anaesthesia. Meyer and Overton were the

first scientists to suggest that hydrophobicity was the main driving force for chemicals binding to

cell membranes.

Octanol was identified as a potential solvent which could better mimic biomembranes because

of its structural similarity of having a polar `head` and nonpolar `tail`35. Hansch and Leo compiled

an extensive database of measured octanol-water partition coefficients and octanol became the

standard descriptor of hydrophobicity36. KOW is now used to estimate the concentration or the

toxicity that a chemical will incur in organisms and in the environment using predictive models.

9

The consequence of this is that methods for calculating KOW must be researched so that it can be

incorporated into predictive models for chemicals that do not have experimental data available.

2.3.2 Estimating partition coefficients using predictive methods

Many different derivations have been applied and methods have been developed in order to

accurately predict partition coefficients since the early 1900s37. Predictive methods have

evolved from a few different, relatively simple calculations in the 1950s to much more intensive

calculations, such as computational methods, which may take hours to complete. Modern

predictive methods for calculation can be grouped into three main approaches: the fragment

approach, the atomic approach, and the whole molecule approach.

The fragment approach is based on the concept that biological activity is additive in nature, and

so a database can be created which contains calculated values associated with molecular

fragments which contribute to chemical reactivity and partitioning38. These fragments are

divided into defined pieces which are often functional groups. Using these fragment values the

molecular property is 'built' out of the contributions from the fragmented pieces by inputting

the values for these pieces into an equation. The main advantage of this approach is that each

fragment piece captures significant electronic interactions occurring within that fragment39.

The atom-based approach considers the molecular property to be due to linear contributions

from the properties of single constituent atoms. Additional parameters must be used for atom-

based approaches, such as for conjugation, proximity, unsaturation, etc. in order to calculate Kow

or other partition coefficients accurately. Atomic contributions are advantageous in that there is

less ambiguity concerning which fragmental value to use. For this method to be effective,

10

however, all different atomic types must be included in the database in order to take the

additional parameters into account.

Whole-molecule approaches are based on using the properties of an entire molecule, such as

charge densities, molecular surface area, volume and free energy40.These methods are

advantageous in that missing/inaccurate fragment values are avoided. Computational methods

are used to employ this approach due to the complexity of the calculations. Whole-molecule

approaches can be divided into two classes: methods that employ 3D-structure representation,

and methods that use topological descriptors. Methods which involve empirical approaches or

3D structure representations are based on free energy calculations. Free energy (G) is a

thermodynamics term which refers to the amount of useful work that the energy produced by a

system could perform. Log P (i.e.LogKow) is proportional to the energy transfer that occurs

between octanol and water:

−2.303𝑅𝑇𝑙𝑜𝑔𝑃 = ∆𝐺𝑜𝑐𝑡 − ∆𝐺𝑤 = ∆𝐺𝑜𝑤 (5)

= ∆𝐺𝑜𝑤𝑒𝑙 + ∆𝐺𝑜𝑤

𝑛𝑒𝑙 (6)

In the equations above Gw and Goct are the solvation-free energies of the solute in water and

octanol, respectively. Gelow and Gnel

ow correspond to electrostatic and nonpolar terms of solute-

solvent interactions.

Some computational programs that can be used to estimate partition coefficients which are

based on either the fragment, atom-based, or whole-molecule estimation methods are listed in

Table 1.

Table 1: Predictive methods used for estimating environmental constants

Estimation Approach Computational program

Fragment CLOGP KOW WIN (EPI-Suite) ACD/LogP AB/LogP

11

KLOGP

Atom-based ALOGP MOLCAD XLOGP

Whole-molecule ABSOLV COSMOtherm SLIPPER SPARC UPPER VLOGP ALOGPS S+LogP

Handbooks that review these types of predictive methods much more extensively include those

of Lyman et al.41, Mackay & Boethling42, and Reinhard & Drefahl43.

2.3.3 Partition coefficient applications, advantages, and limitations

In order to fully understand partitioning phenomena one must first understand how chemicals

behave under ideal laboratory conditions. However, in order to be able to predict partitioning in

more complex conditions, such as with undefined temperature and impure phases, the

partitioning data must be adjusted to be applicable to the specific environment1.

When calculating partition coefficients the properties being considered are at equilibrium, so

using free energy relationships to calculate chemical properties is beneficial because equilibrium

is achieved once the lowest energy system is reached. Free energy can then be translated into

chemical potential, fugacity, and activity values which are equilibrium criteria, meaning that at

equilibrium their values will be equal for two different phases that have come into contact with

each other. Since naturally all systems drive towards equilibrium, these equilibrium criterion

properties can be used to calculate other chemical properties such as partitioning values.

12

Chemical properties can be correlated from values that have been calculated at a fundamental

level using energy-based calculations, and since all chemical properties can be derived using few

but consistent values this reduces inconsistencies or uncertainties in calculations.

Inconsistencies will ultimately result in multiple different values being reported for one system,

and this is a problem that is the task of scientists to reduce as much as possible.

Consistency testing for partition coefficients

It is valuable to correlate partition coefficients with each other to check consistency through the

solubilities (or pseudo-solubilities) of individual chemicals44. The fundamental physicochemical

properties of a substance such as activity coefficients in an aqueous solution have an influence

on partition coefficients, namely the octanol-water partition coefficient and the air-water

partition coefficient (KAW). Mackay & Cole44 suggested the three solubility approach in which

KAW, KOW and KOA (which is the octanol-air partition coefficient) are expressed as ratios of the

corresponding solubilities, which are independently determined. Figure 1 shows the relationship

between the three solubilities, partition coefficients, and related properties.

13

Figure 1: Chemical space diagram showing relationship between solubilities and partition coefficients in the octanol, air, and water phases. From Mackay & Cole44. C is the concentration of the solute in the air (A), water (W) or octanol (O) phase. PS

L is the liquid vapour pressure of the solute, f is the fugacity, and γ is an activity coefficient.

In the three solubility approach a minimum number of fundamental solubility-related properties

are correlated, and from these data multiple properties can be derived. The value in following

this method is that it reduces the number of inconsistencies that may arise from independently

correlating these quantities. The correlated properties include vapour pressure, activity

coefficients, excess Gibbs energies, solubility or pseudosolubility of the liquid or sub-cooled

liquid in all three phases: air, water, and octanol. Using this method KAW, KOA, or KOW can be

deduced if the other two are known. These three partition coefficients must be consistent,

implying that KOA should equal KOW/KAW. Unfortunately, independent empirical measurements of

the three partition coefficients frequently results in an inconsistency.

The three solubility approach is based on the definition of each partition coefficient. In an

octanol-water medium:

𝐾𝑂𝑊 = 𝐶𝑂 𝐶𝑊⁄ (5)

𝐾𝐴𝑊 =𝐶𝐴

𝐶𝑊⁄ (6)

𝐾𝑂𝐴 = 𝐶𝑂/𝐶𝐴 = 𝐾𝑂𝑊

𝐾𝐴𝑊⁄ (7)

Thus it can be seen how partition coefficients can be correlated to each other and tested for

consistency. There have been efforts to correlate consistent thermodynamic values by the

Wania group for multiple different chemical groups including organochlorine pesticides45,

aromatic hydrocarbons46, and other molecules47,48,49,50. In these studies methods for ensuring

14

consistent values are described. For example the use of chemical space plots for ensuring

consistency of partitioning values is recommended48.

Testing for consistency in predicted values should be done when reporting values whether they

be calculated or experimental. It is best to combine experimental and predictive methods

whenever possible such as by using computational chemistry to predict the values that are also

reported by experimental means. When predicting values, inconsistencies can arise depending

on the source of the input parameters and so it is desirable to use multiple predictive methods

to obtain the best possible value and assess the degree of agreement between methods.

Octanol as a surrogate

Although it is known that octanol is not a perfect surrogate for biotissue, it is accepted as part of

a very simplified view of the biopartitioning process5,6,10,51. Some aspects of partitioning that it

does not take into account include 1) it does not consider different types of lipids, 2) all non-

lipid components are ignored, and 3) KOW is the sole descriptor of all molecular interactions

occurring in all biological phases6. Goss et al. emphasizes in their study the importance of

identifying cases where using the lipid-octanol concept could cause systematic errors in

predicting bioaccumulation6. Alternatively, developing models that can overcome these

shortcomings is preferable. Methods for calculating specific tissue-water coefficient (KTW) values

for fish have been reported by Bertelsen et al.5 and by Goss et al.6.

2.3.4 Lipid fraction method for predicting Tissue-water partition constants (KTW)

Bertelsen et al.5 have reported partition coefficients for 6 chemicals in selected tissue of four

species of fish and have developed a relationship between KTW, KOW, water content, and lipids

15

contents. Their data is used in this study to predict KTW but with a slightly different approach. If

the fish tissue is treated as a composite of lipid, water, and other material each with a

corresponding volume fraction νL, νw, and νx, then in principle the tissue-water partitioning

coefficient (KTW) will be given as:

𝐾𝑇𝑊 = 𝜈𝐿𝐾𝐿𝑊 + 𝜈𝑊𝐾𝑊𝑊 + 𝜈𝑋𝐾𝑋𝑊 (8)

Where KLW is the lipid-water partition coefficient, KWW=1.0, νXKXW=0 (i.e. there is no significant

partitioning to phase x), which means that

𝐾𝑇𝑊 = 𝜈𝑊 + 𝜈𝐿𝐾𝐿𝑊 (9)

or

𝐾𝑇𝑊−𝜈𝑊 = 𝜈𝐿𝐾𝐿𝑊 (10)

If we assume that lipid=octanol, then KLW=KOW and KTW-νW=νL'KOW . In practice KLW does not

exactly equal KOW but we can correct for this by rearranging the equation to:

𝐾𝑇𝑊 − 𝜈𝑊

𝐾𝑂𝑊= 𝜈𝐿

′ (11)

νL' is then an 'octanol-equivalent' lipid content. It is expected that νL will be similar in magnitude

to νL'. Using octanol-equivalent lipid values, corrected tissue-water partition coefficients (KTW')

can be calculated using the same equation above but altered to:

𝐾𝑇𝑊′ = (𝜈𝐿′ ∗ 𝐾𝑂𝑊) + 𝜈𝑊 (12)

Using equation 9 and equation 12 two different KTW values can be determined and compared to

experimental data and this approach is adopted in this study.

16

2.3.5 Abraham's Linear Free Energy Relationship (LFER) method

Linear Free Energy Relationships

An LFER is a linear correlation between the logarithm of rate constants (or equilibrium

constants) for a related series of reactions or phase partitioning systems52. These relationships

arise because at a constant pressure and temperature the logarithm of an equilibrium constant

is proportional to the standard free energy change, and the logarithm of a rate constant is a

linear function of the free energy of activation. LFER relationships have been applied to

molecular properties, however it is assumed that contributions of structural components or

property descriptors of a molecule to the overall properties of that molecule are additive and

independent. Abraham has developed a relationship based on LFERs for the calculation of

partition coefficients and has implemented it in a program called ABSOLV52.

ABSOLV: Abraham's Linear Free Energy Method

Using a Linear Solvation Energy Relationship (LSER) approach, this model was designed by

Abraham and colleagues using solute descriptors and are termed Abraham solute descriptors52.

ABSOLV is a computational program which uses solvation parameters to calculate various

solvation-associated properties using Abraham type equations. There are 5 solute descriptors in

the program with values available for solutes ranging from biochemical interactions to

environmental pollutants. These descriptors are combined into the following linear free energy

relationship53:

𝑙𝑜𝑔𝑃 = 𝑐 + 𝑒𝐸 − 𝑠𝑆 + 𝑎𝐴 − 𝑏𝐵 + 𝑣𝑉 (13)

17

The chemical descriptors are:

E = excess molar refraction, which is calculated using the refractive index of the liquid at

20˚C, can be calculated as addition of fragment pieces (i.e. substructures).

S= dipolarity / polarizability; obtained from water-solvent partition coefficients or

experimentally determined by gas liquid chromatographic measurements on stationary

polar phases. It can be obtained also by fragment addition or by analogy to another

compound.

A = H-Bonding acidity parameter; Overall effective Hydrogen bond acidity which can be

obtained by fragment addition or by analogy to another compound, or by measurement

of physicochemical properties such as logP for a number of water-solvent systems.

B= H-Bonding basicity parameter; Overall effective Hydrogen bond basicity, which can

be obtained also by fragment addition or by analogy to another compound, or by

measurement of physicochemical properties such as logP for a number of water-solvent

systems.

V = McGowan volume, which requires only the molecular formula, number of bonds,

and number of rings in a molecule. It is calculated using the algorithm of Abraham, and

has units of (cm3∙ mol-1 )/100 54.

In general the solute descriptors represent the influence of the solute over various solute-

solvent interactions, and the coefficients (represented by lower case letters) correspond to the

complementary effect of the phases on these interactions52. All of the coefficients are calculated

by ABSOLV using linear regression prior to calculation of KOW. The ABSOLV program currently

contains over 15 000 compounds with experimental log P values39.

18

Abraham descriptors have been determined experimentally and applied to chemicals such as

agrochemicals55, commercial chemicals56, drugs and other compounds57 and to many systems

including octanol-water52, air-water and other air- solvent coefficients58, soil systems, biotic

systems, and other systems.

For example, the Abraham solvent coefficients for octanol-water systems have been calculated

and are shown below52:

𝐾𝑂𝑊 = 0.088 + 0.562𝐸 − 1.054𝑆 + 3.814𝑉 + 0.034𝐴 − 3.460𝐵 (14)

𝑛 = 613 𝑟 = 0.9974, 𝑆𝐷 = 0.116,

Abraham LFERs thus have been used extensively in environmental science and there are

experimentally determined solute descriptors for a large number of chemicals and coefficients

have been derived for many different solvent systems. One problem is that recorded

experimental values inevitably contain errors as has been shown in a recent study on

herbicides55. Another potential problem is that for some partitioning systems it can be difficult

to find accurate datasets for 20-30 compounds, which is the minimum required. Considerable

care and experience is required when deriving and using these equations.

In a recent study by Goss et al.6 an approach has been taken to predict tissue-water partition

coefficients in organisms using Abraham parameters. In their study the LFER is used to calculate

partition constants for four tissue types (storage lipid, membrane, serum albumin, muscle

protein), as well as KAW and KOW using coefficients derived by Goss and experimental Abraham

parameters. Each of these LogK values are determined using the generalized Abraham LFER

relationship:

logK = c + eE+ sS+ aA+ bB+ vV (15)

19

Volume fractions of each tissue type are then incorporated to calculate the final tissue-water

partition coefficient for a given solute using the following relationship:

K tissue/water = fstorage lipid *Kstorage lipid/water +f membrane *K membrane/water

+ falbumin*Kalbumin/water + fprotein * Kprotein/water + fwater (16) Goss and his colleagues successfully used this method to calculate tissue-water partition

constants for bovine tissue in their 2013 study.

2.3.6 COSMO-RS (COSMOtherm)

2.3.6a Quantum theory background for predicting electron distribution

Ab initio calculations refer to calculations which are 'first-principle' in nature, its meaning

derived from a Latin expression meaning "from the start"59. First principles calculations only use

physical theory which for molecular systems is quantum mechanics. Therefore in computational

chemistry methods the Schrődinger equation is typically used as a basis for calculations.

The Schrődinger equation is the fundamental equation used in quantum mechanics to calculate

the energy and wavefunction of a molecular system59. The wavefunction is a mathematical

function that can be used to calculate the electron distribution and once this is known

theoretically any other chemical property (such as polarity) can be calculated. The Schrődinger

equation describes how electrons behave, but it cannot actually be solved analytically for a

system that contains more than one electron. Approximations to the Schrődinger equation are

therefore used in order to predict energies of multi-electron molecular systems. The lesser the

degree of the approximation, the 'higher' the level of ab initio calculation is said to be. However

the price for increased predictive accuracy is the time-cost of these calculations. Higher level ab

initio calculations are very slow as the mathematics is very intensive, and it becomes much more

intensive the larger the molecule is and may take days to complete on a personal computer.

20

Hartree-Fock (HF) calculations are the simplest type of ab initio calculations. This method treats

electrons as a continuous charged electric field in order to predict electron energies59. This is not

completely accurate since in reality electrons are repelled by each other and move accordingly.

A more accurate approach is to use a post Hartree-Fock method such as the Moller-Plesset (MP)

method, Configuration Interaction (CI) method, or Coupled Cluster (CC) method. Each of these

methods use the Hartree-Fock energy calculation but it will be modified slightly to account for

electron-electron correlation by use of unoccupied or “virtual orbitals”. Virtual orbitals are

orbitals which valence electrons can potentially occupy and this alters electronic configuration.

Density Functional Theory (DFT) calculations are not based on wavefunction calculations but

instead use an electron probability density function denoted as 𝜌(𝑥, 𝑦, 𝑧) 59. This is based on the

Hohenberg-Kohn theorem which states that the ground state properties of an atom or molecule

are determined by its electron density function. DFT methods use a technique called the Kohn-

Sham approach in which the energy of a system is formulated as a deviation from the energy of

an idealized system with noninteracting electrons. The difference in energy between the ideal

system and a real system must then be approximated since there is a particular functional that is

unknown. This approximation is the main problem with the DFT calculation; the method itself

treats electron correlation properly but the exact functional needed to do this is not known.

Different approximations of this functional are thus used in conjunction with the DFT method,

for example B3LYP is commonly used. This functional has two components, one is an electron

exchange approximation (denoted by B3) and the electron correlation functional (denoted by

LYP).

Hartree-Fock and post Hartree-Fock methods are generally used for predicting molecular

geometries, energies, vibrational frequencies spectra, dipole moments, and other chemical

properties using computational software59. One disadvantage of these methods in comparison

21

to DFT is that the calculations take much longer, and this increases with each level of

calculation. DFT is most often used for calculating spectra (IR, UV, NMR), dipole moments,

ionization energies, and particularly molecular geometries and energies of transition metals,

which ab initio methods have some trouble with. The main advantage of DFT is that it treats

electron correlation properly, so molecular geometries and energies are calculated with an

accuracy comparable to the post-HF MP2 method, and in less time than it takes to run Hartree-

Fock calculations. DFT can do calculations on larger molecules more easily than HF or post-HF

methods because of how their calculations differ. A disadvantage is the unknown mathematical

term that must be approximated, which may introduce inaccuracies into the calculation.

For the current work, the most important properties calculated with DFT are the (1) total energy

of the gas-phase ground state geometry and low-lying conformers, (2) total energy of fully

solvated (COSMO) geometry, and fully solvated low-lying conformers, and (3) the COSMO

charge density distribution or sigma-profile of each molecule. These calculations can be

performed using the computational software TURBOMOLE within the COSMOtherm suite of

programs which can then be used to calculate chemical and environmentally relevant

properties.

2.3.6b COSMOtherm

COSMOtherm is a computational chemistry program which uses DFT type calculations as a basis

for the prediction of physical chemical properties of a molecule in a solvation medium60. There

are nine general COSMO-RS parameters that COSMOtherm uses, and they are listed in Table 2

below:

Table 2: Parameters used by COSMOtherm used for estimating chemical or environmental

properties

22

Parameter Symbol Value

Screening charge average area

rav 0.5 Å

Contact interaction energy a' 1288 kcal/(mol Å2)/e2

Dielectric scaling factor fcorr 2.4

H-bond interaction energy σnb 7400 kcal/(mol Å2)/e2

H-bond interaction area σhb 0.0082 e/ Å2

Contact area aeff 7.1 Å2

Statistical pairing degeneracy Λ 0.14

Ring surface pairing degeneracy

ω -0.21 kcal/mol

Gas-to-liquid entropy change η -9.15

Cavity radius (Å)

Rk H=1.30, C=2.00, N=1.83, O=1.72, Cl=2.05

Dispersion constant (kcal/mol Å2)

Γk H= -0.041, C= -0.037, N= -0.027, O= -0.042, Cl= -0.052

COSMOtherm uses COntinuous Solvation MOdel (COSMO) theory to calculate the molecular

geometry of any given compound60. The idea behind a continuous solvation model is to treat the

compound as if it were inside an infinitely conducting medium. This implies that the dielectric

constant is infinite (ε=∞) and also that the conductor has an endless supply of electrons, and

that these electrons are free to move around in this conductor. This will mean that any molecule

placed inside the conductor will conform to the shape requiring the least amount of energy, and

that any positive or negative charge at a point on a van der Waal’s surface around the molecule

will be balanced by an opposite charge of equal magnitude provided by the conductor. This

enables the molecule to exist in a fully relaxed, fully solvated, lowest-energy state.

Mathematically this is done by defining an envelope around the molecule by essentially fusing

together the van der Waals radii of each constituent atom and then calculating the necessary

charge density from within the conducting medium needed to neutralize or balance the electron

charge density of the molecule over this surface. These results are then optimized using self-

consistency cycles, and what is calculated in the end is the free energy of the molecule in a fully

23

solvated state, called the reference state. This mathematical process is repeated for every

molecule included in the system.

Once the reference value of free energies is known for each molecule then the free energy

change going from one state to another can be deduced using thermodynamics60:

∆GA,B = ∆GRef B − ∆GRef A (17)

COSMOtherm calculations can then be applied to specific molecular environments in order to

calculate molecular properties and environmental constants. For calculating partition

coefficients there will be at least two solvents and one solute involved, so each of these will

have a ΔGRef value. When gas-phase properties are needed, these values are corrected from this

‘COSMO’ phase to gas phase values using chemical potentials. The chemical potential is

calculated for the solute in the solvent mixture and this term can be related to its corresponding

partition coefficient, as will be discussed later.

The basic approach for this calculation is to first calculate the solute’s chemical potential in the

solvent by integrating the solvent sigma potential (σ-potential) over the solute (called the

residual chemical potential) and adding two terms to account for 1) the differences in molecular

size (combinatorial term) and 2) concentration dependence60. The residual chemical potential

calculation is the most intensive as it includes calculating the solvent’s chemical potential in

itself and then calculating the difference in potential when the solute is in the solvent mixture.

Once the chemical potential of the solute in the solvent is calculated, this value can be

converted into a LogK value.

To begin the calculation the molecular surface is divided into segments and the average charge

density for each segment is calculated. This is shown illustratively in Figure 2 below:

24

Figure 2: Molecular surface divided into segments during COSMOtherm calculation61.

A histogram is then constructed showing the number of segments having each charge. This is

called a sigma (σ) profile, and all molecular sigma profiles calculated by COSMOtherm are

calculated this way. The σ-profile for methanol is shown in the Figure 3 below:

Figure 3: σ-profile of methanol (left) generated from segmented molecule (right)61.

25

The chemical potential is calculated iteratively for the solvent (µS) using the following

equation60:

𝜇𝑆(𝜎) =−𝑘𝑇

𝑎𝑒𝑓𝑓𝑙𝑛 (∫ 𝑝𝑠(𝜎′) 𝑒

{𝑎𝑒𝑓𝑓(𝜇𝑆(𝜎′)−𝑒(𝜎,𝜎′)

𝑅𝑇⁄ )}

dσ′) (18)

Where 𝜇𝑆(𝜎) is the chemical potential of a unit of solvent surface with a charge density σ, 𝑎𝑒𝑓𝑓

is the molecular contact area parameter, 𝑝𝑠(𝜎′) is the sigma profile of the solvent, and 𝑒(𝜎, 𝜎′)

is the misfit energy and hydrogen bond parameter for a given surface segment contact pair

interaction60.

The 𝑎𝑒𝑓𝑓 parameter is the area of contact between two molecules for a given calculation. This is

shown illustratively in Figure 4 below:

Figure 4: A visual description of the contact area parameter, aeff 61.

The 𝑒(𝜎, 𝜎′) term accounts for the energy change due to going from the reference state to a

state where the molecule is interacting with another molecule in the system60. This is comprised

of the ‘misfit energy’, which is the energy increase of the contact relative to the perfect

solvation COSMO state, and a second term to account for hydrogen bonding interactions. It is

calculated using the following relation60:

26

𝑒(𝜎, 𝜎′) =𝛼′

2(𝜎 + 𝜎′)2 + 𝑐ℎ𝑏𝑓ℎ𝑏(𝑇)𝑚𝑖𝑛{0, 𝜎𝜎′ + 𝜎ℎ𝑏

2 } (19)

Where α is the misfit energy parameter, chb is the hydrogen bonding energy parameter, fhb(T) is

the calculated temperature-dependent estimate of entropy loss on formation of a hydrogen

bond, and σhb2 is hydrogen bonding onset cut-off parameter.

The𝛼′

2(𝜎 + 𝜎′)2 represents the electrostatic “misfit” contribution which causes an increase in

the energy, and the 𝑐ℎ𝑏𝑓ℎ𝑏(𝑇)𝑚𝑖𝑛{0, 𝜎𝜎′ + 𝜎ℎ𝑏2 } term is the energy decrease caused by

hydrogen bonding. The segment interaction energy is calculated for every segmented piece

interacting with another segmented piece of the molecule, the probability of which is

determined using statistical dynamics. Using these parameters, equation 18 can be solved for

the chemical potential of the solvent (µS(σ)) in its lowest energy state.

Now the ‘residual’ chemical potential can be calculated, which is the chemical potential of

solute i in solvent S. This is done by integrating the solvent σ-potential over the entire solute

using the relationship60:

𝜇𝑖𝑅(𝑆, 𝑇) = ∫ 𝑝𝑖(σ)𝜇𝑆(σ) 𝑑σ (20)

Where 𝜇𝑖𝑅(𝑆, 𝑇) is the chemical potential of solute i in solvent S, 𝑝𝑖(σ)is the σ-profile of solute i,

and 𝜇𝑆(σ) is the σ-potential of solvent S.

Finally the overall chemical potential of the solute i in solvent S can be calculated using the

following relation:

𝜇𝑖(𝑆, 𝑇) = ∫ 𝑝𝑖(σ)𝜇𝑆(σ) 𝑑σ + 𝜇𝑖𝐶(𝑆, 𝑇) + 𝑘𝑇𝑙𝑛𝑥𝑖 (21)

Where 𝜇𝑖(𝑆, 𝑇) is the chemical potential of solute i in solvent S, 𝑝𝑖(σ)𝜇𝑆(σ) is the residual

potential term, 𝜇𝑖𝐶(𝑆, 𝑇) is a combinatorial term, and 𝑘𝑇𝑙𝑛𝑥𝑖 is a concentration-dependence

27

term, as x represents mole fraction. The combinatorial term takes into account the difference in

size of each molecule and is

∆𝜇𝑇 = −𝜆𝑘𝑇𝑙𝑛𝐴𝑆 (22)

Where 𝜆 is a combinatorial parameter which is a function of the relative surface area of the

molecule, and A represents the relative average surface are of the solvent mixture. T is the

temperature in Kelvin and k is the Boltzman constant.

The sum of the residual potential and combinatorial potential are called the pseudo-chemical

potential (𝜇𝑖∗(𝑆, 𝑇)) so the equation reduces to

𝜇𝑖(𝑆, 𝑇) = 𝜇𝑖∗(𝑆, 𝑇) + 𝑘𝑇𝑙𝑛𝑥𝑖 (23)

The concentration term can now be used to derive a partition coefficient between two phases.

The chemical potential of solute i in solvent S is converted into a partition coefficient through

the following manipulation:

𝜇𝑖(𝑆, 𝑇) = 𝜇𝑖(𝑆′, 𝑇) (24)

Therefore

∫ 𝑝𝑖(σ)𝜇𝑆′(σ) 𝑑σ + 𝜇𝑖𝐶(𝑆′, 𝑇) + 𝑘𝑇𝑙𝑛𝑥𝑖(𝑆′) = ∫ 𝑝𝑖(σ)𝜇𝑆(σ) 𝑑σ + 𝜇𝑖

𝐶(𝑆, 𝑇) + 𝑘𝑇𝑙𝑛𝑥𝑖(𝑆) (25)

𝑘𝑇𝑙𝑛 {𝑥𝑖𝑆′

𝑥𝑖𝑆} = ∫ 𝑝𝑖(σ)(𝜇𝑆′(σ) − 𝜇𝑆(σ)) 𝑑σ + 𝜇𝑖

𝐶(𝑆′, 𝑇) − 𝜇𝑖𝐶(𝑆, 𝑇) (26)

𝑙𝑛𝐾 =1

𝑘𝑇(∫ 𝑝𝑖(σ)(𝜇𝑆′(σ) − 𝜇𝑆(σ)) 𝑑σ + 𝜇𝑖

𝐶(𝑆′, 𝑇) − 𝜇𝑖𝐶(𝑆, 𝑇)) (27)

The lnK term is the partition coefficient, and thus it can be seen how COSMOtherm performs a

partition constant calculation. Molecules that are present in one of the COSMOtherm databases

are analyzed this way60.

28

Molecules that are not present in the database can still be analyzed but additional steps need to

be undergone to establish the molecular geometry and related properties. This is done using the

computational software TURBOMOLE62 and COSMOConf63, both which can be used with

COSMOtherm. TURBOMOLE is software that allows the user to build molecules out of atoms or

input a molecular input formula referred to as ‘SMILES’ in order to analyze compounds that are

not present in databases or are theoretical. Once built a geometry optimization calculation is

done using DFT level calculations. Electron exchange calculations are done using correlation

functional called the Becke-Perdew (B-P) functional. After the structure calculation a single

energy calculation is employed using basis sets of triple-zeta valence (TZV) quality. Once this

calculation is complete the file can be sent to COSMOtherm to do a calculation or it can be sent

to COSMOConf for conformer analysis before being sent to COSMOtherm. COSMOConf is a

program designed to determine a representative sample of all possible conformers of a given

compound. This can be an important step because different conformers can have substantially

different molecular properties, for example the LogKOW value of a cyclohexane-based compound

called Mandelic acid varies by 1.26 log units between its two conformers. COSMOConf identifies

possible conformers and also predicts the prevalence in solution based on 1) the free energy in

solution, 2) the quantum chemical energy relative to the lowest energy conformer, and 3) the

chemical potential of the solvent. Once the conformers are identified and weighted according to

prevalence the file can be sent to COSMOtherm for analysis.

COSMOtherm applications

The computational program COSMOtherm is relatively new but it has been applied in many

studies such as a tool to evaluate which solvents for the removal of pyridine derivatives from

29

wastewater streams64, determining solubilities in liquid-liquid and liquid-solid phases65,

determining environmental fate of explosives used by the military66, designing ionic liquids

(ILs)67, finding solvent replacements68 and other studies modeling thermodynamic or chemical

properties.

30

Second object and hypothesis of this study

The second objective of this study is to investigate methods for predicting tissue-water partition

coefficients (KTW). Three different methods will be explored including a lipid fraction method as

discussed by Bertelsen et al.5, a modified Abraham approach as developed by Goss et al.6, and a

solvent surrogate method using the computational method COSMOtherm. It is hypothesized

that KTW values can be predicted within a factor of two of experimental KTW values using one or

more of this methods.

31

3.0 Model development in this study

Here, we develop, test and discuss a novel PBTK model that seeks to extend the description of

uptake kinetics to assess the internal distribution of a neutral organic chemical and the onset of

toxicity, thus providing an estimate of the chemical fate and effects from the starting point in

water to measurable adverse effects. The model can also be used to address the less

demanding task of simulating and predicting bioconcentration. The model input data and

output results are given in conventional concentration units, but the calculations are done in

'fugacity format' in which fugacity provides the driving force for diffusive and advective

transport and for metabolic conversion. Fugacity simplifies the equations, renders them more

transparent and directly expresses the equilibrium status of the chemical between water, blood

and various tissues1. The model is not designed to treat dietary exposure or dermal absorption,

nor can it treat uptake in invertebrates.

The model can also be used to explore the implications of assigning different partition

coefficients to specific phases or organs within the organism. This may help to explain the

variability of toxicity endpoints such as Critical Body Residues on a wet weight or lipid

normalised basis as well as other toxic endpoints such as chemical activity and volume fraction

in target membranes. The model is implemented as an Excel spreadsheet including a macro to

undertake numerical integrations of the differential mass balance equations, giving the time-

course of concentrations in all compartments.

32

3.1 General Model Structure

A schematic diagram of the suggested fish compartments is given in Figure 5. It is assumed that

the concentration of the chemical in the water is completely dissolved and is constant. Uptake

of a chemical occurs through the gills by reversible diffusion from water into the blood. The

chemical is then distributed by blood into a number of internal phases or organs, again by

reversible diffusion. Flow-limited or perfusion-limited transfer from blood to tissue is assumed,

thus the blood exiting from each tissue is in equilibrium with that tissue, implying that the

exiting blood reaches or approaches a fugacity equal to that of the tissue it leaves. A diffusive

resistance could be included if desired.

The capacity of each internal phase is characterized by its volume and an equilibrium partition

coefficient deduced from an estimated octanol-equivalent content that can include non-lipid

components such as water and protein. The gill cavity and all other compartments, including

blood, are assumed to be well-mixed.

The following compartments are defined as shown in Figure 5:

33

Figure 5a: A visual representation of the theoretical fish divided into compartments representing different

biotissue where the arrows represent the pathways in the organism that a chemical could take, as

assumed in this model. Figure 5b shows these pathways in a mathematical sense, where each

compartment has a given fugacity (fx) and transport coefficient (Dx)

The compartments include:

1) A fast-responding target membrane compartment in which narcosis or another adverse

effect occurs when a defined toxic endpoint is reached as discussed later.

2) A compartment (liver) in which all biotransformation or metabolic conversion occurs

3) A relatively “fast responding" or "richly perfused" compartment that may include brain,

kidney, and other highly perfused tissues

4) A relatively “slow responding” or "poorly perfused" compartment which is more slowly

accessed by blood. This compartment may represent storage lipids in adipose fat and

bone tissue, muscle and other poorly perfused tissues.

34

The input data include equilibrium partitioning properties of the chemical, its dissolved

concentration in the water, the properties of the fish including volumes of the compartments

and equilibrium partition coefficients and expressions for the rates of blood-tissue transport,

and the degradation half-life in the liver. All these input quantities are entered using

conventional units. These data are then converted into units suitable for fugacity calculations,

namely fugacity f (Pa), Z-values (mol/ m3∙Pa) used to relate concentration to fugacity and D-

values (mol/Pa∙h) that are essentially rate constants, such that the process rate is Difi (mol/h).

Calculation of steady-state and dynamic conditions is done using these fugacity parameters,

thus simplifying the equations and rendering them more transparent and more readily

interpretable. The compartmental fugacities as a function of time are converted to

concentrations and related units when assessing the onset of toxicity using specified toxic

endpoints. The fugacity quantities employed are defined in Table 3.

35

Table 3: Fugacity-based properties employed in this model

Property Symbol

Fugacity Values (Pa) fx

In water outside fish fw

Gills fg

Blood fb

Membrane fm

Liver fL

Fast-responding ff

Slow-responding fs

Z-Values (mol/m3•Pa) Zx

air Za

water Zw

octanol Zo

blood (2% octanol) Zb

membrane(=ZW*KLWx*LCx) Zm

liver ZL

fast Zf

slow Zs

Total Zt

Blood Flow Rates (m3/h) Gx

Total Cardiac output Gt

Membrane Gm

Liver GL

Fast Gf

Slow Gs

Compartment Blood Residence Times (hours) CTTBx

Membrane CTTBM

Liver CTTBL

Fast CTTBF

Slow CTTBS

D-Value (mol/h*Pa) Dx

Membrane to Blood DBM

Liver to blood DBL

Fast to Blood DBF

Slow to Blood DBS

Metabolism in Liver DML

Respiration intake (ZW*GVLM*EV) DR

Gills DG

36

Each compartment has a calculated fugacity fi (units of Pa) from which the concentration C

(mol.m-3 ) can be deduced as f.Z where Z is the fugacity capacity (mol/ m3∙Pa) as described by

Mackay1. The transport rate coefficients between blood and tissues shown in Figure 1 are DR

(respiration from water to gill cavity contents), DG (transport across the gill from water to

blood), DBM (blood-membrane), DBL (blood-liver), DBF (blood-fast), DBS (blood-slow). No separate

blood or gill cavity compartments with capacity for the chemical are defined since the blood and

water in the gill cavity are assumed to be in a pseudo-steady state condition. The quantity of

chemical associated with blood is regarded as being included in the respective organs.

Differential equations are defined and solved numerically for each compartment (except the

external water), as in Figure 1 yielding output data consisting of the time course of fugacities,

concentrations, and chemical masses for the desired test duration.

3.2 Onset of toxicity

To address the onset of toxic effects a critical concentration (C*) or fugacity (f*) is defined for

the whole fish or for a specific target compartment such as a ‘target membrane’. As the

compartment concentration C rises and as the equal ratios C/C* and f/f* approach 1.0, toxic

effects occur. The onset of toxicity is expressed by a percent probability of mortality P using a

modified Weibull distribution as described by Mackay et al.69. This accounts for differences in

organism susceptibility to the toxicant and to differences in individual size and partitioning

quantities among the population of test organisms. For the present purposes the original

equation is revised to yield P of 50% when C equals C* by inserting 0.693 and the previous

spread factor 1/s is replaced by a “slope factor” S.

P=100[1-exp-(0.693(f/f*)S)] =100[1-exp-(0.693(C/C*)S)] (28)

37

When C equals C*, P is 50%. A large value of S (corresponding to a small value of s) results in a

steeper slope of the mortality vs. time curve. If empirical data are available for the slope then a

value of S can be fitted, a value of 2 to 5 being typical. One option is to estimate the exposure

times corresponding to P of 25%, 50% and 75%. These 25% and 75% values correspond to ratios

C/C* that depend on S, but the 50% value is independent of S. An optimal value of S can be

obtained by trial and error fitting. Alternatively, if the slope at 50% mortality can be determined,

it can be shown by differentiating that dP/dC is 34.6(S/C*), where 34.6 is (100*e-0.693 * 0.693) or

(100*0.5*0.693) and has units of reciprocal concentration. The measured slope dP/dt has units

of reciprocal time and is (dP/dC)∙(dC/dt). The quantity dC/dt can be obtained from the model

output.

The final result is a time course of concentrations and fugacities approaching a steady state or

equilibrium condition with the option of indicating a probability of a toxic effect when a

specified concentration or fugacity reaches a specified critical value.

This compartmentalization thus includes an estimation of delays in the increase in concentration

in the blood and membrane caused by transporting some of the chemical mass into fast and

slow responding reservoirs. When metabolic conversion is included it retards the increase in

concentration at the target membrane site to an extent dependent on the rate of metabolism.

3.3 Toxic Endpoints

It has been argued that toxicity models should use a threshold critical body residue (CBR) as the

most appropriate measure of a toxic endpoint70 and there has been a substantial amount of

research done correlating CBRs to toxic effects in organisms (Barron et al.71, Escher &

Hermens72, Hendricks et al.73. A study done by McCarty et al.77 used both a whole-body

38

concentration and a lipid normalized concentration as a measure of the toxic endpoint. In this

study it was estimated that the toxic endpoint CBR in an organism with 5% lipid content would

be 5 mol/m3 for a neutral organic chemical, assuming an organism density of 1 kg/L.

For this model five potential critical toxic concentrations and corresponding fugacities are

considered:

1) First is a critical whole body wet weight body residue (CBRww) and concentration that is

deduced by summing all the compartment concentrations at the toxic endpoint

weighted using the volume fractions. For narcotics, this is usually in the range 2 to 8

mmol/kg74 or equivalently mol/ m3 and is Σ(ViZifi)/VT where Vi are the compartment

volumes, Zi are the compartment Z values and VT is the total wet weight volume of the

fish. For chemicals which cause a biological response such as pesticides that are

biochemically active and are more toxic, the CBR can be much lower, such as 0.01 or 0.1

mmol/kg74.

2) Second is a critical lipid normalised whole body residue (CBRlw) concentration that is

deduced by summing the lipid concentrations weighted using the lipid volume fractions

(McCarty et al.75). This is usually in the range 40 to 16076 mmol/kg lipid and is Σ(ViZLifi)/VTL

where the Z value is that of the lipids or equivalent lipids and is larger than the Z value

of the whole compartment, and VTL is the total volume of lipids.

3) Third is the concentration in the lipid of the target membrane compartment which is

used because there is evidence that phospholipids making up the membrane tissue

contribute substantially to the sorption capacity of fish (Armitage et al.77). The toxic

endpoint for this compartment is estimated to be in the range 40 to 160 mmol/kg and is

fMZM.

39

4) Fourth is the volume fraction of the chemical in the target membrane lipids. This value

depends on the concentration in the target lipid phase and the chemical’s molar volume

VM (m3/mol).It has been argued that molar volume is a good indicator of membrane

swelling by McGowan78, Mullins79, and more recently by Abernethy et al.80. There are

several methods of calculating molar volume, including the empirical method of dividing

the molar mass by the liquid density, the Van der Waals (or intrinsic) molar volume as

discussed by Leahy81, and the Le Bas method discussed by Reid et al.82 and Abernethy et

al.80. Abernethy concluded that the Le Bas method is accurate enough given the error in

LC50 values. The volume fraction is calculated as CMvM or fMZMvM (m3 chemical/ m3

membrane lipids). It is convenient to express volume fraction as a percent volume

fraction (ie 100CMvM). Abernethy et al. 80 also reported ranges of narcotic toxicity to be

in the range of 0.5% to 1% and for chronic effects the range was 0.05% to 0.1%.

5) Fifth is the chemical activity either in the average lipid or in the target membrane lipids.

The activity is readily calculated by dividing the appropriate compartment fugacity or

the average fish fugacity by the chemical’s liquid or sub-cooled liquid vapour pressure,

i.e., it is f/PL. Ferguson83 demonstrated that narcosis occurs at a constant chemical

activity in the gaseous or liquid phase from which the organism respires. This approach

has been discussed more recently by Mackay et al.84 and Mackay et al.85.

These five metrics of toxicity are closely related but they differ because of different partitioning

properties of the various lipid phases, different volume fractions of the compartments,

differences in the rates of transport to the compartments and the presence or absence of

biotransformation. As the concentration and fugacity approach the critical values (which are

suggested from the literature) there is an increasing probability of lethality as deduced by the

Weibull distribution until with further increases 100% lethality is approached. The model prints

40

out and plots the time course of increasing concentrations and fugacities and the increasing

probability of lethality for each metric listed above.

3.4 Mathematical formulation of the model

3.4.1 Mass balance equations and input parameters

The general differential equation describing the rate of change of fugacity in a compartment is

as follows86:

(29)

Where Vi is the compartment volume (m3) and Zi (mol/ m3Pa) is the fugacity capacity (both of

which are constant) and fi is the chemical fugacity, which changes with time. The input D values,

Dj are by flow or diffusion from adjacent compartments, the chemical flow being Djfj. The output

D values (Di) are defined similarly but in the case of the liver includes loss by reaction, such as

biotransformation. All D values have units of mol/Pa∙h thus each Df product has units of mol/h.

The characteristic time for uptake or loss of a chemical in each compartment is VZ/ΣDi, where

the D values refer to all loss processes from the compartment. These times can vary greatly in

magnitude depending on the compartment volume, partitioning characteristics and blood flow

rates. To facilitate a numerical solution, a steady-state assumption is applied when the

characteristic times are short relative to the test duration. This is applied to the gill water and

the blood. The pseudo-steady-state equations for the gill water is:

(30)

(31)

41

The respiration rate can be estimated from literature data for the specific organism. Here we

adopt the approach used by Arnot and Gobas87 in which an organism-specific oxygen demand

(mg oxygen/day) is estimated as a function of body size. The oxygen concentration in water is

determined from the test temperature and a percentage of saturation. The product of the

oxygen demand and the oxygen concentration yields the water respiration rate GR (m3/h) that is

used to estimate DR as GR.ZW. The uptake efficiency by respiration is obtained from a correlation

including the octanol-water partition coefficient KOW and parameters accounting for the water

and organic resistances of the gill membrane, namely:

1/EG=(1.85+155/KOW) (32)

EG can be shown to be the ratio of the rate of transport through the gills, DG(fG-fB) to the rate of

input to the gills which is also the rate of total losses from the gills (DR+ DG)fG, but initially when

fB<<fG this simplifies to DG/(DR+DG). This enables DG to be calculated from an input EG. For

example, if EG is 0.6 (ie. 60%) then DG is 0.6DR/(1-0.6) which equals 1.5DR.The conventional

uptake rate constant k1 can be shown to be:

1/(V∙ZW∙(1/DR+1/DG)) (33)

Where V is the organism volume and ZW applies to the water.

For blood the steady-state equation below contains the blood-tissue D values Di and the tissue

fugacities fi.

(34)

(35)

(36)

42

(37)

Introducing the steady-state assumptions for blood and the gill contents introduces a

discrepancy in the chemical mass balance, however this is usually small.

The set of mass balance equations is solved in 4 stages

(1) All volumes, Z-values and D-values are defined as is the fugacity in water (fW), and all

other fugacities are set to zero at time t of zero.

(2) A time-step and computing duration are set and the differential equations are then

solved numerically. From an input concentration and fugacity in water, values for

fugacity in gills and blood, fG and fB, are calculated and then each compartment fugacity

is deduced as a function of time. Results are printed out as desired. Integration is done

using a simple Euler routine, but can be done by the more efficient Runge-Kutta

method.

(3) The concentration in the fish, its lipids, and the membrane are calculated. The

probability of mortality is then calculated. The integration is a slight manipulation of

equation 29 and takes the general form:

(38)

Where DMi is the metabolic conversion D-value.

(4) If all reaction DM values are zero, then all fugacities in the fish will approach the fugacity

of water and equilibrium is approached. If metabolism in the liver is included, a steady-

state, non-equilibrium condition is approached. If only one compartment is included the

43

model reduces to a first order one-compartment model as developed by Arnot and

Gobas87.

If all blood-compartment D values are large (or more specifically the corresponding

characteristic times ViZi/Di are short) then equilibrium is rapidly achieved between blood and

the compartments. Large Di values and small ViZi products necessitate selecting a short

integration time-step, such as a minimum value of 0.05 ViZi/Di.1

The metabolic rate constant is calculated as 0.693/(chemical half-life), as suggested by Niimi88.

The model could be extended to include any desired number of compartments; however they

will generally have different volumes, capacities for the chemical, blood-tissue transport D

values and hence different characteristic transfer times. The use of 4 compartments is judged to

be adequate for the present purpose of developing a model as described that is relatively

simple.

Partition coefficients and Z values

The user inputs equilibrium tissue-water partitioning data. Sources can include empirical or

literature data, QSAR estimates and values computed by quantum chemical methods such as

COSMO-RS as described by Klamt et al.89. These partition coefficients can include contributions

from different lipid phases, proteins, and other materials. The model calculates the partition

coefficients KiW from the octanol-water partition coefficient KOW, the lipid content L and a

selected quantity EQ defining the sorptive capacity of the phase relative to octanol, namely:

KiW=L∙KOW∙EQ (39)

44

If EQ is 1.0,KiW is simply L∙KOW. If for example, EQ is 0.9, L is 0.1, and KOW is 1000, then KiW is 90.

The user can thus input any desired value of KiW. It is expected that most EQ values will be close

to 1.0, since previous studies have indicated that partitioning within organisms can be

somewhat estimated using KOW. This enables the user to explore the effect of differences in

sorptive capacity between membrane and storage lipids and materials such as protein can be

included. A Z-value for blood is also defined as an octanol equivalent content such as 2% by

volume.

3.4.2 Blood-tissue transport rates.

For each compartment ‘i' a blood flow rate GBi (m3/h) is estimated from the total cardiac output

and the fraction of the blood flow to each compartment. Alternatively it can be estimated from

the tissue volume and an assumed residence time. This is essentially a flow-limiting transport

assumption. The transport D value is then GBi∙ZB where the Z value is that of the blood. The rate

of flow into the tissue is fB∙D where fB is the inflow blood fugacity. The outflow is D∙fi where fi is

the tissue fugacity. If diffusion limited conditions apply a corresponding reduction in D can be

made.

3.4.3 Compartment residence and characteristic times.

The characteristic uptake and clearance time τ for each compartment is 1/k where k is the rate

constant for all losses. τ can be regarded as approximately a "two-thirds time" and is a factor of

(1/0.693) longer than the half-time. In the fugacity formulation τ is VZ/ΣD, thus it depends on

the tissue volume, its partition coefficient with respect to blood, the blood flow (or perfusion)

45

rate into (and out of) the tissue. The partition coefficient is determined by either the lipid

content or octanol equivalent content of the tissue (EQ∙L). The effective quantity of lipid is thus

V∙EQ∙L m3. The D-value is GZB where ZB is essentially determined by the assumed lipid content of

the blood, and G is the blood flow rate. The corresponding lipid flow rate into the tissue is

termed GL (m3/L). The characteristic time is then V∙EQ∙L/GL and is the ratio of the quantity of lipid

in the tissue to the flow rate of lipid into the tissue. For example, if a tissue contains 1 cm3 of

lipid and the flow rate of blood lipids is 0.01cm3/hour then the characteristic time is 100 hours.

The value of τ characterizes the slow and fast responding tissues. If reactions occur (as in the

liver), then τ is reduced. The total quantity of chemical in the fish can be calculated as ∑V∙Z∙f

from which the average concentration and fugacity can be deduced. Lipid normalised

concentrations in individual compartment and in the whole body are also deduced.

3.4.4 Steady-State Conditions

It is useful to calculate steady-state fugacities and concentrations at long exposure times when

the ∆fi values in equation 8 approach zero. If there are no metabolic losses then all fugacities

become equal to fW. If metabolism occurs only in the liver then fL will be given by fBDBL/(DBL+DML)

and the rate of metabolic loss is fLDML which is also the net uptake rate from blood and the net

rate of uptake from water DR(fW-fG) and through the gills (DR(fW-fG)). It can be shown that for the

liver:

(40)

Clearly fL will be less than fW by a factor primarily dependent on DML, but also influenced by the

sum of the resistance terms (1/DR + 1/DG + 1/DBL) from water to liver. Fugacities in blood, gill,

46

and water can be calculated from fL, for example fB must equal fL/(1+DML/DBL) because at steady-

state the net rate of chemical conversion in the liver fLDML equals DBL(fB-fL); the difference in

input and output rates. For non-metabolizing compartments the blood and compartment

fugacities are equal. The model also calculates and prints out the steady-state conditions. This is

useful as a check of the mass balance and it is of interest when estimating how close the fish is

to steady-state when the toxic endpoint is reached.

3.5 Sensitivity Analysis

A sensitivity analysis can be conducted in which the parameters are varied by selected factors

and the implications of the results assessed. A full sensitivity analysis of all input parameters is

beyond the scope of this thesis, however a sensitivity analysis on the input partition coefficients

on model results is investigated.

The results of the model simulation is generated in the form of concentration believed to be

associated with lethality and the corresponding probability of death during the test. The

concentrations necessary to cause 50% mortality and the time-to-death are considered using

the critical body residue (CBR). A sensitivity analysis can be conducted in which specified input

parameters are changed (such as doubled or halved) in order to test the sensitivity of these

parameters on model results. In this study the partition coefficient KOW value which is inputted

by the user is changed by a factor of 2 in both directions in order to test the sensitivity on model

results for a trial applying naphthalene (NAPH) to a fathead minnow (FHM). Details are given

later in section 5.3.

47

4.0 Predicting partition constants in this study

KTW values were predicted for six different tissues in a rainbow trout, including adipose, liver,

muscle, blood, kidney, and skin for a group of selected neutral organic chemicals. The tissues

were chosen based on available published data found in Bertelsen et al.5. The chemicals

included dichloroethane, trichloroethane, tetrachloroethane, pentachloroethane,

hexachloroethane, and benzene. These chemicals display a range of Log KOW values and were

the six chemicals used for partitioning analysis in Bertelsen et al.5, therefore there is

experimental data available that can be used to compare to results of this study. There are also

data for these chemicals available in Goss et al.6 that can be used to predict KTW values.

The following three predictive methods outlined were applied to estimate KTW values. Linear

regression was done in order to obtain the linear relationships between predicted and

experimental data for all predictive methods. Predictive accuracies were measured using

calculated Root Mean Square Error (RMSE) values, calculated for each predicted KTW value.

4.1 Lipid fraction theory method

This method is based on the relationship reported by Bertelsen et. al.5 as discussed in section

2.3.4. KTW values were calculated for the six different types of fish biotissue (blood, fat, kidney,

liver, muscle, and skin) using equation 9. Lipid fraction (𝜈𝐿) values used were averaged values

taken from Bertelsen et al.5, Lien et al.90, Lien et al.91, and Nichols et al.10. KOW values used were

recommended by Bertelsen et al.5, and νw is the water fraction which is reported for fish in

Bertelsen’s study5.

48

In order to calculate the corrected lipid fraction constant νL' values were calculated for each

tissue using equation 11. In this relationship KTW values are measured tissue-water partition

coefficients and these constants are reported by Bertelsen et al.5, Lien et al.90, Lien et al.90, and

Nichols et al.10 for Trout. νL′ values were then used to calculate new tissue-water partition

coefficients, KTW' using equation 12. KTW' values, KTW values, and KOW values were then graphed

against experimental KTW values for each tissue in order to look at trends and to identify outliers.

4.2 Abraham parameters LFER method

The general Abrahams LFER equation is shown above in equation 13 in section 2.3.5. The solute

descriptors, all in capital letters, are obtained experimentally or calculated. V can be calculated

for a molecular structure based on its molecular formula and the number of rings in the

molecule using an algorithm derived by Abraham92. The E descriptor can be calculated using the

refractive index at 20°C for solids and for liquids the observed value can be taken from the

refractive index56. The remaining three descriptors, S, A, and B need to be determined from

experimental measurements of physicochemical properties. These values may be derived

experimentally using gas or liquid chromatography, or by gas-solvent or water-solvent

partitioning measurements. Databases have been compiled which contain solute descriptors for

many different molecules and recommended values can be found in various studies, for

example Tulp et al.93, van Noort et al. 94, or Stenzel et al. 95. Experimental Abraham parameters

used in this study were recommended by Goss et al.6.

In the study by Goss et al. 6 as mentioned in the literature review, Goss and colleagues

presented a modified Abraham LFER model which can be used to calculate tissue-water

partition coefficients in an organism. Using polyparameter linear free energy relationships (PP-

49

LFERs) this group has calculated coefficients for storage lipids/water, phospholipid membrane

/water, serum albumin/water, and muscle protein/water. Using these coefficients Log K values

can be calculated for each of these tissues using the general LFER equation, shown above. The

phase coefficients are published values taken from Goss and colleague’s 2013 study and the

solute descriptors are either taken from published studies or are predicted computationally,

such as by COSMOtherm. To apply this to a fish, volume fractions for the given fish for each

tissue type are incorporated to calculate the final tissue-water partition coefficient using

equation 16 in section 2.3.5 for calculating KTW values.

4.3 COSMO-RS method

COSMOtherm was used to predict partition coefficients in selected 2-phase solvent systems.

Since the standard measure of biological partitioning is to use KOW the solvent mixtures that

were chosen were variations of the octanol-water system. This mainly involved either varying

the water phase and keeping the octanol phase constant, or varying the octanol phase and

keeping the water phase constant. Water-saturated octanol (which will occur in when

determining KOW experimentally) is tested and so is ‘dry’ octanol, both as phase 1 with the

second phase being pure water (the amount of octanol that dissolves in water is negligible).

Other solvent mixtures in which one or both phases have been modified from the ‘standard’

octanol/water phases predicted and correlated to experimental tissue/water data. Results of

each solvent set applied to each tissue were used as an indicator of what new solvent system

should be tested, and new solvent molecules were chosen based on their hydrophobicity or on

functional groups that were present.

50

Molecules were calculated using TZVPD-Fine parameterization and most molecules were

present in the COSMOtherm TZVPD database. These calculations were relatively fast to perform.

Molecules that were not present were built using TURBOMOLE software. As a result the

configuration requiring the lowest amount of energy is determined and molecular data can be

saved. These data are then sent to COSMOconf, which is a type of COSMO-RS software that

calculates all possible conformers that exist for each molecule and the molecular properties of

each conformer. These calculations are extensive and may take days. Molecules were then

exported back to COSMOtherm so that partition coefficients could be calculated.

4.3.1 Predicting Abraham parameters using COSMOtherm

COSMOtherm can be used to predict Abraham parameters for a given 2-phase system. Using σ-

potential values that have been calculated using the method discussed earlier a Taylor

expansion series can be applied56:

𝜇𝑆(𝜎) ≅ ∑ 𝑐𝑆𝑖𝑓𝑖(𝜎)

𝑚

𝑖=−2

(41)

where

𝜇𝑆(𝜎) = 𝜎𝑖𝑓𝑜𝑟 𝑖 ≥ 0 (42)

and

𝑓−2/−1(𝜎) = 𝑓𝑎𝑐𝑐/𝑑𝑜𝑛(𝜎) ≅ {0 𝑖𝑓 ± 𝜎 < 𝜎ℎ𝑏

∓𝜎 + 𝜎ℎ𝑏𝑖𝑓 ± 𝜎 > 𝜎ℎ𝑏 (43)

The 𝑓−2/−1(𝜎) function is necessary to describe the hydrogen bonding contributions due to the

donor and acceptor behaviour of the solvent. Using this Taylor expansion, each solvent can be

characterized using the 𝑐𝑆𝑖 term which are σ-coefficients.

The partition coefficient is linked to pseudochemical potentials by the equation:

51

𝑘𝑇𝑙𝑛𝐾𝑆,𝑆′𝑋 = [𝜇𝑆′

𝑋 − 𝜇𝑆𝑋] (44)

And combining equation 20 for the definition of 𝜇𝑆𝑋 the partition coefficient between any two

solvent S and S’ should be expressible in the form

𝑙𝑛𝐾𝑆,𝑆′𝑋 =

1

𝑘𝑇[𝑐𝑆,𝑆′ + ∫ 𝑝𝑋(𝜎)(𝜇𝑆′(𝜎) − 𝜇𝑆(𝜎))𝑑𝜎] (45)

≅ �̃�𝑆,𝑆′ + ∫ 𝑝𝑋(𝜎) ∑ �̃�𝑆,𝑆′𝑖 𝑓𝑖(𝜎)

𝑚

𝑖=−2

𝑑𝜎 (46)

= �̃�𝑆,𝑆′ + ∑ �̃�𝑆,𝑆′𝑖 𝑀𝑖

𝑋

𝑚

𝑖=−2

(47)

Where the combinatorial terms have been subsumed by �̃�𝑆,𝑆′ and the σ-moments 𝑀𝑖𝑋are

defined by

𝑀𝑖𝑋 = ∫ 𝑝𝑋(𝜎) 𝑓𝑖(𝜎)𝑑𝜎 (48)

It is implied by equation 44 that the log of a partition coefficient can be expressed as a linear

combination fo sigma moments. The set of sigma moments 𝑀𝑖𝑋, i=0,2,3, complemented by the

hydrogen bond moments 𝑀𝑎𝑐𝑐𝑋 (= 𝑀−2

𝑋 ) and 𝑀𝑑𝑜𝑛𝑋 (= 𝑀−1

𝑋 ) can be used as a set of descriptors

for an LFER. By definition of the σ-profiles, the zeroth moment 𝑀0𝑋is identical with the molecular

surface, the second moment 𝑀2𝑋 is a measure of of the overall electrostatic polarity of the

solute, and the third moment 𝑀3𝑋 is a measure of the asymmetry of the sigma profile. The

hydrogen bond moments 𝑀𝑎𝑐𝑐𝑋 and 𝑀𝑑𝑜𝑛

𝑋 are quantitative measures of the acceptor and donor

capacities of the compound X, respectively.

Using COSMOtherm this calculation can be employed to predict Abraham parameters for any

solute. In this study Abraham parameters were predicted for the six solutes and used in the

method presented by Goss and colleagues6 in addition to using the experimental Abraham

52

parameters suggested in their study. Thus two sets of KTW values are presented which are based

on the study by Goss et al.6.

4.4 Error estimates

Error is calculated using either Root Mean Square Error (RMSE) values or by taking the ratio of

the actual and predicted values. The RMSE equation is as follows:

𝑅𝑀𝑆𝐸 = √∑(𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙)2

𝑛 (49)

Both theoretical and experimental values refer to the KTW values. The RMSE is averaged over

each chemical, meaning n=6. The RMSE was calculated for each type of biotissue, listed above in

section 4.0. To assess the accuracy of predictions made by the model, ratios of experimental to

predicted values are calculated for each set of predicted tissue-water partition coefficients.

53

5.0 Fish model simulation

The model was applied to three situations. First was a hypothetical situation for a fictitious fish

and a fictitious chemical, however the values used are regarded as reasonable for a typical

narcotic substance in a small fish and a 96 hour toxicity test. This is done to display features of

the model and test the mathematical relationships expressed in the mass balance equations.

In the second situation the model is applied to simulate conditions from an experiment

performed by de Maagd and colleagues51. In their toxicity study fathead minnows (FHM) were

exposed to NAPH and trichlorobenzene (TCBz) until the fish were dead. The lethal body burden

(LBB), time of death, and lipid percentage was reported for each fish.

Third, the model was applied to simulate toxicity tests by Nichols et al.10 done on a rainbow

trout. In their study a 48 hour trial was performed exposing the trout to pentachloroethane

(PCE) and the authors reported mean lipid contents, blood concentration over time, and

concentration ratios of PCE in various tissues. The authors also developed a PBTK-type model

and reported results of predicted blood concentration over time.

It is noteworthy that most test organisms are small (i.e. < 1 g) thus it is difficult to obtain

measurements of the distribution of the chemical in blood and various tissues. The advantage of

using small organisms such as the FHM is that the response is generally faster, multiple

organisms can be used, and the cost is reduced. When using larger organisms (i.e.> 100 g), such

as rainbow trout, the cost is greater, fewer fish can be exposed, but information on disposition

of the chemical in the fish is more readily obtained. The strategies of conducting tests and

applying the model to small and large fish are thus regarded as complementary.

54

5.1 Results of fish model

5.1.1 Model simulation sequence

Applying the model requires input of test conditions, organism properties, and chemical

properties. These input parameters and their symbols are listed in Table 4, 5, and 6 below.

Table 4: Input parameters and symbols used in the model to describe test conditions

Symbol

Test Conditions

Water concentration (mg/L, g/m3) CWMGL

Food concentration (mg/kg) CDMGK

Initial fish concentration (mg/kg) CFIMGK

Timestep (hours) deltat

Number of steps N

Time (hours) TIM

Total time (hours) TIMT

Print frequency (1 in x) PRINF

Table 5: Input parameters and symbols used in the model to describe organism properties

Organism Properties

Organism volume (cm3) VFCM

Temperature, degrees (°C) TC

Saturation oxygen concentration (mg/L) LOXS

Respiration efficiency (A-G correlation) EV

Percent oxygen saturation (%) POX

Actual oxygen concentration (mg/L) COX

Growth rate constant (days-1) kG

Gill ventilation rate (L/day, A-G correlation) GVLD

Gill ventilation Rate (m3/h) GVLM

Weibull slope factor S

Respiration rate constant (hour-1) kv

Respiration rate constant (day-1) k1

Organism mass (kg) masskg

Organism total volume, (m3) VFT

Compartment volume fractions VFx

Volume fraction membrane VFM

Volume fraction liver VFL

Volume fraction fast VFF

55

Volume fraction slow VFS

Compartment lipid contents LCx

Membrane LCM

Liver LCL

Fast LCF

Slow LCS

Toxic endpoints input

CBR wet weight (mmol/kg) CBRWW

CBR lipid weight (mmol/kg) CBRLW

Concentration in membrane (mmol/kg) CBRLM

Volume fraction lipid membrane (%) CBRVF

Chemical activity in membrane CBRAC

Table 6: Input parameters and symbols used in the model to describe chemical properties

Chemical Properties

Chemical name NAME

Molar mass(g/mol) MW

Liquid vapour pressure (Pa) VPL

Molar volume (cm3/mol) MV

Octanol-water partition coefficient KOW

Air-water partition coefficient KAW

Octanol-air partition coefficient KOA

Metabolic half-life, whole body (days) TAUM

Metabolic rate constant (days-1) kM

Metabolic rate constant in liver (days-1) kML

Respiration loss rate constant (days-1) kR

Lipid-water partition coefficient scaling factors KLWOEQx

Membrane KLWOEQM

Liver KLWOEQL

Fast KLWOEQF

Slow KLWOEQS

Percent (%) cardiac output to each compartment %Gx

Membrane %Gm

Liver %GL

Fast %Gf

Slow %Gs

56

Only one chemical can be treated at a time. These values are entered into worksheets in the

Excel spreadsheet in which all the compartment volumes, Z values and the D values are

deduced. The fugacity in the water is deduced. When assuming a steady-state for the gill water

and blood, no VZ products need be defined and only four differential equations need be solved.

A suitable time step is 0.05 times the smallest VZ/ΣD product. The value for the time step is

chosen because it is not too large that it will introduce significant errors but a much smaller

timestep will cause the program to become slowly and possible crash. The worksheets include

an estimate of steady-state conditions (including mass balance checks for all compartments)

which can be useful for ensuring that toxic conditions will eventually be reached under the test

conditions.

An Excel Macro then inputs the fugacity in water and all the VZ products and D values from the

worksheets and generates a time course of fugacities in all compartments at specified intervals

for the desired test duration. Simultaneously, the probability of toxicity P is deduced as a

function of time for the suggested toxic endpoints. These data for probability versus time can be

compared directly with empirical data taken from comparative experimental studies.

Illustrative results are given in Figure 6 as the increases in concentrations (and therefore

fugacities) and probabilities of the specific endpoint being reached and exceeded. It is

noteworthy that the different endpoints will yield different times to 50% lethality.

57

Figure 6: Concentration and corresponding probability of death graphical output from the model

developed in this study. For each toxic endpoint described above one set of graphs are produced.

It is possible to run the model and then using initial results adjust the various input parameters

and explore the sensitivity of the results to these changes. The key input parameters are judged

to be the respiratory uptake rate, the volumes of compartments and their partition coefficients

with respect to water (as defined by octanol equivalents), the biotransformation half-life, the

characteristic times for transport between blood and compartments and the suggested toxic

endpoints. These parameters are displayed in the summary sheet below as an example for a

chemical applied to a 1 kg fish.

58

Figure 7: Summary sheet of input parameters and important fugacity-related values, shown as displayed

in the model

The model was run using hypothetical input parameters and mass-balance equations were

applied by calculating the steady-state rates of transport, (defined as described in section 3.4.1)

transferring between each compartment and blood, blood and gills, and gill and water. Steady-

state fugacity values were also printed and checked, since the chemical’s fugacity in the water

should be higher than the fugacity in any part of the fish. The compartmental fugacities should

approach but not surpass the steady-state fugacity in the blood, which in turn may approach but

not surpass the fugacity in the gills. By doing these checks it is ensured that equations have been

inputted correctly and that they appear to be working correctly. Then the model can be applied

to simulate a toxicity test for a hypothetical fish.

Concentration in water: 0.15 fw: 0.031884287 Pa

Test time: 50 hours

Organism mass: 1000 g or cm^3

Parameters Blood Membrane Liver Fast Slow Total

Volume % 3 3 47 47 100

Volume (cm^3) 30 30 470 470 1000

Lipid % 80 10 2 10 102

Lipid volume cm^3 24 3 9.4 47 83.4

% of Cardiac Output 20 10 35 35 100

Blood flow cm^3/h 414 207 724.5 724.5 2070

V 0.00003 0.00003 0.00047 0.00047 0.001

Z 0.6088 23.4219 2.9277 0.5855 2.9277

D 0.0003 0.0001 0.0004 0.0004

VZ 0.0007 0.0001 0.0003 0.0014

T=VZ/D 2.7878 0.6970 0.6239 3.1197

Liver metabolism D-value 0.0000

T=VZ/(Dml+Dbl) for Liver 0.6962

Fugacity (steady-state) 0.0318 0.0318 0.0318 0.0318 0.0318

Concentration (steady-state) 0.0194 0.7450 0.0930 0.0186 0.0931

Fugacity at 50 hours 0.0217 0.0212 0.0217 0.0217 0.0211

Concentration at test time(mol/m^3) 0.0132 0.4966 0.0634 0.0127 0.0618

Concentration at test time(g/m^3) 2.6772 100.4505 12.8342 2.5716 12.5073

Fraction of steady-state completed

(=f @ test time/ f @ steady-state) 0.6834 0.6666 0.6821 0.6826 0.6640

mg/L or g/m 3

59

5.1.2 Simulation of aquatic toxicity tests for naphthalene and trichlorobenzene applied to a

Fathead Minnow

De Maagd et al. 51 performed toxicity studies on fathead minnows (Pimephalespromelas) using

naphthalene (NAPH) and trichlorobenzene (TCBz) in order to study the time-to-death and lethal

body burdens of the fathead minnow. The fish were on average 0.6 g and maintained in an

aquarium which was kept at 20 ± 1 °C and an oxygen content exceeding 5 mg/L. The initial

concentration of NAPH in the tank was approximately 16.6 mg/L, and for TCBz it was

approximately 8.5 mg/L. These parameters were used in our biouptake model in order to

predict lethality of the fathead minnow. In de Maagd’s study the LBB for NAPH was 8.1 ± 3.1

mmol/kg wet weight, and for TCBz the LBB was 14 ± 4.5 mmol/kg, determined empirically using

standard exposure toxicity tests.

The chemical properties for NAPH and TCBz were taken from a Chemical Properties Handbook

(Mackay et al.96), including the chemical's molar mass, liquid vapour pressure, molar volume,

and partition coefficients (including KOW, KAW, and KOA). KOA was also calculated using the

consistency approach described in section 2.3.3 to ensure consistency. These properties are

listed in Table 7:

Table 7: Input parameters relating to chemical properties used in model for fathead minnow trial

Chemical Property Naphthalene Trichlorobenzene

Molar Mass (g/mol) 128.2 181.4

Liquid Vapour Pressure (Pa) 36.2 38.6

Molar Volume (cm3/mol) 123 141

KOW (LogKOW) 1 995 (3.3) 10 471 (4.0)

KAW (LogKAW) 0.0176 (-1.7) 0.0581 (-1.2)

Metabolic half-life values were calculated using a whole-body metabolic half-life of 100 days, as

suggested by Mackay and Gobas for hydrophobic organic chemicals97.

60

Compartment volumes were estimated based on values reported by previous studies (James et

al.98, Lien et al.90). Liver volume was estimated as 1.23% of the entire body weight. Krishnan &

Peyret12 reported lipid volume fractions for blood, fat, liver and muscle compartments for

various fish, including fathead minnows and these values are reported in Table 8.

Table 8: Lipid content fractions reported for compartments in a fathead minnow from Krishnan & Peyret12

Fathead Minnow Blood Fat Muscle

Lipid Content Fraction

0.019 ± 0.001 1.010 ±0.033 0.025 ± 0.001

These values were used as a basis for lipid content input parameter values for fathead minnows

in the model. Compartment-specific input values for volume, lipid content, and blood flow were

selected from the literature12,90. A calculation for total lipid content was included in our model

and was compared to the total lipid content reported in de Maagd et al.51, which was 6.5 ± 2.2%.

The lipid content values for each compartment were adjusted so that the total lipid content of

the fish was matched. The volumes of each compartment had to be adjusted due to the fact

that none of the literature divided the compartments up quite the same way. In particular there

is no multicompartment model defining a membrane compartment and related properties,

however it is known that the lipid content of membranes is quite high77. Values reported for fat

and ‘poorly perfused’ type tissues were averaged for use in the poorly perfused compartment

and values for kidney, muscle, and richly perfused’ type tissues were averaged and used as

starting values for the richly perfused compartment. Values that were available for FHM

specifically included fish volume, water temperature, oxygen saturation, total lipid content, and

oxygen consumption90. Due to a large range in these values and small number of fish tested

(n=3) reported by de Maagd and colleagues FHM-specific values were averaged from values

reported by multiple studies when available, shown in Table 9. In doing this it is hoped that a

more accurate representation of an average FHM will be given.

61

The overall input parameters used to characterize the fathead minnow in this simulation are

summarized in Table 9:

Table 9: Input parameters relating to organism properties used in model for FHM trial

Parameter Symbol Value Source

Organism volume (cm3) VFCM 0.489 de Maagd et al.51

Krishnan & Peyret12

Lien et al.90 Temperature (°C) TC 22.25 de Maagd et al.51

Saturation oxygen concentration (mg/L) LOXS 8.7 Calculated as 14.04-0.24*TC

Respiration efficiency (A-G correlation) EV 0.52 Arnot & Gobas87

Percent oxygen saturation (%) POX 80 de Maagd et al.51

Actual oxygen concentration (mg/L ) COX 6.96 Calculated as POX*LOXS*100

Growth Rate constant (days-1) kG 1.0 E-5 Mackay & Gobas97

Gill Ventilation Rate (L/day, from A-G correlation) GVLD 1.42 Arnot & Gobas87

Gill Ventilation Rate (m3/h) GVLM 5.91 E-05 Calculated as GVLD/24/1000

Weibull slope factor (estimated) S 5 Best fit for probability of death graphs51

Respiration rate constant (h-1) kv 0.06 Mackay & Gobas97

Respiration rate constant (day-1) k1 1.50 kv*24

Organism mass (kg) masskg 4.89 E-4 VCFM/ 1 000

Organism total volume (m3) VFT 4.89 E-7 VCFM/ 1 000 000

Volume fraction membrane VFM 0.001 -

Volume fraction liver VFL 0.3 James et al.98

Volume fraction fast VFF 0.3 Lien et al.90

Volume fraction slow VFS 0.1 Lien et al.90

Lipid fraction - membrane LCM 0.5 Armitage et al.77

Lipid fraction- Liver LCL 0.1 Krishnan & Peyret12

Lipid fraction- Fast LCF 0.1 Krishnan & Peyret12

Lipid fraction- Slow LCS 0.2 Krishnan & Peyret12

The whole-body toxic endpoint was reported in de Maagd et al.51 as 8 ± 3.1 mmol/kg for NAPH

and 14 ± 4.5 mmol/kg for TCBz and these values were used as inputs for the whole-body toxic

endpoints in the model.

62

Results of toxicity simulation for FHM

The model was run using a fathead minnow and the chemicals naphthalene (NAPH) and

trichlorobenzene (TCBz). The lethal body burden predicted by the model is formulated to be the

value inputted as the toxic endpoint, therefore it was expected match the LBB reported by de

Maagd and colleagues. The model simulations were compared with the empirical data from de

Maagd’s study in Tables 10 and 11.

Table 10: Results for fathead minnow from de Maagd51 and from the model using naphthalene as a test

chemical

Naphthalene De Maagd et al.51 Model

Lethal Body Burden (mol/m3) 8.1 ± 3.1 8

Time to 50% death (h) 1.25-4.25 (~2.9) 6.4

Table 11: Results for fathead minnow from the model using trichlorobenzene as a test chemical

Trichlorobenzene De Maagd et al.51 Model

Lethal Body Burden (mol/m3) 14 ± 4.5 14

Time to 50% death (h) 4.5-23.25 (~17) 6.5

The time at which the LBB occurred in de Maagd et al. study determined using graphs which had

been reported in de Maagd’s study, shown below in Figure 8.

Figure 8: Graphs taken from de Maagd et al.51 that have been used in this study to determine the approximate time at which LBB occurred. A) NAPH regressed at LBB=8; t is approximately 3 hours. B) TCBz

regressed at LBB= 14; t is approximately 17 hours

These values are reported in Tables 10 and 11 in brackets.

63

For NAPH the LBB occurs at approximately 6.4 hours, assuming a critical body concentration

(toxic endpoint) of 8 mol/m3. For TCBz the LBB occurred after 6.5 hours, assuming a critical body

concentration of 14 mol/m3. The other toxic endpoints were chosen by using the concentration

reported at the time when the whole-body concentration was equal to the LBB reported in de

Maagd51 and rerunning the model.

The time of death predicted for NAPH is not within the range reported by de Maagd but is

within a factor of 2 of the reported range, as can be seen in Table 10. The time at P(50)

predicted by the model for TCBz was within the range reported by de Maagd’s study, although

it is at the lower end of the range, shown in Table 11.

Outputs of results are reported in the model both as several lists of values and also graphically.

The graphs display the whole body concentration, lipid-normalized whole-body concentration,

concentration in membrane lipids, volume fraction percent in membrane lipids, and chemical

activity in membrane lipids. Probability of death graphs based on each of these are also

produced. These graphs are displayed below in Figures 9 and 10.

64

65

Figure 9: Graphs produced from model output using NAPH as a chemical and a fathead minnow as a test

fish. Model predicts that LBB is 8 mol/m3, and occurs after 6.4 hours.

66

67

Figure 10: Graphs produced from model output using trichlorobenzene as a chemical and a fathead minnow as a test fish. Model predicts that LBB is 14 mol/m3 which occurs after 6.5 hours.

68

5.1.3 Simulation of an aquatic bioconcentration test for pentachloroethane applied to a Trout

A toxicokinetic study performed on rainbow trout was done by Nichols et al.10 where both

empirical results and their own developed model predictions were observed and compared. In

their study the trout were on average 1 kg, and they were kept in an aquarium at a temperature

of 11 ± 1 °C. Trout were exposed to pentachloroethane (PCE) through controlled respirometer-

metabolism chambers and multiple trials were performed over a 48 hour time period. Nichols

reported values including compartment volumes, blood flows, body weight, lipid fractions,

tissue:blood partitioning constants, and a graphical output of the time-course PCE concentration

in the blood of the trout.

In this study the conditions in Nichols et al.10 were simulated closely in the trial that exposed

trout to 150 ug/L PCE, since this was the water concentration for which the most relevant values

were reported. A water concentration of 150 ug/L was therefore used in this model. Parameters

requiring an input for the properties of the organism were chosen based on published literature

(listed in Table 12 below), including compartment volumes, lipid fractions, and blood flow rate.

These values had to be altered to account for the membrane compartment, which is not

separated from its component organs in any of the literature. Therefore the model was run

multiple times before final results were obtained in order to obtain the most logical values for

the membrane compartment. Accordingly, some of the other compartment properties had to be

adjusted as well. Total lipid content reported in Nichols et al.10 and organism volume values

were used to ensure that the values assigned to each compartment made logical sense. Lipid

contents were adjusted to ensure that the total lipid content was approximately the same as

what was reported in Nichols et al.

Table 12 lists input parameters related to Trout that were used in this trial.

69

Table 12: Input parameters relating to organism properties used in this model for trout trial.

Organism Properties Symbol Value Source

Organism volume (g or cm3) VFCM 1000 Nichols et al.10 Lien et al.91 Krishnan & Peyret12

Temperature (˚C) TC 11 Nichols et al.10

Saturation oxygen concentration (mg/L) LOXS 11.4 Calculated as 14.04-0.24*TC

Respiration efficiency A-G correlation EV 0.507 Arnot & Gobas87

Percent oxygen saturation POX 80 Nichols et al.10

Actual oxygen concentration (mg/L) COX 9.12 Calculated as POX*LOXS*100

Growth Rate constant (days-1) kG 0.00001 Mackay & Gobas97

Gill Ventilation Rate (L/day) GVLD 230.3 Arnot & Gobas87

Gill Ventilation Rate (m3/h) GVLM 9.59 Calculated as GVLD/24/1000

Respiration rate constant (hour-1) kv 4.86 Mackay & Gobas97

Respiration rate constant (day-1) k1 116.70 kv*24

Organism mass (kg) masskg 1 VCFM/ 1 000

Organism total volume (m3) VFT 0.001 VCFM/ 1 000 000

Volume fraction membrane VFM 0.03 -

Volume fraction liver VFL 0.03 Nichols et al.10 Lien et al.91

Volume fraction fast VFF 0.47 Nichols et al.10 Lien et al.91 Krishnan & Peyret12

Nichols et al.15

Volume fraction slow VFS 0.47 Nichols et al.10 Lien et al.91 Krishnan & Peyret12

Lipid compartment - membrane LCM 0.8 Armitage et al.77

Lipid compartment - liver LCL 0.1 Nichols et al.10 Lien et al.91 Krishnan & Peyret12

Lipid compartment - fast LCF 0.02 Nichols et al.10 Lien et al.91 Krishnan & Peyret12

Lipid compartment - slow LCS 0.1 Nichols et al.10 Lien et al.91 Krishnan & Peyret12

% cardiac output to membrane %Gm 20 -

% cardiac output to liver %Gl 10 Nichols et al.10

Lien et al.91 Krishnan & Peyret12

Nichols et al.15

% cardiac output to fast responding %Gf 35 Nichols et al.10

Lien et al.91 Krishnan & Peyret12

Nichols et al.15

% cardiac output to slow responding %Gs 35 Nichols et al.10

Lien et al.91 Krishnan & Peyret12

Nichols et al.15

70

The results reported in the Nichols et al study (1990) are shown below, including their

experimental and model predicted results:

Figure 11: A 48 hour time-course for pentachloroethane concentration in 1000g trout in this graph originally reported by Nichols et al.10. Black dots represent values reported from the toxicological study, whereas the smooth line represents Nichols predictive model for the toxicokinetics in a trout.

Chemical properties for PCE were taken from the Chemical Properties Handbook (Mackay et

al.96) including the chemical's molar mass, liquid vapour pressure, molar volume, and partition

coefficients (including KOW, KAW, and KOA). These properties are listed in Table 13:

Table 13: Input parameters relating to chemical properties used in this model for the rainbow

trout trial

Chemical Property Pentachloroethane

Molar Mass (g/mol) 202.3

Liquid Vapour Pressure (Pa) 596

Molar Volume (cm3/mol) 120.4

KOW 1258.9

KAW 0.018

Liquid Solubility (mol/ m3) 2.47

71

Results of bioconcentration simulation applied to a 1 kg Trout

Nichols et al.10 reported results as a time-course concentration of PCE in arterial blood, as well

as tissue:blood PCE concentration ratios after 48 hours. All of these results were compared to

our models results. Thus the concentrations in each compartment as well as blood

concentration was printed, and a time-course plot of PCE in the blood was made. Concentration

values were converted into units of mg/kg in order to compare with Nichols data.

This model predicts a blood concentration of 2.62 mg/kg after 48hours, and Nichols results

show that the concentration in blood at this time is approximately 2.15, as can be seen in Figure

12.

Figure: 12: A 48 hour time-course for pentachloroethane concentration in the blood of a 1000g trout. Results from Nichols10 empirical study are overlaid on top of model results from this study for comparison

Comparing these results a similar trend is observable in concentration uptake in the blood. The

predictions are within a factor of 2 of experimental reported data indicating that the blood

concentration is relatively well simulated. The values and their differences from Figure 12 are

listed in Table 14.

72

Table 14: Chemical concentration in blood reported by Nichols et al.10 and model predicted values at

various times

Time (h) Model Predictions (mg/kg)

Nichols et al.10 (mg/kg)

Ratio (Model: Nichols et al.)

1 0.24 1 4.2 : 1

4 0.50 1.3 2.6 : 1

6 0.65 1.4 2.2 : 1

8 0.79 1.55 2.0 : 1

12 1.05 1.85 1.8 : 1

16 1.30 1.75 1.3 : 1

24 1.72 1.7 0.98 : 1

32 2.07 1.9 0.92 : 1

48 2.62 2.15 0.82 : 1

Compartment concentration ratios were reported by Nichols et al.10 after 48 hours. The

following table compares those ratios to compartment concentration ratios predicted by the

model.

Table 15: Average concentration ratios reported by Nichols et al.10 and concentration ratios predicted by

this model.

Blood:Water Fat:Blood Kidney:Blood Liver:Blood Muscle:Blood

Nichols (1990)

10 100 5 5 3

Model prediction

17 5 1 5 1

73

5.2 Discussion of model performance

For a simple one compartment first-order toxicity model the key output quantities are the

concentration in the whole body as a function of time and the time required to reach a defined

toxic endpoint and the CBR at that time. The key model parameters are as follows:

1. The respiration rate constant, k1, which depends on the flow rate of water to the gills

(G) and the efficiency uptake from water (EG)

2. The sorptive capacity of the whole body for the chemical that is usually expressed as

one or more partition coefficient to lipid phases as well as protein and water (KiW) and

the quantity or volume fraction of these phases (Li). The simplest approach is to define a

lipid content L (as a volume fraction) and KOW then assume that the sorptive capacity of

the whole body with respect to the water is L∙KOW; the equilibrium bioconcentration

factor

3. The rate constant for metabolism and possibly for growth (kG) and whole body basis

For a fish of defined mass, the input parameters are thus G, EG (which can be combined to give

kRor k1), volume fraction of lipid and other phases (Li) and the partition coefficients KiW, kM, and

kG. There are thus at least four input parameters and more if several phases, metabolism, and

growth are included.

Results of Trout and FHM simulation – comparison to experimental values

The results of the FHM trial demonstrate that the model simulates the uptake of a neutral

organic chemical and corresponding probability of death in a fish using realistic input

parameters. The LBB values for both NAPH and TCBz trials were predicted accurately as

74

expected since the LBB was used as the toxic endpoint input parameter for the model. The time-

to-death for both chemicals was within a factor of 2 of the experimental data for the FHM trial.

It is interesting to note that the time-to-death was slightly underestimated for NAPH but

overestimated for TCBz. This might be due to the toxic endpoints (critical concentrations)

chosen for each, which were based on the average LBB values reported by de Maagd. There was

a large range reported for each chemical (2.9-14.0 mol/m3 for NAPH and 5.3-20.0 mol/m3 for

TCBz) in de Maagd et al’s study. The ranges of the times at which death occurred was also quite

large, as previously discussed. It was suggested in their study that the large ranges were likely

connected to the fish’s individual lipid contents, which ranged from 2.5-12.5%. However the

results of their study were presented as averages, not as values associated with a specific fish of

a specific size and lipid content. In addition the number of fish used in each of their trials was 3.

These factors all contribute to uncertainty; the averages presented may not be as reliable as the

ranges reported for analyzing model results. Since our model has reported the probability of

death within the ranges reported, this suggests that the model is capable of predicting LBB and

probability of death for a FHM.

This model does not take any biological responses that a fish may have to a toxin into account,

which may cause differences in reported and actual values. For example, there is a possibility

that as narcosis is approached the organism will become less active and reduce its respiration

rate and blood flow circulation rate. This will slow the onset of toxicity. Another possibility is

that fast exposure to a high concentration will result in a very different CBR from that resulting

from a slow exposure to a lower concentration.

Input parameters that were not available in de Maagd study had to be taken from other studies,

which may have introduced some error into the model calculations. The lipid content of each

compartment was not known and values were estimated, however the total lipid content of the

75

simulated fish in the model (8%) was within the range reported by de Maagd (6.5 % ± 2%).

Compartment divisions differ among studies and some of the input parameter values may be

skewed, especially for an FHM which is quite small and has little experimental data on

characterizing its biotissue.

The trout PCE trial results were analyzed using blood concentrations and a comparison was

made to the toxicological study performed by Nichols et al.10. The concentration of PCE in the

blood predicted by the model were within a factor of 2 of experimental values at any given time

over the 48 hour test period. This shows consistency between the model and experimental

results. The study Nichols et al. (1990) did not report any time-of-death data but did report

concentration ratios in characterized compartments of the trout.

The composition of compartments varies among studies including the definition of richly and

poorly perfused tissues. For the purpose of this study, kidney and muscle tissue values published

in other studies were used for richly perfused biotissue and adipose tissue was mainly

considered as poorly perfused biotissue. Therefore the values predicted by the model for muscle

and kidney tissue are the same and represent results for the richly perfused tissue. Results for

slow-responding tissue is compared to adipose tissue concentration, and membrane

concentration was not analyzed because it is not reported in Nichols et al.10. The predicted

compartment ratios were not within a factor of 2 of the values reported in the Nichols study

(with the exception of liver tissue, which was predicted accurately); the richly perfused

compartment was off by a factor of 4 and the fat tissue in particular is quite different, being off

by a factor of 20.

The possible reasons for these discrepancies will now be discussed in more detail. The definition

of richly perfused and poorly perfused tissue differ in each study and so specific organs had to

be assigned as either richly perfused or poorly perfused. The main problem with this is that the

76

muscle may be assigned one or the other, depending on if the fat layers in between the muscles

are removed10, however this is not typically specified, including the values reported in the

Nichols et al. study. They did go into some detail explaining some of the issues they had with

dealing with the fat tissues, specifically they could not assess the fat in between the muscle

using their chosen method of radiolabelled microspheres. They mention that the radiolabelled

microspheres were a good choice for their study so that they could see the amount of

metabolism that occurs, however they had no way of differentiating the parent from daughter

products. As a result they may have reported values for PCE which were actually an

accumulation of its daughter products. If these daughter products accumulated in the fat then

this would contribute to the discrepancy. The fish was sutured to a respirometer and

anaesthetized which may have caused biological responses not taken into account in this model.

Input parameter values were assigned based on reported experimental values, which differ

among studies. This may introduce any differences in compartment divisions including volume,

lipid content, and tissue composition. For this reason the prediction of the blood concentration

was considered more important than the compartment predictions, especially the fat

compartment which was proven in a sensitivity analysis that it could not be simulated, which

may be due to the reasons just mentioned. KOW was used to characterize partitioning to every

compartment which might not be accurate, since each compartment is characterized by

somewhat different biotissue. This is the primary reason for investigating methods for predicting

tissue-specific partition coefficients, as opposed to using KOW alone to characterize partitioning

to all compartments.

There may be other differences between the two studies that are unknown or unaccounted for,

but it is likely that there are errors in both studies that have caused the discrepancies. However

since the overall concentration in the organism is represented by the blood and the blood

77

concentration is predicted within a factor of 2 at all times reported by Nichols et al. this

indicates accurate prediction of whole-body concentration. The distribution to the poorly

perfused and richly perfused compartment is not simulated as accurately according to these

results, however the possibilities just discussed given insight to the reasons this may be the

case. In addition, the inclusion of a membrane compartment makes predicting the distribution

to compartments much more difficult since there is no data to compare it to.

The inclusion of a membrane compartment may be the biggest reason for any discrepancies

since there have been no experimental studies which divides the membrane section of the

tissue out of the organs, therefore all values reported for these organs includes values for

membranes. The compartment values for volume, lipid content, and blood flow had to be

adjusted based on the sum of these parameters for each compartment. For example the blood

flows were chosen as a fraction of cardiac output to each compartment and so their sum could

not exceed 1.0. The compartment volumes could not exceed the volume of the fish. The lipid

content could not exceed the lipid content of the fish. These values were adjusted several times

and the model was run in order to see how predictions compared to experimental results. The

compartment parameters that had to be altered the most was the lipid contents because when

the membrane compartment’s high lipid content77 is taken into account and the other

compartment values were inputted as averaged empirical values, the lipid content of the fish

totalled 50%. Therefore there was some sensitivity analysis that was done in each trial in order

to get compartment input values that were the most reasonable.

In addition to input parameters for the compartments there is the possibility that the rate

constant for metabolism is not correct, since these values are estimated from the literature.

78

Results of different toxic endpoints:

The results of the toxic endpoints show that the CBRww are related to the concentration in the

target membrane but only approximately and indirectly. The tissue lipid contents and sorptive

capacities differ so the CBRLW is not generally equal to the whole body value. It is recognised that

the lipid phases differ and further they differ in accessibility to the blood. Depending on the test

duration the slowly responding tissue compartment may or may not accumulate an appreciable

quantity of chemical. Generally, high lipid contents result in slower increases in concentration

i.e., the “survival of the fattest” effect.1,Error! Bookmark not defined. Results show that toxic effects

depend on the toxic endpoint critical value selected. Since there was no empirical data for these

other toxic endpoints they could not be compared, however critical concentration values were

chosen based on values corresponding to time-of-death data available from de Maagd et al.51.

Multi-compartment models versus one-compartment models

The main problem with a simple one-compartment model is the inherent assumption following

uptake, which is that the chemical is immediately distributed at equilibrium between all phases

and only an average or whole-body biotransformation rate can be deduced in all phases and

tissues. On the other hand multicompartment toxicokinetic models such as is developed here

specify a number of tissues or tissue groups and their individual sorptive capacities. They do not

assume instantaneous equilibrium between compartments and they can be specific about

biotransformation rates for each compartment. They require, however, estimates of blood

transport rates to each compartment. They can also be specific about where in the fish toxicity

occurs by defining a toxic endpoint specific to a compartment. More detailed insights into the

toxicokinetics can be obtained but this is at the expense of a need for more input parameters

(which may be difficult to estimate) and a more complex model that has greater fidelity to

79

reality5,6,10. The trend in both human and ecotoxicology is to seek insights into the behaviour and

effects of chemical substances in organisms by developing and testing PBTK models of

increasing complexity.

This approach also enables hypotheses to be proposed and tested. For example, it could be

hypothesized that the rate of transport to the target tissues and target tissue-water partition

coefficient are important and require accurate values.

5.3 Sensitivity of partition coefficients to model results

The model was run for NAPH in water using the accepted KOW as reported earlier. It was then re-

run by changing the KOW by a factor of 2 in both directions and predicted concentrations were

compared at time-of-death (3 hours for NAPH). The base case achieved a 50% lethality at a

whole-body concentration of 4.3 mol/ m3 after 3 hours. The toxic endpoint concentrations

corresponding to each KOW value are listed in Table Z to demonstrate the sensitivities.

Table 16: Predicted concentrations of NAPH at 50% lethality when KOW changes by a factor of 2

KOW/2 KOW KOW*2 Time

(hours

)

Whole-body concentration (mol/ m3) 3.82 4.30 4.60 3

Lipid-normalized concentration

(mol/m3)

47.5 53.90 57.70 3

Concentration in membrane lipids

(mol/m3)

33.6 40.40 44.50 3

Volume fraction in membrane lipids

(%)

0.45 0.50 0.59 3

Chemical activity in membrane lipids 0.08 0.05 0.03 3

80

This table shows that altering the KOW value by a factor of 2 affects the results as expected. It is

apparent that as KOW increases, the predicted concentration at time of death also increases. In

order to see how much the concentration is affected these values are presented graphically in

Figure 13.

Figure 13: Plot of the whole body concentration vs. time for the 3 cases. During the first 3 hours the change in KOW (represented in this graph as ‘Z’) has little effect. After 5 hours the Z/2 line begins to deviate and becomes significantly lower. At 10 h the lines are well separated with the 3 cases being 7.9, 11.0 and 13.4 mol/ m3 for Z/2, Z and Z*2 respectively.

The reason for this is that at short times the uptake is controlled by the respiration rate and

there is little loss by respiration. As equilibrium is approached there is increasing loss by

respiration and that rate depends on the capacity of the fish for the chemical. As time increases

and equilibrium is approached the rates of uptake and loss become equal. The times to reach 10

mol/m3 behave similarly and are 22h, 8h, and 7 h for the 3 cases.

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Table 17 contains the equilibrium concentrations at infinite time, or the ‘steady-state’

concentrations. The equilibrium concentrations are, as expected, factors of 2 greater and less

than the base case ‘KOW’.

Table 17: comparison of equilibrium concentrations for each of the 3 cases (KOW, KOW/2, KOW*2)

KOW KOW/2 KOW*2 Ratio KOW:

KOW/2

Ratio KOW:KOW*2

Concentration in Blood at equilibrium (mol/m3)

2.8 2.8 2.8 1:1 1:1

Concentration in Membrane compartment at equilibrium (mol/m3)

132.1 66.1 263.9 2:1 0.5:1

Concentration in Liver compartment at equilibrium (mol/m3)

26.3 13.2 52.4 2:1 0.5:1

Concentration in Fast-reacting tissue compartment at equilibrium (mol/m3)

26.4 13.2 52.8 2:1 0.5:1

Concentration in Slow-reacting tissue compartment at equilibrium (mol/m3)

52.8 26.4 105.5 2:1 0.5:1

To assist interpretation of this sensitivity analysis the change in concentration delta C is

calculated and the ratio deltaC/C base are deduced. The ratio delta C/C to delta KOW / KOW are

then calculated and designated as the sensitivity. This is the fraction that the concentration

changes divided by the fraction that KOW changes. The sensitivity is graphed over time in order

to observe the sensitivity of the change in concentration with respect to the difference in the

KOW value. This graph is shown below in figure 14.

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Figure 14: Graphical display of sensitivity of predicted concentrations over time when KOW has been doubled

In Figure 14 initially S is near zero and as time progresses S increases and reaches 1.0 at

equilibrium. The implication of these results is that high accuracy in KOW is not needed when

kinetics control and exposure times are short. At longer times a more accurate value of KOW is

needed. The required accuracy thus depends on the fractional approach to equilibrium. The

other toxic endpoints show a large variation in predicted concentrations at steady state when

KOW is changed by a factor of 2, shown in Table 17.

83

6.0 Tissue-water partition coefficient prediction method comparison

The model developed in this study for fish toxicity uses KOW as its partitioning parameter for

each chemical and compartment. As noted, this reflects the approximation that chemicals

partition into biotissue according to KOW. In the following section, several approach to

developing tissue-specific partition coefficients that could be used in place of KOW in the model

are explored, with the aim of demonstrating their feasibility for future developmental work in

such models.

Experimental KTW values used in this study

The following experimental KTW values were used for comparison to KTW values that were

predicted as discussed in the methods section. These published empirical values were averaged

from studies were data was available and included Bertelsen et al.5, Lien et al.90,91, and Nichols

et al.10.

Table 18: Experimental KTW values used in this study

DCE TrCE Benzene TCE PCE HCE

Blood 2.40 3.62 9.62 5.52 23.58 79.98

Fat 30.20 118.00 139.00 147.22 514.40 4,607.62

Kidney 3.29 9.09 7.57 14.12 24.42 95.83

Liver 1.35 5.03 3.31 10.63 20.72 100.31

Muscle 2.19 6.84 6.61 7.93 23.02 90.93

Skin 1.95 5.57 7.45 4.32 18.60 37.10

The graphs produced of KTW(predicted) vs. KTW(experimental) for each method are located in Appendix 1.

84

6.1 KOW as a predictor

KOW values were also tested for predictive accuracy for each tissue by calculating the root mean

square error (RMSE) values. An RMSE value was calculated for each of the six tissues and there

were 6 sets of partition coefficients used to calculate each RMSE, meaning n=6. The RMSE

equation is used to determine the average error for each set of partition coefficients being

applied to a biotissue.

Table 19: RMSE of experimental KOW values in comparison to experimental KTW values. Partition

coefficients for six chemicals were used to calculate each RMSE value. These chemicals included 1,2-dichloroethane, 1,1,2-trichloroethane, 1,1,2,2-tetrachloroethane, pentachloroethane, and hexachloroethane.

Tissues RMSE of LOG KOW

adipose 0.24

liver 1.57

muscle 1.50

blood 1.55

kidney 1.41

skin 1.67

Table 19 shows that KOW is within 0.3 log units of the experimental partition coefficient for

adipose, on average. The other tissues have a much larger RMSE value; much greater than the

value of 0.3 that this study hypothesized could be achieved.

6.2 Results of Lipid fraction method

‘Corrected’ lipid fraction values were calculated for fish using equation 11 above for blood, fat,

liver, kidney, muscle, skin, and viscera. These calculated values were compared to experimental

lipid fractions reported by Bertelsen et al.5 by calculating the ratios of the two values. The

following table, Table 20 gives the data reported by Bertelsen et al. containing empirical KTW

85

values, the volume fractions of water (reported here as ϒ), and lipid (νL) for the 7 tissues. The

calculated values of νL' and the ratios of calculated:experimental are also reported. Although KTW

values are only calculated for trout in this study the calculations for corrected νL' values are

reported for all fish species and tissues in order to compare the values for trout with values for

other species of fish, as this data may come in handy for future research of a similar nature.

Table 20: Bertelsen et al.5 partitioning data for different chemicals and fish tissues, with tissue lipid content and calculated tissue content reported

Viscera tissue was discarded from the study calculating KTW values because there was very little

experimental data for it and because its composition is ill-defined.

Equation 9 was used to calculate KTW values for rainbow trout using water content and lipid

content reported in Bertelsen’s study and experimental KOW values. A second set of KTW values

Tissue &

Species

Mean

Fish per

Analysis DCE TrCE Benzene TCE PCE HCE

ϒ

(water

content)

Actual tissue

lipid content

( νL)

Calculated

νL' Per

tissue/fish

Ratio

calculated/

actual

Blood

Catfish 1 - - - 5.71 20.80 88.00 0.839 1.30E-02 1.51E-02 1.16

FHM 28 - - - 9.04 28.20 107.00 0.876 1.90E-02 2.22E-02 1.17

Medaka 175 - - - 17.70 61.60 219.00 0.839 2.30E-02 4.72E-02 2.05

Trout 1 2.40 3.62 9.62 5.17 25.80 56.70 0.839 1.40E-02 3.30E-02 2.36

Fat

Catfish 1 - - - 314.00 1,690.00 7,897.00 0.05 8.99E-01 1.16E+00 1.29

FHM 25 - - - 315.00 1,359.00 5,134.00 0.016 1.01E+00 9.78E-01 0.97

Trout 1 30.20 118.00 139.00 232.00 2,215.00 9,157.00 0.05 9.42E-01 1.21E+00 1.29

Kidney

Catfish 1 - - - 12.30 77.30 168.00 0.788 5.50E-02 4.29E-02 0.78

Trout 1 3.29 9.09 7.57 15.90 81.30 185.00 0.789 5.20E-02 6.52E-02 1.25

Liver

Catfish 1 - - - 12.50 55.60 132.00 0.735 3.90E-02 3.59E-02 0.92

Medaka 175 - - - 65.00 227.00 5,234.00 0.746 1.18E-01 3.12E-01 2.64

Trout 1 1.35 5.03 3.31 13.20 73.10 198.00 0.746 4.50E-02 3.77E-02 0.84

Muscle

Catfish 1 - - - 5.25 12.70 31.70 0.791 9.00E-03 1.05E-02 1.16

FHM 25 - - - 6.27 21.10 77.30 0.806 2.50E-02 1.56E-02 0.63

Trout 1 2.19 6.84 6.61 12.70 83.10 179.00 0.769 3.00E-02 5.11E-02 1.70

Skin

Catfish 1 - - - 4.54 13.80 47.50 0.649 5.70E-02 1.05E-02 0.18

FHM 25 - - - 6.66 19.40 120.00 0.765 4.60E-02 1.70E-02 0.37

Trout 1 1.95 5.57 7.45 4.32 18.60 37.10 0.667 2.90E-02 3.18E-02 1.10

Viscera

FHM 25 - - - 18.40 58.40 285.00 0.766 7.40E-02 4.93E-02 0.67

Medaka 175 - - - 161.00 727.00 1,454.00 0.523 3.77E-01 4.73E-01 1.25

Average= 1.19

86

were calculated using equation 12 and the adjusted lipid values (νL') and are reported at KTW’. To

assess the accuracy of these tissue-water partition constant values their RMSE values were

calculated and these are shown in Table 21 below:

Table 21: RMSE values of predicted and experimental Log KTW values for various tissues in Trout. These

were calculated using the Lipid Fraction method

K(adipose/water)

K(liver/water)

K(muscle/water)

K(blood/water)

K(kidney/water)

K(skin/water)

Lipid fraction LogKTW

0.23 0.36 0.28 0.31 0.38 0.44

Lipid fraction LogKTW '

0.21 0.26 0.41 0.29 0.37 0.45

These RMSE values that are 0.3 log units or less are within a factor of 2 of experimental results.

The RMSE values for all of the tissues and for both methods are consistently low in comparison

with KOW RMSE values, shown in Table 19.

6.3 Results of Goss 2013 modified Abraham approach

KTW values were calculated using the Goss-Abraham method6 and compared to experimental

values by calculating their RMSE values. The following table contains these RMSE values:

Table 22: RMSE values for predicted KTW values using Goss-Abraham method

K(adipose/water)

K(liver/water)

K(muscle/water)

K(blood/water)

K(kidney/water)

K(skin/water)

Goss 2013 model (Goss-recommended Abraham parameters)

0.33 0.63 0.41 0.42 0.53 0.70

Goss 2013 model (COSMOtherm calculated Abraham parameters)

0.69 0.91 0.37 0.71 0.79 0.97

87

None of these RMSE values are within a factor of 2 of experimental values, however both

methods report lower error than the RMSE values reported in Table 19 for LogKOW, with the

exception of the adipose tissue.

6.4 Results of COSMOtherm ‘solvent-surrogate’ approach

First prediction was of octanol-replaced phase. Octanol was replaced with alcohols, beginning

with methanol and increasing in carbon number (up to C22) which represented the 'tissue'

phase. These tests are based on hypothetical mixtures and does not take miscibility of the other

solvent into account, meaning that many of these mixture are not feasible for studying

empirically. Predicted partitioning values were graphed against experimental partition

coefficients reported by Bertelsen et al.5 for each tissue, including blood, fat, liver, kidney,

muscle, and skin. RMSE values were used as a measure of the linear correlation between

experimental and predicted partition coefficients. This process was repeated with alkanes (C1-

C20,C22) and then a few other molecules that were chosen based on initial results. The

following table lists theses RMSE values.

Table 23: Root Mean Square Error (RMSE) values for predicted vs experimental KTW values, where the

tissue phase is represented by the solvent listed and the water phase is pure water (the system has 2

phases)

K(adipose/water)

K(liver/water)

K(muscle/water)

K(blood/water)

K(kidney/water)

K(skin/water)

Methanol 0.53 1.85 1.36 1.83 1.66 1.92

Ethanol 0.46 1.81 1.30 1.79 1.62 1.88

Propanol 0.40 1.75 1.24 1.73 1.57 1.83

Butanol 0.35 1.70 1.20 1.68 1.52 1.78

Pentanol 0.32 1.66 1.15 1.64 1.48 1.74

Hexanol 0.28 1.61 1.12 1.59 1.44 1.70

Heptanol 0.26 1.58 1.08 1.56 1.41 1.67

Octanol (dry) 0.24 1.54 1.05 1.52 1.37 1.63

Nonanol 0.23 1.51 1.02 1.49 1.34 1.60

Decanol 0.22 1.48 0.99 1.46 1.31 1.57

1-Undecanol 0.22 1.46 0.97 1.43 1.29 1.55

1-Dodecanol 0.23 1.44 0.95 1.41 1.27 1.52

88

Tridecanol 0.23 1.41 0.93 1.39 1.25 1.50

Tetradecanol 0.23 1.40 0.91 1.37 1.23 1.48

Pentadecanol 0.24 1.38 0.89 1.35 1.21 1.47

Hexadecanol 0.25 1.36 0.88 1.33 1.20 1.45

Heptadecanol 0.26 1.34 0.85 1.32 1.18 1.43

Nonadecanol 0.27 1.31 0.83 1.29 1.15 1.40

1-Eicosanol 0.28 1.30 0.81 1.27 1.14 1.39

1-Docosanol 0.30 1.27 2.22 1.25 1.11 1.36

Methane 1.30 2.70 1.44 2.67 2.54 2.79

Ethane 0.58 1.93 1.30 1.90 1.77 2.02

Propane 0.46 1.79 1.21 1.75 1.63 1.87

Butane 0.39 1.69 1.14 1.66 1.53 1.78

Pentane 0.35 1.62 1.08 1.59 1.47 1.71

Hexane 0.32 1.56 1.04 1.53 1.41 1.65

Heptane 0.31 1.52 1.00 1.49 1.37 1.61

Octane 0.31 1.48 0.97 1.45 1.33 1.57

Nonane 0.30 1.45 0.94 1.41 1.29 1.54

Decane 0.30 1.42 0.77 1.38 1.27 1.51

Eicosane 0.37 1.25 0.75 1.21 1.10 1.34

Docosane 0.39 1.22 0.75 1.18 1.07 1.31

1-Docosane 0.39 1.22 1.19 1.18 1.07 1.31

1-dodecanethiol 0.34 1.67 1.68 1.65 1.51 1.76

propanediene 0.76 2.16 1.22 2.13 1.99 2.24

1,9-decadiene 0.30 1.69 0.92 1.66 1.52 1.77

1,8-octanediol 0.22 1.36 0.98 1.34 1.18 1.44

1,3,6,8-octanetetrol 0.37 1.39 0.73 1.37 1.19 1.45

1-[1,3,-hydroxylcyclohexane]-3,5-cyclohexane

0.44 1.12 0.88 1.09 0.92 1.18

1-ethyl-3,5-hydroxylcyclohexane

0.23 1.32 1.11 1.293 1.13 1. 9

Water/octanol-heptane (50:50) 0.28 1.58 1.10 1.55 1.41 1.66

Water/octanol-heptane (25:75) 0.29 1.57 1.10 1.54 1.41 1.66

Water/Octanol-heptanol 0.25 1.56 1.05 1.54 1.39 1.64

Water/Octanol-Decane 0.26 1.52 0.79 1.50 1.36 1.61

Water/1-Docosanol-Docosane 0.33 1.26 1.61 1.23 1.11 1.36

Table 24: Root Mean Square Error (RMSE) values for predicted vs experimental KTW values, where the

tissue phase is represented by octanol and the water phase has been replaced by the solvent mixture

listed (the system has 2 phases)

K(adipose/water)

K(liver/water)

K(muscle/water)

K(blood/water)

K(kidney/water)

K(skin/water)

water(.9)-methanol(.1) 0.64 0.82 0.41 0.78 0.64 0.90

water(.85)-methanol(.15)

0.92 0.55 0.28 0.50 0.36 0.61

water(.8)-methanol(.2) 1.17 0.34 0.36 0.26 0.17 0.37

89

water(.75)-methanol(.25)

1.38 0.23 0.53 0.10 0.19 0.19

water(.7)-methanol(.3) 1.56 0.28 0.69 0.19 0.35 0.15

water(.6)-methanol(.4) 1.87 0.51 0.98 0.47 0.64 0.38

water(.5)-methanol(.5) 2.10 0.73 1.20 0.71 0.87 0.61

water(.4)-methanol(.6) 2.28 0.91 1.38 0.89 1.05 0.79

water(.9)-ethanol(.1) 0.88 0.59 0.60 0.55 0.40 0.65

water(.8)-ethanol(.2) 1.46 0.24 0.96 0.14 0.24 0.14

water(.7)-ethanol(.3) 1.84 0.49 1.21 0.46 0.60 0.35

water(.6)-ethanol(.4) 2.10 0.73 1.39 0.71 0.86 0.60

water(.5)-ethanol(.5) 2.28 0.91 1.52 0.89 1.04 0.79

water(.4)-ethanol(.6) 2.42 1.04 0.44 1.03 1.18 0.92

water(.9)-glycol(.1) 0.61 0.86 0.29 0.82 0.68 0.93

water(.8)-glycol(.2) 1.05 0.43 0.50 0.37 0.25 0.48

water(.7)-glycol(.3) 1.35 0.24 0.68 0.11 0.18 0.22

water(.6)-glycol(.4) 1.56 0.27 0.83 0.18 0.34 0.15

water(.5)-glycol(.5) 1.71 0.38 0.94 0.32 0.49 0.25

water(.4)-glycol(.6) 1.83 0.47 0.32 0.44 0.60 0.35

water(.9)-propanone(.1)

1.12 0.37 0.96 0.30 0.21 0.42

water(.8)-propanone(.2)

1.85 0.49 1.40 0.46 0.63 0.38

water(.7)-propanone(.3)

2.31 0.92 1.71 0.91 1.08 0.82

water(.6)-propanone(.4)

2.62 1.23 1.92 1.22 1.38 1.12

water(.5)-propanone(.5)

2.83 1.44 2.07 1.44 1.60 1.34

water(.4)-propanone(.6)

2.99 1.59 0.36 1.59 1.75 1.49

water(.9)-dimethyl ether(.1)

1.17 0.34 1.04 0.26 0.16 0.37

water(.8)-dimethyl ether(.2)

1.93 0.57 1.52 0.54 0.70 0.45

water(.7)-dimethyl ether(.3)

2.43 1.04 1.86 1.03 1.19 0.93

water(.6)-dimethyl ether(.4)

2.76 1.37 2.09 1.37 1.52 1.27

water(.5)-dimethyl ether(.5)

3.00 1.61 2.27 1.61 1.76 1.50

water(.4)-dimethyl ether(.6)

3.17 1.78 1.41 1.78 1.94 1.68

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6.5 Discussion and error analysis

6.5.1 Values within a factor of 2 of experimental data

Based on the sensitivity analysis of partition coefficients to the model results discussed earlier it

was hypothesized that partition coefficients may predict partitioning in various tissues by as

close as a factor of 2 (0.3 log units). The following partition constants are within 0.3 log units of

their corresponding experimental values:

Tables 25-30: For each tissue, predictive methods that were on average within 0.3 log units of corresponding experimental values, measured using the RMSE. For each tissue the lowest RMSE value is bolded. KOW value is included:

Table 25: Adipose Tissue – RMSE values less than 0.3 log units

Phase system RMSE Value

KOW (experimental) 0.24

Lipid fraction method (KTW) 0.23

Lipid fraction corrected method (KTW') 0.21

Hexanol/water 0.28

Heptanol/water 0.26

Octanol (dry) /water 0.24

Nonanol/water 0.23

Decanol/water 0.22

1-Undecanol/water 0.22

1-Dodecanol/water 0.23

Tridecanol/water 0.23

Tetradecanol/water 0.23

Pentadecanol/water 0.24

Hexadecanol/water 0.25

Heptadecanol/water 0.26

Nonadecanol/water 0.27

1-Eicosanol/water 0.28

1,8-octanediol/water 0.22

1-ethyl-3,5-hydroxylcyclohexane/water 0.23

octanol-heptane (50:50) /water 0.28

octanol-heptane (25:75) /water 0.29

Octanol-heptanol/water 0.25

Octanol-Decane/water 0.26

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Table 26: Liver Tissue – RMSE values less than 0.3 log units

Phase System RMSE Value

KOW (experimental) 1.57

Lipid fraction corrected method (KTW') 0.26

Octanol/water(.75)-methanol(.25) 0.23

Octanol/water(.7)-methanol(.3) 0.28

Octanol/water(.8)-ethanol(.2) 0.24

Octanol/water(.7)-glycol(.3) 0.24

Octanol/water(.6)-glycol(.4) 0.27

Table 27: Muscle Tissue – RMSE values less than 0.3 log units

Phase System RMSE Value

KOW (experimental) 1.50

Lipid fraction method (KTW) 0.28

Octanol/water(.85)-methanol(.15) 0.28

Octanol/water(.9)-glycol(.1) 0.29

Table 28: Blood Tissue – RMSE values less than 0.3 log units

Phase System RMSE Value

KOW (experimental) 1.55

Lipid fraction corrected method (KTW') 0.29

Octanol/water(.8)-methanol(.2) 0.26

Octanol/water(.75)-methanol(.25) 0.10

Octanol/water(.7)-methanol(.3) 0.19

Octanol/water(.8)-ethanol(.2) 0.14

Octanol/water(.7)-glycol(.3) 0.11

Octanol/water(.6)-glycol(.4) 0.18

Octanol/water(.9)-propanone(.1) 0.30

Octanol/water(.9)-dimethyl ether(.1) 0.26

Table 28: Kidney Tissue – RMSE values less than 0.3 log units

Phase System RMSE Value

KOW (experimental) 1.41

Octanol/water(.8)-methanol(.2) 0.17

Octanol/water(.75)-methanol(.25) 0.19

Octanol/water(.8)-ethanol(.2) 0.24

Octanol/water(.8)-glycol(.2) 0.25

Octanol/water(.7)-glycol(.3) 0.18

Octanol/water(.9)-propanone(.1) 0.21

Octanol/water(.9)-dimethyl ether(.1) 0.16

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Table 29: Skin Tissue – RMSE values less than 0.3 log units

Phase System RMSE Value

KOW (experimental) 1.67

Octanol/water(.75)-methanol(.25) 0.19

Octanol/water(.7)-methanol(.3) 0.15

Octanol/water(.8)-ethanol(.2) 0.14

Octanol/water(.7)-glycol(.3) 0.22

Octanol/water(.6)-glycol(.4) 0.15

Octanol/water(.5)-glycol(.5) 0.25

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6.4.2 Discussion of KTW predictive methods results

RMSE results of each KTW predictive method are shown in Table 30.

Table 30 showing RMSE results of each KTW predictive method including KOW, lipid fraction KTW, lipid

fraction KTW' Goss-Abraham predicted KTW, Goss-Abraham with COSMO predicted Abraham parameters,

and the closest predicted COSMOtherm mixture KTW value for each tissue.

Tissue Log KOW RMSE

Lipid fraction Log KTW RMSE

Lipid fraction Log KTW' RMSE

Goss-Abraham Log KTW RMSE

Goss-COSMO-Abraham Log KTW RMSE

COSMOtherm best mixture (phase1:phase2) LogK RMSE

Adipose 0.24 0.23 0.21 0.33 0.69 0.22 Decanol:water

Liver 1.57 0.36 0.26 0.63 0.91 0.23 Octanol:water(.75)-methanol(.25)

Muscle 1.50 0.28 0.41 0.41 0.37 0.28 Octanol:water(.85)-methanol(.15)

Blood 1.55 0.31 0.29 0.42 0.71 0.10 Octanol:water(.75) -methanol(.25)

Kidney 1.41 0.38 0.37 0.53 0.79 0.16 Octanol:water(.9)-dimethyl ether(.1)

Skin 1.67 0.44 0.45 0.70 0.97 0.14 Octanol:water(.8)-ethanol(.2)

Ave. RMSE of all tissues for each method

1.32 0.33 0.33 0.50 0.74 0.19

Using Table 30 the partitioning predictive methods can be compared for each tissue, and as an

average taken over all tissues for each method. KOW simulates adipose quite well, being within a

factor of 2 (0.3 log units) of experimental data. However the rest of the tissues are not

simulated as well and the average RMSE is 1.32 when all of the tissues here are considered.

What is not taken into account with this average is that the fat tissue is more responsible for

chemical sorption than other tissues making partitioning in fat an especially important value

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when considering partitioning within organisms. This is in fact the reason that other biotissues

have been largely ignored in terms of researching their partitioning values. With emerging

models that try to describe the distribution of chemicals within an organism, however, obtaining

accurate partitioning values of other tissues is becoming increasingly relevant.

The lipid fraction methods both had an average RMSE value of 0.33, with the largest RMSE value

calculated as 0.45. These results are quite good in that there are no outliers, and that every

tissue was predicted more accurately than using KOW, even the adipose tissue. The benefit to

using the lipid fraction method is that there are few input parameters which may help reduce

inconsistencies in predicted values. It can also potentially be applied to any tissue type. However

in order to use this method lipid fractions (or corrected lipid fractions) and water fractions must

be known for each tissue. These values are specific to each organism and tissue, and finding

published sources for this data may prove difficult. Overall it is a relatively simple method,

applicable across organisms, and can be applied to any tissue type. It would be beneficial to

explore using this method in cases where KTW values are desired.

The LFER approach using experimental Abraham parameters had an average RMSE of 0.50, and

the same LFER approach calculated using COSMOtherm predicted Abraham parameters had an

average RMSE value of 0.74. The muscle tissue was predicted particularly well by both of these

methods, however, and the COSMOtherm predicted Abraham parameters method was more

accurate in this case. The benefit of being able to use predicted Abraham parameters is that in

cases where new or unusual molecules which do not have any experimental data need analysis,

Abraham parameters can be predicted. Although stated in their study that this model should be

able to be applied to fish this model was originally applied to bovine tissue and the serum

albumin coefficient is specifically for bovine tissue. This model is also specific to tissues at 37˚C

which is much higher than the temperature that a fish usually maintains, which is closer to the

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temperature of the water it is in. These reasons may explain why Goss and colleagues were able

to predict partitioning better than could be done in this study. This method was more time-

intensive than the lipid fraction method or COSMOtherm method and requires multiple

calculations be performed to obtain one KTW value. Required inputs include volume fractions for

specified tissue groups and Abraham parameters specific to the solute. However this model can

be applied to any organism as long as volume fractions for tissue groups are known, which may

be easier to obtain than lipid fractions of the tissue.

COSMOtherm had the lowest average RMSE (0.19) and overall it was able to predict the

partitioning most accurately for every tissue group using the specified phase mixture. Due to the

large amount of data that had to be analysed only six solutes were tested; it would be beneficial

to test a larger set of chemicals with varied functional groups on all of these methods to see

how the results are affected. It is quite possible that these solvent systems will not predict KTW

accurately for other chemicals, and since the lowest RMSE values and thus associated solvent

system was chosen for each tissue the data was essentially fit to the desired results. It is an

important point that this is not a validated method and therefore these solvent systems

presented are not suggested for use in calculating KTW values at this point. In addition, these

experiments cannot necessarily be replicated experimentally in a lab setting, as some mixtures

are ‘theoretical’ as they do not account for solubility/insolubilities within one another in these

calculations. These mixtures would have to be investigated theoretically using computational

methods. The results do show, however, that 1) these mixtures may be worth investigating

further for partitioning in liver, blood, muscle, kidney, and skin tissue, and 2) COSMOtherm may

be desirable as a tool to investigate partitioning processes. Using COSMOtherm has a number of

advantages including its large chemical database, its ability to calculate properties for a

molecule that is not in the database or is theoretical, it can predict other properties (such as

96

Abraham parameters, thermodynamic properties, other partitioning constants) that can be used

for checking consistency of results. The time it takes to run a calculation using COSMOtherm is

quite short, unless TURBOMOLE and COSMOConf are employed, in which case the calculation

may take hours or even days. It does appear that other simple mixture similar to octanol-water

may be used to simulate partitioning in other tissues, and that this approach can be investigated

using COSMOtherm. In addition COSMOtherm can be used to find partition constants for an

array of related compounds (for example alcohols) in order to look at trends which may

illuminate information on partitioning. Such graphs have been made using related compounds

of the lowest reported RMSE of a COSMOtherm mixture. These graphs are located in Appendix

2. One disadvantage of using COSMOtherm is that it is a rather complex program and requires

some degree of training for its use.

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7.0 Summary and Conclusions

This study has had two related components. First is the development of a novel fugacity-based

mass balance model describing the time-course of uptake and toxicity of neutral organic

chemicals in a multi-compartment fish and the onset of toxicity. The model, which is

implemented as a spreadsheet, is capable of simulating the bioconcentration and toxicity of the

subject chemical. It requires information on the chemical’s partitioning properties, especially

KOW, the rate of metabolic biotransformation, and parameters describing the uptake parameters

of the fish which may be obtained from allometric relationships. The use of five suggested toxic

endpoints is explored, namely the whole-body critical concentration, the lipid-normalized

critical body burden, the concentration in a suggested target membrane compartment, the

volume fraction in the target membrane compartment, and the whole-body chemical activity. A

unique feature in this model is that it treats the entire sequence of processes from exposure to

probable time of death.

The feasibility of this modeling approach has been demonstrated by applying this model to

empirical data for the uptake and toxicity of naphthalene and trichlorobenzene in a fathead

minnow. The results are within a factor of 2 of empirical data for LBB and time-to-death. The

model was also applied to simulate the bioconcentration of pentachloroethane in a rainbow

trout using empirical data. Simulated concentrations in the blood were within a factor of 2 of

empirical data. These results suggest that with improved parameterization and validation the

model could be used to predict the bioconcentration and toxicity of neutral organic chemicals in

fish. This could assist with empirical toxicity tests, reduce the usage of test animals, and it can

serve as screening-test tool to predict bioconcentration and toxicity in fish.

98

Second, this study demonstrates the critical importance of reliable data concerning organism

partitioning. The lipid fraction method provided consistently low RMSE values for predicting

tissue-water partition coefficients to specified tissues and is already a validated method. For

these main reasons the lipid fraction method is suggested for predicting KTW values in fish. A

new quantum method of predicting partition coefficients has been evaluated and tested for a

variety of solutes and mixed solvent systems which tries to better simulate partitioning into

tissues. As a result of the availability of faster and less expensive computers and improved

insights into processes occurring in chemical solutions this method holds promise for improving

the assessment of bioconcentration and toxicity of existing and new chemicals. An attractive

feature of this approach is that partition coefficients can be estimated a priori from information

on molecular structure. This accuracy is generally within a factor of 2.

The two studies together suggest that it is highly feasible to develop a modeling framework that

relates the molecular structure of neutral organic chemicals to their bioconcentration and

aquatic toxicity with an uncertainty sufficient for screening test regulation purposes.

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