Yolk–Water Partitioning of Neutral Organic Compounds in the Model Organism Danio rerio

Yolk is the most important temporary biological compartment of the early life stages of fish embryos. The sorption strength of a chemical to yolk components may significantly influence the distribution of that chemical in the fish embryo. We determined yolk–water partition coefficients (Kyolk/water, in liters of water per kilogram of yolk, normalized to dry wt) for 70 neutral organic chemicals. The log Kyolk/water values range from 0.76 to 6.56. On the basis of these values, we developed polyparameter linear free energy relationship models to predict yolk–water partitioning for a broad range of neutral organic chemicals with a root mean squared error of 0.37 and r2 of 0.919. These models can be applied for the prediction of internal concentrations at equilibrium (neglecting biotransformation and active transport) in the zebrafish embryo test system. Environ Toxicol Chem 2020;39:1506–1516. © 2020 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.


INTRODUCTION
Fish embryos are used as an alternative model in toxicology in various areas, for instance, to determine the acute toxicity of chemicals (Embry et al. 2010;Strähle et al. 2012;Belanger et al. 2013;Busquet et al. 2014), to study bioconcentration (Kühnert et al. 2013), and to identify developmental toxicity (Brannen et al. 2010;Weigt et al. 2011), endocrine disruption (Segner 2009;Brion et al. 2012), or neurotoxicity (Linney et al. 2004;de Esch et al. 2012). Often, the intention is to enable small-scale screening of chemicals and/or to extrapolate the effects to juvenile and adult fish or even mammals. Typically, embryos of the zebrafish Danio rerio are used because of the ease of zebrafish maintenance, the large number of produced eggs, and the transparency of early life stages (Scholz et al. 2008). For a mechanistic understanding of chemical effects, knowledge of the concentration of a chemical at the target site for the respective endpoint as well as the freely dissolved concentration of a chemical in the test system is crucial. However, because of the small scale, direct measurement at the target site is difficult; therefore, internal concentrations of chemicals in fish embryos (Kühnert et al. 2013;Brox et al. 2014) are typically derived from whole-body homogenates. Furthermore, embryonic stages of oviparous vertebrates such as fish are characterized by a specific compartment, the yolk. The yolk functions as a nutrition source for the developing embryo. Its major component, vitellogenin (VTG), represents a high-molecular weight glycolipoprotein of approximately 2140 amino acids with a molecular weight of approximately 250 kDa. It is synthesized in the liver of females and transported via the blood to the ovary. After receptor-mediated endocytosis, VTGs are cleaved to lipovitellins I and II as well as phosvitin. Besides these proteins, the yolk includes various lipids like cholesterol (40% of the total lipid), phosphatidylcholine (17% of the total lipid), and triglycerides (9% of the total lipid) (Fraher et al. 2016;Sant and Timme-Laragy 2018). The exact composition is not known, and there might be high variability with respect to species or nutrition. In zebrafish, depending on the incubation temperature of the embryo, the yolk reservoir is depleted by approximately 5 d postfertilization (Strähle et al. 2012).
Proteins and lipids can represent an important source for sorption of chemicals; hence, a significant amount of a test chemical may be bound to the yolk fraction of the embryo. This would be of particular importance if internal concentrations are derived from whole-body analysis because chemicals with differential distribution between the yolk and body could mask the concentrations relevant at the target site. Understanding of the yolk-body distribution of a chemical would allow one to correct internal concentrations from whole-body chemical analytics.
To describe the distribution of a chemical in the fish or fish embryo at equilibrium, the fish-water partition coefficient can be calculated for a chemical using Equation 1 (according to Endo et al. 2013). The respective composition of the fish has to be known therefore (volume fraction f of the component) as well as partition coefficients for different biological components like transport proteins (serum albumin, e.g.; Henneberger et al. 2016a), structural proteins Henneberger et al. 2016b), storage lipids , and membrane lipids . Note that all partition coefficients are in units of liters of water per liter of component.
Partition coefficients (biological compartment-water) for transport proteins (especially serum albumin), structural proteins, storage lipids, and membrane lipids are known for some hundreds of compounds; but in general the chemical universe is much broader and diverse, and all of the different compounds of interest cannot be covered by these experimental data sets. Models for the prediction of partition coefficients are therefore needed. For neutral chemicals, the polyparameter linear free energy relationship (pp-LFER) equations were successfully applied to predict the respective partition coefficients Endo et al. , 2012Endo et al. , 2013Geisler et al. 2012). The pp-LFER equations were developed in the 1980s by M. Abraham and coworkers to predict various physicochemical properties of organic compounds (Abraham et al. 1994a(Abraham et al. , 1999. These models describe the partition coefficient (in terms of log K) mechanistically based on the interaction possibilities of a respective chemical (represented by uppercase letters in Equations 2 and 3) with the 2 phases of a partition system (represented by lowercase letters in Equations 2 and 3). The interactions covered in the equations are hydrogen bond acidity A, hydrogen bond basicity B, polarizability and dipolarity S, excess molar refraction E (only Equation 2), McGowan's molar volume V, and the logarithmic gas/hexadecane partition coefficient L (only Equation 3). The lowercase letters of the equation describe the complementary interactions of the surrounding 2-phase system and the system constant c (Abraham et al. 2004;Goss 2005;Vitha and Carr 2006;Endo and Goss 2014a). In comparison to Equation 2, Equation 3 does not include the eE term; the nonspecific interactions are described by vV and lL instead. Advantages of Equation 3 are the potential application for highly fluorinated compounds as well as for organosilicon compounds and that it gives slightly better fits (Endo and Goss 2014b).
In comparison to a juvenile or adult fish water system, where the composition of the fish (e.g., rainbow trout) can be described by available equations for the biological compartments (proteins and lipids) as mentioned, it is not yet possible to describe the zebrafish embryo in the same way. The sorption properties of the yolk as one important compartment of the embryo have not been characterized experimentally. But there is a strong demand to understand the sorption behavior of chemicals to the yolk compartment and the distribution of chemicals between water and the yolk in the early stages of the fish embryo. Knowing the yolk-water partition coefficients, a detailed description of the distribution of a chemical is possible. This enables a precise prediction of internal concentration at the early life stages of the zebrafish and helps in experimental designs and setups. Further, the distribution of a chemical between the yolk and the embryonic body can be characterized, which is essential for the interpretation of toxicological effects observed in the test organism. And yolk-water partition coefficients are needed for physiologically based toxicokinetic modeling to describe the alternative test system.
For this reason, we decided to characterize the yolk as one complete biological compartment to enable a mechanistically based description of the equilibrium situation for neutral chemicals in zebrafish embryos. Based on the experimentally determined partition coefficients, we developed pp-LFER equations to enable a prediction of yolk-water partitioning for neutral organic compounds.

Reagents
Test medium for incubation of embryos was prepared according to Organization for Economic Co-operation and Development guideline 236 (International Organization for Standardization 1996; Organization for Economic Co-operation and Development 2013). To buffer the pH, Hanks' balanced salt solution (Sigma-Aldrich; 10 mM, pH 7.4) or MES hydrate (Sigma Aldrich; 10 mM, pH 5.8) was used.

Preparation of yolk
Eggs (fertilized and nonfertilized) of D. rerio at 2 to 3 h postfertilization (hpf) were rinsed with tank water and test medium and finally transferred with a pipette to a 15-or 50-mL polypropylene tube. Water was completely removed, and eggs were homogenized with an Ultra Turrax (speed 6.0, 2 × 2 min, T10 basic; IKA) and centrifuged at 13 000 rpm for 5 min at 4°C to remove food remains, feces, and chorion parts. The supernatant (yolk) was used for the determination of the yolk-water partition coefficients.

Determination of dry weight
Dry weight for each batch of yolk (each experimental approach) was determined from 3 replicates in 1.5-mL glass vials. In brief, 300 µL of yolk were weighed on an analytical balance. Water was removed in an oven at 100°C for 3 h. After cooling down, the weight of the remaining yolk components was determined; and to confirm the result, the weight of the remaining yolk components was determined again after heating at 100°C for another 2 h.

Determination of partition coefficients by dialysis experiments
Dialysis experiments were performed with custom-made dialysis cells at 25°C under constant stirring at 250 rpm (a picture of the dialysis cells is given in Supplemental Data, S1). These cells are composed of two 5-mL glass chambers, which were separated by a dialysis membrane (Spectra/Por ® 3 Standard Grade Regenerated Cellulose Membrane, Standard RC Sheets with a molecular weight cutoff of 3.5 kDa; to ensure that yolk components with low molecular weight were retained, we selected the low-molecular weight cutoff). For each experimental setup, 3 replicates were prepared, where 5 mL of yolk or a yolk dilution were used on one side of the dialysis cells and 5 mL of a spiked solution of test medium or buffer were used on the other side of the cells (sample cells). In addition, 3 reference cells were prepared, where 5 mL of test medium or buffer were used instead of yolk or yolk dilution. The concentration of each compound was 0.5 mg/L in the dialysis system; spiking was done using 50 µL of a respective methanol solution, which results in 0.5% (v/v) of methanol in the system. Recoveries can be found in Supplemental Data, S1. After 48 h (first sampling) and 72 h (second sampling), samples were taken from the dialysis cells to check whether equilibrium was reached and to determine the yolk-water partition coefficient. Both chambers of the reference cells were sampled, whereas only the yolk-free side was sampled for the sample cells. At the first time point, 100 µL of the cells were sampled, to avoid an influence on the system by volume loss. At the second time point, 200 µL were sampled.

Sample preparation and analysis for the dialysis setup
Samples were analyzed via gas chromatography (GC)-mass selective detection (MSD) or liquid chromatography tandem mass spectrometry (LC-MS/MS) depending on the chemical. The LC-MS/MS analysis of the aqueous samples was performed directly without sample preparation; for GC analysis an extraction step with cyclohexane or ethyl acetate was applied prior to analysis. Selection of the extraction solvent was based on the calculation of the extraction efficiency by the respective solvent-water partition coefficient for each chemical (extraction tool [Ulrich et al. 2017]). In addition, naphthalene or hexachlorobenzene was added as an internal standard for the extraction procedure. Details can be found in Supplemental Data, S1. Equations for the calculation of the yolk-water partition coefficients are given in Supplemental Data, S2.

Determination of partition coefficients by headspace-GC-flame-ionization detection measurements for volatile compounds
Yolk-water partition coefficients of volatile compounds could not be investigated by dialysis experiments. Crimped vials were used for a 2-phase (reference: water as one phase and air as another phase) and a 3-phase (sample: yolk components like lipoproteins, lipids, and proteins comprised one phase, water as the main component of yolk as the second phase, and air as the third phase) setup, where the air phase was analyzed by headspace measurements on a 6890 GC (Hewlett-Packard) with a 7694 headspace sampler (Hewlett-Packard). Volumes of both the 2-and 3-phase approaches were kept the same. Between 0.1 mL (0.1 mL yolk diluted with 0.9 mL test medium to obtain a volume of 1 mL) and 5 mL yolk were used in the experiments. A minimal volume of 0.5 mL (yolk and/or test medium) was used in the setup. Concentrations used in the headspace measurements were 1 mg/L for the different compounds; the content of methanol was maximal 1% (v/v). Recoveries can be found in Supplemental Data, S1. The prepared 20-mL headspace vials were shaken for 2 h on an orbital shaker at 220 rpm and at room temperature. After equilibration, the samples were placed in the headspace sampler and equilibrated for 2 h at 35°C before headspace analysis (for details see Supplemental Data, S1). Two hours of equilibration in the headspace oven was selected to keep the conditions the same for all samples within an approach. Equations for the calculation of the yolk-water partition coefficients are given in Supplemental Data, S2.

Selection of compounds
Compounds investigated by the dialysis approach were analyzed by GC-MSD or LC-MS/MS. The main advantage of the LC-MS/MS measurements was that no sample preparation was needed before analysis. The aqueous samples could be analyzed directly. However, the selection of compounds was determined by the availability of experimental pp-LFER compound descriptors, which are mainly available for organic chemicals with lower molecular weights (m/z < 150). Often, it is difficult to analyze such compounds by LC-MS/MS, and LC-diode array detector (DAD) systems are preferred for the quantification of these compounds. However, often the sensitivity is the limiting factor for the quantification by LC-DAD systems. Our preselection included many compounds with different functional groups, to get a chemically diverse data set and a broad application domain for the model; but some of the selected compounds could not be detected by LC-MS/MS. Other compounds were volatile, and the log yolk-water partition coefficient (K yolk/water ) could not be investigated by the dialysis experiments because of the loss of compounds during the experiment. For these compounds the headspace approach was used to determine the K yolk/water values.

Statistics and graphs
Multiple regressions for the determination of the system parameters of the yolk-water partition system were performed in Statistica (Ver 13; TIBCO Software). The solute descriptors used in the multiple regressions are given in Supplemental Data, S3. The solute descriptors were derived from the LSER database (Ulrich et al. 2017). In the multiple regressions log K yolk/water values were used as dependent variables and the respective compound descriptors E, S, A, B, V (with regard to Equation 2) or L, S, A, B, V (with regard to Equation 3) as independent variables. Graphs were created with Python Ver 3.6 (Python Software Foundation n.d.) using the libraries Matplotlib Ver 3.1.1 (Hunter 2007) and Seaborn Ver 0.9.0 (Waskom et al. 2018).

RESULTS AND DISCUSSION
Determination of dry weights and protein content of the yolk The protein content was determined by Lowry protein assay (Supplemental Data, S4). Protein content and dry weight (Supplemental Data, S4) showed smaller differences for the different dialysis experiments.
The dry weight ranged from 24.9 to 65.8 mg/mL yolk, the interbatch variability was 26%, and the maximum of the intrabatch variability was 3%. The respective protein content ranged from 15.8 to 57.7 mg protein/mL yolk, with an interbatch variability of 30% and a maximum in the intrabatch variability of 27%. The protein content and the dry weight did not correlate (r 2 = 0.21; Supplemental Data, S4). Other components like lipids are also present in the yolk and might have a sorption capacity as well (Wang et al. 2000;Hachicho et al. 2015;Bittner et al. 2019). For this reason, we decided to refer the determined partition coefficients to the dry weight.
The yolk extracted from fish eggs varied slightly in its composition for several reasons. 1) Because of the different amounts of eggs processed on individual days, the yolk extraction was conducted at slightly different stages of development, ranging from 2 to 3 hpf. 2) Homogenization mechanically disrupted the chorion (egg shell) of the embryo. The chorion represents a nonsoluble, highly crosslinked protein layer, which could not be completely removed by centrifugation. Hence, the different extracts may contain variable fractions of remaining chorion pieces (see pictures of the yolk in Supplemental Data, S5). 3) In addition to the developmental stage or chorion contaminations, there might be other sources of variability such as nutritional status or amount of food taken up by the females producing the eggs.

Determination of yolk-water partition coefficients by dialysis experiments
Dialysis experiments were performed for 46 aromatic compounds individually; results are given in Table 1. The compounds were spiked in methanol solution to the dialysis system, resulting in a 0.5 volume (v/v) of methanol in the buffer solution. This should have no impact on the yolk-water partition coefficient. The log K yolk/water values ranged from 0.76 (aniline) to 3.95 (phenanthrene). We tried to keep the fraction of compound which was sorbed to the yolk components between 20 and 80% to avoid larger errors attributable to analytical limitations (Allendorf et al. 2019). For smaller log K yolk/water values, the amount of yolk which could be used in the dialysis experiment was the limiting factor. For aniline, for example, the fraction bound to yolk was between 7 and 21% (Supplemental Data, S6), and the respective log K yolk/water values were between 0.46 and 1.01. The standard deviation (SD) of the log K yolk/water values was 0.23 (all samplings included, SD = 0.27 for the first sampling, SD = 0.21 for the second sampling), which is relatively high in this case. To determine these values, 5 mL yolk were used without dilution in the dialysis experiments. A fraction bound to yolk <20% for aniline leads to greater errors in the estimation of the yolk-water partition coefficient (Allendorf et al. 2019). Compared to other biological compartments like serum albumin, which had been investigated by dialysis experiments in earlier work Henneberger et al. 2016a;Allendorf et al. 2019) and can be purchased as purified protein, the amount of nonaqueous compartments of the yolk cannot be obtained in higher concentrations to improve determination of partition coefficients for compounds with log K yolk/water values <1. To obtain 5 mL of yolk per replicate, a minimum of 17 mL of yolk is required (including the setup of 3 dialysis cells and the determination of the corresponding dry wt), which means that approximately 80 000 to 100 000 eggs are needed. For this reason, we also decided to include the log K yolk/water values where the fraction sorbed to the yolk components is close to 20%, and we also accepted higher SDs in some cases (e.g., aniline).
To determine the relatively high log K yolk/water value of phenanthrene (3.95), yolk was diluted 1:50. The yolk was not completely homogeneous, and smaller chorion constituents were still present (see Supplemental Data, S5). To avoid inhomogeneous solutions in the dialysis cells, the dilutions with buffered or nonbuffered test medium were prepared in a volumetric flask (0.5 mL yolk in 50 mL test medium) and well mixed before adding them to the 3 dialysis cells. We tried to avoid higher dilutions because the error in the determination of the yolk-water partition coefficient is also influenced by the dilution step. According to our experience, a log K yolk/water value of 4 is the largest one can determine with the dialysis experiments.
We tested the reproducibility of the results from the dialysis experiments for the compound naphthalene (Supplemental Data, S7). Five independent dialysis experiments were performed. The results for log K yolk/water ranged from 2.24 to 2.71. The mean log K yolk/water value of all measurements was 2.48, with an SD of 0.06. For each experiment, different preparations of yolk were used, which may explain the observed differences. Related to the variability of the yolk compositions, the same sources of variability (e.g., developmental stage) may also impact the determination of the partition coefficients (see section Determination of dry weights and protein content of the yolk, and Supplemental Data, S4).
Determination of yolk-water partition coefficients for volatile compounds using headspace analysis Aliphatic compounds were selected to enhance the diversity of the compounds in the training set of the model and to extend the application domain of the pp-LFER model. These compounds are more volatile compared to the aromatic compounds which were selected for the dialysis experiments. Because of their volatility, we decided to determine the yolk-water partition coefficients by headspace measurements. By the headspace approach higher log K yolk/water values could be determined, with a range from 1.82 (hexafluorobenzene, the only aromatic compound determined by headspace measurements) to 6.56 (n-tridecane). By means of headspace analysis the total data set was expanded by 24 compounds (Table 2). For 3 compounds the fraction of chemical sorbed to the yolk components (Table 2, fraction bound) was <20%. A consistency test suggests that also these values were valid (Supplemental Data, S8).
The minimal temperature which could be applied for the equilibration in the headspace oven was 35°C, which means there is a temperature difference of 10°C between the dialysis approach (25°C) and the headspace approach (35°C). To answer the question whether there could be a shift in the log K yolk/water values, we performed the dialysis experiment for naphthalene at different temperatures. Results are shown in Table 3. The log K yolk/water values ranged from 2.33 to 2.80; in comparison, the values of the different dialysis setups at 25°C for the compound naphthalene ranged from 2.24 to 2.71 (Supplemental Data, S7). The results for naphthalene indicated that no clear shift could be observed for different temperatures applied at the dialysis experiments. For this reason, we included the headspace data in the whole data set for the development of a pp-LFER equation.

Potential impact of aging on the determination of partition coefficients
A potential confounding factor of the partition coefficient determination could be introduced by aging of the yolk. It is likely that lipoproteins, proteins, and lipids may degrade over time in the nonsterile experimental system, whereas a living fish egg of the early life stage does not foul. A potential change in the protein structure or composition was indeed indicated by odor and appearance as well as a change in the pH values in the dialysis cells. The pH of the yolk preparations changed from 6.5 at the beginning of the dialysis experiments to 5.8 at the end of the dialysis experiments (72 h, second sampling). We also tested the pH in yolk, which was older than 1 wk (not used for partition coefficient determination) and found a further decrease to 5.0, indicating a potential degradation of yolk components and/or microbial contamination.
The potential changes in the composition may have affected the sorption behavior of chemicals to the yolk components. This can be seen especially for amines (e.g., 2-bromoaniline, N,N-diethylaniline; Table 1), where strong differences occurred in the partition coefficients determined for the first and second samplings.

Description of the yolk-water system by pp-LFER equations
A pp-LFER model was obtained by a multiple regression using the experimentally determined log K yolk/water values from Experimentally determined values for the first and second samplings and values calculated from both samplings are given; the SD for each log K yolk/water value is given in parentheses, and the fraction of compound which is sorbed to the yolk components is given as fraction bound. CAS = Chemical Abstracts Service.
Yolk-water partitioning of neutral organic compounds-Environmental Toxicology and Chemistry, 2020;39:1506-1516 both approaches of all chemicals as dependent variables and the respective solute descriptors as independent variables. In total, 70 partition coefficients of the respective chemicals were used to obtain the pp-LFER model. The model was developed based on the log K yolk/water values of the first sampling. Values from the second sampling were avoided because of the aging effects of the yolk, which appeared during the experiment and may affect the yolk-water partition coefficients of some compounds (e.g., phenol, 4-nitroaniline). Two different pp-LFER equations were obtained based on Equation 2 or 3. In Equation 5 the lL term is used instead of the eE term (Equation 4). The coefficients of determination (r 2 ) as well as the root mean squared errors (RMSE) are the same for both models.
Multiple regressions were also performed based on the log K yolk/water values of the second sampling and for the mean log K yolk/water values of both samplings (Supplemental Data, S9). The range of the compound descriptors can be found in Supplemental Data, S2. The model should only be applied for predictions of yolk-water partition coefficients within this application domain. Slight differences can be seen for the phase parameters determined; differences are on the order of approximately 0.2. The r 2 value is lower for the model based on the log K yolk/water values achieved from the second sampling (0.880/0.886), and the respective RMSE is higher (0.44/0.43). This confirms the uncertainties based on the aged yolk system, and we recommend applying Equation 4 or 5 for the prediction of yolk-water partition coefficients. As can be seen from Figure 1, the log K yolk/water values determined by dialysis experiments and by the headspace approach cover different ranges and different application domains regarding the chemical space or potential intermolecular interactions. We also performed multiple regressions on the smaller data set of the log K yolk/water values determined in the dialysis experiments (Supplemental Data, S9, Table S9-1) to show the influence of the additional values on the results of the multiple regression. Overall, we tried to cover a broad application domain and included fluorinated compounds and chemicals with 2 or more functional groups.
To check whether the sorption capacity of the yolk is similar to that of other biocompartments or can be described by the octanol-water partition coefficient, linear regressions were The linear regression with the membrane lipid-water partition coefficient shows a slope of 0.98 and an intercept of -0.57; the partition coefficients seem to be relatively similar compared to the other equations. For larger partition coefficients, both systems (yolk-water and membrane lipid-water) correlate well, and membrane lipids show relatively similar sorption properties compared to the yolk components. In contrast, larger differences were observed for the comparison of the yolk-water partition coefficients with the octanol-water partition coefficients, the serum albumin-water partition coefficients, and the storage lipid-water partition coefficients of the respective compound data set. This means that these sorption phases FIGURE 2: Experimentally determined log K yolk/water values (of the first sampling) were plotted against log K octanol/water (first row, left), log K albumin/water (first row, right), log K storage lipid/water (second row, left), and log K membrane lipid/water (second row, right) values. K albumin/water = albumin-water partition coefficient; K membrane lipid/water = membrane lipid-water partition coefficient; K octanol/water = octanol-water partition coefficient; K storage lipid/water = storage lipid-water partition coefficient; K yolk/water = yolk-water partition coefficient. cannot be used as surrogates to describe the sorption behavior of yolk components, although the RMSE value of Equation 6 is close to the RMSE values of the pp-LFER equations. Because there are also slight differences for membrane lipids and yolk components, the mechanistically based pp-LFER approach is an appropriate model to predict yolk-water partition coefficients over a broad range.
We further compared the pp-LFER equations of the respective systems (Table 4), the phase parameters of the 5 systems are different from each other (Abraham et al. 1994b;Geisler et al. 2012); also, parameters of the membrane lipid-water show larger differences for the a, b, and s parameters. The yolk-water system is described by greater a and b parameters and a smaller s parameter. The a parameter is even positive, indicating that there are strong H-bond acceptors present in the nonaqueous compartments of the yolk-water system.

Validation of the model
To validate our model, we calculated yolk-water partition coefficients from zebrafish embryos obtained by whole-embryo measurement in a study by Kühnert et al. (2013). In the present study the internal concentrations of napththalene, fluorene, benz[a]anthracene, and fluoranthene of the whole embryo in a defined exposure medium were determined to calculate bioconcentration factors. We excluded benz[a]anthracene for the validation because its internal concentrations decreased over time, indicating increasing biotransformation. We calculated the yolk-water partition coefficient assuming that the dry weight of one zebrafish embryo is 61 µg/egg at 96 hpf (Hachicho et al. 2015). The study of Kühnert et al. was performed until 72 hpf. The dry weight between the 2 time points is relatively constant (Hachicho et al. 2015). The internal concentrations in the study were determined at different time points (3-72 hpf). From 21 to 72 hpf the internal concentrations of the compounds naphthalene, fluorene, and fluoranthene did not change significantly, although the amount of yolk decreased during these developmental stages, so we assumed an equal distribution of the chemicals between yolk and embryonic body for these 3 compounds. In Table 5 the calculated log K yolk/water values are given; based on Equations 4 and 5, we predicted the log K yolk/water values for the 3 compounds. For naphthalene we could further compare our experimentally determined yolk-water partition coefficient to the calculated one. The results of our prediction differ only slightly from the calculated values, which strongly indicates that the yolk-water partition coefficient can be used to describe the sorption to the total zebrafish embryo at later time points of the test.
Our predicted values (Table 5, predictions based on Equations 4 and 5) and the experimentally determined values are in good agreement with the calculated log K yolk/water values from the data set of Kühnert et al. (2013), the differences between predicted and calculated log K yolk/water values are in the range of 0.1 to 0.3 log units. For this example, it can be seen that the yolk-water partition coefficients can be predicted quite well by our pp-LFER equations. The value for albumin-water partitioning is given in liters of water per kilogram of albumin; recalculation of the equation by assumption of a density of 1.4 kg/L will result in c = 0.29 for a unit conversion to liters of water per liter of albumin (Endo et al. 2013). For membrane lipids a density of 1.0 kg/L is assumed; there is no problem in unit conversion to liters of water per liter of membrane lipid for the equation. Storage lipids have a density of 0.93 kg/L; for comparison of the equations with log K values having equal units, the constant c of the equation will be different. a = hydrogen bond acidity; b = hydrogen bond basicity; c = system constant; e = excess molar refraction; K albumin/water = albumin-water partition coefficient; K membrane lipid/water = membrane lipid-water partition coefficient; K octanol/water = octanol-water partition coefficient; K storage lipid/water = storage lipid-water partition coefficient; K yolk/ water = yolk-water partition coefficient; s = polarizability and dipolarity; l = logarithmic gas/hexadecane partition coefficient; v = McGowan's molar volume. For naphthalene, the experimentally determined log K yolk/water value is also given; for each compound, the experiments were conducted at 2 different concentrations, and we calculated the respective log K yolk/water value for each concentration. n.a. = not analyzed.

CONCLUSIONS
Yolk-water partitioning can be described by the pp-LFER approach for neutral organic chemicals. The equations for the prediction of the partition coefficients can be used to describe the thermodynamic equilibrium situation in the fish embryo. The application domain of the model is broad; however, it cannot be applied for high-molecular weight compounds where steady state is not reached in the fish embryo. Greater differences between the predicted yolk-water partition coefficients are expected if biotransformation plays an important role for the test compound in the fish embryo and at the later developmental stages (100-120 hpf). Especially for the late developmental stages, the yolk will play a minor role as a sorbent, and the body-water partition coefficient should be calculated as an alternative to describe steady state. Further, it cannot be applied for ionic compounds because the pp-LFER approach is only applicable for neutral chemicals. For ionic chemicals there is a strong demand for other valuable prediction tools. Within the application domain, we could demonstrate that the models can be successfully applied to predict the steady-state partitioning for neutral organic compounds and may serve as a helpful tool for the description of a chemical's behavior in the fish embryo test systems.