Mechanistic modeling of the bioconcentration of (super)hydrophobic compounds in Hyalella azteca

Bioconcentration tests using the freshwater amphipod Hyalella azteca as an alternative to conventional fish tests have recently received much attention. An appropriate computational model of H. azteca could help in understanding the mechanisms behind bioconcentration, in comparison to the fish as test organism. We here present the first mechanistic model for H. azteca that considers the single diffusive processes in the gills and gut. The model matches with the experimental data from the literature quite well when appropriate physiological information is used. The implementation of facilitated transport was essential for modeling. Application of the model for superhydrophobic compounds revealed binding to organic matter and the resulting decrease in bioavailable fraction as the main reason for the observed counterintuitive decrease in uptake rate constants with increasing octanol/water partition coefficient. Furthermore, estimations of the time needed to reach steady state indicated that durations of more than a month could be needed for compounds with a log Kow > 8, limiting the experimental applicability of the test. In those cases, model-based bioconcentration predictions could be a preferable approach, which could be combined with in vitro biotransformation measurements. However, our sensitivity analysis showed that the uncertainty in determining the octanol/water partition coefficients is a strong source of error for superhydrophobic compounds. Supplementary Information The online version contains supplementary material available at 10.1007/s11356-023-25827-7.

Albumin-like protein concentration assumed the same as albumin in fish. The diffusion coefficient of the albumin-like protein in water is assumed equal to that of albumin 6.3*10 -7 cm 2 /s (Gaigalas et al., 1992). Note that this is a very rough assumption. Total plasma flow , 252 Lplasma/kg/d Cardiac output QB was calculated as for fish after (Erickson & McKim, 1990): To covert Lblood in Lplasma, QB was multiplied by 0.7 as in fish (Gingerich et al., 1987).
Agut 0.07 cm 2 For Gammarus pulex, the gut was reported as of cylindrical shape with a diameter of 0.28-0.6 mm for animals of 10-15 mm length (Welton et al., 1983). Scaling down to a bodylength of 4.5 mm for Hyalella azteca, this amounts to a diameter of about 0.2 mm. The surface area of a cylinder of diameter 0.2 mm and length of approximately 4.5 mm amounts to 9.6*10 -3 cm 2 . Assuming the presence of villi in the gut, we multiply by a factor of 7.5 as is done for fish (Larisch & Goss, 2018a). Micro-villi have been observed in amphipods (Halcrow, 2001), we therefore apply a factor of 24 on the apical membrane permeability.
Note that this is a very rough estimation.

S1 Diffusion
Diffusion is the driving force for the uptake (and elimination) of chemicals into the organism. Although borders between areas of diffusion and advection are not sharp in reality (Erickson & McKim, 1990), for simplicity we will strictly separate both processes. Diffusion will be deemed insignificant in areas dominated by water-or blood flow, and transport in the unstirred water layers or the membrane is assumed solely governed by diffusion. The diffusive flux is related to the concentration gradient by Fick's first law: Where J is the diffusive flux (in chemical mass/area/time), D is the diffusion constant, c the chemical concentration and x the position. Diffusion constants in water were estimated from molecular weight (MW), according to (Avdeef, 2010): Modeled compounds, molecular weight and calculated diffusion constants are listed in Table S3 and S4. We assumed equal diffusion coefficients in blood and water, but a reduction by a factor of 0.25 for the diffusion in the cytosol (Verkman, 2002).    (Tomlin, 2003) j Experimental (Baker et al., 1992)

S2 Facilitation factor in ABLblood
For the calculation of the facilitation factor in blood, albumin-like proteins with similar binding properties were assumed to be present in H. azteca at the same concentration as in fish. Albumin/water partition coefficients were either calculated with LSERD (Ulrich et al., 2017) using experimental descriptors, or the following correlation with the log Kow (Endo & Goss, 2011): The desorption rate constant from albumin was calculated from an empirical correlation with the chemical's molecular weight according to Eq. (S4) (Krause et al., 2018): Where MWchemical is the chemical's molecular weight in g/mol, and kdes is the desorption rate constant in 1/s.

The relation between solute bound to albumin
, and solute freely dissolved in water in equilibrium can be expressed as: Where / is the albumin/water partition coefficient, is the concentration of albumin in water, and ksorb,ALB is the sorption rate constant to albumin in 1/s.
To calculate the influence of facilitated transport by the carrier albumin in blood, compound both freely dissolved in water and bound to albumin must be considered separately. Only the unbound fraction can move across cell membranes, but both fractions may traverse the unstirred water layer, see scheme in Figure S2 on the right. Figure S2 Diffusion steps in gills (left) and facilitated transport of the chemical across the ABL in blood (right). Vertical arrows on the right depict diffusion of the chemical (unbound and bound to the carrier), horizontal arrows de-/sorption processes from/to the carrier. Only the unbound species can traverse the cell membrane and enter layer 1 from the membrane side, but both can traverse into the gill blood compartment (Bloodgills), hence the asymmetrical depiction of arrows.
Transport rate constants for the diffusion through the ABL in blood differ from the free chemical, because the transport of the bound chemical is limited by the diffusion of the carrier: Where Dcarrier is the diffusion constant of the carrier, in this case albumin.
We separated the ABL into 10 layers. Sorption kinetics are slow in relation to the residence time in the respective layers, we are thus limited by de-/sorption kinetics. Sorption processes will take place during the whole diffusion process, but a molecule only carried the last little stretch of the way by a carrier will not contribute the same way to the facilitation factor as a molecule picked up from the start. For an ABL of 286 nm, the arising difference between 1 and 10 layers in the calculations amounted to a factor of about 10.
For the unbound and bound chemical, mass balance equations can be set up in each layer, as each form can move from or to the neighboring layer, or sorb or desorb from albumin in the respective layer. Solving the system of equations in Table S5 via the Gauss algorithm, we get the rate constant considering facilitated transport. Comparing this rate constant to the one without considering facilitated transport, we can calculate FACABL.
The resulting facilitation factors FACABL are then used to calculate the rate constant of diffusion through the ABL in blood: Where Dw is the diffusion constant of the chemical in blood (assumed equal to water) and dABL the total thickness of the ABL. Vlayer =A*dABL,blood,layer*0.7 = A*dABL,blood/10*0.7 the volume of a single ABL-layer, kABL,blood,unbound/ kABL,blood,bound rate constant for diffusion in the ABL in blood for freely dissolved chemical/chemical bound to albumin-like proteins for an ABL layer of thickness dABL/10, kx rate constant for diffusion from water to the first layer of the ABL (combines all preceding diffusion steps, for simplicity), cw,unbound is the chemical concentration in water of the unbound chemical. Vblood is the volume of the organ blood pool, which is assumed well mixed and is big enough for the bound and unbound chemical to be in equilibrium with each other. The factor 0.7 is used to transform blood volume to plasma volume.

S3 Bile acids as carriers in the gut
The facilitated transport via bile acids in the gut was estimated from subcooled solubility according to (Larisch, 2019;Larisch & Goss, 2018b;Westergaard & Dietschy, 1976): Where Ssubcooled is the subcooled solubility in mM. It is calculated approximatively according to (Liu et al., 2013) from aqueous solubility Sw and melting temperature Tm (in K): Note the uncertainty of these predictions, because the prediction model of the FACmic by micellar transport is an empirical model based solely on fatty acids as input data. Although the FAC depends on log Kow, there is wide scatter, see Figure S3. Thus, the estimated FAC depending on log Kow can only be considered as a rough estimate, and specific FACs should be calculated for specific chemicals for better results. For resulting FAC below 1, FAC was set to 1. Figure S3 Correlation between calculated log FAC and experimental log Kow. Micelle facilitation factors were calculated at 297 K using Eq. (S9) and (S10) for 1601 chemicals for which experimental log Kow (Mansouri et al., 2016), experimental water solubilities and experimental melting temperatures were available (QSAR Toolbox version 4.4.1, which is freely available on the OECD website (http://www.qsartoolbox.org/)). Trendline: log FAC =0.58*log Kow -2.18.

Figure S7
Differences in modeled k1 if transport by blood flow is reduced due to a reduced binding to albumin and thus a reduction in sorption capacity of the blood, or by an actual reduction in blood flow. Figure S8 Differences in k1 due to organism age at the start of the experiment. Young, immature amphipods tend to have higher k1 than mature ones. If a datapoint is not marked, no age was available in the respective publication.  Figure S12. Different models predicting k1: this work (calculated with adapted blood flow), and models from literature (Arnot & Gobas, 2004), (Lee et al., 2002) and (Chen & Kuo, 2018); models that did not consider a reduced bioavailable fraction were multiplied by funbound. Figure S13. Predicted k2 according to Eq. (6), in the absence (blue) or presence (green) of metabolism, alongside experimental k2 (red) for blood flow modeled as in fish. Same chemicals taken from different literature are marked with a cross. Figure S14. Relative importance of elimination paths in H. azteca in the absence of growth or metabolism. Blood flow is calculated with adapted blood flow. Figure S15. Predicted log BCF according to Eq.(7), in the absence (blue) or presence (green) of metabolism, alongside experimental k2 (red) for blood flow modeled as in fish. Same chemicals taken from different literature are marked with a cross.