As an independent compartment. Based upon a mass balance for eachAs an independent compartment. Based

As an independent compartment. Based upon a mass balance for each
As an independent compartment. Based upon a mass balance for each chemical of interest, a set of coupled ordinary differential equations were formulated in each compartment following the principles of physiologically based pharmacokinetic modeling. A detailed description of the differential equations can be found in Additional File 1: Differential equations used in the HPG axis model. In the brain, gonad, and liver compartments, we simulated both ER and AR dynamics. The AR component was not included in the model for male FHM published by Watanabe et al. [20]. ER binds estrogens (e.g., E2 and EE2), and bound ER affects the production of VTG. AR binds androgens (e.g., T and TB), and subsequently regulates biochemical processes such as the production of gonadotropins [21]. A general mathematical formulation of ligand-receptor binding is shown in Equation 1.d(CiR,j Vj ) = k1 dtiR,j Ci,j CR,j Vj- Kd iR,j kiR,j CiR,j Vj(1)where, C iR, j (nmol/L) is the OPC-8212 clinical trials concentration of compound i (e.g. T, TB, E2 and EE2) bound to its receptor in compartment j (e.g. brain, liver, gonad, and venous blood) ; Vj (L) is the volume of compartment j; k1_iR, j (L/nmol/hr) is the association rate constant of compound i with its receptor in compartment j; Ci, j (nmol/ L) is the concentration of free compound i in compartment j; CR, j (nmol/L) is PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/28914615 the concentration of unbound receptor of compound i in compartment j; K d_iR, j (nmol/L) is the equilibrium dissociation constant of compound i with its receptor in compartment j.GillIn the gill compartment, we did not simulate any production of proteins (e.g., VTG), hormones (e.g.,Li et al. BMC Systems Biology 2011, 5:63 http://www.biomedcentral.com/1752-0509/5/Page 3 ofFigure 1 Conceptual model of the HPG axis in adult female FHMs. Tissues in adult female FHMs are categorized into six compartments: gill, brain, gonad, liver, venous blood, and other. Each compartment is defined by volume, blood flow, and partition coefficient, and performs multiple physiological functions.Li et al. BMC Systems Biology 2011, 5:63 http://www.biomedcentral.com/1752-0509/5/Page 4 ofluteinizing hormone, LH), or hormone receptors (e.g, ER and AR). ER mRNA is present in FHM gills, however, we did not simulate ER in the gill compartment because the gill expression of ER is very low compared to other tissues [22]. We simulated the exposure of female FHMs to TB and/or EE2 in water, and the gill compartment is where the exogenous chemicals are absorbed. The concentration of each chemical in exposure water was represented as a function of time. Then, equilibrium partitioning was assumed, and the FHM arterial blood concentration was calculated from the water concentration using an equilibrium partition coefficient assigned for each chemical (Equation 2). In addition, we assumed that the gill compartment did not accumulate any chemical(s).CArti = FWgil ?Ci,H20 + Fcar ?CVeni FWgil + Fcar i,bld(2)Second, we assumed an up-regulation of LH synthesis by bound ER in the brain compartment. This assumption was based upon observations of estrogen response elements PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/26795252 (EREs) in the promoter region of the lh gene and reports of estrogen-stimulated LH production in fish [25]. Equation 3 describes the LH production rate in the brain compartment as a function of bound AR and ER. In the equation, PLH, brn (nmol/hr) is the production rate of LH in brain; Pb_LH, brn (nmol/hr) is the background production rate of LH in brain, which was formulated as a diurnal cycle; CER_bd, brn.