American Institute of Mathematical Sciences

Advanced
2014, 11(3): 621-639. doi: 10.3934/mbe.2014.11.621

Modeling the endocrine control of vitellogenin production in female rainbow trout

Kaitlin Sundling 1, , Gheorghe Craciun 2, , Irvin Schultz 3, , Sharon Hook 3, , James Nagler 4, , Tim Cavileer 4, , Joseph Verducci 5, , Yushi Liu 5, , Jonghan Kim 6, and  William Hayton 7,

1. 

Department of Pathology, University of Wisconsin Hospital and Clinics, Madison WI 53792, United States
2. 

Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison, Madison, WI 53706
3. 

Battelle Pacific Northwest National Laboratory, Marine Sciences Laboratory, Sequim, WA 98382, United States, United States
4. 

Department of Biological Sciences and Center for Reproductive Biology, University of Idaho, Moscow, ID 83844, United States, United States
5. 

Department of Statistics, Ohio State University, Columbus, OH 43210, United States, United States
6. 

Department of Pharmaceutical Sciences, Northeastern University, Boston, MA 02115, United States
7. 

Division of Pharmaceutics, Ohio State University, Columbus, OH 43210, United States

Received  March 2011 Revised  May 2013 Published  January 2014

The rainbow trout endocrine system is sensitive to changes in annual day length, which is likely the principal environmental cue controlling its reproductive cycle. This study focuses on the endocrine regulation of vitellogenin (Vg) protein synthesis, which is the major egg yolk precursor in this fish species. We present a model of Vg production in female rainbow trout which incorporates a biological pathway beginning with sex steroid estradiol-17β levels in the plasma and concluding with Vg secretion by the liver and sequestration in the oocytes. Numerical simulation results based on this model are compared with experimental data for estrogen receptor mRNA, Vg mRNA, and Vg in the plasma from female rainbow trout over a normal annual reproductive cycle. We also analyze the response of the model to parameter changes. The model is subsequently tested against experimental data from female trout under a compressed photoperiod regime. Comparison of numerical and experimental results suggests the possibility of a time-dependent change in oocyte Vg uptake rate. This model is part of a larger effort that is developing a mathematical description of the endocrine control of reproduction in female rainbow trout. We anticipate that these mathematical and computational models will play an important role in future regulatory toxicity assessments and in the prediction of ecological risk.
Keywords: Endocrine control, pharmacokinetic/pharmacodynamic model., vitellogenin.
Mathematics Subject Classification: Primary: 92C45, 92B05; Secondary: 37N25, 92C30, 92C4.
Citation: Kaitlin Sundling, Gheorghe Craciun, Irvin Schultz, Sharon Hook, James Nagler, Tim Cavileer, Joseph Verducci, Yushi Liu, Jonghan Kim, William Hayton. Modeling the endocrine control of vitellogenin production in female rainbow trout. Mathematical Biosciences & Engineering, 2014, 11 (3) : 621-639. doi: 10.3934/mbe.2014.11.621
References:
[1]

G. T. Ankley, R. S. Bennett, R. J. Erickson, D. J. Hoff, M. W. Hornung, R. D. Johnson, D. R. Mount, J. W. Nichols, C. L. Russom, P. K. Schmieder, J. A. Serrrano, J. E. Tietge and D. L. Villeneuve, Adverse outcome pathways: A conceptual framework to support ecotoxicology research and risk assessment,, Environmental Toxicology and Chemistry, 29 (2010), 730.  doi: 10.1002/etc.34.  Google Scholar

[2]

E. Bon, B. Breton, M. Govoroun and F. Le Menn, Effects of accelerated photoperiod regimes on the reproductive cycle of the female rainbow trout: II Seasonal variations of plasma gonadotropins (GTH I and GTH II) levels correlated with ovarian follicle growth and egg size,, Fish Physiology and Biochemistry, 20 (1999), 143.   Google Scholar

[3]

J. Boyce-Derricott, J. J. Nagler and J. G. Cloud, Variation among rainbow trout (Oncorhynchus mykiss) estrogen receptor isoform 3' untranslated regions and the effect of 17 $\beta$-estradiol on mRNA stability in hepatocyte culture,, DNA and cell biology, 29 (2010), 229.   Google Scholar

[4]

N. Bromage, C. Randall, B. Davies, M. Thrush, J. Duston, M. Carillo and S. Zanuy, Photoperiodism and the control of reproduction and development in farmed fish,, in Aquaculture: Fundamental and Applied Research, (1993), 81.   Google Scholar

[5]

N. Bromage, M. Porter and C. Randall, The environmental regulation of maturation in farmed finfish with special reference to the role of photoperiod and melatonin,, Aquaculture, 197 (2001), 63.  doi: 10.1016/S0044-8486(01)00583-X.  Google Scholar

[6]

S. Choi, C. H. Lee, W. Park, D.-J. Kim and Y. C. Sohn, Effects of shortened photoperiod on gonadotropin-releasing hormone, gonadotropin, and vitellogenin gene expression associated with ovarian maturation in rainbow trout,, Zoological Science (Tokyo), 27 (2010), 24.  doi: 10.2108/zsj.27.24.  Google Scholar

[7]

K. S. Cunningham, R. E. Dodson, M. A. Nagel, D. J. Shapiro and D. R. Schoenberg, Vigilin binding selectively inhibits cleavage of the vitellogenin mRNA 3'-untranslated region by the mRNA endonuclease polysomal ribonuclease 1,, Proceedings of the National Academy of Sciences of the United States of America, 97 ().  doi: 10.1073/pnas.220425497.  Google Scholar

[8]

B. Davies, N. Bromage and P. Swanson, The brain-pituitary axis of female rainbow trout Oncorhynchus mykiss: Effects of photoperiod manipulation,, General and Comparative Endocrinology, 115 (1999), 155.   Google Scholar

[9]

J. Duston and N. R. Bromage, Photoperiodic mechanisms and rhythms of reproduction in the female rainbow trout,, Fish Physiology and Biochemistry, 2 (1986), 35.   Google Scholar

[10]

J. Duston and N. R. Bromage, The entrainment and gating of the endogenous circannual rhythm of reproduction in the female rainbow trout (Salmo gairdneri),, Journal of Comparative Physiology A, 164 (1988), 259.   Google Scholar

[11]

G. Flouriot, F. Pakdel and Y. Valotaire, Transcriptional and post-transcriptional regulation of rainbow trout estrogen receptor and vitellogenin gene expression,, Molecular and cellular endocrinology, 124 (1996), 173.  doi: 10.1016/S0303-7207(96)03960-3.  Google Scholar

[12]

S. Hook, J. Nagler, T. Cavileer, J. Verducci, Y. Liu, K. Sundling, W. Hayton, J. Kim and I. Schultz, Gene expression profiles in the pituitary, ovary, and liver of female rainbow trout during the reproductive cycle,, (submitted)., ().   Google Scholar

[13]

J. Y. Jin, R. R. Almon, D. C. DuBois and W. J. Jusko, Modeling of corticosteroid pharmacogenomics in rat liver using gene microarrays,, Journal of Pharmacology and Experimental Therapeutics, 307 (2003), 93.  doi: 10.1124/jpet.103.053256.  Google Scholar

[14]

W. J. Jusko and H. C. Ko, Physiologic indirect response models characterize diverse types of pharmacodynamic effects,, Clinical pharmacology and therapeutics, 56 (1994), 406.  doi: 10.1038/clpt.1994.155.  Google Scholar

[15]

J. Kim, Pharmacokinetics and Pharmacodynamics of Protein Turnover and Production in Vivo,, Doctoral Thesis, (2004).   Google Scholar

[16]

J. Kim, W. L. Hayton and I. R. Schultz, Modeling the brain-pituitary-gonad axis in salmon,, Marine environmental research, 62 (2006).  doi: 10.1016/j.marenvres.2006.04.022.  Google Scholar

[17]

V. J. Kramer, M. A. Etterson, M. Hecker, C. A. Murphy, G. Roesijadi, D. J. Spade, J. A. Spromberg, M. Wang and G. T. Ankley, Adverse outcome pathways and ecological risk assessment: Bridging to population-level effects,, Environmental Toxicology and Chemistry, 30 (2011), 64.  doi: 10.1002/etc.375.  Google Scholar

[18]

Y. Katsu, A. Lange, S. Miyagawa, H. Urushitani, N. Tatarazako, Y. Kawashima, C. R. Tyler and T. Iguchi, Cloning, expression and functional characterization of carp (Cyprinus carpio) estrogen receptors and their differential activations by estrogens,, Journal of Applied Toxicology, 33 (2013), 41.   Google Scholar

[19]

O. Leanos-Castaneda and G. Van Der Kraak, Functional characterization of estrogen receptor, ERa and ERb, mediating vitellogenin production in the liver of rainbow trout,, Toxicology and Applied Pharmacology, 224 (2007), 116.   Google Scholar

[20]

Y. Liu, J. Verducci, I. Schultz, S. Hook, J. Nagler, G. Craciun, K. Sundling and W. Hayton, Time course analysis of microarray data for the pathway of reproductive development in female rainbow trout,, Stat. Anal. Data Min., 2 (2009), 192.  doi: 10.1002/sam.10047.  Google Scholar

[21]

C. Mao, K. G. Flavin, S. Wang, R. Dodson, J. Ross and D. J. Shapiro, Analysis of RNA-protein interactions by a microplate-based fluorescence anisotropy assay,, Analytical Biochemistry, 350 (2006), 222.  doi: 10.1016/j.ab.2005.12.010.  Google Scholar

[22]

C. A. Murphy, K. A. Rose, M. S. Rahman and P. Thomas, Testing and applying a fish vitellogenesis model to evaluate laboratory and field biomarkers of endocrine disruption in atlantic croaker (micropogonias undulatus) exposed to hypoxia,, Environmental Toxicology and Chemistry, 28 (2009), 1288.  doi: 10.1897/08-304.1.  Google Scholar

[23]

C. A. Murphy, K. A. Rose and P. Thomas, Modeling vitellogenesis in female fish exposed to environmental stressors: Predicting the effects of endocrine disturbance due to exposure to a PCB mixture and cadmium,, Reproductive Toxicology, 19 (2005), 395.  doi: 10.1016/j.reprotox.2004.09.006.  Google Scholar

[24]

J. J. Nagler, T. Cavileer, J. Sullivan, D. G. Cyr and C. R. III, The complete nuclear estrogen receptor family in the rainbow trout: Discovery of the novel ER $\alpha$2 and both ER $\beta$ isoforms,, Gene (Amsterdam), 392 (2007), 164.   Google Scholar

[25]

J. J. Nagler, T. L. Davis, N. Modi, M. M. Vijayan and I. Schultz, Intracellular, not membrane, estrogen receptors control vitellogenin synthesis in the rainbow trout,, General and comparative endocrinology, 167 (2010), 326.  doi: 10.1016/j.ygcen.2010.03.022.  Google Scholar

[26]

E. R. Nelson and H. R. Habibi, Functional significance of nuclear estrogen receptor subtypes in the liver of goldfish,, Endocrinology, 151 (2010), 1668.  doi: 10.1210/en.2009-1447.  Google Scholar

[27]

L. K. Opresko and H. S. Wiley, Receptor-mediated endocytosis in Xenopus oocytes. I. Characterization of the vitellogenin receptor system,, Journal of Biological Chemistry, 262 (1987), 4109.   Google Scholar

[28]

L. M. Perazzolo, K. Coward, B. Davail, E. Normand, C. R. Tyler, F. Pakdel, W. J. Schneider and F. L. Menn, Expression and localization of messenger ribonucleic acid for the vitellogenin receptor in ovarian follicles throughout oogenesis in the rainbow trout, Oncorhynchus mykiss,, Biology of reproduction, 60 (1999), 1057.  doi: 10.1095/biolreprod60.5.1057.  Google Scholar

[29]

F. Piferrer, E. M. Donaldson, Uptake and clearance of exogenous estradiol-17 beta and testosterone during the early development of coho salmon (Oncorhynchus kisutch), including eggs, alevins and fry,, Fish Physiology and Biochemistry, 13 (1994), 219.   Google Scholar

[30]

J. N. Rodriguez, E. Bon and F. L. Menn, Vitellogenin receptors during vitellogenesis in the rainbow trout Oncorhynchus mykiss,, The Journal of experimental zoology, 274 (1996), 163.   Google Scholar

[31]

I. R. Schultz, G. Orner, J. L. Merdink and A. Skillman, Dose-response relationships and pharmacokinetics of vitellogenin in rainbow trout after intravascular administration of 17[alpha]-ethynylestradiol,, Aquatic Toxicology, 51 (2001), 305.   Google Scholar

[32]

A. D. Skillman, J. J. Nagler, S. E. Hook, J. A. Small and I. R. Schultz, Dynamics of 17$\alpha$-ethynylestradiol exposure in rainbow trout (oncorhynchus mykiss): absorption, tissue distribution, and hepatic gene expression pattern,, Environmental toxicology and chemistry / SETAC, 25 (2006), 2997.   Google Scholar

[33]

C. M. Taylor, B. Blanchard, and D. T. Zava, A Simple Method to Determine Whole Cell Uptake of Radiolabeled Estrogen and Progesterone and Their Subcellular-Localization in Breast-Cancer Cell-Lines in Monolayer-Culture,, Journal of Steroid Biochemistry and Molecular Biology, 20 (1984), 1083.   Google Scholar

[34]

C. Tyler, J. Sumpter and R. Handford, The dynamics of vitellogenin sequestration into vitellogenic ovarian follicles of the rainbow trout, salmo gairdneri,, Fish Physiology and Biochemistry, 8 (1990), 211.  doi: 10.1007/BF00004460.  Google Scholar

[35]

C. R. Tyler and J. P. Sumpter, Oocyte growth and development in teleosts,, Reviews in Fish Biology and Fisheries, 6 (1996), 287.  doi: 10.1007/BF00122584.  Google Scholar

[36]

C. R. Tyler, J. P. Sumpter and N. R. Bromage, In vivo ovarian uptake and processing of vitellogenin in the rainbow trout, salmo gairdneri,, Journal of Experimental Zoology, 246 (1988), 171.  doi: 10.1002/jez.1402460209.  Google Scholar

[37]

C. R. Tyler, J. P. Sumpter and N. R. Bromage, Selectivity of protein sequestration by vitellogenic oocytes of the rainbow trout, salmo gairdneri,, Journal of Experimental Zoology, 248 (1988), 199.  doi: 10.1002/jez.1402480211.  Google Scholar

[38]

K. H. Watanabe, M. E. Andersen, N. Basu, M. J. Carvan, K. M. Crofton, K. A. King, C. Suñol, E. Tiffany-Castiglioni and I. R. Schultz, Defining and modeling known adverse outcome pathways: Domoic acid and neuronal signaling as a case study,, Environmental Toxicology and Chemistry, 30 (2011), 9.  doi: 10.1002/etc.373.  Google Scholar

[39]

K. H. Watanabe, Z. Li, K. J. Kroll, D. L. Villeneuve, N. Garcia-Reyero, E. F. Orlando, M. S. Sepúlveda, T. W. Collette, D. R. Ekman, G. T. Ankley and N. D. Denslow, A computational model of the hypothalamic-pituitary-gonadal axis in male fathead minnows exposed to 17$\alpha$-ethinylestradiol and 17$\beta$-estradiol,, Toxicological Sciences, (2009).   Google Scholar

[40]

Y. Zohar, J. A. Munoz-Cueto, A. Elizur and O. Kah, Neuroendocrinology of reproduction in teleost fish,, General and Comparative Endocrinology, 165 (2010), 438.  doi: 10.1016/j.ygcen.2009.04.017.  Google Scholar

show all references

References:
[1]

G. T. Ankley, R. S. Bennett, R. J. Erickson, D. J. Hoff, M. W. Hornung, R. D. Johnson, D. R. Mount, J. W. Nichols, C. L. Russom, P. K. Schmieder, J. A. Serrrano, J. E. Tietge and D. L. Villeneuve, Adverse outcome pathways: A conceptual framework to support ecotoxicology research and risk assessment,, Environmental Toxicology and Chemistry, 29 (2010), 730.  doi: 10.1002/etc.34.  Google Scholar

[2]

E. Bon, B. Breton, M. Govoroun and F. Le Menn, Effects of accelerated photoperiod regimes on the reproductive cycle of the female rainbow trout: II Seasonal variations of plasma gonadotropins (GTH I and GTH II) levels correlated with ovarian follicle growth and egg size,, Fish Physiology and Biochemistry, 20 (1999), 143.   Google Scholar

[3]

J. Boyce-Derricott, J. J. Nagler and J. G. Cloud, Variation among rainbow trout (Oncorhynchus mykiss) estrogen receptor isoform 3' untranslated regions and the effect of 17 $\beta$-estradiol on mRNA stability in hepatocyte culture,, DNA and cell biology, 29 (2010), 229.   Google Scholar

[4]

N. Bromage, C. Randall, B. Davies, M. Thrush, J. Duston, M. Carillo and S. Zanuy, Photoperiodism and the control of reproduction and development in farmed fish,, in Aquaculture: Fundamental and Applied Research, (1993), 81.   Google Scholar

[5]

N. Bromage, M. Porter and C. Randall, The environmental regulation of maturation in farmed finfish with special reference to the role of photoperiod and melatonin,, Aquaculture, 197 (2001), 63.  doi: 10.1016/S0044-8486(01)00583-X.  Google Scholar

[6]

S. Choi, C. H. Lee, W. Park, D.-J. Kim and Y. C. Sohn, Effects of shortened photoperiod on gonadotropin-releasing hormone, gonadotropin, and vitellogenin gene expression associated with ovarian maturation in rainbow trout,, Zoological Science (Tokyo), 27 (2010), 24.  doi: 10.2108/zsj.27.24.  Google Scholar

[7]

K. S. Cunningham, R. E. Dodson, M. A. Nagel, D. J. Shapiro and D. R. Schoenberg, Vigilin binding selectively inhibits cleavage of the vitellogenin mRNA 3'-untranslated region by the mRNA endonuclease polysomal ribonuclease 1,, Proceedings of the National Academy of Sciences of the United States of America, 97 ().  doi: 10.1073/pnas.220425497.  Google Scholar

[8]

B. Davies, N. Bromage and P. Swanson, The brain-pituitary axis of female rainbow trout Oncorhynchus mykiss: Effects of photoperiod manipulation,, General and Comparative Endocrinology, 115 (1999), 155.   Google Scholar

[9]

J. Duston and N. R. Bromage, Photoperiodic mechanisms and rhythms of reproduction in the female rainbow trout,, Fish Physiology and Biochemistry, 2 (1986), 35.   Google Scholar

[10]

J. Duston and N. R. Bromage, The entrainment and gating of the endogenous circannual rhythm of reproduction in the female rainbow trout (Salmo gairdneri),, Journal of Comparative Physiology A, 164 (1988), 259.   Google Scholar

[11]

G. Flouriot, F. Pakdel and Y. Valotaire, Transcriptional and post-transcriptional regulation of rainbow trout estrogen receptor and vitellogenin gene expression,, Molecular and cellular endocrinology, 124 (1996), 173.  doi: 10.1016/S0303-7207(96)03960-3.  Google Scholar

[12]

S. Hook, J. Nagler, T. Cavileer, J. Verducci, Y. Liu, K. Sundling, W. Hayton, J. Kim and I. Schultz, Gene expression profiles in the pituitary, ovary, and liver of female rainbow trout during the reproductive cycle,, (submitted)., ().   Google Scholar

[13]

J. Y. Jin, R. R. Almon, D. C. DuBois and W. J. Jusko, Modeling of corticosteroid pharmacogenomics in rat liver using gene microarrays,, Journal of Pharmacology and Experimental Therapeutics, 307 (2003), 93.  doi: 10.1124/jpet.103.053256.  Google Scholar

[14]

W. J. Jusko and H. C. Ko, Physiologic indirect response models characterize diverse types of pharmacodynamic effects,, Clinical pharmacology and therapeutics, 56 (1994), 406.  doi: 10.1038/clpt.1994.155.  Google Scholar

[15]

J. Kim, Pharmacokinetics and Pharmacodynamics of Protein Turnover and Production in Vivo,, Doctoral Thesis, (2004).   Google Scholar

[16]

J. Kim, W. L. Hayton and I. R. Schultz, Modeling the brain-pituitary-gonad axis in salmon,, Marine environmental research, 62 (2006).  doi: 10.1016/j.marenvres.2006.04.022.  Google Scholar

[17]

V. J. Kramer, M. A. Etterson, M. Hecker, C. A. Murphy, G. Roesijadi, D. J. Spade, J. A. Spromberg, M. Wang and G. T. Ankley, Adverse outcome pathways and ecological risk assessment: Bridging to population-level effects,, Environmental Toxicology and Chemistry, 30 (2011), 64.  doi: 10.1002/etc.375.  Google Scholar

[18]

Y. Katsu, A. Lange, S. Miyagawa, H. Urushitani, N. Tatarazako, Y. Kawashima, C. R. Tyler and T. Iguchi, Cloning, expression and functional characterization of carp (Cyprinus carpio) estrogen receptors and their differential activations by estrogens,, Journal of Applied Toxicology, 33 (2013), 41.   Google Scholar

[19]

O. Leanos-Castaneda and G. Van Der Kraak, Functional characterization of estrogen receptor, ERa and ERb, mediating vitellogenin production in the liver of rainbow trout,, Toxicology and Applied Pharmacology, 224 (2007), 116.   Google Scholar

[20]

Y. Liu, J. Verducci, I. Schultz, S. Hook, J. Nagler, G. Craciun, K. Sundling and W. Hayton, Time course analysis of microarray data for the pathway of reproductive development in female rainbow trout,, Stat. Anal. Data Min., 2 (2009), 192.  doi: 10.1002/sam.10047.  Google Scholar

[21]

C. Mao, K. G. Flavin, S. Wang, R. Dodson, J. Ross and D. J. Shapiro, Analysis of RNA-protein interactions by a microplate-based fluorescence anisotropy assay,, Analytical Biochemistry, 350 (2006), 222.  doi: 10.1016/j.ab.2005.12.010.  Google Scholar

[22]

C. A. Murphy, K. A. Rose, M. S. Rahman and P. Thomas, Testing and applying a fish vitellogenesis model to evaluate laboratory and field biomarkers of endocrine disruption in atlantic croaker (micropogonias undulatus) exposed to hypoxia,, Environmental Toxicology and Chemistry, 28 (2009), 1288.  doi: 10.1897/08-304.1.  Google Scholar

[23]

C. A. Murphy, K. A. Rose and P. Thomas, Modeling vitellogenesis in female fish exposed to environmental stressors: Predicting the effects of endocrine disturbance due to exposure to a PCB mixture and cadmium,, Reproductive Toxicology, 19 (2005), 395.  doi: 10.1016/j.reprotox.2004.09.006.  Google Scholar

[24]

J. J. Nagler, T. Cavileer, J. Sullivan, D. G. Cyr and C. R. III, The complete nuclear estrogen receptor family in the rainbow trout: Discovery of the novel ER $\alpha$2 and both ER $\beta$ isoforms,, Gene (Amsterdam), 392 (2007), 164.   Google Scholar

[25]

J. J. Nagler, T. L. Davis, N. Modi, M. M. Vijayan and I. Schultz, Intracellular, not membrane, estrogen receptors control vitellogenin synthesis in the rainbow trout,, General and comparative endocrinology, 167 (2010), 326.  doi: 10.1016/j.ygcen.2010.03.022.  Google Scholar

[26]

E. R. Nelson and H. R. Habibi, Functional significance of nuclear estrogen receptor subtypes in the liver of goldfish,, Endocrinology, 151 (2010), 1668.  doi: 10.1210/en.2009-1447.  Google Scholar

[27]

L. K. Opresko and H. S. Wiley, Receptor-mediated endocytosis in Xenopus oocytes. I. Characterization of the vitellogenin receptor system,, Journal of Biological Chemistry, 262 (1987), 4109.   Google Scholar

[28]

L. M. Perazzolo, K. Coward, B. Davail, E. Normand, C. R. Tyler, F. Pakdel, W. J. Schneider and F. L. Menn, Expression and localization of messenger ribonucleic acid for the vitellogenin receptor in ovarian follicles throughout oogenesis in the rainbow trout, Oncorhynchus mykiss,, Biology of reproduction, 60 (1999), 1057.  doi: 10.1095/biolreprod60.5.1057.  Google Scholar

[29]

F. Piferrer, E. M. Donaldson, Uptake and clearance of exogenous estradiol-17 beta and testosterone during the early development of coho salmon (Oncorhynchus kisutch), including eggs, alevins and fry,, Fish Physiology and Biochemistry, 13 (1994), 219.   Google Scholar

[30]

J. N. Rodriguez, E. Bon and F. L. Menn, Vitellogenin receptors during vitellogenesis in the rainbow trout Oncorhynchus mykiss,, The Journal of experimental zoology, 274 (1996), 163.   Google Scholar

[31]

I. R. Schultz, G. Orner, J. L. Merdink and A. Skillman, Dose-response relationships and pharmacokinetics of vitellogenin in rainbow trout after intravascular administration of 17[alpha]-ethynylestradiol,, Aquatic Toxicology, 51 (2001), 305.   Google Scholar

[32]

A. D. Skillman, J. J. Nagler, S. E. Hook, J. A. Small and I. R. Schultz, Dynamics of 17$\alpha$-ethynylestradiol exposure in rainbow trout (oncorhynchus mykiss): absorption, tissue distribution, and hepatic gene expression pattern,, Environmental toxicology and chemistry / SETAC, 25 (2006), 2997.   Google Scholar

[33]

C. M. Taylor, B. Blanchard, and D. T. Zava, A Simple Method to Determine Whole Cell Uptake of Radiolabeled Estrogen and Progesterone and Their Subcellular-Localization in Breast-Cancer Cell-Lines in Monolayer-Culture,, Journal of Steroid Biochemistry and Molecular Biology, 20 (1984), 1083.   Google Scholar

[34]

C. Tyler, J. Sumpter and R. Handford, The dynamics of vitellogenin sequestration into vitellogenic ovarian follicles of the rainbow trout, salmo gairdneri,, Fish Physiology and Biochemistry, 8 (1990), 211.  doi: 10.1007/BF00004460.  Google Scholar

[35]

C. R. Tyler and J. P. Sumpter, Oocyte growth and development in teleosts,, Reviews in Fish Biology and Fisheries, 6 (1996), 287.  doi: 10.1007/BF00122584.  Google Scholar

[36]

C. R. Tyler, J. P. Sumpter and N. R. Bromage, In vivo ovarian uptake and processing of vitellogenin in the rainbow trout, salmo gairdneri,, Journal of Experimental Zoology, 246 (1988), 171.  doi: 10.1002/jez.1402460209.  Google Scholar

[37]

C. R. Tyler, J. P. Sumpter and N. R. Bromage, Selectivity of protein sequestration by vitellogenic oocytes of the rainbow trout, salmo gairdneri,, Journal of Experimental Zoology, 248 (1988), 199.  doi: 10.1002/jez.1402480211.  Google Scholar

[38]

K. H. Watanabe, M. E. Andersen, N. Basu, M. J. Carvan, K. M. Crofton, K. A. King, C. Suñol, E. Tiffany-Castiglioni and I. R. Schultz, Defining and modeling known adverse outcome pathways: Domoic acid and neuronal signaling as a case study,, Environmental Toxicology and Chemistry, 30 (2011), 9.  doi: 10.1002/etc.373.  Google Scholar

[39]

K. H. Watanabe, Z. Li, K. J. Kroll, D. L. Villeneuve, N. Garcia-Reyero, E. F. Orlando, M. S. Sepúlveda, T. W. Collette, D. R. Ekman, G. T. Ankley and N. D. Denslow, A computational model of the hypothalamic-pituitary-gonadal axis in male fathead minnows exposed to 17$\alpha$-ethinylestradiol and 17$\beta$-estradiol,, Toxicological Sciences, (2009).   Google Scholar

[40]

Y. Zohar, J. A. Munoz-Cueto, A. Elizur and O. Kah, Neuroendocrinology of reproduction in teleost fish,, General and Comparative Endocrinology, 165 (2010), 438.  doi: 10.1016/j.ygcen.2009.04.017.  Google Scholar

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