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Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells
1.  Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, United States, United States, United States 
References:
[1] 
A. Atri, J. Amundson, D. Clapham and J. Sneyd, A singlepool model for intracellular calcium oscillations and waves in the Xenopus laevis Oocyte, Biophys. J., 65 (1993), 17271739. 
[2] 
F. Bronner, Cytoplasmic transport of calcium and other inorganic ions, Comp. Biochem. Physiol., 115B (1996), 313317. 
[3] 
J. Buchanan, R. P. Gilbert and M. J. Ou, The kinetics of vitamin $D_3$ in the osteoblastic cell, Submitted to J. Theor. Biol., (2012). 
[4] 
E. M. Costa and D. Feldman, Measurement of 1,25Dihydroxyvitamin D3 receptor turnover by dense amino acid labeling: Changes during receptor upregulation by vitamin D metabolites, Endocrinology, 120 (1987), 11731178. 
[5] 
M. C. FarachCarson and P. J. Davis, Steroid hormone interactions with target cells: Cross talk between membrane and nuclear pathways, J. Pharm. Exp. Therap., 307 (2003), 839845. 
[6] 
R. Gilbert, A. Panasenko and A. Vasilic, Acoustic Propagation in a Random Saturated Medium: The Monophasic Case, Math. Mehods Appl. Sciences, 33 (2010), 22062214. 
[7] 
K. Hackl and S. Ilic, Application of the multiscale FEM to the modeling of cancellous bone, Biomechan. Model. Mechanobiol., 9 (2010), 87102. 
[8] 
V. V. Jikov, S. M. Kozlov and O.A. Oleinik, "Homogenization of Differential Operators and Integral Functionals," Springer, Berlin 1994. 
[9] 
J. Keener and J. Sneyd, "Mathematical Physiology," Springer, Berlin, 1998. 
[10] 
S. V. Komarova, R. J. Smith, S. J. Dixon, S. M. Sims and L. M. Wahl, Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling, Bone, 33 (2003), 206215. 
[11] 
D. L. Lacey, E. Timms, h.L. Tan, M. J. Kelley, C. R. Dunstan, T. Burgess, R. Elliott, A. Columbero, G. Elliott, S. Scully, H. Hsu, J. Sullivan, N. Hawkins, E. Davy, C. Capparelli, A. Eli, Y. X. Qian, S. Kaufman, I. Sarosi, V. Shalhoub, G. Senaldi, J. Guo, J. Delaney and W. J. Boyle, Osteoprotegerin ligand is a cytokine that regulates osteoclast differentiation and activation, Cell, 93 (1998), 165176. 
[12] 
D. A. Lauffenburger and J. Linderman, "Receptors: Models for Binding, Trafficking and Signaling," Oxford University Press, New York, 1996. 
[13] 
V. Lemaire, F. L. Tobin, L. D. Greller, C. R. Cho and L. J. and Suva, Modeling the interactions between osteoblast and osteoclast activities in bone remodeling, J. Theor. Biol., 229 (2004), 293309. doi: 10.1016/j.jtbi.2004.03.023. 
[14] 
I. Nemere, 24,25Dihydroxyvitamin D3 suppresses the rapid actions of 1,25 Dihydroxyvitamin D3 and parathyroid hormone on calcium transport in chick intestine, Bone Miner. Res., 14 (1999), 15431549. 
[15] 
I. Nemere, N. Garbi, G. J. Hammerling and R. C. Khanal, Intestinal cell calcium uptake and the targeted knockout of the 1,25D3MARRS (Membraneassociated, rapid response steroidbinding) receptor/PDIA3/Erp57, J. Biol. Chem., 285 (2010), 3185931866. 
[16] 
I. Nemere, R. J. Pietras and P. F. Blackmore, Membrane receptors for membrane hormones: Signal transduction and physiological significance, J. Cell Biochem., 88 (2003), 438445. 
[17] 
A. W. Norman, "Rapid Biological Responses Mediated by $1\alpha,25$Dihydroxyvitamin D$_3$," In Vitamin D (D. Feldman and F. H. Glorieux and J. W. Pike), Academic Press, New York, 1997. 
[18] 
I. Novak, P. Kraikivski and B. Slepchenko, Diffusion in cytoplasm: Effects of excluded volume due to internal membranes and cytoskeletal structures, Biophys. J., 97 (2009), 758767. 
[19] 
I. L. Novak, F. Gao, P. Kraikivski and B. Slepchenko, B. M. Diffusion amid random overlapping obstacles: Similarities, invariants, aproximations, J. Chem. Phys., 134 (2011), 154104. 
[20] 
J. W. Pike, "The Vitamin D Receptor and Its Gene," In Vitamin D (D. Feldman, F. H. Glorieux and J. W. Pike), Academic Press, New York, 1997, 105125. 
[21] 
W. S. Simonet, D. L. Lacey, C. R. Dunstan, M. Kelley, M.S. Chang, R. Lothy, H. Q. Nguyen, S. Wooden, L. Bennett, T. Boone, G. Shimamoto, M. DeRose, R. Elliott, A. Columbero, H.L. Tan, G. Trail, J. Sullivan, E. Davy, N. Bucay, L. RenshawGregg, T. M. Hughes, D. Hill, W. Pattison, P. Campbell, S. Sander, G. Van, J. Tarpley, P. Derby, R. Lee and W. J. Boyle, Osteoprotegerin: A novel secreted protein involved in the regulation of bone density, Cell, 89 (1997), 309319. 
[22] 
P. Slepchenko, I. Semenova, I. Zaliopin. and V. Rodianaov, Switching of membrane organelles between cytoskeletal transport systems is determined by regulation of the microtubulebased transport, J. Cell Biol., 179 (2007), 635641. 
[23] 
G. K. Witfield, P. W. Jurutka, C. A. Hausler, J.C. Hsieh, T. K. Barthel, E. T. Jacobs, C. E. Dominguez, M. L. Thatcher and M. R. Hausler, "Nuclear Vitamin D Receptor: Control of Gene Transcription, and Novel Bioactions," In Vitamin D (D. Feldman, F. H. Glorieux and J. W. Pike), Academic Press, New York, 1997, 219261. 
show all references
References:
[1] 
A. Atri, J. Amundson, D. Clapham and J. Sneyd, A singlepool model for intracellular calcium oscillations and waves in the Xenopus laevis Oocyte, Biophys. J., 65 (1993), 17271739. 
[2] 
F. Bronner, Cytoplasmic transport of calcium and other inorganic ions, Comp. Biochem. Physiol., 115B (1996), 313317. 
[3] 
J. Buchanan, R. P. Gilbert and M. J. Ou, The kinetics of vitamin $D_3$ in the osteoblastic cell, Submitted to J. Theor. Biol., (2012). 
[4] 
E. M. Costa and D. Feldman, Measurement of 1,25Dihydroxyvitamin D3 receptor turnover by dense amino acid labeling: Changes during receptor upregulation by vitamin D metabolites, Endocrinology, 120 (1987), 11731178. 
[5] 
M. C. FarachCarson and P. J. Davis, Steroid hormone interactions with target cells: Cross talk between membrane and nuclear pathways, J. Pharm. Exp. Therap., 307 (2003), 839845. 
[6] 
R. Gilbert, A. Panasenko and A. Vasilic, Acoustic Propagation in a Random Saturated Medium: The Monophasic Case, Math. Mehods Appl. Sciences, 33 (2010), 22062214. 
[7] 
K. Hackl and S. Ilic, Application of the multiscale FEM to the modeling of cancellous bone, Biomechan. Model. Mechanobiol., 9 (2010), 87102. 
[8] 
V. V. Jikov, S. M. Kozlov and O.A. Oleinik, "Homogenization of Differential Operators and Integral Functionals," Springer, Berlin 1994. 
[9] 
J. Keener and J. Sneyd, "Mathematical Physiology," Springer, Berlin, 1998. 
[10] 
S. V. Komarova, R. J. Smith, S. J. Dixon, S. M. Sims and L. M. Wahl, Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling, Bone, 33 (2003), 206215. 
[11] 
D. L. Lacey, E. Timms, h.L. Tan, M. J. Kelley, C. R. Dunstan, T. Burgess, R. Elliott, A. Columbero, G. Elliott, S. Scully, H. Hsu, J. Sullivan, N. Hawkins, E. Davy, C. Capparelli, A. Eli, Y. X. Qian, S. Kaufman, I. Sarosi, V. Shalhoub, G. Senaldi, J. Guo, J. Delaney and W. J. Boyle, Osteoprotegerin ligand is a cytokine that regulates osteoclast differentiation and activation, Cell, 93 (1998), 165176. 
[12] 
D. A. Lauffenburger and J. Linderman, "Receptors: Models for Binding, Trafficking and Signaling," Oxford University Press, New York, 1996. 
[13] 
V. Lemaire, F. L. Tobin, L. D. Greller, C. R. Cho and L. J. and Suva, Modeling the interactions between osteoblast and osteoclast activities in bone remodeling, J. Theor. Biol., 229 (2004), 293309. doi: 10.1016/j.jtbi.2004.03.023. 
[14] 
I. Nemere, 24,25Dihydroxyvitamin D3 suppresses the rapid actions of 1,25 Dihydroxyvitamin D3 and parathyroid hormone on calcium transport in chick intestine, Bone Miner. Res., 14 (1999), 15431549. 
[15] 
I. Nemere, N. Garbi, G. J. Hammerling and R. C. Khanal, Intestinal cell calcium uptake and the targeted knockout of the 1,25D3MARRS (Membraneassociated, rapid response steroidbinding) receptor/PDIA3/Erp57, J. Biol. Chem., 285 (2010), 3185931866. 
[16] 
I. Nemere, R. J. Pietras and P. F. Blackmore, Membrane receptors for membrane hormones: Signal transduction and physiological significance, J. Cell Biochem., 88 (2003), 438445. 
[17] 
A. W. Norman, "Rapid Biological Responses Mediated by $1\alpha,25$Dihydroxyvitamin D$_3$," In Vitamin D (D. Feldman and F. H. Glorieux and J. W. Pike), Academic Press, New York, 1997. 
[18] 
I. Novak, P. Kraikivski and B. Slepchenko, Diffusion in cytoplasm: Effects of excluded volume due to internal membranes and cytoskeletal structures, Biophys. J., 97 (2009), 758767. 
[19] 
I. L. Novak, F. Gao, P. Kraikivski and B. Slepchenko, B. M. Diffusion amid random overlapping obstacles: Similarities, invariants, aproximations, J. Chem. Phys., 134 (2011), 154104. 
[20] 
J. W. Pike, "The Vitamin D Receptor and Its Gene," In Vitamin D (D. Feldman, F. H. Glorieux and J. W. Pike), Academic Press, New York, 1997, 105125. 
[21] 
W. S. Simonet, D. L. Lacey, C. R. Dunstan, M. Kelley, M.S. Chang, R. Lothy, H. Q. Nguyen, S. Wooden, L. Bennett, T. Boone, G. Shimamoto, M. DeRose, R. Elliott, A. Columbero, H.L. Tan, G. Trail, J. Sullivan, E. Davy, N. Bucay, L. RenshawGregg, T. M. Hughes, D. Hill, W. Pattison, P. Campbell, S. Sander, G. Van, J. Tarpley, P. Derby, R. Lee and W. J. Boyle, Osteoprotegerin: A novel secreted protein involved in the regulation of bone density, Cell, 89 (1997), 309319. 
[22] 
P. Slepchenko, I. Semenova, I. Zaliopin. and V. Rodianaov, Switching of membrane organelles between cytoskeletal transport systems is determined by regulation of the microtubulebased transport, J. Cell Biol., 179 (2007), 635641. 
[23] 
G. K. Witfield, P. W. Jurutka, C. A. Hausler, J.C. Hsieh, T. K. Barthel, E. T. Jacobs, C. E. Dominguez, M. L. Thatcher and M. R. Hausler, "Nuclear Vitamin D Receptor: Control of Gene Transcription, and Novel Bioactions," In Vitamin D (D. Feldman, F. H. Glorieux and J. W. Pike), Academic Press, New York, 1997, 219261. 
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