-
Previous Article
Uniqueness of limit cycles and multiple attractors in a Gause-type predator-prey model with nonmonotonic functional response and Allee effect on prey
- MBE Home
- This Issue
-
Next Article
Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation
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 single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis Oocyte, Biophys. J., 65 (1993), 1727-1739. |
[2] |
F. Bronner, Cytoplasmic transport of calcium and other inorganic ions, Comp. Biochem. Physiol., 115B (1996), 313-317. |
[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 1,25-Dihydroxyvitamin D3 receptor turnover by dense amino acid labeling: Changes during receptor up-regulation by vitamin D metabolites, Endocrinology, 120 (1987), 1173-1178. |
[5] |
M. C. Farach-Carson and P. J. Davis, Steroid hormone interactions with target cells: Cross talk between membrane and nuclear pathways, J. Pharm. Exp. Therap., 307 (2003), 839-845. |
[6] |
R. Gilbert, A. Panasenko and A. Vasilic, Acoustic Propagation in a Random Saturated Medium: The Monophasic Case, Math. Mehods Appl. Sciences, 33 (2010), 2206-2214. |
[7] |
K. Hackl and S. Ilic, Application of the multiscale FEM to the modeling of cancellous bone, Biomechan. Model. Mechanobiol., 9 (2010), 87-102. |
[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), 206-215. |
[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), 165-176. |
[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), 293-309.
doi: 10.1016/j.jtbi.2004.03.023. |
[14] |
I. Nemere, 24,25-Dihydroxyvitamin D3 suppresses the rapid actions of 1,25 Dihydroxyvitamin D3 and parathyroid hormone on calcium transport in chick intestine, Bone Miner. Res., 14 (1999), 1543-1549. |
[15] |
I. Nemere, N. Garbi, G. J. Hammerling and R. C. Khanal, Intestinal cell calcium uptake and the targeted knockout of the 1,25D3-MARRS (Membrane-associated, rapid response steroid-binding) receptor/PDIA3/Erp57, J. Biol. Chem., 285 (2010), 31859-31866. |
[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), 438-445. |
[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), 758-767. |
[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, 105-125. |
[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. Renshaw-Gregg, 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), 309-319. |
[22] |
P. Slepchenko, I. Semenova, I. Zaliopin. and V. Rodianaov, Switching of membrane organelles between cytoskeletal transport systems is determined by regulation of the microtubule-based transport, J. Cell Biol., 179 (2007), 635-641. |
[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, 219-261. |
show all references
References:
[1] |
A. Atri, J. Amundson, D. Clapham and J. Sneyd, A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis Oocyte, Biophys. J., 65 (1993), 1727-1739. |
[2] |
F. Bronner, Cytoplasmic transport of calcium and other inorganic ions, Comp. Biochem. Physiol., 115B (1996), 313-317. |
[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 1,25-Dihydroxyvitamin D3 receptor turnover by dense amino acid labeling: Changes during receptor up-regulation by vitamin D metabolites, Endocrinology, 120 (1987), 1173-1178. |
[5] |
M. C. Farach-Carson and P. J. Davis, Steroid hormone interactions with target cells: Cross talk between membrane and nuclear pathways, J. Pharm. Exp. Therap., 307 (2003), 839-845. |
[6] |
R. Gilbert, A. Panasenko and A. Vasilic, Acoustic Propagation in a Random Saturated Medium: The Monophasic Case, Math. Mehods Appl. Sciences, 33 (2010), 2206-2214. |
[7] |
K. Hackl and S. Ilic, Application of the multiscale FEM to the modeling of cancellous bone, Biomechan. Model. Mechanobiol., 9 (2010), 87-102. |
[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), 206-215. |
[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), 165-176. |
[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), 293-309.
doi: 10.1016/j.jtbi.2004.03.023. |
[14] |
I. Nemere, 24,25-Dihydroxyvitamin D3 suppresses the rapid actions of 1,25 Dihydroxyvitamin D3 and parathyroid hormone on calcium transport in chick intestine, Bone Miner. Res., 14 (1999), 1543-1549. |
[15] |
I. Nemere, N. Garbi, G. J. Hammerling and R. C. Khanal, Intestinal cell calcium uptake and the targeted knockout of the 1,25D3-MARRS (Membrane-associated, rapid response steroid-binding) receptor/PDIA3/Erp57, J. Biol. Chem., 285 (2010), 31859-31866. |
[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), 438-445. |
[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), 758-767. |
[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, 105-125. |
[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. Renshaw-Gregg, 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), 309-319. |
[22] |
P. Slepchenko, I. Semenova, I. Zaliopin. and V. Rodianaov, Switching of membrane organelles between cytoskeletal transport systems is determined by regulation of the microtubule-based transport, J. Cell Biol., 179 (2007), 635-641. |
[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, 219-261. |
[1] |
Ching-Shan Chou, Yong-Tao Zhang, Rui Zhao, Qing Nie. Numerical methods for stiff reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2007, 7 (3) : 515-525. doi: 10.3934/dcdsb.2007.7.515 |
[2] |
Leilei Wei, Yinnian He. A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4907-4926. doi: 10.3934/dcdsb.2020319 |
[3] |
M. Grasselli, V. Pata. A reaction-diffusion equation with memory. Discrete and Continuous Dynamical Systems, 2006, 15 (4) : 1079-1088. doi: 10.3934/dcds.2006.15.1079 |
[4] |
Hideki Murakawa. Fast reaction limit of reaction-diffusion systems. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1047-1062. doi: 10.3934/dcdss.2020405 |
[5] |
Hirotoshi Kuroda, Noriaki Yamazaki. Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations. Conference Publications, 2009, 2009 (Special) : 486-495. doi: 10.3934/proc.2009.2009.486 |
[6] |
Yuliya Gorb, Dukjin Nam, Alexei Novikov. Numerical simulations of diffusion in cellular flows at high Péclet numbers. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 75-92. doi: 10.3934/dcdsb.2011.15.75 |
[7] |
Keng Deng. On a nonlocal reaction-diffusion population model. Discrete and Continuous Dynamical Systems - B, 2008, 9 (1) : 65-73. doi: 10.3934/dcdsb.2008.9.65 |
[8] |
Piermarco Cannarsa, Giuseppe Da Prato. Invariance for stochastic reaction-diffusion equations. Evolution Equations and Control Theory, 2012, 1 (1) : 43-56. doi: 10.3934/eect.2012.1.43 |
[9] |
Zhiting Xu, Yingying Zhao. A reaction-diffusion model of dengue transmission. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 2993-3018. doi: 10.3934/dcdsb.2014.19.2993 |
[10] |
Martino Prizzi. A remark on reaction-diffusion equations in unbounded domains. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 281-286. doi: 10.3934/dcds.2003.9.281 |
[11] |
Laurent Desvillettes, Klemens Fellner. Entropy methods for reaction-diffusion systems. Conference Publications, 2007, 2007 (Special) : 304-312. doi: 10.3934/proc.2007.2007.304 |
[12] |
Narcisa Apreutesei, Vitaly Volpert. Reaction-diffusion waves with nonlinear boundary conditions. Networks and Heterogeneous Media, 2013, 8 (1) : 23-35. doi: 10.3934/nhm.2013.8.23 |
[13] |
Angelo Favini, Atsushi Yagi. Global existence for Laplace reaction-diffusion equations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (5) : 1473-1493. doi: 10.3934/dcdss.2020083 |
[14] |
A. Dall'Acqua. Positive solutions for a class of reaction-diffusion systems. Communications on Pure and Applied Analysis, 2003, 2 (1) : 65-76. doi: 10.3934/cpaa.2003.2.65 |
[15] |
Zhaosheng Feng. Traveling waves to a reaction-diffusion equation. Conference Publications, 2007, 2007 (Special) : 382-390. doi: 10.3934/proc.2007.2007.382 |
[16] |
Feng-Bin Wang. A periodic reaction-diffusion model with a quiescent stage. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 283-295. doi: 10.3934/dcdsb.2012.17.283 |
[17] |
Nick Bessonov, Gennady Bocharov, Tarik Mohammed Touaoula, Sergei Trofimchuk, Vitaly Volpert. Delay reaction-diffusion equation for infection dynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2073-2091. doi: 10.3934/dcdsb.2019085 |
[18] |
Thomas I. Seidman. Interface conditions for a singular reaction-diffusion system. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 631-643. doi: 10.3934/dcdss.2009.2.631 |
[19] |
Wilhelm Stannat, Lukas Wessels. Deterministic control of stochastic reaction-diffusion equations. Evolution Equations and Control Theory, 2021, 10 (4) : 701-722. doi: 10.3934/eect.2020087 |
[20] |
Guangying Lv, Jinlong Wei, Guang-an Zou. Noise and stability in reaction-diffusion equations. Mathematical Control and Related Fields, 2022, 12 (1) : 147-168. doi: 10.3934/mcrf.2021005 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]