Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells
A one-dimensional model for the transport of vitamin D$_3$ in anosteoblast cell is proposed, from its entry through the membraneto its activation of RANKL synthesis in the nucleus. In themembrane and cytoplasm, the transport of D$_3$ and RANKL isdescribed by a diffusion process, while their interact...
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AIMS Press
2012-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.319 |
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| author | Robert P. Gilbert Philippe Guyenne Ying Liu |
| author_facet | Robert P. Gilbert Philippe Guyenne Ying Liu |
| author_sort | Robert P. Gilbert |
| collection | DOAJ |
| description | A one-dimensional model for the transport of vitamin D$_3$ in anosteoblast cell is proposed, from its entry through the membraneto its activation of RANKL synthesis in the nucleus. In themembrane and cytoplasm, the transport of D$_3$ and RANKL isdescribed by a diffusion process, while their interaction in thenucleus is modeled by a reaction-diffusion process. For thelatter, an integral equation involving the boundary conditions, aswell as an asymptotic solution in the regime of smallconcentrations, are derived. Numerical simulations are alsoperformed to investigate the kinetics of D$_3$ and RANKL throughthe entire cell. Comparison between the asymptotics and numericsin the nucleus shows an excellent agreement. To our knowledge,this is the first time, albeit using a simple model, a descriptionof the complete passage of D$_3$ through the cell membrane, thecytoplasm, into the cell nucleus, and finally the production ofRANKL with its passage to the exterior of the cell, has beenmodeled. |
| format | Article |
| id | doaj-art-514653dbf15b48c3a7eed27ab5f55c80 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-514653dbf15b48c3a7eed27ab5f55c802025-01-24T02:25:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-12-0110231934410.3934/mbe.2013.10.319Modeling of the kinetics of vitamin D$_3$ in osteoblastic cellsRobert P. Gilbert0Philippe Guyenne1Ying Liu2Department of Mathematical Sciences, University of Delaware, Newark, DE 19716Department of Mathematical Sciences, University of Delaware, Newark, DE 19716Department of Mathematical Sciences, University of Delaware, Newark, DE 19716A one-dimensional model for the transport of vitamin D$_3$ in anosteoblast cell is proposed, from its entry through the membraneto its activation of RANKL synthesis in the nucleus. In themembrane and cytoplasm, the transport of D$_3$ and RANKL isdescribed by a diffusion process, while their interaction in thenucleus is modeled by a reaction-diffusion process. For thelatter, an integral equation involving the boundary conditions, aswell as an asymptotic solution in the regime of smallconcentrations, are derived. Numerical simulations are alsoperformed to investigate the kinetics of D$_3$ and RANKL throughthe entire cell. Comparison between the asymptotics and numericsin the nucleus shows an excellent agreement. To our knowledge,this is the first time, albeit using a simple model, a descriptionof the complete passage of D$_3$ through the cell membrane, thecytoplasm, into the cell nucleus, and finally the production ofRANKL with its passage to the exterior of the cell, has beenmodeled.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.319numerical simulations.receptorsreaction-diffusionosteoblastsrankl |
| spellingShingle | Robert P. Gilbert Philippe Guyenne Ying Liu Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells Mathematical Biosciences and Engineering numerical simulations. receptors reaction-diffusion osteoblasts rankl |
| title | Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells |
| title_full | Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells |
| title_fullStr | Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells |
| title_full_unstemmed | Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells |
| title_short | Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells |
| title_sort | modeling of the kinetics of vitamin d 3 in osteoblastic cells |
| topic | numerical simulations. receptors reaction-diffusion osteoblasts rankl |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.319 |
| work_keys_str_mv | AT robertpgilbert modelingofthekineticsofvitamind3inosteoblasticcells AT philippeguyenne modelingofthekineticsofvitamind3inosteoblasticcells AT yingliu modelingofthekineticsofvitamind3inosteoblasticcells |