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Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells

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  • A one-dimensional model for the transport of vitamin D$_3$ in an osteoblast cell is proposed, from its entry through the membrane to its activation of RANKL synthesis in the nucleus. In the membrane and cytoplasm, the transport of D$_3$ and RANKL is described by a diffusion process, while their interaction in the nucleus is modeled by a reaction-diffusion process. For the latter, an integral equation involving the boundary conditions, as well as an asymptotic solution in the regime of small concentrations, are derived. Numerical simulations are also performed to investigate the kinetics of D$_3$ and RANKL through the entire cell. Comparison between the asymptotics and numerics in the nucleus shows an excellent agreement. To our knowledge, this is the first time, albeit using a simple model, a description of the complete passage of D$_3$ through the cell membrane, the cytoplasm, into the cell nucleus, and finally the production of RANKL with its passage to the exterior of the cell, has been modeled.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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