Mathematical Biosciences and Engineering, 2013, 10(2): 319-344. doi: 10.3934/mbe.2013.10.319

Primary: 58F15, 58F17; Secondary: 53C35.

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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

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.
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