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

Robert P. Gilbert; Philippe Guyenne; Ying Liu

doi:10.3934/mbe.2013.10.319

Article Contents

2013, Volume 10, Issue 2: 319-344. Doi: 10.3934/mbe.2013.10.319

This issue Previous Article Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation Next Article Uniqueness of limit cycles and multiple attractors in a Gause-type predator-prey model with nonmonotonic functional response and Allee effect on prey

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

1.
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716

Received: May 2012

Revised: November 2012

Published: January 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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