Systems analysis of bone remodelling as a homeostatic regulator

Abstract

Bone remodelling in adult skeleton is a process of maintaining bone mass through combined activities of bone forming osteoblasts and bone resorbing osteoclasts. Focusing on a molecular pathway mediated by osteoprotegerin, the authors derived a mathematical formulation for molecular interactions and cellular behaviours. The authors also treated this remodelling process as a homeostatic regulator in a framework of linear quadratic problems. A primary question was: does a solution of a matrix Riccati equation provide a guideline for therapeutic interventions for prevention of bone loss? In order to elucidate the systems dynamics, the authors analysed the perturbed set of equations around a stable equilibrium state together with the original equations. The results demonstrate that a homeostatic regulator with the selected control variables effectively reduces bone degradation activities and restore a physiological remodelling process. To partially validate efficacy of the described intervention strategy, biological experiments were conducted with an osteoblast cell line using one of the control variables, salubrinal (chemical agent). The authors observed that administration of salubrinal activated mRNA levels of transcription factors and an osteogenic marker gene as well as enhancement of mineralisation. Taken together, the current study supports a potential usage of control theories in active regulation of bone remodelling homeostasis.