On allosteric control model of bone turnover cycle containing osteocyte regulation loop

One approach to developing a mathematical model that predicts osteoactivity both in bio-scaffolds, as well as the in bone tissue in vivo, is based on a bio-cybernetic vision of basic multicellular unit (BMU) action. In the case of the model presented in this paper, some of the loops of regulation have been modified to reflect the range of allosteric control mechanisms: Michaelis–Menten, Hill, Adair, Koshland–Nemethy–Filmer (KNF), Monod–Wyman–Changeux (MWC). This approach has resulted in a four-dimensional system that shows steady cyclic behaviour using a range of constants with clear biological meaning. The initial findings suggesting that a steady state appears as a cycle in multidimensional phase space and this is discussed in this paper. The existence of this cycle in the osteoclasts–osteoblasts–osteocytes–bone subspace indicates that there is a conservative value along steady trajectories for this dynamic system. Biophysical interpretation of this conservative value has been proposed as a kind of substrate-energy regenerative potential of the bone remodelling system with a similarity to the classical physical value—energy. Such a recovery “potential” is directed against both mechanical and biomechanical damage to the bone. The current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Michaelis–Menten mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This finding demonstrates the viability of the suggestion of the subsistence of conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. The results indicate that the robust behaviour of the model is maintained from the simple cellular level to the molecular biochemical level of regulation.