In Silico Stochastic Network Models that Emulate the Molecular Sieving Characteristics of Bone

Abstract

Recent studies implicate bone's extracellular matrix as a "living electrophoresis and ion exchange column" with low pass filter function at the matrix level; whereas small molecules pass through the matrix microporosity, larger molecules penetrate the tissue through the pericellular space. In this study, stochastic network modeling principles were applied, for the first time to our knowledge, to build in silico, nano- to microscale models of bone. Small volumes of bone were modeled to include hierarchical levels of porosity comprising the bone matrix microporosity and the pericellular network. Flow and transport through the network was calculated for molecules from 1,000 to 100,000 datons (Da). On the basis of this study, two contrasting effects determine the rate and direction of transport of different size molecules through the hierarchical porous network of bone. Whereas diffusivity of a given molecule decreases with increasing molecular size, the size exclusion effects of bone's low pass molecular sieve translate into increasing flow velocities for large molecular species along transport paths located in the immediate vicinity of the cells. Both phenomena are expected to have a profound effect on the formation of molecular gradients at a tissue level, providing cues for tissue generation and repair by cellular "micromachines," i.e., osteoclasts and osteoblasts.