Ordinary Differential Equation-based Modeling of Cells in Human Cartilage

AbstractChondrocytes produce the extracellular cartilage matrix required for smooth joint mobility. As cartilage is not vascularised, and chondrocytes are not innervated by the nervous system, chondrocytes are therefore generally considered non-excitable. However, chondrocytes do express a range of ion channels, ion pumps, and receptors involved in cell homeostasis and cartilage maintenance. Dysfunction in these ion channels and pumps has been linked to degenerative disorders such as arthritis. Because the electrophysiological properties of chondrocytes are difficult to measure experimentally, mathematical modelling can instead be used to investigate the regulation of ionic currents. Such models can provide insight into the finely tuned parameters underlying fluctuations in membrane potential and cell behaviour in healthy and pathological conditions. Here, we introduce an open-source, intuitive, and extendable mathematical model of chondrocyte electrophysiology, implementing key proteins involved in regulating the membrane potential. Because of the inherent biological variability of cells and their physiological ranges of ionic concentrations, we describe a population of models that provides a robust computational representation of the biological data. This permits parameter variability in a manner mimicking biological variation, and we present a selection of parameter sets that suitably represent experimental data. Our mathematical model can be used to efficiently investigate the ionic currents underlying chondrocyte behaviour.