Bone models following the mass action kinetics approach capture the effects of signaling factors on cell dynamics with π terms. These terms represent the fraction of occupied receptors and are defined by . The model by simplifies the π terms using Hill functions that represent ligand-receptor binding kinetics as activating or repressing processes, generalizing the work of . Despite some differences between the π terms and models of and , they share fundamental derivation steps. In the mass action kinetics approach, bone signaling factor actions are commonly represented by the reversible ligand-receptor relationship: