Simulation of the haptotactic effect on chondrocytes in the Boyden chamber assay

Tissue growth, wound healing, inflammation response and cancer spread are closely related to cell movement phenomena. Cell movement often exhibits random walks as well as tactic responses to certain chemicals. Boyden chamber assays have been widely used to measure the cell diffusive and tactic coefficients for cell motion assessments. We develop a mathematical model based on the mass conservation principle, and apply it to carefully elucidate the Boyden chamber experiment conducted by Shimizu et al. (1997), in which chondrocytes were tested for their haptotactic behavior responding to type II collagen. The whole process including cells sediment through the cell suspension in the upper well and the consequential migration within the collagen-coated membrane is well simulated using the developed model. To our knowledge, cell sediment phenomena have so far been neglected in previous literature. The haptotactic effect is treated by the receptorkinetic model, and the cell random walk is characterized macroscopically as cell diffusion. Finally, the values of cell diffusive, haptotactic coefficients and saturation constant of haptotaxis are determined by regression. Results show the chondrocytes perform the maximal haptotactic response when the Boyden chamber membrane is coated with a linearly distributed type II collagen with the maximal concentration, 35 μg/ml. As the collagen concentration increases, the effect of haptotaxis turns to gradually decrease. It's also found that the haptotactic velocity has the same order of the cell migration velocity (10^-7 cm/s). The saturation constant of haptotaxis to type II collagen is found to be quite small (10^-6 g/cm³), therefore we speculate the haptotaxis is possible to impose an influential impact on the migration of chondrocytes in the early stage of cartilage formation.