Measurement of chondrocyte chemotaxis using a Boyden chamber: a model of receptor-mediated cell migration combined with cell sedimentation

The Boyden chamber assay measures the coefficients of cell motility by fitting the experiments with theoretical calculations. Under the circumstance of rapid receptor kinetics, the distribution of chemical-receptor complexes on the cell surface can be treated as being quasi-steady and chemotaxis is directly related to the biochemical concentration, leading to the celebrated Keller–Segel model, which has been shown to be an approximation to the full receptor-mediated form. No matter approximate or full, these approaches have ignored cell sedimentation in the upper chamber, assuming that all the cells have already resided on the filter top at the beginning of the test. However, the time required for all the cells to settle through the suspension can be close to the entire incubation time of just several hours. In order to amend such a deficiency, the present work combines the receptor-based model with cell sedimentation for modeling the chemotaxis assay using the Boyden chamber. Simulations were performed to fit the experimental data in the literature, which tested the chondrocyte chemotactic motility in response to collagen. Results show that once cell sedimentation is involved, the assumption of quasi-steady receptor distribution may be invalid for the Boyden assay. This is because the formation of the chemical-receptor complexes is profoundly retarded by the process of cell sedimentation. To estimate the parameters of cell motility and receptor kinetics, cell sedimentation should be incorporated in modeling the chemotaxis assay using the Boyden chamber.