Cell-cell adhesion in limb-formation, estimated from photographs of cell sorting experiments based on a spatial stochastic model

We developed a new method to estimate the magnitude of differential cell-cell adhesion of two tissues based on the spatial patterns in cell- sorting experiments, and applied it to experimental data on progress-zone cells of avian limb bud at stages 20-26. The change in cell distribution in the experiment was recorded, and statistics q(B/B) for the degree of cell sorting was calculated from the photographs. Based on extensive computer simulations of spatial Markov processes on a 2-D lattice, we derived a formula for q(B/B) increasing with time. Using least square fitting, differential adhesion A and cell motility m are estimated from the time series data of q(B/B) obtained from the experiment. The estimated A was close to 0 (the spatial pattern remained random) if the mixed cells were from two tissues of the same stage. If the mixed cells were from different stages, and the estimated A was positive (cell sorting occurred). Estimated A increased with the difference in the stage number of the two tissues from which the cells were sampled. This result can be explained both by the stage-specific change in adhesion molecules and by a linear increase (or decrease) in the amount of adhesion molecules on cell surface.