Effective mechanical potential of cell–cell interaction explains three-dimensional morphologies during early embryogenesis
Fig 1
Overview of strategy for inferring the effective potential of cell–cell interactions.
A. Relationship between microscopic forces and attractive/repulsive forces in isolated two cell systems. i) Microscopic forces are exemplified. ii) The microscopic forces are approximated as attractive/repulsive forces where cells are described as particles with the mean size. iii) Both the repulsive and attractive forces are provided as cell–cell distance–dependent functions, and the summation (black broken line) is the distance–force curve of the two particles. The relationship between the curve and the mean diameters of the cells is shown. iv) A distance–potential curve is shown where the mean diameters of cells correspond to the distance at the potential minimum. B. Strategy for inferring effective forces of cell–cell interactions. i) Particle model. A blue sphere corresponds to a cell. Attractive or repulsive force between the particles (blue spheres #1–4), was considered; vectors of cell–cell interaction forces (Fi) are illustrated by black arrows in the case of particle #3. The net force (FC|p) of particle #3 is shown by a red vector. The summation of Fi results in FC|p which determines the velocity (VC|p) of pth particle. ii) Nuclear tracking data were obtained and used as a reference data during the inference. iii) Effective forces of cell–cell interactions were inferred by fitting. Red line, attractive; blue line, repulsive. iv) From the inferred effective forces, we examined whether distance–force/potential curves are detected. Related figure: S1 Fig (inference method).