(A) Cell-cell interaction. Two cells, centered at and , respectively, are in contact with each other. The shortest distance between the central cylindrical lines of the two cells is with and two points on the cylindrical central lines of these two cells, respectively. The amount of the overlap of these two cells is . We shall denote by the center of the line segment connecting and The total interaction force, exerted at center , is the sum of the normal force in the normal direction and the tangential force in a direction orthogonal to that is determined by the relative velocities of these two cells; see the details in Appendix 1.4 on force calculations. (B) Cell-agar interaction. A cell, centered at , touches the agar surface that has the mean position at and the roughness (the maximum fluctuation around the mean), with the amount of the overlap of the cell and agar. If the center of the hemispherical cap of the cell corresponding to the end that dips into the agar is , then . Denote , which is the midpoint of the line segment along the vertical line passing through the point between and . The total cell-agar interaction force , exerted at the center , is the superposition of a normal force in the vertical direction and the tangential force in a direction along the plane that is determined by the velocity of the cell; cf. Appendix 1.4.