Fig. 14: Calculating the bond angle constraint.
The energy change ΔE when a bond is made or broken is a function of the actual angles between existing bonds, and a target angle. a Everywhere except along the leading edge of the EVL, the target angle is 60° based on the angle between uniformly sized circles in a perfectly hexagonal packing arrangement. b Schematic of the EVL leading edge as seen in vegetal view. The target angle along the leading edge takes into account the curvature of the embryo surface, and is adjusted dynamically as the leading edge contracts. The leading edge forms an irregular polygon encircling the embryo, with particles located at its vertices. Thus, the number of vertices and edges (N) equals the number of particles and bonds in the leading edge; in the diagram, polygon edges are numbered. The target angle between consecutive bonds is the vertex angle of a planar, regular N-gon, equal to 180° – (360°/N). This value depends only on the number of edge particles present, and therefore decreases gradually as particles leave the leading edge during epiboly. c In the absence of a bond between the two indicated particles, the energy depends on bond angles θ1 and θ2. d In the presence of a bond (dashed line), the energy depends on bond angles θ1a, θ1b, θ2a, and θ2b, such that θ1 = θ1a + θ1b and θ2 = θ2a + θ2b. ΔE is the difference between the energies of the two configurations (c, d); hence ΔEbond formation = –ΔEbond breaking, and one configuration (presence or absence of the bond) will be favored over the other.
