Figure 3.

Analysis of cell–cell interaction mechanisms in a system of two cells i and j. Phase plane analysis (a,b) and time plots of gene expression dynamics (c,d). (a) Nullclines of X (where dX/dt = 0) under lateral inhibition. One symmetric unstable steady state (open box) and two asymmetric stable steady states (filled boxes) coexist. (b) Nullclines of X_i (solid line) and Y_i (dashed line) under lateral stabilization where Y_j = 1. One unstable steady state (open box) and three stable steady states (filled boxes) exist. Arrowhead indicates a ‘new’ steady state dependent on lateral stabilization. (c) Symmetry breaking in X expression. After induction, a transient of intermediate expression at the symmetric unstable steady state (arrowhead) is followed by symmetry breaking (arrow, at t = τ_X) into one X⁺ and one X⁻ cell. (d) Biphasic growth of Y in the deterministic system (η = 0 to exclude symmetry breaking of X). After induction, expression of Y remains at a plateau level (arrowhead) followed by super-induction (arrow, at t = τ_Y) through lateral stabilization. Parameter values as in table 1. (Online version in colour.)