Fig 6. The stochastic switching trajectory and the rate change with the burst size.

(a) Changing the relative burst size ν_A = 1, 3, 5, 10 for both switching processes A → B (top) and B → A (bottom) alters the MAP. The actions for the transitions (coloured lines) decrease and hence switching becomes more rapid as ν_A increases. The position of the different steady expression states are marked with colour circles for state A (orange) and B (blue) as well as the saddle points (black). Parameters are those of Fig 4. Morphogen signal is M = 0.45. For this value of M the effect on the action is more dramatic for the transition A→B. (b) Burst size modifies the change of action along the tissue. The action along the tissue evaluated for different values of ν_B (indicated by the different colours) for both switching transitions: B → A (solid line) and A → B (dashed lines) (top panel). The derivative of the action for B → A with respect to morphogen concentration level is shown in the bottom panel. Increasing the morphogen level biases the cells towards state A. The steady state position of the boundary is close to the value of M where dotted and dashed lines cross. The burst size has very little effect on these positions (value of M), but does affect how quickly they are approached. Parameters are those of Fig 4.