Fig. 8: Construction of regulatory program matrices in the AGRN framework.

a Three elementary stage transition types of the model. Linear (upper), fork (middle), and conditional transitions (bottom). Uppercase letters with rounded background represent developmental stages with the corresponding expression profile of the developmental stage vectors in which genes with an on, or off state are indicated by value 1, or 0, respectively. Black outline of the squares denotes stage-specific genes; gray outline refers to triggers (tr). The elements of the corresponding regulatory matrix M indicate the nature of the pairwise regulatory interactions (negative: repressor, positive: activator, zero: neutral). b Illustration of the model functionality on a simple differentiation hierarchy. Due to the fork transition in stage C, there are two possible developmental pathways depending on tr-1. C → D is the default pathway that needs no trigger, while C → F is the triggered branch that the differentiation process follows, if the tr-1 trigger is on. The conditional transition between D and E stages requires a second signal (tr-2 +). We used minimal expression representation: stage A corresponds to a stage vector in which the first element is 1, while in stage F the 6th value is 1; the 7th and 8th values of the stage vectors correspond to triggers tr-1 and tr-2, respectively. The lower left panel shows the system’s state as a function of time, as measured by the expression levels of the stage-specific genes in case of the two possible developmental pathway realizations (line colors correspond to the colors of the stages as shown in the upper panel). Arrows denote the time of the induction of the trigger signals. The regulatory program matrix M corresponding to this system is shown in the rightmost panel. This matrix is derived by a combination of the elementary transition rules depicted in (a) and defined in Eqs. 4–6. We used the standard parameter set (see Methods).