Figure 3. Cascade propagator network motifs and typology of double cascades.

(a–e) Illustration of possible interference patterns between individual cascades: additive, interference without overlap or amplification, interference with overlap and without amplification, interference without overlap and with amplification, interference with overlap and amplification, respectively. Blue and yellow stand for single cascades, green for interference, and red for overlap and amplification, depending on whether the red zone is in the interference zone (green) or not. (f–k) Metabolic network motifs in the interference of two individual cascades that induce amplification. Cases (f–g) Motif caused by a metabolite which loses its only generating reaction and at the same time it is the reactant of several reactions. These reactions are going to be become non-viable. Case g is equivalent to f but inverting the sense of the links. Case (h) Metabolite which has been left with one connection to a reversible reaction. This reversible reaction has zero net flux and becomes inviable. Cases (i–j) This motif appears when a modified metabolite is lead with only one incoming connection coming from a reversible direction. This fixes the reversible reaction towards the production of this metabolite. If this step turns a metabolite of the reversible reaction inviable, the reversible reaction becomes inviable. Therefore, this motif is a potential trigger of amplification. Case j is equivalent to case i when the senses of the reactions are inverted. Case k) The individual cascades fix the sense of a reversible reaction oppositely, one cascade forwards (k top) and the other backwards (k bottom) (note that the pictures illustrate the effects of both cascades individually). After superimposing the effects of the two cascades, one can see that this reversible reaction becomes inviable. Thus, metabolites surrounding the reaction may become inviable as well, depending on their degrees. It is also a potential trigger, as in cases i–j.