Composition of Petri nets from controled reactions. a) The algorithm described with the help of Figure 6 provides the complete set of possible controled reactions Rc = (r,fr) for each difference vector dm, here arrayed in a table where all possible controled reactions of subsequent difference vectors are listed in subsequent columns. Any arbitrary sequence of controled reactions obtained by taking one difference vector from each of the subsequent columns gives one functional extended Petri net which is compatible with the time series data set that originally served as input . There are no combinations of controled reactions generated in the described way that would give dysfunctional Petri nets because all invalid or contradictory reaction vectors have been filtered out as described. Red arrows indicate one possible trajectory of assembling a valid Petri net. Panel b) shows two reconstructed network motifs according to sets of controled reactions computed by the algorithm for difference vector d1 (see Figure 6) both of which are compatible with the input data: in a molecular interpretation, chemical reaction of B to C may depend on the absence of F (left) or the presence of A (right). A vanishes in a separate reaction in both cases. The two network motifs shown correspond to the decomposition d1 = r4 + r5 (see Figure 6g). None of the two displays the wiring of the original Petri net (Figure 6a) which can be retrieved using the decomposition d1 = r1.
Durzinsky et al. BMC Systems Biology 2011 5:113 doi:10.1186/1752-0509-5-113