Figure 6
From: Inferring branching pathways in genome-scale metabolic networks
ReTrace example run. Example ReTrace run for query m1 → m10 with k = 3 in a database of 9 reactions and 10 metabolites. Atoms numbered from top to bottom as shown in figure. Dashed arrows indicate edges connecting vΔ and v
U
to atom nodes. Otherwise atom graph edges are not drawn; instead, arrows indicate substrates and products in reactions and atoms are mapped in linear fashion. For example, in reaction r9, atom nodes v7,1, v8,1 and v8,2 are connected to nodes v9,1, v9,2 and v9,3, respectively. At first, U = {m10,1, m10,2, m10,3} are the unresolved nodes. Top: algorithm state after first call to Procedure FindPath. The three shortest atom paths found are 
= (vΔ, v1,1, v8,1, v9,2, v10,2, v
U
), 
= (vΔ, v1,2, v8,2, v9,3, v10,3, v
U
) and 
= (vΔ, v1,2, v4,2, v7,1, v9,1, v10,1, v
U
), with path length ties broken arbitrarily. Choosing to process first, the reaction set corresponding to the atom path is P' = {r3, r8, r9}. Tracing back from v
U
, ReTrace finds that v10,2 and v10,3 can be traced back to vΔ, while v7,1 is added to U. Procedure FindPath is then called recursively. Bottom: algorithm state after second call to Procedure FindPath. Edges to v
U
are updated to reflect U = {v7,1}. Shortest paths from vΔ to v
U
are computed. However, only two paths are found: 
= (vΔ, v1,2, v4,2, v7,1, v
U
) and 
= (vΔ, v1,2, v3,1, v7,1, v
U
). Choosing arbitrarily to process next, ReTrace finds out that the reaction set P' = {r2, r6} resolves the remaining atom in U and a complete pathway {r2, r3, r6, r8, r9} has been discovered.