STEPP – Search Tool for Exploration of Petri net Paths: A New Tool for Petri Net-Based Path Analysis in Biochemical Networks - Biological Petri Nets - page 119

Table 1
Abbreviations used for enzymes, metabolites, summarised reactions, and environment reactions

Abbr. Enzyme name Abbr. Summarised reactions Abbr. Metabolite name

Adk adenylate kinase ATPcons(b) ATP consumption ADP adenosine diphosphate

FK fructokinase Glyc(b) glycolysis AMP adenosine monophosphate

HK hexokinase StaSy(b) starch synthesis ATP adenosine triphosphate

Inv invertase Abbr. Environmental reactions eSuc external sucrose

NDPkin NDP kinase geSuc generate eSuc F6P fructose 6-phosphate

PGI phosphoglucoisomer rStarch remove starch Frc fructose

PGM phosphoglucomutase G1P glucose 1-phosphate

PPase pyrophosphatase G6P glucose 6-phosphate

SPP sucrose phosphate phosphatase Glc glucose

SPS sucrose phosphate synthase Pi phosphate ion

SucTrans sucrose transporter PP pyrophosphate

SuSy sucrose synthase S6P sucrose 6-phosphate

UGPase UDP-glucose pyrophosphorylase starch starch

Suc sucrose

UDP uridine diphospate

UDPglc uridine diphosphate-glucose

UTP uridine triphosphate

”: There is no path from eSuc to starch including Glc and
excluding HK. This is obvious, because Glc can only be converted into G6P through HK.
eSuc -> starch “l

eSuc-> starch “i { Glc } &e { HK }

{ <, 11 } ” searches for all paths with at most eleven vertices and finds sixteen possible

paths, see Table 2.
The search for the shortest paths:

eSuc -> starch “shortest” yields one result: SucTrans, Inv, HK,

StaSy(b).

Biologically Motivated Path Search

Mutation of sucrose synthase
The question is to get all alternative paths, when sucrose synthase is not available, because, e.g., of
a loss-of-function mutation. Start and end vertices are sucrose and starch. As mentioned earlier, 171
paths exist. Now, we have to exclude sucrose synthase by the constraint “e ” . The result consists

of 51 paths, which are far too much to be evaluated manually. One possibility for path reduction is the
exclusion of all PP/Pi bridges, formulated as constraint by “e

{ SuSy }

&no ppi” , which results into 39
paths. To restrict the path length, because many very long paths occur, we add the constraint “ e

{ SuSy }

{ }

SuSy

&no ppi & lmax ” , whereby the length 11 is chosen heuristically. Using length nine, we get only

one path, using length thirteen, we get fourteen paths, while for the length eleven we get the following
nine paths:
1: Suc, Inv, Frc, FK, ADP, Glyc(b), ATP, StaSy, starch,
2: Suc, Inv, Frc, FK, ADP, NDPkin rev, ATP, StaSy, starch,
3: Suc, Inv, Frc, FK, ADP, AdK rev, ATP, StaSy, starch,
4: Suc, Inv, Frc, FK, F6P, Glyc(b), ATP, StaSy, starch,
5: Suc, Inv, Frc, FK, F6P, PGI rev, G6P, StaSy, starch,
6: Suc, Inv, Frc, Glc, HK, ADP, Glyc(b), ATP, StaSy, starch,
7: Suc, Inv, Frc, Glc, HK, ADP, NDPkin rev, ATP, StaSy, starch,
8: Suc, Inv, Frc, Glc, HK, ADP, AdK rev, ATP, StaSy, starch,
9: Suc, Inv, Frc, Glc, HK, G6P, StaSy, starch.

{ 11 }