10.3. Derivations and Reaction Networks

10.3.1. Application Constraints

We may want to impose constraints on which reactions are accepted. E.g., in formose the molecules should not have too many carbon atoms.

Explore in the playground.

include("../000_basics/050_formoseGrammar.py")
strat = (
   addUniverse(formaldehyde)
   >> addSubset(glycolaldehyde)
   # Constrain the reactions:
   # No molecules with more than 20 atoms can be created.
   >> rightPredicate[
      lambda derivation: all(g.numVertices <= 20 for g in derivation.right)
   ](
      # Iterate until nothing new is found.
      repeat(
         inputRules
      )
   )
)
dg = DG(graphDatabase=inputGraphs)
dg.build().execute(strat)
dg.print()

10.3.2. Advanced Printing

Reaction networks can become large, and often it is necessary to hide parts of the network, or in general change the appearance.

Explore in the playground.

include("212_dgPredicate.py")
# Create a printer with default options:
p = DGPrinter()
# Hide "large" molecules: those with > 4 Cs:
p.pushVertexVisible(lambda v: v.graph.vLabelCount("C") <= 4)
# Hide the reactions with the large molceules as well:
def edgePred(e):
   if any(v.graph.vLabelCount("C") > 4 for v in e.sources): return False
   if any(v.graph.vLabelCount("C") > 4 for v in e.targets): return False
   return True
p.pushEdgeVisible(edgePred)
# Add the number of Cs to the molecule labels:
p.pushVertexLabel(lambda v: "#C=" + str(v.graph.vLabelCount("C")))
# Highlight the molecules with 4 Cs:
p.pushVertexColour(lambda v: "blue" if v.graph.vLabelCount("C") == 4 else "")
# Print the network with the customised printer.
dg.print(p)

10.3.3. Repetition

A sub-strategy can be repeated.

Explore in the playground.

include("../000_basics/050_formoseGrammar.py")
strat = (
   addUniverse(formaldehyde)
   >> addSubset(glycolaldehyde)
   # Iterate the rule application 4 times.
   >> repeat[4](
      inputRules
   )
)
dg = DG(graphDatabase=inputGraphs)
dg.build().execute(strat)
dg.print()

10.3.4. Rule Application

Transformation rules (reaction patterns) can be applied to graphs (molecules) to create new graphs (molecules). The transformations (reactions) implicitly form a directed (multi-)hypergraph (chemical reaction network).

Explore in the playground.

include("../000_basics/050_formoseGrammar.py")
# Reaction networks are expaned using a strategy:
strat = (
   # A molecule can be active or passive during evaluation.
   addUniverse(formaldehyde) # passive
   >> addSubset(glycolaldehyde) # active
   # Aach reaction must have a least 1 active educt.
   >> inputRules
)
# We call a reaction network a 'derivation graph'.
dg = DG(graphDatabase=inputGraphs)
dg.build().execute(strat)
# They can also be visualised.
dg.print()

10.3.5. Double Pushout Printing

Each reaction/derivation can be visualised as a DPO diagram.

Explore in the playground.

include("212_dgPredicate.py")
for e in dg.edges:
   e.print()