Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Efficient Reconstruction of Metabolic
Pathways by Bidirectional Chemical Search
Liliana Félix
Francesc Rosselló
Gabriel Valiente
Algorithms, Bioinformatics, Complexity and Formal Methods Research
Group, Technical University of Catalonia
Computational Biology and Bioinformatics Research Group, Research
Institute of Health Science, University of the Balearic Islands
Results
Protocol
New Pathways
Discussion
5th Int. Conf. Computational Methods in Systems
Biology, Edinburgh, Scotland, 20–21 September 2007
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph Transformations
Reconstructing Metabolic Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Results
Protocol
New Pathways
Discussion
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
• Benkö et al. J. Chem. Inf. Comput. Sci. 43 (2003) 1085
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
• Benkö et al. J. Chem. Inf. Comput. Sci. 43 (2003) 1085
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
High throughput view of metabolism
METABOLIC PATHWAYS
Gabriel Valiente
Glycan Biosynthesis
and Metabolism
Biodegradation of
Xenobiotics
Introduction
Nucleotide
Metabolism
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Carbohydrate
Metabolism
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Metabolism of
Other Amino Acids
Lipid
Metabolism
Amino Acid
Metabolism
Results
Protocol
New Pathways
Discussion
Energy
Metabolism
Metabolism of
Cofactors and Vitamins
Biosynthesis of
Secondary Metabolites
01100
5/31/04
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
High throughput view of metabolism
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
High throughput view of metabolism
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Definition
A chemical graph is a variation to the classical representation
of chemical graphs used in computational chemistry
Gabriel Valiente
• Bonds between pairs of atoms are not classified
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
according to certain categories: they are distinguished
by their order only
• Aromaticity is discarded
• A single bond is allowed to match (be contained in) a
double or a triple bond in chemical substructure search
• Hydrogen atoms are not explicitly represented unless
they are directly involved in a biochemical reaction
• Chemical graphs need not be connected: they represent
the disjoint union of chemical compounds
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (KEGG compound C00221, β-D-Glucose, with
molecular formula C6 H12 O6 , and corresponding chemical
graph with explicit hydrogen atoms)
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Definition
A biochemical reaction describes the transformation of a
substrate chemical graph into a product chemical graph, and
can be described by a mapping of substrate to product
atoms
• Bonds between mapped atoms are preserved by the
biochemical reaction
• Bonds between unmapped atoms are either broken (in
the substrate) or created (in the product)
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Definition
Given a substrate and a product chemical graph, which need
not be connected, an atom mapping between them is optimal
if it entails the least possible number of broken and created
bonds in a transformation of the substrate into the product
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Definition
Given a substrate and a product chemical graph, which need
not be connected, an atom mapping between them is optimal
if it entails the least possible number of broken and created
bonds in a transformation of the substrate into the product
Remark
There is always an optimal atom mapping between a
substrate and a product chemical graph, as long as they are
compatible: they share the same molecular formula
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (Lactose 6-phosphate + H2 O ↔
β-D-Glucose + D-Galactose 6-phosphate)
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Remark
The constraints we impose on the reconstruction process are
threefold
Gabriel Valiente
• The initial chemical graphs represent all sets of at most
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
m metabolites among those involved in the set R or
reactions, for some fixed, but arbitrary, m
• The reconstruction process is restricted to a fixed, but
arbitrary, number k of derivation steps
• The initial and final sets of metabolites of every
metabolic pathway belong to the set of initial chemical
graphs
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Given a set R of biochemical reactions and a number k of
derivation steps, obtain the set of all derivation paths of
length up to 2k using the metabolites and reactions in R
Gabriel Valiente
Introduction
(0)
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
(1)
CF
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
(1)
CF
CR
(0)
CR
• Length 1
(0)
(1)
(0)
CF → CF ∩ CR
• Length 2
(0)
(1)
(1)
(0)
CF → CF ∩ CR → CR
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Given a set R of biochemical reactions and a number k of
derivation steps, obtain the set of all derivation paths of
length up to 2k using the metabolites and reactions in R
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
(0)
(1)
CF
(2)
CF
(2)
CF
CR
(1)
CR
(0)
CR
• Length 3
(0)
(1)
(2)
(1)
(0)
CF → CF → CF ∩ CR → CR
• Length 4
(0)
(1)
(2)
(2)
(1)
(0)
CF → CF → CF ∩ CR → CR → CR
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Given a set R of biochemical reactions and a number k of
derivation steps, obtain the set of all derivation paths of
length up to 2k using the metabolites and reactions in R
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
(0)
CF
···
IF
(i−1)
CF
CF
(i)
CF
CR
(i)
CR
IR
(0)
···
CR
(i−1)
CR
• Length 2i − 1
(0)
(0)
CF → · · · → IF → CF ∩ IR → · · · → CR
• Length 2i
(0)
(0)
CF → · · · → IF → CF ∩ CR → IR → · · · → CR
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Example
Toy artificial chemistry given by the metabolites
a, b, c, d, e, f (where b, d, e, f are compatible with each
other, a is compatible with bb and c is compatible with bbb)
and the following reactions (where only the first four
reactions are reversible)
ab ↔ c
a ↔ de
bd ↔ be
bb ↔ df
c → ebb
dd → a
af → bee
Discussion
Look for metabolic pathways starting and ending in the class
C = {c, ab, ad, ae, af } of metabolites and pairs of
metabolites a, b, c, d, e globally compatible with bbb
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Example (cont.)
(0)
• CF
• One step derivations
Introduction
(0)
c → (ab, bbe)
ab → (c, bde)
ad → dde
ae → dee
af → (def , bee)
Reconstructing
Metabolic
Pathways
Results
Protocol
New Pathways
Discussion
(1)
CF → CF
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
(0)
= CR = C = {c, ab, ad, ae, af }
(1)
(def , ddf ) → af
(dde, dee) → ae
(dde, ddd) → ad
(c, bde, bdd) → ab
ab → c
(1)
∩ CR = {ab, c}
(1)
∩ CR = {ab, c, bde, dde, dee, def }
• CF
• CF
(0)
(1)
(0)
CR → CR
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Example (cont.)
• Metabolic pathways of length 1 starting and ending in C
(0)
Introduction
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
(0)
c → ab
ab → c
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
(1)
CF → CF ∩ CR
• Metabolic pathways of length 2 starting and ending in C
(0)
(1)
(1)
(0)
CF → CF ∩ CR → CR
c
ab
ab
ad
ad
ae
af
→
→
→
→
→
→
→
ab
c
bde
dde
dde
dee
def
→c
→ ab
→ ab
→ ad
→ ae
→ ae
→ af
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (cont.)
• Two step derivations
(0)
CF
c
ab
ad
ae
af
(1)
→
CF
→ (ab, bbe)
→ (c, bde)
→
dde
→
dee
→ (def , bee)
(2)
CR
((af , bbe), bbd)
(ad, ae)
(ad, ∅)
(ab, (ab, bdd, bee), bde)
(c, bde, bdd)
(2)
→
CF
→
((c, bde), (bbd, def ))
→ ((ab, bbe), (ab, bdd, bee))
→
(ad, ae)
→
ae
→
((af , bbe), bde)
→
(1)
CR
→
(def , ddf )
→
(dde, dee)
→ (dde, ddd)
→ (c, bde, bdd)
→
ab
(0)
→ CR
→
→
→
→
→
af
ae
ad
ab
c
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (cont.)
(2)
• CF
(2)
(1)
∩ CR = {c, ab, bdd, bde, def }
(2)
• CF ∩ CR
= {c, ab, ad, ae, af , bbd, bbe, bdd, bde, bee}
• Metabolic pathways of length 3 starting and ending in C
(0)
(1)
(2)
(1)
(0)
CF → CF → CF ∩ CR → CR
c→
ab →
ab →
ab →
c→
af →
c→
ab
c
bde
bde
ab
bee
bbe
→
→
→
→
→
→
→
c
ab
ab
bdd
bde
bde
def
→ ab
→c
→c
→ ab
→ ab
→ ab
→ af
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (cont.)
• Metabolic pathways of length 4 starting and ending in C
(0)
(1)
(2)
(2)
(1)
(0)
CF → CF → CF ∩ CR → CR → CR
c→
ab →
ab →
ab →
ab →
ad →
ad →
ad →
ae →
af →
ab
c
c
bde
bde
dde
dde
dde
dee
def
→
→
→
→
→
→
→
→
→
→
c
ab
ab
ab
ab
ad
ad
ae
ae
af
→
→
→
→
→
→
→
→
→
→
ab
c
bde
c
bde
dde
dde
dde
dde
def
→c
→ ab
→ ab
→ ab
→ ab
→ ad
→ ae
→ ae
→ ae
→ af
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (cont.)
• Metabolic pathways of length 4 starting and ending in C
(0)
(1)
(2)
(2)
(1)
(0)
CF → CF → CF ∩ CR → CR → CR
c→
ab →
af →
ab →
ab →
c→
c→
af →
af →
ab →
bbe
c
def
bde
bde
ab
ab
bee
bee
bde
→
→
→
→
→
→
→
→
→
→
bbd
bbe
bbe
bdd
bdd
bde
bde
bde
bde
bee
→ ddf
→ def
→ def
→ ab
→ bde
→ ab
→ bdd
→ ab
→ bdd
→ bde
→ af
→ af
→ af
→c
→ ab
→c
→ ab
→c
→ ab
→ ab
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Algorithm 1
Given a set R of biochemical reactions and a number k of
derivation steps, obtain the set of all metabolic pathways of
length up to 2k using the metabolites and reactions in R
starting and ending in sets of at most m metabolites among
those involved in the reactions in R
M ← metabolites
of the reactions in R
S
j
M← m
M
j=1
0
∼ 0
E ← M/∼
= where m = m iff m and m are compatible
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
foreach C ∈ E do
IF ← IR ← C
foreach i ← 1 to k do
NF ← ∅
foreach m ∈ IF do
foreach r ∈ R do
foreach n ← forward appl. of r to m do
NF ← NF ∪ {n}
NR ← ∅
foreach m ∈ IR do
foreach r ∈ R do
foreach n ← reverse appl. of r to m do
NR ← NR ∪ {n}
output C → · · · → IF → NF ∩ IR → · · · → C
output C → · · · → IF → NF ∩ NR → IR → · · · → C
IF ← NF ; IR ← NR
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Algorithm 2
Given a set R of biochemical reactions and a number k of
derivation steps, obtain the metabolic network (X , Y )
containing all metabolic pathways of length up to 2k, using
the metabolites and reactions in R starting and ending in
sets of at most m metabolites among those involved in the
reactions in R
M ← metabolites
of the reactions in R
S
j
M← m
M
j=1
0
∼ 0
E ← M/∼
= where m = m iff m and m are compatible
X ←Y ←∅
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
foreach C ∈ E do
IF ← IR ← C
foreach i ← 1 to k do
NF ← ∅
foreach m ∈ IF do
foreach r ∈ R do
foreach n ← forward appl. of r to m do
NF ← NF ∪ {n}
X ← X ∪ {m, n}; Y ← Y ∪ {(m, n)}
NR ← ∅
foreach m ∈ IR do
foreach r ∈ R do
foreach n ← reverse appl. of r to m do
NR ← NR ∪ {n}
X ← X ∪ {m, n}; Y ← Y ∪ {(n, m)}
IF ← NF ; IR ← NR
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Example (cont.)
Toy artificial chemistry obtained from the class
C = {c, ab, ad, ae, af } of the initial chemical graphs
compatible with bbb by bidirectional search of metabolic
pathways of length up to 4
c
ad
ddd
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
ab
bde
dde
ae
bbe
bdd
dee
bee
bbd
Discussion
ddf
def
af
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Example (cont.)
Derivations produced by the enumeration of all-pairs shortest
paths in (X , Y ) starting and ending in the elements of
C = {c, ab, ad, ae, af }
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
c → ab
c → bbe → def → af
ab → c
ab → c → bbe → def → af
ad → dde → ae
af → bee → bde → ab
af → bee → bde → ab → c
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Example (cont.)
Derivations produced by the enumeration of all-pairs shortest
paths in (X , Y ) starting and ending in the elements of
C = {c, ab, ad, ae, af }
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
c → ab
c → bbe → def → af
ab → c
ab → c → bbe → def → af
ad → dde → ae
af → bee → bde → ab
af → bee → bde → ab → c
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Remark
The following shortest path derivation is not minimal
ab → c → bbe → def → af
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Algorithm 3
Given a metabolic network (X , Y ) and a set C of initial and
final metabolite sets, enumerate all minimal acyclic
metabolic pathways contained in (X , Y ) which start and end
in metabolite sets from C
foreach v ∈ C do
p ← {v }
acyclic(C , Y , v , p)
foreach (v , w ) ∈ Y do
if w ∈
/ p then
if w ∈ C then
print p ∪ {w }
else
p ← p ∪ {w }
acyclic(C , Y , w , p)
p ← p \ {w }
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Example (cont.)
Derivations produced by the enumeration of minimal acyclic
paths starting and ending in the elements of
C = {c, ab, ad, ae, af }
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
c → ab
c → bbe → bbd → ddf → af
c → bbe → def → af
ab → c
ad → dde → ae
af → bee → bde → ab
af → bee → bde → bdd → ab
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Example (cont.)
Derivations produced by the enumeration of minimal acyclic
paths starting and ending in the elements of
C = {c, ab, ad, ae, af }
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
c → ab
c → bbe → bbd → ddf → af
c → bbe → def → af
ab → c
ad → dde → ae
af → bee → bde → ab
af → bee → bde → bdd → ab
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Remark
The following minimal acyclic derivation is not shortest
c → bbe → bbd → ddf → af
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Experimental protocol used to reconstruct metabolic
pathways for all known reference pathway maps
• Obtain reference pathway maps from the KEGG
database
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
• Solve the optimal atom mapping problem for all of the
reactions in the reference pathways
• Reconstruct metabolic pathways of length up to 8 for
each reference pathway
• Orient the reactions according to previous studies of
irreversibility of reactions in KEGG
• Filter out those metabolic pathways that involve
irreversible reactions applied in the reverse direction
• Identify the new metabolites thus obtained by chemical
structure search in public databases
• Analyze the new metabolic pathways for coexistence of
metabolites and enzymes in each particular organism
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
New pathways of length up to 2k using the metabolites and
reactions in KEGG reference pathway maps
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
map
00020
00030
00100
00120
00251
00260
00290
00330
00340
00360
00410
00590
00906
k=0
order
82
314
229
292
24
604
161
289
129
157
106
870
594
order
253
1,148
229
1,901
44
841
350
376
323
244
264
3,128
1,181
size
350
1,678
0
3,254
44
482
390
180
390
178
320
4,672
1,250
k=1
shortest
8
6
0
24
2
8
12
6
2
4
4
156
76
minimal
8
10
0
36
4
8
12
6
2
4
4
156
76
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
New pathways of length up to 2k using the metabolites and
reactions in KEGG reference pathway maps
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
map
00020
00030
00100
00120
00251
00260
00290
00330
00340
00360
00410
00590
00906
k=0
order
82
314
229
292
24
604
161
289
129
157
106
870
594
order
458
2,284
229
3,442
52
915
350
383
385
246
293
5,501
1,345
size
818
4,788
0
7,680
60
632
390
194
536
182
382
10,278
1,780
k=2
shortest
8
6
0
30
2
8
12
6
2
4
4
156
76
minimal
8
44
0
192
4
8
12
6
2
4
6
180
78
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
New pathways of length up to 2k using the metabolites and
reactions in KEGG reference pathway maps
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
map
00020
00030
00100
00120
00251
00260
00290
00330
00340
00360
00410
00590
00906
k=0
order
82
314
229
292
24
604
161
289
129
157
106
870
594
order
737
2,988
229
3,442
52
929
350
383
385
246
316
7,052
1,357
size
1,712
6,770
0
7,680
60
676
390
194
536
182
428
14,456
1,818
k=3
shortest
8
6
0
30
2
8
12
6
2
4
4
156
76
minimal
8
326
0
984
4
8
12
6
2
4
6
228
78
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
New pathways of length up to 2k using the metabolites and
reactions in KEGG reference pathway maps
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
map
00020
00030
00100
00120
00251
00260
00290
00330
00340
00360
00410
00590
00906
k=0
order
82
314
229
292
24
604
161
289
129
157
106
870
594
order
785
3,021
229
3,442
52
929
350
383
385
246
316
7,189
1,357
size
1,876
6,836
0
7,680
60
676
390
194
536
182
428
14,824
1,818
k=4
shortest
8
6
0
30
2
8
12
6
2
4
4
156
76
minimal
8
1,714
0
4,716
4
8
12
6
2
4
6
228
78
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
New pathways of length up to 2k using the metabolites and
reactions in KEGG reference pathway maps
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (KEGG pathway 00100, k = 1)
C13455 + C15971
⇒ R06958 ⇒
C13456 + C15971
⇐ R07577 ⇐
C09707 + C13456
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (KEGG pathway 00100, k = 1)
C13455 + C15932
⇒ R06958 ⇒
C13456 + C15932
⇐ R07551 ⇐
C13456 + C15928
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (KEGG pathway 00260, k = 1)
C00022 + C00065
⇒ R00369 ⇒
C02115 + C00048
⇐ R00588 ⇐
C00041 + C00168
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (KEGG pathway 00030, k = 2)
C00198 + C00629
⇒ R01519 ⇒
C00618 + C00198
⇒ R01538 ⇒
OCC(OC(CO)C(O)C(=O)C(O)C(O)=O)C(O)C(O)C(O)C(O)=O
⇐ R01538 ⇐
OCC(OC(CO)C(O)C(O)C(=O)C(O)=O)C(O)C(O)C(O)C(O)=O
⇐ R01519 ⇐
C00257 + C06440
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (KEGG pathway 00100, k = 1)
C14146 + C13455
⇒ R06958 ⇒
C14146 + C13456
⇐ R06961 ⇐
C08586 + C13456
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Example (KEGG pathway 00100, k = 1)
C14146 + C13455 => R06958 => C14146 + C13456
<= R06961 <= C08586 + C13456
alpha-Zeacarotene + Abscisic aldehyde
=> alpha-Zeacarotene + Abscisic alcohol
<= delta-Carotene + Abscisic alcohol
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Example (KEGG pathway 00100, k = 1)
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
• Estevez et al. J. Biol. Chem. 276 (2001) 22901
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Discussion
• Bidirectional chemical search is an efficient method to
build a substantial portion of the artificial chemistry
defined by the metabolites and biochemical reactions in
a given metabolic pathway
• Computational results upon several reference pathway
maps in KEGG reveal a number of new biochemical
pathways
• The artificial chemistry reconstruction starting from all
sets of at most m metabolites among those involved in
the set of reactions might reveal the existence of a much
larger number of new biochemical pathways for m > 2
Efficient
Reconstruction of
Metabolic
Pathways by
Bidirectional
Chemical Search
Gabriel Valiente
Introduction
Artificial Chemistries
Metabolic Pathways
Chemical Graphs
Chemical Graph
Transformations
Reconstructing
Metabolic
Pathways
Constraints
Bidirectional Search
Example
Algorithm 1
Algorithm 2
Algorithm 3
Results
Protocol
New Pathways
Discussion
Discussion
Number of potential biochemical reactions (number of
classes with two or more molecules)
map
00020
00030
00100
00120
00251
00260
00290
00330
00340
00360
00410
00590
00906
m=1
1
7
14
10
3
5
8
6
1
7
3
10
18
m=2
97
263
285
396
209
624
274
490
255
364
234
213
786
m=3
2,250
3,696
20,756
6,685
5,512
23,630
3,895
14,025
7,897
6,230
6,273
2,178
13,100
m=4
24,833
28,860
285,566
67,353
74,831
424,027
33,131
203,409
104,759
55,100
81,546
14,417
120,642
m=5
170,858
151,233
2,439,893
471,120
604,301
4,252,609
196,273
1,741,156
763,662
309,536
610,070
70,620
719,545