example problems: chapters 6 & 7
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Example Problems: Chapters 6 & 7. Systems Biology Study Group Sarah Munro 11-19-2007. Examples. Drawing networks Creating the S Matrix Verifying the S Matrix Topological Properties of the network S for E. coli core metabolism S for Glycolysis. Reaction Network Map. byp. v 1. v 2. - PowerPoint PPT PresentationTRANSCRIPT
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Example Problems:Chapters 6 & 7
Systems Biology Study Group
Sarah Munro
11-19-2007
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Examples
• Drawing networks
• Creating the S Matrix
• Verifying the S Matrix
• Topological Properties of the network
• S for E. coli core metabolism
• S for Glycolysis
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E
Axt
Ext
bypxt
A B C
byp
v1 v22b1
D
cof
byp
2cof
b3
b2v3v5
v4
v6
Reaction Network Map
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E
Axt
Ext
bypxt
A B C
byp
2
D
cof
byp
2
cof
Metabolite Connectivity Map
b1 v1 v2
v3
v4
v6
v5
b3
b2
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100000000bypxt
010000000Ext
001-000000Axt
1-00000110byp
00001-11-00cof
01-0101000E
000011-100D
0001-1-0010C
0000002-2-1B
001000001-A
bbbvvvvvv
S
321654321
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1000
1100
0100
0110
0010
0011
1001
0001
1353123454363312
Urea
Arginine
Fumarate
ccinateArgininosu
Aspartate
Citrulline
Ornithine
P-Carbamoyl
............
S1
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Create E1, the elemental matrix for S1:
Ornithine C5H13N2O2
Carbamoyl Phosphate CH2NO5P
Citrulline C6H13N3O3
Aspartate C4H6NO4
Argininosuccinate C10H17N4O6 Fumarate C4H2O4
Arginine C6H15N4O2 Urea CH4N2O
00000001P
24041321N
12464325O
415217613132H
164104651C
UreaArgFumsucc-ArgAspCitrulOrnithP-Carb
E1
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Multiply the elemental and stoichiometric matrices in MATLAB:
0001P
0000N
1014O
2022H
0000C
1.3.5.31.2.3.45.4.3.63.3.1.2
S1E1
E1·S1 ≠ 0 Something is missing!
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0001H
1-010OH
0001HPO
1000Urea
1100Arginine
0100Fumarate
0110ccinateArgininosu
0010Aspartate
0011Citrulline
1001Ornithine
0001P-Carbamoyl
1.3.5.31.2.3.45.4.3.63.3.1.2
2
4
S2
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00000001P
24041321N
12464325O
415217613132H
164104651C
UreaArgFumsucc-ArgAspCitrulOrnithP-Carb
E2
001
000
014
121
000
HOHHPO 24
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Multiply the new elemental and stoichiometric matrices in MATLAB:
0000P
0000N
0000O
0000H
0000C
1.3.5.31.2.3.45.4.3.63.3.1.2
S2E2
E2·S2 = 0 The S matrix is now correct !
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H2O
HPO4
H+
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1
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1-001-10000E
00011-1-100D
01-0000010C
0000011-1-1B
001-000001-A
vvvvvvvvv
S
eca654321
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100110000E
000111100D
010000010C
000001111B
001000001A
vvvvvvvvv
S
eca654321
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1-010C
001-1B
01-01-A
vvvv
S
ca21
2
1010C
0011B
0101A
vvvv
S
ca21
2
100v
001v
110v
011v
CBA
S
c
a
2
1T2
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1010v
0101v
1021v
0112v
vvvv
SS A
c
a
2
1
ca21
2T2v
Reaction Adjacency Matrix, Av:
How many compounds participate in va? In v1?
How many compounds do v2 and vc have in common?
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210C
121B
012A
CBA
SS A T22x
Compound Adjacency Matrix, Ax:
How many reactions does compound A participate in?
How many reactions do A and B participate in together? What about compounds A and C?
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1Teusink et al. Eur. J. Biochem. (267) 2000
Teusink_Glycolysis
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1Teusink et al. Eur. J. Biochem. (267) 2000
Teusink_Glycolysis_core
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Rxn Name Rxn Abbrev Rxn #'Hexokinase' 'vGLK' 1'Glucose-6-phosphate isomerase' 'vPGI' 2'Phosphofructokinase' 'vPFK' 3'Aldolase' 'vALD' 4'Glyceraldehyde 3-phosphate dehydrogenase' 'vGAPDH' 5'Phosphoglycerate kinase' 'vPGK' 6'Phosphoglycerate mutase' 'vPGM' 7'Enolase' 'vENO' 8'Pyruvate kinase' 'vPYK' 9'Pyruvate decarboxylase' 'vPDC' 10'Glucose transport' 'vGLT' 11'Alcohol dehydrogenase' 'vADH' 12'ATPase activity' 'vATP' 13
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Metab Names Metab Abbrev Metab #'Glucose in Cytosol‘ 'GLCi' 1'Glucose 6 Phosphate' 'G6P' 2'Fructose 6 Phosphate' 'F6P' 3'Fructose-1,6 bisphosphate' 'F16P' 4'Triose-phosphate' 'TRIO' 5'1,3-bisphosphoglycerate' 'BPG' 6'3-phosphoglycerate' 'P3G' 7'2-phosphoglycerate' 'P2G' 8'Phosphoenolpyruvate' 'PEP' 9'Pyruvate' 'PYR' 10'Acetaldehyde' 'ACE' 11'High energy phosphates' 'P' 12'NAD' 'NAD' 13'NADH' 'NADH' 14'CO2' 'CO2' 15'Extracellular Glucose' 'GLCo' 16'Ethanol' 'ETOH' 17
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function [Ax, Av, Sbin] = topo_properties(S)%Plots the number of metabolites y that participate in x reactions%Function file input is a mxn matrix that defines the stoichiometry of a%reaction network%Function file outputs include: Ax = compound adjacency matrix, %Av = reactions adjacency matrix, Sbin = binary form of Smatrix %Generate binary form of S matrix[m,n] = size(S);Sbin = zeros(m,n);for i= 1:m for j= 1:n if S(i,j)~=0; Sbin(i,j) = 1; if S(i,j) == 0; Sbin(i,j) = 0; end endendend
%calculate transpose of SbinSbinT = transpose(Sbin);
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%calculate Ax, the compound adjacency matrixAx = Sbin*SbinT; %calculate Av, the reaction adjacency matrixAv = SbinT*Sbin; % bar plot of the number of metabolites y, that participate in x reactions[m,n] = size(Ax);y = [];for i = 1:my = [y Ax(i,i)];endmaxreactions = max(y);minreaction = min(y);reactions = [minreactions:1:maxreactions]; compounds = zeros(1,length(reactions));for j = 1:length(reactions);I = find(y == reactions(j));compounds(j) = [length(I)];end bar(reactions,compounds)xlabel('number of reactions')ylabel('number of compounds')
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1 2 3 4 50
2
4
6
8
10
12
14
number of reactions
num
ber
of c
ompo
unds
Participation of Compounds in Reactions for Glycolysis Core
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0 5 10 15 20 25 300
5
10
15
20
25
30
number of reactions
num
ber
of c
ompo
unds
Participation of Compounds in Reactions in E. coli Core
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What’s Next?Singular Value Decomposition?
Calculating Extreme Pathways?
Running Simulations using ODE solvers?