Using Pathway Tools & Matlab for Flux Balance Analysis Kent - PowerPoint PPT Presentation

Using Pathway Tools & Matlab for Flux Balance Analysis Kent Peterson 25 Aug. 2009

Summary • Flux Balance Analysis (FBA) • Workflow: from Ptools to Matlab, and back again • A simple example • What next? 2

Let’s start at the very beginning ... Krebs cycle in A. thaliana (from Widipedia) E 12 X 1 X 2 k 12 Bio Chemical Reaction Network

Flux Balance Analysis (FBA) • Flux = “rate at which chemicals are transformed or transported” • Balanced = “input & output rates are equal” (a.k.a. steady-state) • Analysis = “optimize (balanced) flux with constraints” • Example: maximize product synthesis per unit feedstock, while satisfying maintenance (biomass) requirements Biomass Feedstock Product Cell

Software components • Pathway Tools 1 (PGDB for organism) • SBML 2 Toolbox (export metabolic description files) • COBRA 3 (setup the LP) • GLPK 4 (solve the LP) • Matlab 5 (math’s programming & graphics) 1. http://bioinformatics.ai.sri.com/ptools/ 2. http://sbml.org/Software/SBMLToolbox 3. Palsson lab @ UCSD, http://gcrg.ucsd.edu/Downloads/Cobra_Toolbox 4. GNU Linear Programming Kit, http://glpkmex.sourceforge.net/ 5. http://www.mathworks.com/

Workflow • Load PGDB into PathwayTools • Export metabolic network into SBML file • Import SBML file into Matlab • Compute FBA solution in Matlab • Examine network & flux sol’n, using Matlab GUIs • Iterate • Write FBA sol’n to text file • Import sol’n to Pathway Tools Omics Viewer Export Pathway Iterate Matlab tools Import 8

Example Maximize anabolic “biomass” produced from a “feedstock” 9

Getting the data from Ptools to Matlab • SBML export from Pathway Tools • SBML import into Matlab 10

What a mess! 1 (29) FRUCTOSE � 16 � DIPHOSPHATE (23) 1.18.1.2 (9) MET � 0001 (25) NADP (28) DIHYDROXY � ACETONE � PHOSPHATE (11) 1.2.1.13 (2) PHOSPHORIBULOKINASE 0.9 (3) RIBULP3EPIM (19) RXN � 0006 (10) CMP (14) RXN � 0001 (18) MET � 0006 (2) CDP (33) 3.6.3.14 (34) BiomassFormation (6) OXYGEN � MOLECULE (15) RXN � 0002 0.8 (3) PHOSPHO � ENOL � PYRUVATE (8) SEDOBISALDOL (1) RIB5PISOM (24) RXN490 � 3650 (37) XYLULOSE � 5 � PHOSPHATE 0.7 (5) 2TRANSKETO (28) 2PGADEHYDRAT (4) 2 � PG (12) MET � 0002 (13) RUBISCO (12) PHOSGLYPHOS (36) D � SEDOHEPTULOSE � 7 � P 0.6 (34) D � SEDOHEPTULOSE � 1 � 7 � P2 (13) CTP (16) RXN � 0003 (11) MET � 0004 (7) E � (31) CMPKIN (1) PROTON C CO � THY � LUM � CYA (43) Biomass (25) PSII 0.5 (9) F16ALDOLASE (21) RXN � 0008 (10) TRIOSEPISOMERIZATION (26) RXN � 0010 (16) MET � 0007 Reaction (30) ERYTHROSE � 4P (23) PROTON (26) NADPH (42) RIBULOSE � 5P (33) WATER Metabolite 0.4 (5) MET � 0009 Substrate flux (8) PYRUVATE (4) SEDOHEPTULOSE � BISPHOSPHATASE Product flux (41) RIBOSE � 5P (24) G3P 0.3 (15) PPI (40) ADP (35) Pi (32) GAP (18) RXN � 0005 (17) MET � 0008 (22) CARBON � DIOXIDE (20) MET � 0005 (38) ATP (14) MET � 0003 0.2 (6) 1TRANSKETO (19) Oxidized � ferredoxins (27) DPG (17) RXN � 0004 (21) Reduced � ferredoxins (22) RXN � 0009 (39) D � RIBULOSE � 15 � P2 (31) FRUCTOSE � 6P 0.1 (32) INORGPYROPHOSPHAT (30) CDPKIN (27) 3PGAREARR (29) PEPDEPHOS (7) F16BDEPHOS (20) RXN � 0007 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 11

Matlab tools (1): Met/Rxn graph 1 (22) CARBON � DIOXIDE (13) CTP (39) D � RIBULOSE � 15 � P2 (30) CDPKIN (13) RUBISCO (2) PHOSPHORIBULOKINASE 0.9 (24) G3P (27) 3PGAREARR (2) CDP (4) 2 � PG (42) RIBULOSE � 5P Calvin (28) 2PGADEHYDRAT (3) RIBULP3EPIM (12) PHOSGLYPHOS cycle (3) PHOSPHO � ENOL � PYRUVATE (1) RIB5PISOM 0.8 (37) XYLULOSE � 5 � PHOSPHATE (29) PEPDEPHOS (8) PYRUVATE (41) RIBOSE � 5P (27) DPG (31) CMPKIN (6) 1TRANSKETO (22) RXN � 0009 (11) 1.2.1.13 (5) 2TRANSKETO (32) GAP 0.7 (9) MET � 0001 (36) D � SEDOHEPTULOSE � 7 � P (10) CMP (21) RXN � 0008 (4) SEDOHEPTULOSE � BISPHOSPHATASE (12) MET � 0002 (34) D � SEDOHEPTULOSE � 1 � 7 � P2 (10) TRIOSEPISOMERIZATION 0.6 (18) RXN � 0005 Reaction (14) MET � 0003 (30) ERYTHROSE � 4P (28) DIHYDROXY � ACETONE � PHOSPHATE (19) RXN � 0006 (31) FRUCTOSE � 6P (11) MET � 0004 Metabolite (8) SEDOBISALDOL (9) F16ALDOLASE (20) RXN � 0007 0.5 Substrate flux (20) MET � 0005 Product flux (7) F16BDEPHOS (14) RXN � 0001 (29) FRUCTOSE � 16 � DIPHOSPHATE 0.4 (33) WATER (18) MET � 0006 (15) PPI (16) RXN � 0003 (15) RXN � 0002 0.3 (16) MET � 0007 (38) ATP (17) RXN � 0004 (17) MET � 0008 (32) INORGPYROPHOSPHAT (40) ADP (25) PSII 0.2 (26) RXN � 0010 (7) E � (33) 3.6.3.14 (26) NADPH (19) Oxidized � ferredoxins (23) PROTON (5) MET � 0009 (24) RXN490 � 3650 (25) NADP 0.1 (34) BiomassFormation (23) 1.18.1.2 (21) Reduced � ferredoxins (43) Biomass (1) PROTON C CO � THY � LUM � CYA (35) Pi (6) OXYGEN � MOLECULE 12 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Matlab tools (2): Met/Rxn browser 13

Final product: an FBA solution 1 (22) CARBON � DIOXIDE (13) CTP (39) D � RIBULOSE � 15 � P2 (30) CDPKIN (13) RUBISCO (2) PHOSPHORIBULOKINASE (24) G3P 0.9 (27) 3PGAREARR (2) CDP (4) 2 � PG (42) RIBULOSE � 5P (28) 2PGADEHYDRAT (3) RIBULP3EPIM (12) PHOSGLYPHOS (3) PHOSPHO � ENOL � PYRUVATE (1) RIB5PISOM 0.8 (37) XYLULOSE � 5 � PHOSPHATE (29) PEPDEPHOS (8) PYRUVATE (41) RIBOSE � 5P (27) DPG (31) CMPKIN (6) 1TRANSKETO (22) RXN � 0009 (11) 1.2.1.13 (5) 2TRANSKETO (32) GAP 0.7 (9) MET � 0001 (36) D � SEDOHEPTULOSE � 7 � P (10) CMP (21) RXN � 0008 (4) SEDOHEPTULOSE � BISPHOSPHATASE (12) MET � 0002 (34) D � SEDOHEPTULOSE � 1 � 7 � P2 (10) TRIOSEPISOMERIZATION 0.6 (18) RXN � 0005 (14) MET � 0003 (30) ERYTHROSE � 4P (28) DIHYDROXY � ACETONE � PHOSPHATE (19) RXN � 0006 (31) FRUCTOSE � 6P (11) MET � 0004 (8) SEDOBISALDOL (9) F16ALDOLASE (20) RXN � 0007 0.5 (20) MET � 0005 (7) F16BDEPHOS (14) RXN � 0001 (29) FRUCTOSE � 16 � DIPHOSPHATE 0.4 (33) WATER (18) MET � 0006 (15) PPI (16) RXN � 0003 (15) RXN � 0002 0.3 (16) MET � 0007 (38) ATP (17) RXN � 0004 (17) MET � 0008 (32) INORGPYROPHOSPHAT (40) ADP (25) PSII 0.2 (26) RXN � 0010 (7) E � (33) 3.6.3.14 (26) NADPH (19) Oxidized � ferredoxins (23) PROTON (5) MET � 0009 (24) RXN490 � 3650 (25) NADP 0.1 (34) BiomassFormation (23) 1.18.1.2 (21) Reduced � ferredoxins (43) Biomass (1) PROTON C CO � THY � LUM � CYA (35) Pi 14 (6) OXYGEN � MOLECULE 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Import to Omics Viewer 15

Recap • What have we accomplished? – From stoichiometry (structure) of reaction network ... • Steady-state flux “subspace”, v ∈ N ( S ) x ∈ N ( S T ) • Conserved “motifs”, ˙ – From flux constraints ... • Unique steady-state operating point (solution of LP) • We used “biomass” optimization, but there are many variations on the theme (e.g., MOMA, ROOM) • What is not represented? – Quantity (Concentrations) – Thermodynamics (chemical potentials) – Dynamics (approach to steady-state, stability,...) – Spatial inhomogeneities – Regulation (neither metabolic nor transcriptional) 16

Network dynamics (1): Linearized 17

Network dynamics (2): Nonlinear 18

A network model can (should?) include: • Structure (connections, stoichiometric weights) • Flux (chemical flow) • Concentration (chemical potential) • Kinetics (flux/potential constitutive model) • Regulatory “feedback” Ref: Krappmann, Lipscomb, Braus (2000) PNAS 97(25): 13585.

Example of “Metabolic Control” from EcoCyc T r a n s c r i p t i o n a l c o n t r o l Modulatory control