Faulon J.L., Bender A. Handbook of Chemoinformatics Algorithms

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418 Handbook of Chemoinformatics Algorithms

Ri5P(C1 ∼0,C2 ∼0,C3 ∼0,C4 ∼0,C5 ∼0) V_Ri5P

S17P(C1 ∼0,C2 ∼0,C3 ∼0,C4 ∼0,C5 ∼0,C6 ∼0,C7 ∼0) V_S17P

S7P(C1 ∼0,C2 ∼0,C3 ∼0,C4 ∼0,C5 ∼0,C6 ∼0,C7 ∼0) V_S7P

I 1

NULL 0

end species

begin reaction rules

R5DP(C1%1,C2%2,C3%3,C4%4,C5%5) + CO2(C1%6) -> \

G3P(C1%2,C2%4,C3%6) + G3P(C1%1,C2%3,C3%5) v_R00024/(V_R5DP*V_CO2)

G3P(C1%1,C2%2,C3%3) -> P13G(C1%1,C2%2,C3%3) v_R01512/V_G3P

T3P(C1%1,C2%2,C3%3) < − > P13G(C1%2,C2%3,C3%1) v_R01063_f/V_T3P,

v_R01063_b/V_P13G

T3P(C1%1,C2%2,C3%3) < − > DHAP(C1%1,C2%2,C3%3) v_R01015_f/V_T3P,

v_R01015_b/V_DHAP

F16P(C1%1,C2%2,C3%3,C4%4,C5%5,C6%6) < − > \

DHAP(C1%5,C2%2,C3%6) + T3P(C1%4,C2%1,C3%3) v_R01068_f/V_F16P,

v_R01068_b/(V_DHAP*V_T3P)

F16P(C1%1,C2%2,C3%3,C4%4,C5%5,C6%6) -> \

F6P(C1%1,C2%2,C3%3,C4%4,C5%5,C6%6) v_R00762/V_F16P

F6P(C1%1,C2%2,C3%3,C4%4,C5%5,C6%6) + \

T3P(C1%7,C2%8,C3%9)< − > E4P(C1%5,C2%1,C3%4,C4%3)+\

X5P(C1%2,C2%8,C3%6,C4%9,C5%7) v_R01067_f/(V_F6P*V_T3P),

v_R01067_b/(V_E4P*V_X5P)

S17P(C1%1,C2%2,C3%3,C4%4,C5%5,C6%6,C7%7) < − > \

DHAP(C1%6,C2%2,C3%4) +

E4P(C1%7,C2%1,C3%5,C4%3) v_R01829_f/V_S17P,

v_R01829_b/(V_DHAP*V_E4P)

S17P(C1%1,C2%2,C3%3,C4%4,C5%5,C6%6,C7%7) -> \

S7P(C1%2,C2%1,C3%4,C4%3,C5%6,C6%5,C7%7) v_R01845/V_S17P

S7P(C1%1,C2%2,C3%3,C4%4,C5%5,C6%6,C7%7) +\

T3P(C1%8,C2%9,C3%10) < − > \

Ri5P(C1%2,C2%4,C3%6,C4%7,C5%5) +

X5P(C1%1,C2%9,C3%3,C4%10,C5%8) v_R01641_f/(V_S7P*V_T3P),

v_R01641_b/(V_Ri5P*V_X5P)

R5P(C1%1,C2%2,C3%3,C4%4,C5%5) < − > \

X5P(C1%1,C2%2,C3%3,C4%4,C5%5) v_R01529_f/V_R5P,

v_R01529_b/V_X5P

Ri5P(C1%1,C2%2,C3%3,C4%4,C5%5) < − > \

R5P(C1%5,C2%1,C3%4,C4%2,C5%3) v_R01056_f/V_Ri5P,

v_R01056_b/V_R5P

R5P(C1%11,C2%12,C3%13,C4%14,C5%15) -> \

R5DP(C1%12,C2%11,C3%14,C4%13,C5%15) v_R01523/V_R5P

T3P() -> NULL vs_T3P/V_T3P

F6P() -> NULL vs_F6P/V_F6P

R5P() -> NULL vs_R5P/V_R5P

E4P() -> NULL vs_E4P/V_E4P

G3P() -> NULL vs_G3P/V_G3P

I-> I + CO2(C1 ∼0) v_vi_CO2_unlabeled

I-> I + CO2(C1 ∼1) v_vi_CO2_labeled

end reaction rules

begin observables

Molecules T3P_0 T3P(C1∼0,C2∼0,\

C3∼0)/V_T3P

Molecules T3P_1 T3P(C1∼1,C2∼0,\ T3P(C1∼0,C2∼1,\ T3P(C1∼0,C2∼0,C3∼1)/\

C3∼0)/V_T3P C3∼0)/V_T3P V_T3P

Molecules T3P_2 T3P(C1∼1,C2∼1,\ T3P(C1∼1,C2∼0,\ T3P(C1∼0,C2∼1,C3∼1)/\

C3∼0)/V_T3P C3

∼1)/V_T3P V_T3P

Molecules T3P_3 T3P(C1∼1,C2∼1,\

C3∼1)/V_T3P

end observables

Using Systems Biology Techniques to Determine Metabolic Fluxes 419

generate_network({overwrite=>1});

writeSBML();

writeMfile();

simulate_ode({prefix=>"equil", t_end=>10000, n_steps=>10});

setParameter("v_vi_CO2_unlabeled", 0.9);

setParameter("v_vi_CO2_labeled", 0.1);

simulate_ode({t_end=>200, n_steps=>200});

writeNET();

With reference to the Calvin cycle and BioNetGen input file given above, we can

now recap the method of setting up a BioNetGen input file to perform a forward sim-

ulation of

C labeling dynamics, which is the core component of any flux estimation

procedure.

1. Define the list of molecular species and reactions of interest and specify the

atom fate maps for these reactions. In our example, there are 13 internal

reactions and six exchange reactions defined in the reaction rules block of the

BioNetGen input file.

2. In the parameters block, for each reaction, specify a flux consistent with the

stoichiometric constraints. For reversible reactions, we need to specify both

the forward and backward fluxes. Metabolite pool sizes are also specified in

the parameters block. For this example, we use the default pool size of one.

3. Next, specify the observables. These should be experimentally measurable

quantities of interest. We specified T3P based on the mass differences of the

isotopomers.

4. Run the forward simulation to obtain the steady state.

5. Change the input feed to isotope-labeled fluxes and simulate the

C labeling

dynamics.

15.5 DISCUSSION AND CONCLUSION

Systems biology is the integration of experimental and computational approaches

to achieve the overall goal of explaining and predicting complex cellular behaviors

of biological systems. Using different “omics” technologies—genomics, proteomics,

and metabolomics—a wealth of information is becoming available about many dif-

ferent cellular components and, to some extent, on the interaction between some of

these components. These approaches are providing a static view of biological systems.

However, it is of growing importance to augment these analyses with a higher-level

understanding of cellular dynamics. Fluxes are an integrated functional output of

a metabolic network, which are highly relevant for understanding how the network

operates as a system and for applications that focus on manipulating metabolic behav-

iors, as in metabolic engineering. In recent years, MFA has become an important tool

for quantifying metabolic pathways.

MFA allows the detailed quantification of all intracellular fluxes in the metabolism

of a biological system.Among the developed tools,

C MFA, which uses

C labeling

patterns of metabolic products that result from feeding

C-labeled substrates, is a

powerful quantitative method for intracellular pathway flux determination within

420 Handbook of Chemoinformatics Algorithms

metabolic networks. We have provided an algorithmic overview of the procedure of

CMFA.

C-based MFA requires the knowledge of fate of carbons in metabolic

reactions, and the carbon atom fate information is transferred into isotopomer balance

equations, which describe the mathematical relationship between unknown fluxes and

the available measurement dataset. Using these equations, fluxes can be computed

from the measurements through nonlinear parameter fitting.

In recent years, with the development of experimental techniques and computa-

tional methods, steady-state

C MFA has reached a state of relative maturity. The

experiments themselves have become a routine procedure, the measurement tech-

niques are well established, and sophisticated mathematical evaluation algorithms are

available. However,

C MFA is still a time-consuming and low-throughput process.

Typically, modeling carbon isotopomer networks, such as central carbon pathways,

involves an equation system containing a few to several thousand variables to balance

reactions between isotopomers. This problem is addressed by the BNGL/BioNetGen-

based approach to

C MFA reviewed here. The BNGL/BioNetGen-based approach

allows isotopomer balance equations to be constructed quickly from a database of

carbon fate maps and then simulated.

Metabolic steady state is a precondition for current flux analysis methods. The

routine methods for flux analysis are based on

C steady state using isotopic label-

ing patterns of proteinogenic amino acids, which is reflective of their 12 precursors

in central metabolism. Detecting the labeling patterns of free intracellular metabolic

intermediates can dramatically shorten the labeling experiments because these inter-

mediates can reach

C steady state much faster than proteinogenic amino acids.

The labeling patterns can also go beyond the 12 precursors. Dynamic

C labeling

patterns of intracellular metabolic intermediates contain more information than the

C steady-state isotopic labeling patterns. For example, intracellular metabolite pool

sizes affect the dynamic labeling patterns, whereas they have no effect on steady-state

labeling patterns.

ACKNOWLEDGMENTS

This work was supported in part by the NIH, under grants GM080216, CA132629,

and GM076570, and by the DOE, under contract DE-AC52-06NA25396. We thank

P.J. Unkefer, C.J. Unkefer, and R.F. Williams for helpful discussions.

REFERENCES

1. Feist A. M., Henry C. S., Reed J. L., Krummenacker M., Joyce A. R., Karp P.

D., Broadbelt L. J., Hatzimanikatis V., and Palsson B. O., A genome-scale metabolic

reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and

thermodynamic information, Molecular Systems Biology 2007, 3: 121.

2. Forster J., Famili I., Fu P., Palsson B. O., and Nielsen J., Genome-scale reconstruction of

the Saccharomyces cerevisiae metabolic network, Genome Research 2003, 13: 244–253.

3. Duarte N. C., Becker S.A., Jamshidi N., Thiele I., Mo M. L.,VoT. D., SrivasR., and Palsson

B. O., Global reconstruction of the human metabolic network based on genomic and

bibliomic data, Proceedings of the National Academy of Sciences 2007, 104: 1777–1782.

Using Systems Biology Techniques to Determine Metabolic Fluxes 421

4. Segre D., Vitkup D., and Church G. M., Analysis of optimality in natural and perturbed

metabolic networks, Proceedings of the National Academy of Sciences 2002, 99: 15112–

15117.

5. Sauer U., High-throughput phenomics: Experimental methods for mapping fluxomes,

Current Opinion in Biotechnology 2004, 15: 58–63.

6. Sauer U., Metabolic networks in motion: 13C-based flux analysis, Molecular Systems

Biology 2006, 2:62.

7. Schmidt K., Carlsen M., Nielsen J., and Villadsen J., Modeling isotopomer distribu-

tions in biochemical networks using isotopomer mapping matrices, Biotechnology and

Bioengineering 1997, 55: 831–840.

8. Zupke C. and Stephanopoulos G., Modeling of isotope distribution and intracellular fluxes

in metabolic networks using atom mapping matrices, Biotechnology Progress 1994, 10:

489–498.

9. Wiechert W., 13C Metabolic flux analysis, Metabolic Engineering 2001, 3: 195–206.

10. Arauzo-Bravo M. J. and Shimizu K., An improved method for statistical analysis of

metabolic flux analysis using isotopomer mapping matrices with analytical expressions,

Journal of Biotechnology 2003, 105: 117–133.

11. Wiechert W., Mollney M., Petersen S., and de Graaf A., A universal framework for 13C

metabolic flux analysis, Metabolic Engineering 2001, 3: 265–283.

12. Szyperski T., Biosynthetically directed fractional 13C-labeling of proteinogenic amino

acids. An efficient analytical tool to investigate intermediary metabolism, European

Journal of Biochemistry 1995, 232: 433–448.

13. Szyperski T., 13C-NMR, MS and metabolic flux balancing in biotechnology research,

Quarterly Reviews of Biophysics 1998, 31: 41–106.

14. Goto S., Okuno Y., Hattori M., Nishioka T., and Kanehisa M., LIGAND: Database of

chemical compounds and reactions in biological pathways, Nucleic Acids Research 2002,

30: 402–404.

15. Krieger C. J., Zhang P., Mueller L. A., Wang A., Paley S., Arnaud M., Pick J., Rhee S. Y.,

and Karp P. D., MetaCyc: Recent enhancements to a database of metabolic pathways and

enzymes in microorganisms and plants, Nucleic Acids Research 2004, 32: D438–D442.

16. Schomburg I., Chang A., Ebeling C., Gremse M., Heldt C., Huhn G., and Schomburg D.,

BRENDA, the enzyme database: updates and major new developments, Nucleic Acids

Research 2004, 32: D431–D433.

17. Michal G., Biochemical Pathways: An Atlas of Biochemistry and Molecular Biology.

Wiley: New York, Heidelberg, Germany, 1999.

18. Arita M., In silico atomic tracing by substrate-product relationships in Escherichia coli

intermediary metabolism, Genome Research 2003, 13: 2455–2466.

19. Mu F., Williams R. F., Unkefer C. J., Unkefer P. J., Faeder J. R., and Hlavacek W.S.,

Carbon fate maps for metabolic reactions, Bioinformatics (Oxford) 2007, 23: 3193–3199.

20. Arita M., The metabolic world of Escherichia coli is not small, Proceedings of the

National Academy of Sciences 2004, 101: 1543–1547.

21. http://bionetgen.org.

22. Faeder J. R., Blinov M. L., Goldstein B., and Hlavacek W. S., Rule-based modeling of

biochemical networks, Complexity 2005, 10: 22–41.

23. Blinov M. L., Yang J., Faeder J. R., and Hlavacek W. S., Graph theory for rule-based

modeling of biochemical networks. Transactions on Computational Systems Biology VII,

2006, 89–106.

24. Hlavacek W. S., Faeder J. R., Blinov M. L., Posner R. G., Hucka M., and Fontana W.,

Rules for modeling signal-transduction systems, Science’s STKE 2006, p. re6.

25. FateMapViewer Software http://cellsignaling.lanl.gov/FateMaps

422 Handbook of Chemoinformatics Algorithms

26. Faeder J. R., Blinov M. L., and Hlavacek W. S., Rule-based modeling of biochemical

systems with BioNetGen, Methods in Molecular Biology 2009, 500: 113–169.

27. Wiechert W. and de Graaf A. A., Bidirectional reaction steps in metabolic networks:

I. Modeling and simulation of carbon isotope labeling experiments, Biotechnology and

Bioengineering 1997, 55: 101–117.

28. Dauner M., Bailey J. E., and Sauer U., Metabolic flux analysis with a comprehen-

sive isotopomer model in Bacillus subtilis, Biotechnology and Bioengineering 2001, 76:

144–156.

29. Forbes N. S., Clark D. S., and Blanch H. W., Using isotopomer path tracing to quantify

metabolic fluxes in pathway models containing reversible reactions, Biotechnology and

Bioengineering 2001, 74: 196–211.

30. Schmidt K., Nielsen J., and Villadsen J., Quantitative analysis of metabolic fluxes in

Escherichia coli using two-dimensional NMR spectroscopy and complete isotopomer

models, Journal of Biotechnology 1999, 71: 175–190.

31. Zhao J. and Shimizu K., Metabolic flux analysis of Escherichia coli K12 grown on 13C-

labeled acetate and glucose using GC-MS and powerful flux calculation method, Journal

of Biotechnology 2003, 101: 101–117.

32. Schaub J., Mauch K., and Reuss M., Metabolic flux analysis in Escherichia coli by inte-

grating isotopic dynamic and isotopic stationary 13C labeling data, Biotechnology and

Bioengineering 2008, 99: 1170–1185.

33. Young J. D., Walther J. L., Antoniewicz M. R., Yoo H., and Stephanopoulos G., An ele-

mentary metabolite unit (EMU) based method of isotopically nonstationary flux analysis,

Biotechnology and Bioengineering 2008, 99: 686–699.

34. Yuan J., Fowler W. U., Kimball E., Lu W., and Rabinowitz J. D., Kinetic flux profiling of

nitrogen assimilation in Escherichia coli, Nature Chemical Biology 2006, 2: 529–530.

35. Wahl S. A., Dauner M., and Wiechert W., New tools for mass isotopomer data evaluation

in (13)C flux analysis: Mass isotope correction, data consistency checking, and precursor

relationships, Biotechnology and Bioengineering 2004, 85: 259–268.

36. http://vimss.lbl.gov/DvHFlux.

37. Steinbeck C., Hoppe C., Kuhn S., Floris M., Guha R., and Willighagen E. L., Recent

developments of the chemistry development kit (CDK)—an open-source java library for

chemo- and bioinformatics, Current Pharmaceutical Design 2006, 12: 2111–2120.

38. Yang J., Monine M. I., Faeder J. R., and Hlavacek, W. S., Kinetic Monte Carlo method for

rule-based modeling of biochemical networks, Physical Review E 2008, 78: 031910.