# Introduction to Metabolic Control Analysis (MCA)

• Maliackal Poulo Joy
• Timothy C. Elston
• Andrew N. Lane
• Jeffrey M. Macdonald
• Marta Cascante
Protocol
Part of the Methods in Pharmacology and Toxicology book series (MIPT)

## Abstract

Metabolic Control Analysis (MCA) provides a conceptual framework for understanding the control of fluxes though metabolic pathways at the molecular level. It further provides a theoretical underpinning for an experimental approach to determining metabolic control. In this chapter, the basic principles of MCA are introduced, and the kinds of applications that are accessible to this approach. The relationship to flux analysis and measurement of metabolic fluxes is outlined.

## Key words

Metabolic control analysis Flux control Elasticity

## Glossary

Disequilibrium ratio

Deviation of a reaction from equilibrium as expressed by the ratio of the actual reactants to the values they have at equilibrium, under the prevailing conditions Γ = (p/s)/Keq. This is related to the available free energy difference for driving a reaction: ΔG = ΔG 0−RTln Γ

Elasticity

Is a property of an enzyme and determines how the flux through a particular step depends on the substrate concentration: ∂lnv i/∂lns i

Flux

Net rate of a reaction or of a pathway. Flux is the difference between the forward rate and the reverse rate, J = v fv r

Flux Control

The extent to which flux is determined and is a system property. If J is the net flux, the control is determined by the sensitivity of the net flux to changes in activity at individual steps

Flux Control Coefficient (FCC)

Fractional change in flux due to a fractional change in enzyme activity a: FCC = ∂lnJ/∂lna

Hill equation

Proteins that interact with multiple substrates or ligands, such as hemoglobin, may show cooperativity between binging sites. The Hill equation represents an all or none cooperative binding equation of the form F = s n /(K + s n ) where n is the Hill coefficient. A value n > 1 implies positive cooperativity, and n < 1 is negative cooperativity. N is always less than the number of binding sites. Cf. Monod–Wyman–Changeux and Koshland–Nemethy–Filmer models (15)

kcat, Km

In the Michaelis–Menten mechanism, k cat is the turnover number for an enzyme and represents the apparent first order rate constant for the breakdown of ES complexes. K m is operationally the concentration of substrate at which the reaction velocity is half its maximum possible, as determined by V max = k cat.[enzyme]. k cat/K m is the apparent second order rate constant or substrate-enzyme complex formation and determines the specificity of the enzyme for its substrate (15)

Rate

Speed of a reaction. For a Michaelis–Menten reaction, the initial rate is v i  = V max.s/(K m + s)

Regulation

In MCA, control and regulation are distinct properties. Control is defined through the coefficients such as FCC. In contrast, regulation refers to the maintenance of homeostasis (i.e., resistance change), and a regulated enzyme is one that performs this task. Such an enzyme does not have to have a high FCC

Response

How flux changes with respect to a local parameter p such as an effector Ri = ∂lnJ/∂lnpi

## References

1. 1.
Savageau MA, Voit EO, Irvine DH. Biochemical systems-theory and metabolic control-theory.1. fundamental similarities and differences. Math Biosci. 1987;86(2):127–45.
2. 2.
Savageau MA, Voit EO, Irvine DH. Biochemical systems-theory and metabolic control-theory. 2. the role of summation and connectivity relationships. Math Biosci. 1987;86(2):147–69.
3. 3.
Savageau MA. Design of molecular control mechanisms and demand for gene-expression. Proc Natl Acad Sci USA. 1977;74(12):5647–51.
4. 4.
Voit EO. Computational analysis of biochemical systems: a practical guide for biochemists & molecular biologists. Cambridge, UK: Cambridge University Press; 2000.Google Scholar
5. 5.
Fell DA. Metabolic control analysis—a survey of its theoretical and experimental development. Biochem J. 1992;286:313–30.
6. 6.
Fell D. Understanding the control of metabolism. In: Snell K, editor. Frontiers in metabolism. London: Portland Press; 1997.Google Scholar
7. 7.
Cascante M, Boros LG, Comin-Anduix B, de Atauri P, Centelles JJ, Lee PWN. Metabolic control analysis in drug discovery and disease. Nat Biotechnol. 2002;20(3):243–9.
8. 8.
Cornishbowden A. Metabolic control-theory and biochemical systems-theory—different objectives, different assumptions, different results. J Theor Biol. 1989;136(4):365–77.
9. 9.
Cascante M, Franco R, Canela EI. Use of implicit methods from general sensitivity theory to develop a systematic-approach to metabolic control.1. unbranched pathways. Math Biosci. 1989;94(2):271–88.
10. 10.
Cascante M, Franco R, Canela EI. Use of implicit methods from general sensitivity theory to develop a systematic-approach to metabolic control.2. complex-systems. Math Biosci. 1989;94(2):289–309.
11. 11.
Heinrich R, Schuster S. The regulation of cellular systems. New York: Chapman & Hall; 1996.
12. 12.
13. 13.
Hall D, Minton AP. Macromolecular crowding: qualitative and semiquantitative successes, quantitative challenges. Biochim Biophys Acta-Proteins and Proteomics. 2003;1649(2):127–39.
14. 14.
Roberts JKM, Lane AN, Clark RA, Nieman RH. Relationships between the rate of synthesis of ATP and the concentrations of reactants and products of ATP hydrolysis in maize root-tips, determined by P-31 nuclear magnetic-resonance. Arch Biochem Biophys. 1985;240(2):712–22.
15. 15.
Fersht A. Structure and mechansim in protein science. Structure and mechansim in protein science. New York: W.H. Freeman & Co; 1999.Google Scholar
16. 16.
Albe KR, Butler MH, Wright BE. Cellular concentrations of enzymes and their substrates. J Theor Biol. 1990;143(2):163–95.
17. 17.
Srivastava DK, Bernhard SA. Enzyme enzyme interactions and the regulation of metabolic reaction pathways. Curr Top Cell Regul. 1986;28:1–68.
18. 18.
Werle M, Jahn L, Kreuzer J, Hofele J, Elsasser A, Ackermann C, Katus HA, Vogt AM. Metabolic control analysis of the Warburg-effect in proliferating vascular smooth muscle cells. J Biomed Sci. 2005;12(5):827–34.
19. 19.
Marin-Hernandez A, Rodriguez-Enriquez S, Vital-Gonzalez PA, Flores-Rodriguez FL, Macias-Silva M, Sosa-Garrocho M, Moreno-Sanchez R. Determining and understanding the control of glycolysis in fast-growth tumor cells—flux control by an over-expressed but strongly product-inhibited hexokinase. FEBS J. 2006;273(9):1975–88.
20. 20.
Suarez RK, Staples JF, Lighton JRB, West TG. Relationships between enzymatic flux capacities and metabolic flux rates: Nonequilibrium reactions in muscle glycolysis. Proc Natl Acad Sci USA. 1997;94(13):7065–9.
21. 21.
Kacser H, Burns J. The control of flux. Symp Soc Exp Biol. 1973;27:65–104.
22. 22.
Kacser H, Burns J, Fell D. The control of flux. Biochem Soc Trans. 1995;1923:1341–66.Google Scholar
23. 23.
Heinrich R, Rapoport TA. Linear steady-state treatment of enzymatic chains—general properties, control and effector strength. Eur J Biochem. 1974;42(1):89–95.
24. 24.
Heinrich R, Rapoport TA. Linear steady-state treatment of enzymatic chains—critique of crossover theorem and a general procedure to identify interaction sites with an effector. Eur J Biochem. 1974;42(1):97–105.
25. 25.
Rapoport TA, Heinrich R, Jacobasc G, Rapoport S. Linear steady-state treatment of enzymatic chains—mathematical-model of glycolysis of human erythrocytes. Eur J Biochem. 1974;42(1):107–20.
26. 26.
Kholodenko BN, Brown GC. Paradoxical control properties of enzymes within pathways: Can activation cause an enzyme to have increased control? Biochem J. 1996;314:753–60.
27. 27.
de Atauri P, Acerenza L, Kholodenko BN, de la Iglesia N, Guinovart JJ, Agius L, Cascante M. Occurrence of paradoxical or sustained control by an enzyme when overexpressed: necessary conditions and experimental evidence with regard to hepatic glucokinase. Biochem J. 2001;355:787–93.
28. 28.
Kacser H, Sauro HM, Acerenza L. Enzyme-enzyme interazctions and control analysis.1. the case of nonadditivity—monomer-oligomer associations. Eur J Biochem. 1990;187(3):481–91.
29. 29.
Kohdolenko BN, Lyubarev AE, Kurganov BI. Control of the metabolic flux in a system with high enzyme concentrations and moiety-conserved cycles. Eur J Biochem. 1992;210:147–53.
30. 30.
Kholodenko BN, Cascante M, Westerhoff HV. Control-theory of metabolic channeling. Mol Cell Biochem. 1995;143(2):151–68.
31. 31.
Kholodenko BN, Westerhoff HV, Puigjaner J, Cascante M. Control in channeled pathways—a matrix-method calculating the enzyme control coefficients. Biophys Chem. 1995;53(3):247–58.
32. 32.
Cornish-Bowden A, Cárdenas ML. Technological and medical implications of metabolic control analysis. Dordrecht: Kluwer; 2000.
33. 33.
Comin-Anduix B, Boren J, Martinez S, Moro C, Centelles JJ, Trebukhina R, Petushok N, Lee WNP, Boros LG, Cascante M. The effect of thiamine supplementation on tumour proliferation—a metabolic control analysis study. Eur J Biochem. 2001;268(15):4177–82.
34. 34.
Boren J, Montoya AR, de Atauri P, Comin-Anduix B, Cortes A, Centelles JJ, Frederiks WM, Van Noorden CJF, Cascante M. Metabolic control analysis aimed at the ribose synthesis pathways of tumor cells: a new strategy for antitumor drug development. Mol Biol Rep. 2002;29(1–2):7–12.
35. 35.
Bowden AC. Metabolic control analysis in biotechnology and medicine. Nat Biotechnol. 1999;17(7):641–3.
36. 36.
Ramos-Montoya A, Lee WNP, Bassilian S, Lim S, Trebukhina RV, Kazhyna MV, Ciudad CJ, Noe V, Centelles JJ, Cascante M. Pentose phosphate cycle oxidative and nonoxidative balance: a new vulnerable target for overcoming drug resistance in cancer. Int J Cancer. 2006;119(12):2733–41.
37. 37.
Weinberg RA. The Biology of Cancer. Garland Science: New York; 2007.Google Scholar
38. 38.
Summerton JE. Morpholino, siRNA, and S-DNA compared: impact of structure and mechanism of action on off-target effects and sequence specificity. Curr Top Med Chem. 2007;7(7):651–60.
39. 39.
Robu ME, Larson JD, Nasevicius A, Beiraghi S, Brenner C, Farber SA, Ekker SC. p53 activation by knockdown technologies. PLoS Genet. 2007;3(5):787–801.
40. 40.
Du LT, Pollard JM, Gatti RA. Correction of prototypic ATM splicing mutations and aberrant ATM function with antisense morpholino oligonucleotides. Proc Natl Acad Sci USA. 2007;104(14):6007–12.
41. 41.
Liu YM, Borchert GL, Donald SP, Surazynski A, Hu CA, Weydert CJ, Oberley LW, Phang JM. MnSOD inhibits proline oxidase-induced apoptosis in colorectal cancer cells. Carcinogenesis. 2005;26(8):1335–42.
42. 42.
Monroe DG, Getz BJ, Johnsen SA, Riggs BL, Khosla S, Spelsberg TC. Estrogen receptor isoform-specific regulation of endogenous gene expression in human osteoblastic cell lines expressing either ER alpha or ER beta. J Cell Biochem. 2003;90(2):315–26.
43. 43.
Acerenza L. Design of large metabolic responses. Constraints and sensitivity analysis. J Theor Biol. 2000;207(2):265–82.
44. 44.
Acerenza L, Ortega F. Metabolic control analysis for large changes: extension to variable elasticity coefficients. Iee Proceedings Systems Biology Syst Biol (Stevenage). 2006;153(5):323–6.
45. 45.
Nicholls DG, Ferguson SJ, The chemiosmotic proton circuit. In: Bioenergetics3. San Diego: Academic Press; 2001Google Scholar
46. 46.
Hatzimanikatis V, Bailey JE. Effects of spatiotemporal variations on metabolic control: approximate analysis using (log)linear kinetic models. Biotechnol Bioeng. 1997;54(2):91–104.
47. 47.
Wu L, Wang WM, van Winden WA, van Gulik WM, Heijnen JJ. A new framework for the estimation of control parameters in metabolic pathways using lin-log kinetics. Eur J Biochem. 2004;271(16):3348–59.
48. 48.
Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U. COPASI—a complex pathway simulator. Bioinformatics. 2006;22:3067–74.

## Authors and Affiliations

• Maliackal Poulo Joy
• 1
• Timothy C. Elston
• 1
• Andrew N. Lane
• 2
Email author
• Jeffrey M. Macdonald
• 3
• Marta Cascante
• 4
1. 1.Department of PharmacologyUniversity of North Carolina School of MedicineChapel HillUSA
2. 2.Departments of Medicine and Chemistry, Center for Regulatory and Environmental Analytical Metabolomics (CREAM), and James Graham Brown Cancer CenterUniversity of LouisvilleLouisvilleUSA
3. 3.Department of Biomedical EngineeringUniversity of North Carolina School of MedicineChapel HillUSA
4. 4.Department of Biochemistry and Molecular Biology, Associated Unit to CSICInstitute of Biomedicine of University of Barcelona (IBUB) and IDIBAPS (Institut d’Investigacions Biomèdiques August Pi i Sunyer)BarcelonaSpain