Metabolic control analysis

Plot of steady state flux versus enzyme activity with flux control coefficients at various points.

In biochemistry, metabolic control analysis (MCA) is a mathematical framework for describing metabolic, signaling, and genetic pathways. MCA quantifies how variables, such as fluxes and species concentrations, depend on network parameters. In particular, it is able to describe how network-dependent properties, called control coefficients, depend on local properties called elasticities or elasticity coefficients.[1][2][3]

MCA was originally developed to describe the control in metabolic pathways but was subsequently extended to describe signaling and genetic networks. MCA has sometimes also been referred to as Metabolic Control Theory, but this terminology was rather strongly opposed by Henrik Kacser, one of the founders[citation needed].

More recent work[4] has shown that MCA can be mapped directly on to classical control theory and are as such equivalent.

Biochemical systems theory[5] (BST) is a similar formalism, though with rather different objectives. Both are evolutions of an earlier theoretical analysis by Joseph Higgins.[6]

Chemical reaction network theory is another theoretical framework that has overlap with both MCA and BST but is considerably more mathematically formal in its approach.[7] Its emphasis is primarily on dynamic stability criteria[8] and related theorems associated with mass-action networks. In more recent years the field has also developed [9] a sensitivity analysis which is similar if not identical to MCA and BST.

  1. ^ Fell D., (1997) Understanding the Control of Metabolism, Portland Press.
  2. ^ Heinrich R. and Schuster S. (1996) The Regulation of Cellular Systems, Chapman and Hall.
  3. ^ Salter, M.; Knowles, R. G.; Pogson, C. I. (1994). "Metabolic control". Essays in Biochemistry. 28: 1–12. PMID 7925313.
  4. ^ Ingalls, B. P. (2004) A Frequency Domain Approach to Sensitivity Analysis of Biochemical Systems, Journal of Physical Chemistry B, 108, 1143-1152.
  5. ^ Savageau M.A (1976) Biochemical systems analysis: a study of function and design in molecular biology, Reading, MA, Addison–Wesley.
  6. ^ Higgins, J. (1963). "Analysis of sequential reactions". Annals of the New York Academy of Sciences. 108 (1): 305–321. Bibcode:1963NYASA.108..305H. doi:10.1111/j.1749-6632.1963.tb13382.x. PMID 13954410. S2CID 30821044.
  7. ^ Feinberg, Martin (1987). "Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems". Chemical Engineering Science. 42 (10): 2229–2268. doi:10.1016/0009-2509(87)80099-4.
  8. ^ Clarke, Bruce L. (January 1980), Prigogine, I.; Rice, Stuart A. (eds.), "Stability of Complex Reaction Networks", Advances in Chemical Physics, vol. 43 (1 ed.), Wiley, pp. 1–215, doi:10.1002/9780470142622.ch1, ISBN 978-0-471-05741-3, retrieved 2023-12-06
  9. ^ Shinar, Guy; Alon, Uri; Feinberg, Martin (2009). "Sensitivity and Robustness in Chemical Reaction Networks". SIAM Journal on Applied Mathematics. 69 (4): 977–998. ISSN 0036-1399.