50 Years of metabolic control analysis

Open AccessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Sauro Herbert M. 202450 Years of metabolic control analysisInterface Focus.142023008020230080http://doi.org/10.1098/rsfs.2023.0080SectionOpen AccessIntroduction50 Years of metabolic control analysis Herbert M. Sauro Herbert M. Sauro http://orcid.org/0000-0002-3659-6817 Department of Bioengineering, University of Washington, PO Box 355061, Seattle, WA 98195-5061, USA [email protected] Contribution: Conceptualization, Investigation, Methodology, Resources, Writing – original draft, Writing – review & editing Google Scholar Find this author on PubMed Search for more papers by this author Herbert M. Sauro Herbert M. Sauro http://orcid.org/0000-0002-3659-6817 Department of Bioengineering, University of Washington, PO Box 355061, Seattle, WA 98195-5061, USA [email protected] Contribution: Conceptualization, Investigation, Methodology, Resources, Writing – original draft, Writing – review & editing Google Scholar Find this author on PubMed Published:09 February 2024https://doi.org/10.1098/rsfs.2023.0080 It has been 50 years since the publication of the seminal works by Savageau [1], Kacser & Burns [2,3] and Heinrich & Rapoport [4], on the control of biochemical networks. What is remarkable about these three publications (especially the two papers by Kacser et al. and Rapoport et al.) is that they independently developed almost the same approach and came to the same conclusions. This approach is today called metabolic control analysis (MCA), and is a body of work that uses mathematics to reason about the properties of biochemical pathways in a deductive manner. Although originally focused on metabolic pathways, it was realized early on that it could be equally applied to genetic and signalling networks [5,6]. In fact anything that one could associate a stoichiometry matrix with. In recent years, others have reinvented MCA [7–9], using different notation, highlighting the fact that there has been a good deal of conceptual convergence in this area. Although some aspects of MCA had been published previous to the original primary publications [10,11], the papers by Kacser, Burns, Heinrich and Rapoport were focused on how metabolites and fluxes in metabolic pathways are affected by changes in enzyme activities and other external factors. The work by Savageau [1], in contrast, emphasized the effect on species concentrations with no mention of fluxes but also uniquely discussed the dynamic stability of dynamical models. The article by Kacser & Burns [2], titled 'The control of flux', was particularly influential because it presented its ideas in a clear, readable and mathematically accessible way. It spoke directly to the community of biochemists and molecular biologists, who only had a passing familiarity with differential calculus and, at that time, were largely non-quantitative. Even though the Kacser & Burns article was clearly written, it was ignored for many years (as was the work by Heinrich & Rapoport [4] and Savageau [1]). Only in the early 1980s did the work begin to be noticed particularly by individuals such as Groen, Wanders, Westerhoff and coworkers at the Amsterdam school [12]. At this point, the paper's impact rose rapidly and remained highly cited for the next 15 years and continues to be cited today at a rate of about 20 citations per year. To date (December 2023), according to Google Scholar, the article has been cited 2622 times. Similar numbers can be found for the work by Heinrich & Rapoport [4], Savageau [1] and their coworkers. There have of course been criticisms, always unfounded, due to misunderstanding the theory; either because it could not handle large changes, had no predictive value or simply could not be true [13]. Many of the conclusions made by MCA went against orthodoxy and even today there is resistance. However resistance is often for the wrong reason. MCA certainly does make claims but these are based on a deductive approach using fundamental and largely accepted statements about the nature of enzymes and chemical kinetics. Rather than dismiss the claims of MCA, the scientific approach would be to refute the claims by experimentation. As far as I am aware, not a single result in MCA has been refuted by experimental observation, quite the contrary. This is not to say that MCA is therefore true, that would be a ridiculous statement to make. However, until a better explanation and predictor of the behaviour of cellular pathways emerges, MCA is currently the best we have. One idea that has caused the most consternation, even today, is the ingrained idea of the rate-limiting step. Interestingly, prior to the 1960s, there was an active literature that spoke against the idea, of what was then called, the 'master reaction'. The paper by Burton [14] is a good example but there are others. Burton's paper alone, published in 1936, should convince anyone that the idea of a rate-limiting step makes no logical sense. Somehow in the 1960s, and perhaps earlier, experimentalists took the opposite view and saw metabolism in very simple terms where one only had to identify the single step that controlled the pathway in order to understand it. Interestingly, the revival in the argument against the idea of the rate limiting step arose entirely from experimental observations of the arginine pathway in Neurospora at Edinburgh in the Waddington school; but by geneticists, not biochemists. Fig. 5 in one of the early publications by Kacser & Burns [11], shows how various doses of enzymes in the arginine pathway had little or no effect on growth. As an anecdote, Kacser once told me, while I worked with him in Edinburgh, that what inspired his interest was the observation that Neurospora could lose 95% of a given enzyme and appear virtually unchanged phenotypically. This work was presented in a PhD thesis by Tateson in 1972 [15] under the guidance of Waddington, Falconer and Kacser and is available online at the Edinburgh thesis archive. My own experience of MCA was not based on experimental science but on my first attempts to run computer simulations. I thought at the time, that if I could run a computer simulation of say glycolysis, I could understand how it worked. Unfortunately the computer outputted reams of numbers and graphs, which I had no idea how to interpret. Searching the university library, I stumbled upon the work by Kacser and Burns and realized this was the language I needed to interpret what was happening for my simulation. For me personally, this is what was important. MCA helps one understand why a given biochemical pathway has certain phenotype properties based on the properties of the component parts. In a small sense, it bridged genotype to phenotype. Today there are thousands of papers published on MCA and a growing number of textbooks. There are even pages on Wikipedia that describe MCA. In relation to other fields, work by Ingalls [16] in 2004 showed that MCA and engineering control theory [17] were one and the same thing. Unlike electrical and mechanical systems, which are the mainstay of engineering control theory, biochemical networks have unique properties such as stoichiometry and mass conservation, which warrant special treatment not found in engineering control theory. This difference is partly manifest in the various summation and connectivity theorems that emerge from the analysis, which give additional insight into the properties of biochemical pathways. There are also definite connections with both the pioneering works of Clarke [18] and Feinberg [19] in the area of chemical network theory but which have yet to be made clear. To commemorate the 50 years since the publication of the work by Kacser, Heinrich and Savageau, we have received two papers that continue the development of MCA and a historical note from Tom Rapoport [20]. The first paper is by Liebermeister & Noor [21], who describe the use of MCA to discover optimally principles in the distribution of protein across metabolic networks. A second paper by Kochen et al. [22] describes how MCA, can provide interesting and useful insights into the dynamic properties of protein signalling pathways. Finally, Tom Rapoport [20] gives a historical perspective on how field developed in Berlin. It is worth mentioning that a special theme is also being published in Biosystems and includes additional papers of interest. Data accessibility This article has no additional data. Declaration of AI use I have not used AI-assisted technologies in creating this article. Conflict of interest declaration I declare I have no competing interests. Funding This work was supported by Department of Energy (DOE) award DE-EE0008927. The content expressed here is solely the responsibility of the authors and does not necessarily represent the official views of the DOE or the University of Washington. Acknowledgements I wish to thank the many colleagues and friends who I have had the fortune to work with over the years. Finally, I wish to acknowledge funding for this work by the Department of Energy awards BER DE-SC0023091 and DE-EE0008927 through my good colleague James Carothers at UW. FootnotesOne contribution of 4 to a theme issue '50 Years of metabolic control analysis'. © 2024 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. References1.Savageau MA. 1972 The behavior of intact biochemical control systems. In Current topics in cellular regulation (eds Bernard L. Horecker, Earl R. Stadtman), vol. 6, pp. 63–130. Amsterdam, The Netherlands: Elsevier. Google Scholar2.Kacser H, Burns JA. 1973 The control of flux. Symp. Soc. Exp. Biol. 27, 65-104. PubMed, Google Scholar3.Kacser H, Burns JA, Kacser H, Fell D. 1995 The control of flux. Biochem. Soc. Trans. 23, 341-366. (doi:10.1042/bst0230341) Crossref, PubMed, ISI, Google Scholar4.Heinrich R, Rapoport TA. 1974 A linear steady-state treatment of enzymatic chains: general properties, control and effector strength. Eur. J. Biochem. 42, 89-95. (doi:10.1111/j.1432-1033.1974.tb03318.x) Crossref, PubMed, Google Scholar5.Kahn D, Westerhoff HV. 1991 Control theory of regulatory cascades. J. Theor. Biol. 153, 255-285. (doi:10.1016/S0022-5193(05)80426-6) Crossref, PubMed, ISI, Google Scholar6.Small JR, Fell DA. 1990 Covalent modification and metabolic control analysis: modification to the theorems and their application to metabolic systems containing covalently modifiable enzymes. Eur. J. Biochem. 191, 405-411. (doi:10.1111/j.1432-1033.1990.tb19136.x) Crossref, PubMed, Google Scholar7.Mochizuki A. 2022 A structural approach to understanding enzymatic regulation of chemical reaction networks. Biochem. J. 479, 1265-1283. (doi:10.1042/BCJ20210545) Crossref, PubMed, ISI, Google Scholar8.Shinar G, Alon U, Feinberg M. 2009 Sensitivity and robustness in chemical reaction networks. SIAM J. Appl. Math. 69, 977-998. (doi:10.1137/080719820) Crossref, ISI, Google Scholar9.Vassena N. 2020 Sensitivity of metabolic networks: perturbing metabolite concentrations. arXiv 2012.10687 (https://arxiv.org/abs/2012.10687) Google Scholar10.Higgins J. 1963 Analysis of sequential reactions. Ann. NY Acad. Sci. 108, 305-321. (doi:10.1111/j.1749-6632.1963.tb13382.x) Crossref, PubMed, ISI, Google Scholar11.Kacser H, Burns J. 1968 Causality, complexity and computers. In Quantitative biology of metabolism: models of metabolism, metabolic parameters, damage to metabolism, metabolic control, pp. 11–23. Berlin, Germany: Springer. Google Scholar12.Groen AK, Wanders R, Westerhoff H, Van der Meer R, Tager J. 1982 Quantification of the contribution of various steps to the control of mitochondrial respiration. J. Biol. Chem. 257, 2754-2757. (doi:10.1016/S0021-9258(19)81026-8) Crossref, PubMed, ISI, Google Scholar13.Hue L. 2000 From control to regulation: a new prospect for metabolic control analysis. In Technological and medical implications of metabolic control analysis, pp. 329–338. Berlin, Germany: Springer. Google Scholar14.Burton AC. 1936 The basis of the principle of the master reaction in biology. J. Cell. Comp. Physiol. 9, 1-14. (doi:10.1002/jcp.1030090102) Crossref, Google Scholar15.Tateson R. 1972 Control of biosynthetic pathways in neurospora. PhD thesis, The University of Edinburgh, Edinburgh, UK. See https://era.ed.ac.uk/handle/1842/14527. Google Scholar16.Ingalls BP. 2004 A frequency domain approach to sensitivity analysis of biochemical networks. J. Phys. Chem. B 108, 1143-1152. (doi:10.1021/jp036567u) Crossref, ISI, Google Scholar17.Ogata K. 2010 Modern control engineering, 5th edn. London, UK: Pearson. Google Scholar18.Clarke BL. 1980 Stability of complex reaction networks. Adv. Chem. Phys. 43, 1-215. (doi:10.1002/9780470142622.ch1) Google Scholar19.Feinberg M. 2019 Foundations of chemical reaction network theory. vol. 202, Applied Mathematical Sciences. Cham, Switzerland: Springer. (doi:10.1007/978-3-030-03858-8_20) Google Scholar20.Rapoport T. 2024 A Berlin-sided retrospective of the origins of metabolic control theory. Interface Focus 14, 20230024. (doi:10.1098/rsfs.2023.0024) Link, Google Scholar21.Noor E, Liebermeister W. 2024 Optimal enzyme profiles in unbranched metabolic pathways. Interface Focus 14, 20230029. (doi:10.1098/rsfs.2023.0029) Link, Google Scholar22.Kochen MA, Hellerstein JL, Sauro HM. 2024 First-order ultrasensitivity in phosphorylation cycles. Interface Focus 14, 20230045. (doi:10.1098/rsfs.2023.0045) Link, Google Scholar Next Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetails This Issue15 February 2024Volume 14Issue 1Theme issue '50 Years of metabolic control analysis' organised by Herbert M. Sauro Article InformationDOI:https://doi.org/10.1098/rsfs.2023.0080Published by:Royal SocietyOnline ISSN:2042-8901History: Manuscript received22/12/2023Manuscript accepted22/12/2023Published online09/02/2024 License:© 2024 The Authors.Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Citations and impact Subjectssystems biology