Research CommentariesBiochemistry

The Era of Pathway Quantification

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Science  08 May 1998:
Vol. 280, Issue 5365, pp. 852-853
DOI: 10.1126/science.280.5365.852

On page 895 of this issue, Ferrell and Machleder (1) highlight a new era in our understanding of cellular metabolism. Knowledge of metabolic processes in cells can be roughly divided into three eras: the Era of Pathway Identification (1890–1950), the Era of Pathway Regulation (1950–1980), and the Era of Pathway Quantification (1980-?). In the first era, the individual steps in the biochemical pathways were identified. In now classical studies, the substrates, products, and enzymes of pathways such as glycolysis, [HN2], [HN3], [HN4], [HN5], [HN6] fatty acid metabolism, [HN7], [HN8] and nucleic acid metabolism were identified by Emden, Meyerhoff, Warburg, Kornberg, Cori, [HN9] Brown, Goldstein, [HN10] and many others (2). In the second era, the control of pathways through feedback, feed-forward, cooperativity, allostery, phosphorylation, and covalent modification was delineated by Pardee, [HN11] Krebs, Fischer, [HN12] Stadtman, Jacob, Monod, this author, and many others (3)[HN13]. In the third era, now in its childhood, the quantification of pathways is being examined to calculate the rates at which metabolites and substrates are produced and degraded in cells and in organs.

Ferrell and Machleder (1) examine the turning on and off of the cell cycle in oocytes, showing that this control process is quantitatively “ultrasensitive” (4) and that the enzymes responsible are the mitogen-activated protein kinase (MAP kinase) cascade. In their report, they examine this process in intact oocytes (1); in a previous paper, Huang and Ferrell analyzed a cell-free system of the same MAP kinase cascade (5).[HN14], [HN15] Because individual enzymes of the cascade do not show cooperativity, it seems clear that some form of zero-order ultrasensitivity or multistep ultrasensitivity (4) is at work in this pathway, likely involving the kinetics of phosphorylation and dephosphorylation in the enzymes of the kinase cascade.

Enzyme responses to changes in ligand concentration.

Relative differences in ligand concentration(s) that give 10% saturation (S0.1) versus 90% saturation (S0.9) of the response to a stimulus.

Ultrasensitivity has been defined (4) as the response of a system that is more sensitive to changes in the concentration of the ligand than is the normal hyperbolic response given by the Michaelis-Menten equation.[HN16], [HN17] A Michaelis-Menten or hyperbolic response requires an 81-fold change in ligand S (the ligand can be a substrate or an effector of an inhibitor) to generate a ninefold change in response [for example, V0.9/V0.1 = 9 when S0.9/S0.1 = 81, where V is velocity and S is substrate concentration (see figure above)]. The ratio, 81, will be true of any Michaelis-Menten curve (which is a hyperbola) regardless of the midpoint of the curve. An ultrasensitive response is defined as that in which the change from 10% to 90% can be achieved with less than an 81-fold change in ligand concentration, and a subsensitive response is one in which it can be achieved only with a greater than 81-fold change in ligand concentration. One can also use the Hill coefficient (nH), [HN18] as Ferrell and Machleder have done, to indicate Michaelis-Menten or hyperbolic sensitivity (nH = 1.0), ultrasensitivity (nH > 1), and subsensitivity (nH < 1).

One known mechanism of ultrasensitivity is the cooperativity observed in hemoglobin (6); others are zero-order ultrasensitivity, as observed in kinase reactions running near saturation (7), and multistep ultrasensitivity, in which there are multiple regulators of the same enzyme (8). Ferrell and Machleder show that the change in Hill coefficient in the oocyte cell cycle response is very high (nH = 5.0, compared to 2.8 for hemoglobin) to illustrate the powerful ultrasensitivity of this system. They also illustrate an important principle in this quantitation: Individual oocytes show an even greater ultrasensitivity than the ensemble as a whole, and they declare that this is caused by the individual systems having different midpoints to their saturation curves—that is, the average of highly sensitive systems with different S0.5 values will give a much less sensitive overall response to a stimulus than would the individual systems themselves. They also postulate a feed-forward phenomenon to explain the added ultrasensitivity in the intact oocytes beyond that in the cell-free system.

Explanation of threshold effects.

A typical drug response curve produced with decreasing concentrations of a drug until the analytical method is no longer accurate (dashed line). The extrapolation (seen frequently) implies a threshold. A truly accurate assay would give a sigmoid curve as shown for ultrasensitivity in the figure above.

Ferrell and Machleder use some terms that will become increasingly important in the new Era of Quantification. Terms such as “switchlike” or “all-or-none” give the flavor of switch phenomena in mechanical systems—a good analogy and one that implies a very high ultrasensitivity. Switches in nonbiological systems refer to such phenomena as light switches that go from darkness to light in an instant or a melting point that goes from one state to another with a small change in temperature. In both of these cases, either in the mechanical device or the melting solution, millions of molecules are involved, and therefore the sigmoid character of the response is obscured. As shown in the figure directly above, with smaller numbers of molecules (for example, four subunits in hemoglobin), the change is gradual but is markedly more sensitive than a hyperbolic curve to changes in the environment. Thus, a lack of knowledge of the mathematics would lead one to suggest that a drug acts only when it exceeds a threshold. In fact, low concentrations of a drug will have an effect, but it will be undetectable against the large background of a biological system (see figure below).

Some steps have already been made in the new Era of Quantification. Calcium spiking has been quantitated and allows the cell to set a sharp threshold to stimuli (9). The pathway of chemotaxis [HN19] in Escherichia coli [HN20] has been calculated in relation to the actual concentrations of the components of that response (10). The switch between the Krebs cycle [HN21], [HN22] and the glyoxalate shunt has been correlated quantitatively with the rates through each of the individual steps in the Krebs cycle and glyoxalate bypass (8). The use of energy in maintaining a phosphorylation system has also been quantitated (11). These are just a few illustrative examples of the quantitative conclusions that are possible when quantitation and the mathematics of quantitation become part of the arsenal of investigators of metabolic interactions. Investigators will be increasingly concerned with responses initiated by small fluctuations in the environment or cellular media, small changes in hormone supplies, and increases or decreases in enzyme levels, for example, as cells differentiate and dedifferentiate. We have gone from the era of “who” to that of “how” and are now entering the era of “how much”. Ferrell and Machleder's report is a prime example of excellent data and thinking applied to a very important problem.

HyperNotes Related Resources on the World Wide Web

General Hypernotes

Fundamentals of Enzyme Kinetics, chapter 10, by Athel Cornish-Bowden (Portland Press, London, 1995) presents a discussion of enzymes and their role in metabolic pathways.

EcoCyc is an encyclopedia of Escherichia coli genes and metabolism. The EcoCyc knowledge base describes each pathway and biochemical reaction of E. coli metabolism, and the enzyme that carries out each reaction, including its cofactors, activators, inhibitors, and the subunit structure of the enzyme. Registration is required for use of this site, and free accounts are available to users in academic and nonprofit organizations.

The Metabolic Database is the metabolic component of SoyBase, a soybean genetic database, containing reaction and pathway descriptions and diagrams for a number of basic metabolic pathways.

Pedro's BioMolecular Research Tools is a collection of WWW links to information and services useful to molecular biologists. It provides links to molecular biology search and analysis tools; bibliographic, text, and Web search services; guides and tutorials; and biological and biochemical journals and newsletters.

The World Wide Web Virtual Library: Biosciences points to virtual library pages for Biological Molecules, and Biochemistry and Molecular Biology. Each of these pages presents a long list of Web resources. The World Wide Web Virtual Library: Biomolecules covers molecular sequence and structure databases, metabolic pathway databases, and other lists of Web resources. The World Wide Web Virtual Library: Biochemistry and Molecular Biology is a list of resources listed by provider.

Numbered Hypernotes

1. Daniel E. Koshland's Web page describes his research interests and current projects and lists selected publications.

2. Metabolic Pathways of Biochemistry by Karl Miller illustrates glycolysis and gluconeogenesis, beta-oxidation of fatty acids, and other major metabolic pathways, primarily those important to human biochemistry.

3. Glycolysis is outlined by the Neuromuscular Disease Center at Washington University School of Medicine. An animation shows changes in the glucose molecule in glycolysis.

4. Design-it-yourself Glycolysis is an item in the Biochemical Designs Collection and was produced by Jon Maber, a member of the department of Biochemistry & Molecular Biology in the University of Leeds. Glycolysis is described in a fact sheet, an outline of the reaction, and an animation.

5. Glycolysis at a Glance focuses on the enzymes involved in each step of glycolysis.

6. Glucose Metabolism is described in Lecture 9 of Cell Biology at Illinois State University.

7. Metabolic pathways, including fatty acid metabolism and nucleotide metabolism, are presented by BioTech. The BioTech Web site, located at Indiana University, is a hybrid biology/chemistry educational resource and research tool on the Web. It is designed to serve everyone from high school students to professional researchers.

8. Fatty acid metabolism is one of several metabolic maps available from the Kyoto Encyclopedia of Genes and Genomes (KEGG). The KEGG project is an effort to computerize current knowledge of molecular and cellular biology in terms of the information pathways that consist of interacting molecules or genes and to provide links from the gene catalogs produced by genome sequencing projects. KEGG is being undertaken in the Institute for Chemical Research, Kyoto University as part of the Japanese Human Genome Program.

9. Carl and Gerty Cori is a brief biography of the two researchers who shared a Nobel prize in 1947 for their discovery of the mechanism for blood glucose regulation. An obituary of Carl Cori that appeared in the Boston Globe in 1984 also describes their work.

10. Two Texas Doctors Celebrate Nobel Medicine Prize at MIT is an article from the Boston Globe that describes the work of Michael S. Brown and Joseph L. Goldstein on cholesterol metabolism.

11. Arthur Pardee outlines his research and lists a few of his publications on his Web page at Harvard University.

12. Edmond H. Fischer and Edwin G. Krebs describe their work at the University of Washington. Photographs of the two Nobel laureates are also available.

13. The Nobel Foundation provides biographies of Nobel laureates, including researchers in metabolic pathways cited in this commentary: Otto Fritz Meyerhof, Otto Heinrich Warburg, Carl Ferdinand Cori and Gerty Theresa Cori, Arthur Kornberg, Francois Jacob and Jacques Monod, Michael S Brown and Joseph L Goldstein, Edmond H. Fischer and Edwin G. Krebs.

14. Structure and Overview of Various MAP Kinases provides an introduction to this family of proteins.

15. Mammalian MAPK Signaling Pathways illustrates the main components of the signal transduction pathways that are structurally related to the mitogen-activated protein kinase pathway and includes a brief description of MAP kinase.

16. Michaelis-Menten Kinetics explains the Michaelis-Menten constant. This page is included in Enzyme Kinetics, a chapter of the MIT Biology Hypertextbook.

17. The Michaelis-Menten equation is outlined in An Enzyme Kinetics Tutorial by Robert Metrione Anthony J. Frisby, and Matthew J. Watson.

18. The Hill coefficient is defined in the Glaxo Wellcome Pharmacology Guide.

19. Chemotaxis in E. coli is described by Carl Jason Morton-Firth.

20. The E. coli Index provides links to Internet resources for the study of E. coli. This site is a part of the World Wide Web Virtual Library.

21. Step by Step Krebs Cycle illustrates this metabolic pathway.

22. Mitochondria Overview—Krebs Cycle outlines the steps of the Krebs cycle.

23. Department of Molecular and Cell Biology, University of California, Berkeley

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