Box 153 Working In Biochemistry

Metabolic Control Analysis: Quantitative Aspects

The factors that influence the flow of intermediates (flux) through a pathway may be determined quantitatively by experiment and expressed in terms useful for predicting the change in flux when some factor involved in the pathway changes. Consider the simple reaction sequence in Figure 1, in which a substrate X (say, glucose) is converted in several steps to a product Z (perhaps pyruvate, formed glycolytically). A later enzyme in the pathway is a dehydrogenase (ydh) that acts on substrate Y. Because the action of a dehydrogenase is easily measured (see Fig. 13-15), we can use the flux (J) through this step (Jydh) to measure the flux through the whole path. We manipulate experimentally the level of an early enzyme in the pathway (xase, which acts on the substrate X) and measure the flux through the path (Jydh) for several levels of the enzyme xase.

Jxase Jydh

FIGURE 1 Flux through a hypothetical multienzyme pathway.

The relationship between the flux through the pathway from X to Z in the intact cell and the concentration of each enzyme in the path should be hyperbolic, with virtually no flux at infinitely low enzyme and near-maximum flux at very high enzyme activity. In a plot of Jydh against the concentration of xase, Exase, the change of flux with a small change of enzyme is 3Jydh/3Exase, which is simply the slope of the tangent to the curve at any concentration of enzyme, Exase, and which tends toward zero at saturating Exase. At low Exase, the slope is steep; the flux increases with each incremental increase in enzyme activity. At very high Exase, the slope is much smaller; the system is less responsive to added xase, because it is already present in excess over the other enzymes in the pathway.

To show quantitatively the dependence of flux through the pathway, 3Jydh, on 3Exase, we could use the ratio 3Jydh/^.Exase. However, its usefulness is limited because its value depends on the units used to express flux and enzyme activity. By expressing the fractional changes in flux and enzyme activity, 3Jydh/Jydh, and 3Exase/Exase, we obtain a unitless expression for the flux control coefficient, C Jydh:

This can be rearranged to

/O Jydh_ Jydh E xase

Cxase _ ^ * f oE xase Jydh which is mathematically identical to

CJydh= 0ln Jydh xase dln E xase

This equation suggests a simple graphical means for determining the flux control coefficient: C^diis the slope of the tangent to the plot of ln Jydh versus ln Exase, which can be obtained by replotting the experimental data in Figure 2a to obtain Figure 2b. Notice that CJydehis not a constant; it depends on the starting Exase from which the change in enzyme level takes place. For the cases shown in Figure 2, C^yse1 is about 1.0 at the lowest Exase, but only about 0.2 at high Exase. A value near 1.0 for C^ade1 means that the enzyme's concentration wholly determines the flux through the pathway; a value near 0.0 means that the enzyme's concentration does not limit the flux through the path. Unless the flux control coefficient is greater than about 0.5, changes in the activity of the enzyme will not have a strong effect on the flux.

The elasticity, e, of an enzyme is a measure of how that enzyme's catalytic activity changes when the concentration of a metabolite—substrate, product, or effector—changes. It is obtained from an experimental plot of the rate of the reaction catalyzed by the enzyme versus the concentration of the metabolite, at metabolite concentrations that prevail in the cell. By arguments analogous to those used to derive C, we can show e to be the slope of the tangent to a plot of revealed an unexpectedly low flux control coefficient for PFK-1, which, because of its known elaborate allosteric regulation, has been viewed as the main point of flux control—the "rate-determining step"—in glycolysis. Experimentally raising the level of PFK-1 fivefold led to a change in flux through glycolysis of less than 10%, suggesting that the real role of PFK-1 regulation is not to control flux through glycolysis but to mediate metabolite homeostasis—to prevent large changes in metabolite concentrations when the flux through gly-colysis increases in response to elevated blood glucose or insulin. Recall that the study of glycolysis in a liver ln V versus ln [substrate, or product, or effector]:

dln V

3ln S

For an enzyme with typical Michaelis-Menten kinetics, the value of e ranges from about 1 at substrate concentrations far below Km to near 0 as Vmax is approached. Allosteric enzymes can have elasticities greater than 1.0, but not larger than their Hill coefficients (p. 167).

Finally, the effect of controllers outside the pathway itself (that is, not metabolites) can be measured and expressed as the response coefficient, R. The change in flux through the pathway is measured for changes in the concentration of the controlling parameter P, and R is defined in a form analogous to that of Equation 1, yielding the expression dJydh P dP Jydh

RPydh

Using the same logic and graphical methods as described above for determining C, we can obtain R as the slope of the tangent to the plot of ln J versus ln P.

The three coefficients we have described are related in this simple way:

Thus the responsiveness of each enzyme in a pathway to a change in an outside controlling factor is a simple function of two things: the control coefficient, a variable that expresses the extent to which that enzyme influences the flux under a given set of conditions, and the elasticity, an intrinsic property of the enzyme that reflects its sensitivity to substrate and effector concentrations.

Concentration of enzyme, Ex

FIGURE 2 The flux control coefficient. (a) Typical variation of the pathway flux, Jydh, measured at the step catalyzed by the enzyme ydh, as a function of the amount of the enzyme xase, Exase, which catalyzes an earlier step in the pathway. The flux control coefficient at (e,j) is the slope of the product of the tangent to the curve, 3/ydh/3£xase, and the ratio (scaling factor), e/j. (b) On a double-logarithmic plot of the same curve, the flux control coefficient is the slope of the tangent to the curve.

Concentration of enzyme, Ex dln Jydh = cJydh dln Jydh = cJydh

FIGURE 2 The flux control coefficient. (a) Typical variation of the pathway flux, Jydh, measured at the step catalyzed by the enzyme ydh, as a function of the amount of the enzyme xase, Exase, which catalyzes an earlier step in the pathway. The flux control coefficient at (e,j) is the slope of the product of the tangent to the curve, 3/ydh/3£xase, and the ratio (scaling factor), e/j. (b) On a double-logarithmic plot of the same curve, the flux control coefficient is the slope of the tangent to the curve.

e extract (Fig. 15-33) also yielded a flux control coefficient that contradicted the conventional wisdom; it showed that hexokinase, not PFK-1, is most influential in setting the flux through glycolysis. We must note here that a liver extract is far from equivalent to a hepato-cyte; the ideal way to study flux control is by manipu lating one enzyme at a time in the living cell. This is already feasible in some cases.

Investigators have used nuclear magnetic resonance (NMR) as a noninvasive means to determine the concentration of glycogen and metabolites in the five-step pathway from glucose in the blood to glycogen in myocytes

Capillary

Glucose

Plasma ' membrane

Myocyte

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