Fundamentals of Biochemistry Third Edition Donald Voet • Judith G. Voet • Charlotte W. Pratt Chapter 12 Enzyme Kinetics, Inhibition, and Control Copyright © 2008 by John Wiley & Sons, Inc.

Enzyme kinetics begins with measuring reaction rates For instance, measuring the disappearance of reactant A by monitoring its concentration over time yields a rate constant k.

In an enzyme-catalyzed reaction, the concentrations of four species are measured: the enzyme (E), the substrate (S), the product (P) and the enzyme-substrate complex (ES).

In an enzyme-catalyzed reaction, the concentrations of four species are measured: the enzyme (E), the substrate (S), the product (P) and the enzyme-substrate complex (ES). Importantly, the concentration of both the “free” enzyme (E) and the “bound” enzyme (ES) are constant during most of the reaction: this is called the steady-state assumption

In an enzyme-catalyzed reaction, the concentrations of four species are measured: the enzyme (E), the substrate (S), the product (P) and the enzyme-substrate complex (ES). More interestingly, [S] decreases linearly with time, so the reaction is first order in [S] Importantly, the concentration of both the “free” enzyme (E) and the “bound” enzyme (ES) are constant during most of the reaction: this is called the steady-state assumption

If these criteria are followed: • Reaction is first order in substrate • The assumption of steady state holds • The “backward” reaction from ES  E + S is much more favored than the “forward” reaction ES  E + P (in other words, k-1 >> k2 Then the reaction is said to follow Michaelis-Menten kinetics (Leonor Michaelis and Maud Mentem, 1913). Most enzymatic reactions are described by Michaelis-Menten kinetics.

v0 is the initial velocity of the reaction; as substrate concentration grows, so does this velocity. It is asymptotic with a value called Vmax. Note the units of [S] are in terms of the Michaelis constant KM

kcat = catalytic constant = turnover number (number of rxns/site/s) = Vmax/[E]total units of inverse seconds; for simple Michaelis-Menten enzymes (one substrate) kcat = k2 kcat/KM = catalytic efficiency; values near 109 show the enzyme’s efficiency is near the diffusion-controlled limit

From the class handout, you derived the classic Michaelis-Menten equation: which has the form y = mx + b; in other words, a line, if you plot 1/[S] as the independent variable and 1/v0 as the dependent variable

The Lineweaver-Burk plot can yield an estimate of Vmax and KM easily Lineweaver, H and Burk, D. (1934). "The Determination of Enzyme Dissociation Constants". Journal of the American Chemical Society 56 (3): 658–666

The Lineweaver-Burk plot Plot 1/[S] vs. 1/v0 (so it’s sometimes called a double-reciprocal plot), then regress a best-fit line through the points

The Lineweaver-Burk plot Plot 1/[S] vs. 1/v0 (so it’s sometimes called a double-reciprocal plot), then regress a best-fit line through the points Extrapolate the best-fit line back to its x-intercept

The x-intercept is –1/KM The y-intercept is 1/Vmax The Lineweaver-Burk plot The x-intercept is –1/KM The y-intercept is 1/Vmax Plot 1/[S] vs. 1/v0 (so it’s sometimes called a double-reciprocal plot), then regress a best-fit line through the points Extrapolate the best-fit line back to its x-intercept

Problems with the Lineweaver-Burk plot: • Because reciprocals are plotted, small errors in the measurements of v0 and [S] lead to large errors in Vmax and KM • Since S is usually not extremely soluble, there are no points with large values of 1/[S], which means the extrapolation to obtain Vmax and KM can lead to large errors

Problems with the Lineweaver-Burk plot: • Because reciprocals are plotted, small errors in the measurements of v0 and [S] lead to large errors in Vmax and KM • Since S is usually not extremely soluble, there are no points with large values of 1/[S], which means the extrapolation to obtain Vmax and KM can lead to large errors There are other methods of obtaining Vmax and KM but the most used method is nonlinear regression on the standard [S] vs v0 curve.

Because the mathematics developed so far hinges on the rate-determining step, it is impossible to derive what the other steps in the mechanism are, from the math alone

Enzymatic reaction usually require two substrates, A and B

Enzymatic reaction usually require two substrates, A and B The typical bisubstrate reaction involves a transfer of a functional group

A couple of examples:

The mechanism for a bisubstrate reaction is categorized: An ordered mechanism has a specific order for the binding of substrates An random mechanism has no specific order for the binding

An ping-pong (double displacement) mechanism binds substrates one at a time to produce the two products

Enzyme inhibition Enzymes can bind substances that slow down or stop their catalytic function — these substances are called inhibitors Malonate, for instance, inhibits succinate dehydrogenase

Another example: adenosine deaminase converts adenosine to inosine

Another example: adenosine deaminase converts adenosine to inosine The enzyme can be inhibited by the transition-state analog 1,6-dihydroinosine

How to incorporate enzymes into Michaelis-Menten kinetics: Include an inhibitor (I) reaction to the enzyme, and invent a new equilibrium constant KI to show how effectively the inhibitor binds to the enzyme

Enzyme inhibition falls into a couple of different categories Competitive inhibition occurs when an inhibitor is competing with the substrate for access to the enzyme’s active site α is a measure of how competitive the inhibitor is; bigger α means more competitive. α is dependent on [I] and KI

An example of competitive inhibition is liver alcohol dehydrogenase’s interaction with ethanol and methanol; both ethanol and methanol compete for the same active site on the enzyme

An example of competitive inhibition is liver alcohol dehydrogenase’s interaction with ethanol and methanol; both ethanol and methanol compete for the same active site on the enzyme This product is toxic

An example of competitive inhibition is liver alcohol dehydrogenase’s interaction with ethanol and methanol; both ethanol and methanol compete for the same active site on the enzyme This product is toxic So upon ingestion of methanol, a large quantity of ethanol is administered to compete with methanol for the enzyme

Uncompetitive inhibition: the inhibitor binds to the ES complex only, distorting the active site with the substrate in place The statin class of drugs are uncompetitive inhibitors of serine proteases

The Lineweaver-Burk plot allows a straightforward comparison of inhibition mechanisms Competitive inhibition: slope varies; y-intercept does not Uncompetitive inhibition: y-intercept varies; slope does not

Mixed inhibition: the inhibitor binds both to the free enzyme and to the ES complex. This is also confusing known as noncompetitive inhibition. Metal ions that don’t bind to the substrate binding site are mixed inhibitors.

Mixed inhibition: slope varies; y-intercept also varies Figure 12-9

Kapp = the apparent Michaelis constant = α KM

Enzyme activity may be regulated by controlling the amount of enzyme, or by using allosteric effectors or covalent modification. Aspartate transcarbamoylase (ATCase) can be regulated by both adenosine triphosphate (ATP) and cytidine triphosphate (CTP)

Look at the shape of the curves and determine if either substance is an allosteric effector, and, if so, whether it is an activator or an inhibitor

Look at the shape of the curves and determine if either substance is an allosteric effector, and, if so, whether it is an activator or an inhibitor activator inhibitor

CTP is a feedback inhibitor because its production inhibits a previous step

The structure of ATCase yields an explanation of the effector control: the enzyme has a symmetric arrangement of 3 catalytic subunits (red/blue) and 3 regulatory subunits (yellow) ATP binds to the regulatory subunit in its R-state (active); CTP binds to it in its T-state (inactive)

Does the bisubstrate analog on the left bind to ATCase’s R-state or T-state?

Does the bisubstrate analog on the left bind to ATCase’s R-state or T-state? R-state (active)!

Enzyme activity control by covalent modification There is a class of enzyme called kinases, which catalyze the phosphorylation of other enzymes (including other kinases). The source of the phosphate is typically ATP.

Enzyme activity control by covalent modification There is a class of enzyme called kinases, which catalyze the phosphorylation of other enzymes (including other kinases). The source of the phosphate is typically ATP. There is also a class of enzyme called phosphatases, which dephosphorylate enzymes. The reaction is a hydrolysis.

An example is the production of glucose-1-phosphate (G1P) from glycogen (a polymer of glucose). This reaction is the rate-determining step of the glycogen breakdown pathway, and is catalyzed by muscle glycogen phosphorylase. phosophorylase b is phosphorylated (which involves a kinase) into phosphorylase a, which catalyzes the G1P production reaction.

Muscle glycogen phosphorylase and its critical Ser 14 which gets phosphorylated

inactive active

AMP, ATP, G6P are all effectors of muscle glycogen phosphorylase; phosphorylase b is the inactive form because ATP and G6P will bind and inactivate it. Phosphorylase a is only inactivated by glucose.