Lehninger Principles of Biochemistry

David L. Nelson, Michael M. Cox

Chapter 6

Enzymes - all with Video Answers

Educators

Chapter Questions

Problem 1

The sweet taste of freshly picked corn (maize) is due to the high level of sugar in the kernels. Store-bought corn (several days after picking) is not as sweet, because about $50 \%$ of the free sugar is converted to starch within one day of picking. To preserve the sweetness of fresh corn, the husked ears can be immersed in boiling water for a few minutes ("blanched") then cooled in cold water. Corn processed in this way and stored in a freezer maintains its sweetness. What is the biochemical basis for this procedure?

Dana Tsai

Dana Tsai

Numerade Educator

Problem 2

To approximate the actual concentration of enzymes in a bacterial cell, assume that the cell contains equal concentrations of 1,000 different enzymes in solution in the cytosol and that each protein has a molecular weight of 100,000 . Assume also that the bacterial cell is a cylinder (diameter $1.0 \mu \mathrm{m}$, height $2.0 \mu \mathrm{m}$ ), that the cytosol (specific gravity 1.20) is $20 \%$ soluble protein by weight, and that the soluble protein consists entirely of enzymes. Calculate the average molar concentration of each enzyme in this hypothetical cell.

Lottie Adams

Numerade Educator

Problem 3

The enzyme urease enhances the rate of urea hydrolysis at pH 8.0 and $20^{\circ} \mathrm{C}$ by a factor of $10^{14}$. If a given quantity of urease can completely hydrolyze a given quantity of urea in 5.0 min at $20^{\circ} \mathrm{C}$ and pH 8.0 , how long would it take for this amount of urea to be hydrolyzed under the same conditions in the absence of urease? Assume that both reactions take place in sterile systems so that bacteria cannot attack the urea.

Lottie Adams

Numerade Educator

Problem 4

When enzyme solutions are heated, there is a progressive loss of catalytic activity over time due to denaturation of the enzyme. A solution of the enzyme hexokinase incubated at $45^{\circ} \mathrm{C}$ lost $50 \%$ of its activity in 12 min , but when incubated at $45^{\circ} \mathrm{C}$ in the presence of a very large concentration of one of its substrates, it lost only $3 \%$ of its activity in 12 min . Suggest why thermal denaturation of hexokinase was retarded in the presence of one of its substrates.

Prashant Bana

Numerade Educator

Problem 5

Carboxypeptidase, which sequentially removes carboxyl-terminal amino acid residues from its peptide substrates, is a single polypeptide of 307 amino acids. The two essential catalytic groups in the active site are furnished by $\mathrm{Arg}^{145}$ and $\mathrm{Glu}^{270}$.
(a) If the carboxypeptidase chain were a perfect $\alpha$ helix, how far apart (in $\AA$ ) would $\operatorname{Arg}^{145}$ and Glu ${ }^{270}$ be? (Hint: See Fig. 4-4b.)
(b) Explain how the two amino acid residues can catalyze a reaction occurring in the space of a few angstroms.

Lottie Adams

Numerade Educator

Problem 6

The muscle enzyme lactate dehydrogenase catalyzes the reaction
Structure can't copy
NADH and $\mathrm{NAD}^{+}$are the reduced and oxidized forms, respectively, of the coenzyme NAD. Solutions of NADH, but not $\mathrm{NAD}^{+}$, absorb light at 340 nm . This property is used to determine the concentration of NADH in solution by measuring spectrophotometrically the amount of light absorbed at 340 nm by the solution. Explain how these properties of NADH can be used to design a quantitative assay for lactate dehydrogenase.

Lottie Adams

Numerade Educator

Problem 7

(a) At what substrate concentration would an enzyme with a $k_{\text {cat }}$ of $30.0 \mathrm{~s}^{-1}$ and a $K_{\mathrm{m}}$ of 0.0050 m operate at one-quarter of its maximum rate? (b) Determine the fraction of $V_{\max }$ that would be obtained at the following substrate concentrations: $[\mathrm{S}]=\frac{1}{2} K_{\mathrm{m}}, 2 K_{\mathrm{m}}$, and $10 K_{\mathrm{m}}$.

Lottie Adams

Numerade Educator

Problem 8

Although graphical methods are available for accurate determination of the $V_{\max }$ and $K_{\mathrm{m}}$ of an enzyme-catalyzed reaction (see Box $6-1$ ), sometimes these quantities can be quickly estimated by inspecting values of $V_0$ at increasing [ S$]$. Estimate the $V_{\max }$ and $K_{\mathrm{m}}$ of the enzyme-catalyzed reaction for which the following data were obtained.
$$
\begin{array}{cc}
{[\mathrm{S}](\mathrm{m})} & V_0(\mu \mathrm{m} / \mathrm{min}) \\
\hline 2.5 \times 10^{-6} & 28 \\
4.0 \times 10^{-6} & 40 \\
1 \times 10^{-5} & 70 \\
2 \times 10^{-5} & 95 \\
4 \times 10^{-5} & 112 \\
1 \times 10^{-4} & 128 \\
2 \times 10^{-3} & 139 \\
1 \times 10^{-2} & 140 \\
\hline
\end{array}
$$

Lottie Adams

Numerade Educator

Problem 9

Prostaglandins are a class of eicosanoids, fatty acid derivatives with a variety of extremely potent actions on vertebrate tissues. They are responsible for producing fever and inflammation and its associated pain. Prostaglandins are derived from the 20 -carbon fatty acid arachidonic acid in a reaction catalyzed by the enzyme prostaglandin endoperoxide synthase. This enzyme, a cyclooxygenase, uses oxygen to convert arachidonic acid to $\mathrm{PGG}_2$, the immediate precursor of many different prostaglandins (prostaglandin synthesis is described in Chapter 21).
(a) The kinetic data given below are for the reaction catalyzed by prostaglandin endoperoxide synthase. Focusing here on the first two columns, determine the $V_{\max }$ and $K_{\mathrm{m}}$ of the enzyme.
$$
\begin{array}{lcc}
\begin{array}{l}
\text { [Arachidonic } \\
\text { acid] } \\
(\mathrm{mm})
\end{array} & \begin{array}{l}
\text { Rate of formation } \\
\text { of } \mathrm{PGG}_2 \\
(\mathrm{mM} / \mathrm{min})
\end{array} & \begin{array}{l}
\text { Rate of formation } \\
\text { of } \mathrm{PGG}_2 \text { with } 10 \\
\mathrm{mg} / \mathrm{mL} \text { ibuprofen } \\
(\mathrm{mM} / \mathrm{min})
\end{array} \\
\hline 0.5 & 23.5 & 16.67 \\
1.0 & 32.2 & 25.25 \\
1.5 & 36.9 & 30.49 \\
2.5 & 41.8 & 37.04 \\
3.5 & 44.0 & 38.91
\end{array}
$$
(b) Ibuprofen is an inhibitor of prostaglandin endoperoxide synthase. By inhibiting the synthesis of prostaglandins, ibuprofen reduces inflammation and pain. Using the data in the first and third columns of the table, determine the type of inhibition that ibuprofen exerts on prostaglandin endoperoxide synthase.

Rashmi Sinha

Numerade Educator

Problem 10

The following experimental data were collected during a study of the catalytic activity of an intestinal peptidase with the substrate glycylglycine: $\square$
$$
\text { Glycylglycine }+\mathrm{H}_2 \mathrm{O} \longrightarrow 2 \text { glycine }
$$
$$
\begin{array}{cc}
\text { [S] (mm) } & \begin{array}{c}
\text { Product formed } \\
(\mu \mathrm{mol} / \mathrm{min})
\end{array} \\
\hline 1.5 & 0.21 \\
2.0 & 0.24 \\
3.0 & 0.28 \\
4.0 & 0.33 \\
8.0 & 0.40 \\
16.0 & 0.45
\end{array}
$$
Use graphical analysis (see Box 6-1 and its associated Living Graph) to determine the $K_{\mathrm{m}}$ and $V_{\text {max }}$ for this enzyme preparation and substrate.

Ronald Prasad

Numerade Educator

Problem 11

One transformation of the Michaelis-Menten equation is the Lineweaver-Burk, or double-reciprocal, equation. Multiplying both sides of the Lineweaver-Burk equation by $V_{\max }$ and rearranging gives the Eadie-Hofstee equation:
$$
V_0=\left(-K_{\mathrm{m}}\right) \frac{V_0}{[\mathrm{~S}]}+V_{\text {max }}
$$
A plot of $V_0$ vs. $V_0 /[\mathrm{S}]$ for an enzyme-catalyzed reaction is shown below. The blue curve was obtained in the absence of inhibitor. Which of the other curves (A, B, or C) shows the enzyme activity when a competitive inhibitor is added to the reaction mixture? Hint: See Equation 6-30.
Graph can't copy

Lottie Adams

Numerade Educator

Problem 12

Carbonic anhydrase of erythrocytes $\left(M_{\mathrm{r}} 30,000\right)$ has one of the highest turnover numbers we know of. It catalyzes the reversible hydration of $\mathrm{CO}_2$ :
$$
\mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2 \rightleftharpoons \mathrm{H}_2 \mathrm{CO}_3
$$

This is an important process in the transport of $\mathrm{CO}_2$ from the tissues to the lungs. If $10.0 \mu \mathrm{g}$ of pure carbonic anhydrase catalyzes the hydration of 0.30 g of $\mathrm{CO}_2$ in 1 min at $37^{\circ} \mathrm{C}$ at $V_{\max }$, what is the turnover number ( $\left.k_{\text {cat }}\right)$ of carbonic anhydrase (in units of $\mathrm{min}^{-1}$ )?

Lottie Adams

Numerade Educator

Problem 13

The rate equation for an enzyme subject to competitive inhibition is
$$
V_0=\frac{V_{\text {max }}[\mathrm{S}]}{\alpha K_{\mathrm{m}}+[\mathrm{S}]}
$$

Beginning with a new definition of total enzyme as
$$
[\mathrm{E}]_{\mathrm{t}}=[\mathrm{E}]+[\mathrm{EI}]+[\mathrm{ES}]
$$
and the definitions of $\alpha$ and $K_{\mathrm{I}}$ provided in the text, derive the rate equation above. Use the derivation of the MichaelisMenten equation as a guide.

Lottie Adams

Numerade Educator

Problem 14

Many enzymes are inhibited irreversibly by heavy metal ions such as $\mathrm{Hg}^{2+}, \mathrm{Cu}^{2+}$, or $\mathrm{Ag}^{+}$, which can react with essential sulfhydryl groups to form mercaptides:
$$
\text { Enz-SH }+\mathrm{Ag}^{+} \longrightarrow \text { Enz-S-Ag }+\mathrm{H}^{+}
$$

The affinity of $\mathrm{Ag}^{+}$for sulfhydryl groups is so great that $\mathrm{Ag}^{+}$ can be used to titrate - SH groups quantitatively. To 10.0 mL of a solution containing $1.0 \mathrm{mg} / \mathrm{mL}$ of a pure enzyme, an investigator added just enough $\mathrm{AgNO}_3$ to completely inactivate the enzyme. A total of $0.342 \mu \mathrm{mol}$ of $\mathrm{AgNO}_3$ was required.
Calculate the minimum molecular weight of the enzyme. Why does the value obtained in this way give only the minimum molecular weight?

Lottie Adams

Numerade Educator

Problem 15

Human blood serum contains a class of enzymes known as acid phosphatases, which hydrolyze biological phosphate esters under slightly acidic conditions (pH 5.0):
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Acid phosphatases are produced by erythrocytes, the liver, kidney, spleen, and prostate gland. The enzyme of the prostate gland is clinically important, because its increased activity in the blood can be an indication of prostate cancer. The phosphatase from the prostate gland is strongly inhibited by tartrate ion, but acid phosphatases from other tissues are not. How can this information be used to develop a specific procedure for measuring the activity of the acid phosphatase of the prostate gland in human blood serum?

Rashmi Sinha

Numerade Educator

Problem 16

Carbonic anhydrase is strongly inhibited by the drug acetazolamide, which is used as a diuretic (i.e., to increase the production of urine) and to lower excessively high pressure in the eye (due to accumulation of intraocular fluid) in glaucoma. Carbonic anhydrase plays an important role in these and other secretory processes, because it participates in regulating the pH and bicarbonate content of several body fluids. The experimental curve of initial reaction velocity (as percentage of $V_{\text {max }}$ ) versus [S] for the carbonic anhydrase reaction is illustrated below (upper curve). When the experiment is repeated in the presence of acetazolamide, the lower curve is obtained. From an inspection of the curves and your knowledge of the kinetic properties of competitive and mixed enzyme inhibitors, determine the nature of the inhibition by acetazolamide. Explain your reasoning.
Graph can't copy

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 17

Derive the expression for the effect of a reversible inhibitor on observed $K_{\mathrm{m}}$ (apparent $K_{\mathrm{m}}=\alpha K_{\mathrm{m}} / \alpha^{\prime}$ ). Start with Equation 6-30 and the statement that apparent $K_{\mathrm{m}}$ is equivalent to the [S] at which $V_0=V_{\max } / 2 \alpha^{\prime}$.

Lottie Adams

Numerade Educator

Problem 18

The active site of lysozyme contains two amino acid residues essential for catalysis: $\mathrm{Glu}^{35}$ and $\mathrm{Asp}^{52}$. The $\mathrm{p} K_{\mathrm{a}}$ values of the carboxyl side chains of these residues are 5.9 and 4.5 , respectively. What is the ionization state (protonated or deprotonated) of each residue at pH 5.2 , the pH optimum of lysozyme? How can the ionization states of these residues explain the pH -activity profile of lysozyme shown below?
Graph can't copy

Sana Riaz

Numerade Educator

Problem 19

Go to the Living Graphs for Chapter 6 .
(a) Using the Living Graph for Equation 6-9, create a $V$ versus [S] plot. Use $V_{\max }=100 \mu \mathrm{m} \mathrm{s}^{-1}$, and $K_{\mathrm{m}}=10 \mu \mathrm{m}$. How much does $V_0$ increase when $[\mathrm{S}]$ is doubled, from 0.2 to $0.4 \mu \mathrm{m}$ ? What is $V_0$ when $[\mathrm{S}]=10 \mu \mathrm{m}$ ? How much does the $V_0$ increase when [S] increases from 100 to $200 \mu \mathrm{m}$ ? Observe how the graph changes when the values for $V_{\max }$ or $K_{\mathrm{m}}$ are halved or doubled.
(b) Using the Living Graph for Equation 6-30 and the kinetic parameters in (a), create a plot in which both $\alpha$ and $\alpha^{\prime}$ are 1.0. Now observe how the plot changes when $\alpha=2.0$; when $\alpha^{\prime}=3.0$; and when $\alpha=2.0$ and $\alpha^{\prime}=3.0$.
(c) Using the Living Graphs for Equation 6-30 and the Lineweaver-Burk equation in Box 6-1, create LineweaverBurk (double-reciprocal) plots for all the cases in (a) and (b). When $\alpha=2.0$, does the $x$ intercept move to the right or to the left? If $\alpha=2.0$ and $\alpha^{\prime}=3.0$, does the $x$ intercept move to the right or to the left?

Rabeya Zahid

Numerade Educator