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Lehninger Principles of Biochemistry

David L. Nelson, Michael M. Cox

Chapter 6

Enzymes - all with Video Answers

Educators


Chapter Questions

02:13

Problem 1

Keeping the Sweet Taste of Corn 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
03:10

Problem 2

Intracellular Concentration of Enzymes To approximate the 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 çell.

Lottie Adams
Lottie Adams
Numerade Educator
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Problem 3

Rate Enhancement by Urease The enzyme urease enhances the rate of urea hydrolysis at $\mathrm{pH} 8.0$ 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 $\mathrm{pH} 8.0,$ 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.

Taylor Jordan
Taylor Jordan
Numerade Educator
01:19

Problem 4

Protection of an Enzyme against Denaturation by Heat 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
Prashant Bana
Numerade Educator
02:11

Problem 5

Requirements of Active Sites in Enzymes 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 $\operatorname{Arg}^{145}$ and $\mathrm{Glu}^{270}$
(a) If the carboxypeptidase chain were a perfect $\alpha$ helix, how far apart (in $\AA$ ) would $\mathrm{Arg}^{145}$ and Glu $^{270}$ be? (Hint: See Fig. 4-4a.)
(b) Explain how the two amino acid residues can catalyze a reaction occurring in the space of a few angstroms.

Lottie Adams
Lottie Adams
Numerade Educator
03:56

Problem 6

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

Lottie Adams
Lottie Adams
Numerade Educator
01:31

Problem 7

Effect of Enzymes on Reactions Which of the listed effects would be brought about by any enzyme catalyzing the following simple reaction?
(a) Decreased $\boldsymbol{K}_{\mathbf{e q}}^{\prime} ;$ (b) increased $k_{1} ;$ (c) increased $\boldsymbol{K}_{\mathbf{e q}}^{\prime} ;$ (d) increased $\Delta G^{\dagger}$ decreased $\Delta G^{\dagger} ;$ (f) more negative $\Delta G^{\prime \circ} ;(g)$ increased $k_{2}$

Prashant Bana
Prashant Bana
Numerade Educator
04:46

Problem 8

8. Relation between Reaction Velocity and Substrate Concentration: MichaelisMenten Equation (a) At what substrate concentration would an enzyme with a $k_{\mathrm{cat}}$ of 30.0 $\mathrm{s}^{-1}$ and a $K_{\mathrm{m}}$ of $0.0050 \mathrm{M}$ operate at one-quarter of its maximum rate?
(b) Determine the fraction of $V_{\max }$ that would be obtained at the following substrate concentrations $[\mathrm{S}]: 1 / 2 K_{\mathrm{m}}, 2 K_{\mathrm{m}},$ and $10 K_{\mathrm{m}}$
(c) An enzyme that catalyzes the reaction $X \rightleftharpoons Y$ is isolated from two bacterial species. The enzymes have the same $V_{\max }$ but different $K_{\mathrm{m}}$ values for the substrate X. Enzyme A has a $K_{\mathrm{m}}$ of $2.0 \mu \mathrm{M},$ and enzyme $\mathrm{B}$ has a $K_{\mathrm{m}}$ of $0.5 \mu \mathrm{M}$. The plot below shows the kinetics of reactions carried out with the same concentration of each enzyme and with $[\mathrm{X}]=1 \mu \mathrm{M}$ Which curve corresponds to which enzyme?

Lottie Adams
Lottie Adams
Numerade Educator
02:02

Problem 9

Applying the Michaelis-Menten Equation I An enzyme catalyzes the reaction $A \rightleftharpoons B$. The enzyme is present at a concentration of $2 \mathrm{nM}$, and the $V_{\max }$ is $1.2 \mu \mathrm{M} \mathrm{s}^{-1} .$ The $K_{\mathrm{m}}$ for substrate $\mathrm{A}$ is $10 \mu \mathrm{M}$. Calculate the initial velocity of the reaction, $V_{0},$ when the substrate concentration is (a) $2 \mu \mathrm{M},$ (b) $10 \mu \mathrm{M},(\mathrm{c}) 30 \mu \mathrm{M}$

Lottie Adams
Lottie Adams
Numerade Educator
01:49

Problem 10

Applying the Michaelis-Menten Equation II An enzyme catalyzes the reaction $\mathrm{M} \rightleftharpoons$ N. The enzyme is present at a concentration of $1 \mathrm{nM}$, and the $V_{\max }$ is $2 \mu \mathrm{M} \mathrm{s}^{-1}$. The $K_{\mathrm{m}}$ for substrate $\mathrm{M}$ is $4 \mu \mathrm{M}$. (a) Calculate $k_{\mathrm{cat}}$. (b) What values of $V_{\max }$ and $K_{\mathrm{m}}$ would be observed in the presence of sufficient amounts of an uncompetitive inhibitor to generate an $\alpha^{\prime}$ of $2.0 ?$

Lottie Adams
Lottie Adams
Numerade Educator
05:23

Problem 11

Applying the Michaelis-Menten Equation III A research group discovers a new version of happyase, which they call happyase*, that catalyzes the chemical reaction HAPPY $\rightleftharpoons$ SAD. The researchers begin to characterize the enzyme.
(a) In the first experiment, with $\left[\mathrm{E}_{\mathrm{t}}\right]$ at $4 \mathrm{nM}$, they find that the $V_{\max }$ is $1.6 \mu \mathrm{M} \mathrm{s}^{-1}$. Based on this experiment, what is the $k_{\mathrm{cat}}$ for happyase $^{*} ?$ ( Include appropriate units.)
(b) In another experiment, with $\left[\mathrm{E}_{\mathrm{t}}\right]$ at $1 \mathrm{nM}$ and $[\mathrm{HAPPY}]$ at $30 \mu \mathrm{M}$, the researchers find that $V_{0}=300 \mathrm{nM} \mathrm{s}^{-1} .$ What is the measured $K_{\mathrm{m}}$ of happyase* for its substrate HAPPY? (Include appropriate units.)
(c) Further research shows that the purified happyase* used in the first two experiments was actually contaminated with a reversible inhibitor called ANGER. When ANGER is carefully removed from the happyase* preparation and the two experiments repeated, the measured $V_{\max }$ in (a) is increased to $4.8 \mu \mathrm{M} \mathrm{s}^{-1},$ and the measured $K_{\mathrm{m}}$ in (b) is now $15 \mu \mathrm{M}$ For the inhibitor ANGER, calculate the values of $\alpha$ and $\alpha^{\prime}$

Banhishikha Sinha
Banhishikha Sinha
Numerade Educator
03:35

Problem 12

Applying the Michaelis-Menten Equation IV An enzyme is found that catalyz reaction $\mathrm{X} \rightleftharpoons \mathrm{Y}$. Researchers find that the $K_{\mathrm{m}}$ for the substrate $\mathrm{X}$ is $4 \mu \mathrm{M}$, and the $k_{\mathrm{ca}}$ $\min ^{-1}$
(a) In an experiment, $[\mathrm{X}]=6 \mathrm{mM},$ and $V_{0}=480 \mathrm{nM} \min ^{-1} .$ What was the $\left[\mathrm{E}_{\mathrm{t}}\right]$ the experiment?
(b) In another experiment, $\left[\mathrm{E}_{\mathrm{t}}\right]=0.5 \mu \mathrm{M},$ and the measured $V_{0}=5 \mu \mathrm{M} \min ^{-1} . \mathrm{Wh}$ the $[\mathrm{X}]$ used in the experiment?
(c) The compound $Z$ is found to be a very strong competitive inhibitor of the en. with an $\alpha$ of $10 .$ In an experiment with the same $\left[\mathrm{E}_{\mathrm{t}}\right]$ as in (a), but a different $[\mathrm{x}$ amount of $Z$ is added that reduces $V_{0}$ to $240 \mathrm{nM} \min ^{-1}$. What is the $[\mathrm{X}]$ in this experir
(d) Based on the kinetic parameters given above, has this enzyme evolved to ac catalytic perfection? Explain your answer briefly, using the kinetic parameter(s) that

Lottie Adams
Lottie Adams
Numerade Educator
01:43

Problem 13

Estimation of $V_{\max }$ and $K_{\mathrm{m}}$ by Inspection 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
Lottie Adams
Numerade Educator
06:15

Problem 14

Properties of an Enzyme of Prostaglandin Synthesis 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.
$$\begin{array}{ccc}
\begin{array}{c}
\text { [Arachidonic } \\
\text { acid] (mM) }
\end{array} & \begin{array}{c}
\text { Rate of formation of } \\
\text { PGG }_{2} \text { (mM min }^{-1} \text {) }
\end{array} & \begin{array}{c}
\text { Rate of formation of PGG }_{2} \text { with 10 } \\
\text { mg/mL ibuprofen (mM min }^{-1} \text {) }
\end{array} \\
\hline 0.5 & 23.5 & 16.67 \\
1.0 & 32.2 & 25.25 \\
1.5 & 36.9 & 30.49 \\
2.5 & 41.8 & 37.04 \\
3.5 & 44.0 & 38.91 \\
\hline
\end{array}$$
(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
Rashmi Sinha
Numerade Educator
02:33

Problem 15

Graphical Analysis of $V_{\max }$ and $K_{\mathrm{m}}$ The following experimental data were collected during a study of the catalytic activity of an intestinal peptidase with the substrate glycylglycine:
\[
\text { Glycylglycine }+\mathrm{H}_{2} \mathrm{O} \rightarrow 2 \text { glycine }
\]
Use graphical analysis (see Box $6-1$ ) to determine the $V_{\max }$ and $K_{\mathrm{m}}$ for this enzyme preparation and substrate.

Ronald Prasad
Ronald Prasad
Numerade Educator
02:18

Problem 16

The Eadie-Hofstee Equation There are several ways to transform the MichaelisMenten equation so as to plot data and derive kinetic parameters, each with different advantages depending on the data set being analyzed. One transformation of the MichaelisMenten 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:
\[
V_{0}=\left(-K_{\mathrm{m}}\right) \frac{V_{0}}{[\mathrm{S}]}+V_{\mathrm{max}}
\]
A plot of $V_{0}$ versus $V_{0} /[\mathrm{S}]$ 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 was added to the reaction mixture? Hint: See Equation $6-30$

Lottie Adams
Lottie Adams
Numerade Educator
01:37

Problem 17

The Turnover Number of Carbonic Anhydrase Carbonic anhydrase of erythrocytes $\left(M_{\mathrm{r}} 30,000\right)$ has one of the highest turnover numbers known. It catalyzes the reversible hydration of $\mathrm{CO}_{2}$
\[
\mathbf{H}_{2} \mathbf{O}+\mathbf{C O}_{2} \rightleftharpoons \mathbf{H}_{2} \mathbf{C O}_{3}
\]
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 $0.30 \mathrm{g}$ of $\mathrm{CO}_{2}$ in $1 \mathrm{min}$ at $37^{\circ} \mathrm{C}$ at $V_{\max },$ what is the turnover number $\left(k_{\text {cat }}\right)$ of carbonic anhydrase (in units of $\min ^{-1}$ )?

Hailey Tomashek
Hailey Tomashek
Numerade Educator
04:04

Problem 18

Deriving a Rate Equation for Competitive Inhibition The rate equation for an enzyme subject to competitive inhibition is
\[
V_{0}=\frac{V_{\max }[\mathbf{S}]}{\alpha K_{\mathrm{m}}+[\mathbf{S}]}
\]
Beginning with a new definition of total enzyme as
\[
\left[\mathbf{E}_{t}\right]=[\mathbf{E}]+[\mathbf{E S}]+[\mathbf{E I}]
\]
and the definitions of $\alpha$ and $K_{1}$ provided in the text, derive the rate equation above. Use the derivation of the Michaelis-Menten equation as a guide.

Lottie Adams
Lottie Adams
Numerade Educator
01:54

Problem 19

Irreversible Inhibition of an Enzyme 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:
\[
\text { Enz-SH }+\mathbf{A g}^{+} \rightarrow \mathbf{E n z}-\mathbf{S}-\mathbf{A g}+\mathbf{H}^{+}
\]
The affinity of $\mathrm{Ag}^{+}$ for sulfhydryl groups is so great that $\mathrm{Ag}^{+}$ can be used to titrate $-\mathrm{SH}$ groups quantitatively. To $10.0 \mathrm{mL}$ 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
Lottie Adams
Numerade Educator
02:12

Problem 20

Clinical Application of Differential Enzyme Inhibition Human blood serum contains a class of enzymes known as acid phosphatases, which hydrolyze biological phosphate esters under slightly acidic conditions (pH 5.0):
Acid phosphatases are produced by erythrocytes and by 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
Rashmi Sinha
Numerade Educator
01:14

Problem 21

Inhibition of Carbonic Anhydrase by Acetazolamide 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 $\mathrm{pH}$ and bicarbonate content of several body fluids. The experimental curve of initial reaction velocity (as percentage of $V_{\max }$ ) 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.

Adriano Chikande
Adriano Chikande
Numerade Educator
02:39

Problem 22

The Effects of Reversible Inhibitors Derive the expression for the effect of a reversible inhibitor on observed $K_{\mathrm{m}}\left(\text { apparent } K_{\mathrm{m}}=\alpha K_{\mathrm{m}} / \alpha^{\prime}\right) .$ Start with Equation 6-30 and the statement that apparent $K_{\mathrm{m}}$ is equivalent to the $[\mathrm{S}]$ at which $V_{0}=V_{\max } / 2 \alpha^{\prime}$

Lottie Adams
Lottie Adams
Numerade Educator
00:51

Problem 23

pH Optimum of Lysozyme The active site of lysozyme contains two amino acid residues essential for catalysis: 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 $\mathrm{pH} 5.2,$ the $\mathrm{pH}$ optimum of lysozyme? How can the ionization states of these residues explain the pH-activity profile of lysozyme shown below?

Sana Riaz
Sana Riaz
Numerade Educator
23:09

Problem 24

Exploring and Engineering Lactate Dehydrogenase Examining the structure of an enzyme can lead to hypotheses about the relationship between different amino acids in the protein's structure and the protein's function. One way to test these hypotheses is to use recombinant DNA technology to generate mutant versions of the enzyme and then examine the structure and function of these altered forms. The technology used to do this is described in Chapters 8 and 9 One example of this kind of analysis is the work of A. R. Clarke and colleagues on the enzyme lactate dehydrogenase, published in $1989 .$ Lactate dehydrogenase (LDH) catalyzes the reduction of pyruvate with NADH to form lactate (see Section 14.3). A schematic of the enzyme's active site is shown below; the pyruvate is in the center:
The reaction mechanism is similar to that of many NADH reductions (see Fig. $13-24$ ); it is approximately the reverse of steps 2 and 3 of Figure $14-8 .$ The transition state involves a strongly polarized carbonyl group of the pyruvate molecule:
(a) A mutant form of LDH in which Arg $^{109}$ is replaced with Gln shows only $5 \%$ of the pyruvate binding and $0.07 \%$ of the activity of wild-type enzyme. Provide a plausible explanation for the effects of this mutation.
(b) A mutant form of LDH in which Arg $^{171}$ is replaced with Lys shows only $0.05 \%$ of the wild-type level of substrate binding. Why is this dramatic effect surprising?
(c) In the crystal structure of LDH, the guanidinium group of Arg $^{171}$ and the carboxyl group of pyruvate are aligned, as shown above, in a co-planar "forked" configuration. Based on this structure, explain the dramatic effect of substituting Arg 171 with Lys.
(d) A mutant form of LDH in which Ile $^{250}$ is replaced with Gln shows reduced binding of NADH. Provide a plausible explanation for this result.

Clarke and colleagues also set out to engineer a mutant version of LDH that would bind and reduce oxaloacetate rather than pyruvate. They made a single substitution, replacing $\mathrm{Gln}^{102}$ with Arg; the resulting enzyme would reduce oxaloacetate to malate and would no longer reduce pyruvate to lactate. They had therefore converted LDH to malate dehydrogenase.
(e) Sketch the active site of this mutant LDH with oxaloacetate bound.
(f) Why does this mutant enzyme now use oxaloacetate as a substrate instead of pyruvate?
(g) The authors were surprised that substituting a larger amino acid in the active site allowed a larger substrate to bind. Explain this result.

Andres Roman
Andres Roman
Numerade Educator