Fundamentals of Biochemistry

Donald Voet, Judith G. Voet, Charlotte W. Pratt

Chapter 12

Enzyme Kinetics, Inhibition, and Control - all with Video Answers

Educators

Chapter Questions

Problem 1

Consider the nonenzymatic elementary reaction $A \rightarrow B$. When the concentration of $\mathrm{A}$ is $20 \mathrm{mM}$, the reaction velocity is measured as $5 \mu \mathrm{M}$
B produced per minute.
(a) Calculate the rate constant for this reaction.
(b) What is the molecularity of the reaction?

Niamat Khuda

Niamat Khuda

Numerade Educator

Problem 2

The hypothetical elementary reaction $2 \mathrm{A} \rightarrow \mathrm{B}+\mathrm{C}$ has a rate constant of $10^{-6} \mathrm{M}^{-1} \cdot \mathrm{s}^{-1} .$ What is the reaction velocity when the concentration of $\mathrm{A}$ is $10 \mathrm{mM} ?$

Niamat Khuda

Numerade Educator

Problem 3

If there is $10 \mu$ mol of the radioactive isotope $^{32}$ P (half-life 14 days) at $t=0,$ how much $^{32} \mathrm{P}$ will remain at $(\mathrm{a}) 7$ days
(b) 14 days,
(c) 21 days, and
(d) 70 days?

Niamat Khuda

Numerade Educator

Problem 4

Calculate the half-life, in years, for the reaction $2 \mathrm{X} \rightarrow \mathrm{Y}$ when the starting concentration of $X$ is $6 \mu M$ and the rate constant is $3.6 \times$ $10^{-3} \mathrm{M}^{-1} \cdot \mathrm{s}^{-1}$

Niamat Khuda

Numerade Educator

Problem 5

From the reaction data below, determine whether the reaction is first order or second order and calculate the rate constant.
$$\begin{array}{cc}
\hline \text { Time (s) } & \text { Reactant (mM) } \\
\hline 0 & 6.2 \\
\hline 1 & 3.1 \\
\hline 2 & 2.1 \\
\hline 3 & 1.6 \\
\hline 4 & 1.3 \\
\hline 5 & 1.1 \\
\hline
\end{array}$$

Rabeya Zahid

Numerade Educator

Problem 6

From the reaction data below, determine whether the reaction is first order or second order and calculate the rate constant.
$$\begin{array}{cc}
\hline \text { Time (s) } & \text { Reactant (mM) } \\
\hline 0 & 5.4 \\
\hline 1 & 4.6 \\
\hline 2 & 3.9 \\
\hline 3 & 3.2 \\
\hline 4 & 2.7 \\
\hline 5 & 2.3 \\
\hline
\end{array}$$

Rabeya Zahid

Numerade Educator

Problem 7

For an enzymatic reaction, draw curves that show the appropriate relationships between the variables in each plot below.

Niamat Khuda

Numerade Educator

Problem 8

Explain why it is usually easier to calculate an enzyme's reaction velocity from the rate of appearance of product rather than the rate of disappearance of a substrate.

Niamat Khuda

Numerade Educator

Problem 9

At what concentration of S (expressed as a multiple of $K_{M}$ ) will $\nu_{\mathrm{o}}=$ $0.95 V_{\max } ?$

Niamat Khuda

Numerade Educator

Problem 10

Identify the enzymes in Table $12-1$ whose catalytic efficiencies are near the diffusion-controlled limit.

Niamat Khuda

Numerade Educator

Problem 11

Calculate $K_{M}$ and $V_{\max }$ from the following data:
$$\begin{array}{cc}
\hline \text { [S] }(\mu \text { M }) & v_{0}\left(\mathrm{mM} \cdot \mathrm{s}^{-1}\right) \\
\hline 0.1 & 0.34 \\
\hline 0.2 & 0.53 \\
\hline 0.4 & 0.74 \\
\hline 0.8 & 0.91 \\
\hline 1.6 & 1.04 \\
\hline
\end{array}$$

Niamat Khuda

Numerade Educator

Problem 12

Explain why each of the following data sets from a Lineweaver Burk plot are not individually ideal for determining $K_{M}$ for an enzymecatalyzed reaction that follows Michaelis-Menten kinetics.

Hailey Tomashek

Hailey Tomashek

Numerade Educator

Problem 13

The $K_{M}$ for the reaction of chymotrypsin with $N$ -acetylvaline ethyl ester is $8.8 \times 10^{-2} \mathrm{M}$, and the $K_{M}$ for the reaction of chymotrypsin with $N$ -acetyltyrosine ethyl ester is $6.6 \times 10^{-4} \mathrm{M}$. (a) Which substrate has the higher apparent affinity for the enzyme? (b) Which substrate is likely to give a higher value for $V_{\max } ?$

Niamat Khuda

Numerade Educator

Problem 14

Enzyme A catalyzes the reaction $S \rightarrow P$ and has a $K_{M}$ of $50 \mu \mathrm{M}$ and $\mathrm{a} V_{\max }$ of $100 \mathrm{nM} \cdot \mathrm{s}^{-1} .$ Enzyme $\mathrm{B}$ catalyzes the reaction $\mathrm{S} \rightarrow \mathrm{Q}$ and has
a $K_{M}$ of $5 \mathrm{mM}$ and a $V_{\max }$ of $120 \mathrm{nM} \cdot \mathrm{s}^{-1} .$ When $100 \mu \mathrm{M}$ of $\mathrm{S}$ is added to a mixture containing equivalent amounts of enzymes $A$ and $B$, after 1 minute which reaction product will be more abundant: $\mathrm{P}$ or $\mathrm{Q}$ ?

Rabeya Zahid

Numerade Educator

Problem 15

In a bisubstrate reaction, a small amount of the first product $P$ is isotopically labeled (P*) and added to the enzyme and the first substrate A. No $\mathrm{B}$ or $\mathrm{Q}$ is present. Will $\mathrm{A}(=\mathrm{P}-\mathrm{X})$ become isotopically labeled $\left(\mathrm{A}^{*}\right)$ if the reaction follows a Ping Pong mechanism?

Niamat Khuda

Numerade Educator

Problem 16

In a bisubstrate reaction, a small amount of the first product $P$ is isotopically labeled (P*) and added to the enzyme and the first substrate A. No B or $Q$ is present. Will $A(=P-X)$ become isotopically labeled $\left(A^{*}\right)$ if the reaction follows a Sequential mechanism?

Niamat Khuda

Numerade Educator

Problem 17

How would diisopropylphosphofluoridate (DIPF; Section $11-5 \mathrm{A}$ ) affect the apparent $K_{M}$ and $V_{\max }$ of a sample of chymotrypsin?

Rabeya Zahid

Numerade Educator

Problem 18

Molecule A is the substrate for enzyme X. Which is more likely to be a competitive inhibitor of enzyme X: molecule B or molecule C? Explain.

Jennifer Stoner

Jennifer Stoner

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Problem 19

Determine the type of inhibition of an enzymatic reaction from the following data collected in the presence and absence of the inhibitor. $$\begin{array}{ccc}
\hline & & v_{0} \text { with I present } \\
{[\mathrm{S}](\mathrm{mM})} & v_{0}\left(\mathrm{mM} \cdot \min ^{-1}\right) & \left(\mathrm{m} \mathrm{M} \cdot \min ^{-1}\right) \\
\hline 1 & 1.3 & 0.8 \\
\hline 2 & 2.0 & 1.2 \\
\hline 4 & 2.8 & 1.7 \\
\hline 8 & 3.6 & 2.2 \\
\hline 12 & 4.0 & 2.4 \\
\hline
\end{array}$$

Rabeya Zahid

Numerade Educator

Problem 20

Estimate $K_{\mathrm{I}}$ for a competitive inhibitor when $[\mathrm{I}]=5 \mathrm{mM}$ gives an apparent value of $K_{M}$ that is three times the $K_{M}$ for the uninhibited reaction.

Hailey Tomashek

Hailey Tomashek

Numerade Educator

Problem 21

Is it necessary for measurements of reaction velocity to be expressed in units of concentration per time $\left(\mathrm{M} \cdot \mathrm{s}^{-1}, \text {for example }\right)$ to calculate an enzyme's $K_{M} ?$

Rabeya Zahid

Numerade Educator

Problem 22

Is it necessary to know [E], to determine
(a) $K_{M},$ (b) $V_{\max },$ or $(\mathrm{c}) k_{\mathrm{cat}} ?$

Rabeya Zahid

Numerade Educator

Problem 23

You are trying to determine the $K_{M}$ for an enzyme. Due to a lab mishap, you have only two usable data points:
$$\begin{array}{cc}
\hline \text { Substrate } & \text { Reaction velocity } \\
\text { concentration }(\boldsymbol{\mu} \mathbf{M}) & \left(\boldsymbol{\mu} \mathbf{M} \cdot \mathbf{s}^{-1}\right) \\
\hline 1 & 5 \\
\hline 100 & 50 \\
\hline
\end{array}$$
Use these data to calculate an approximate value for $K_{M}$. Is this value likely to be an overestimate or an underestimate of the true value? Explain.

Hailey Tomashek

Hailey Tomashek

Numerade Educator

Problem 24

You are attempting to determine $K_{M}$ by measuring the reaction velocity at different substrate concentrations, but you do not realize that the substrate tends to precipitate under the experimental conditions you have chosen. How would this affect your measurement of $K_{M} ?$

Rabeya Zahid

Numerade Educator

Problem 25

You are constructing a velocity versus [substrate] curve for an enzyme whose $K_{M}$ is believed to be about $2 \mu$ M. The enzyme concentration is $200 \mathrm{nM}$ and the substrate concentrations range from $0.1 \mu \mathrm{M}$ to $10 \mu \mathrm{M}$ What is wrong with this experimental setup and how could you fix it?

Rabeya Zahid

Numerade Educator

Problem 26

Enzyme X and enzyme Y catalyze the same reaction and exhibit the $\nu_{0}$ versus [S] curves shown below. Which enzyme is more efficient at low $[\mathrm{S}] ?$ Which is more efficient at high $[\mathrm{S}] ?$

Rabeya Zahid

Numerade Educator

Problem 27

. Based on some preliminary measurements, you suspect that a sample of enzyme contains an irreversible enzyme inhibitor. You decide to dilute the sample 100 -fold and remeasure the enzyme's activity. What would your results show if an irreversible inhibitor is present?

Rabeya Zahid

Numerade Educator

Problem 28

For the same enzyme sample described in Problem 27, what would your results show if a reversible inhibitor is present?

Rabeya Zahid

Numerade Educator

Problem 29

For an enzyme-catalyzed reaction, the presence of 5 nM of a reversible inhibitor yields a $V_{\max }$ value that is $80 \%$ of the value in the absence of the inhibitor. The $K_{M}$ value is unchanged.
(a) What type of inhibition is likely occurring?
(b) What proportion of the enzyme molecules have bound inhibitor?
(c) Calculate the inhibition constant.

Rabeya Zahid

Numerade Educator

Problem 30

Sphingosine-1-phosphate (S1P) is important for cell survival. The synthesis of S1P from sphingosine and ATP is catalyzed by the enzyme sphingosine kinase. An understanding of the kinetics of the sphingosine kinase reaction may be important in the development of drugs to treat cancer. The velocity of the sphingosine kinase reaction was measured in the presence and absence of threo-sphingosine, a stereoisomer of sphingosine that inhibits the enzyme. The results are shown below.
$$\begin{array}{ccc}
\hline \begin{array}{c}
\text { Sphingosine] } \\
\text { ( } \mathbf{\mu} \mathbf{M} \text { ) }
\end{array} & \begin{array}{c}
\boldsymbol{v}_{\mathbf{o}}\left(\mathbf{m g} \cdot \mathbf{m i n}^{-\mathbf{1}}\right) \\
\text { (no inhibitor) }
\end{array} & \begin{array}{c}
\boldsymbol{v}_{\mathbf{o}}\left(\mathbf{m g} \cdot \mathbf{m i n}^{-1} \mathbf{)}\right. \\
\text { (with } \text {threo} \text { -sphingosine) }
\end{array} \\
\hline 2.5 & 32.3 & 8.5 \\
\hline 3.5 & 40 & 11.5 \\
\hline 5 & 50.8 & 14.6 \\
\hline 10 & 72 & 25.4 \\
\hline 20 & 87.7 & 43.9 \\
\hline 50 & 115.4 & 70.8 \\
\hline
\end{array}$$
Construct a Lineweaver-Burk plot to answer the following questions:
(a) What are the apparent $K_{M}$ and $V_{\max }$ values in the presence and absence of the inhibitor?
(b) What kind of an inhibitor is threo -sphingosine? Explain.

Rabeya Zahid

Numerade Educator

Problem 31

Ethanol in the body is oxidized to acetaldehyde $\left(\mathrm{CH}_{3} \mathrm{CHO}\right)$ by liver alcohol dehydrogenase (LADH). Other alcohols are also oxidized by LADH. For example, methanol $\mathrm{CH}_{3} \mathrm{OH}$ ), which is mildly intoxicating, is oxidized by LADH to the quite toxic product formaldehyde $\left(\mathrm{CH}_{2} \mathrm{O}\right)$. The toxic effects of ingesting methanol (a component of many commercial solvents) can be reduced by administering ethanol. The ethanol acts as a competitive inhibitor of the methanol by displacing it from LADH. This provides sufficient time for the methanol to be harmlessly excreted by the kidneys. If an individual has ingested $100 \mathrm{mL}$ of methanol (a lethal dose $),$ how much 100 proof whiskey ( $50 \%$ ethanol by volume) must he imbibe to reduce the activity of his LADH toward methanol to $5 \%$ of its original value? The adult human body contains $\sim 40 \mathrm{L}$ of aqueous fluids throughout which ingested alcohols are rapidly and uniformly mixed. The densities of ethanol and methanol are both $0.79 \mathrm{g} \cdot \mathrm{cm}^{-3}$. Assume the $K_{M}$ values of LADH for ethanol and methanol to be $1.0 \times 10^{-3} \mathrm{M}$ and $1.0 \times 10^{-2} \mathrm{M},$ respectively, and that $K_{\mathrm{I}}=K_{M}$ for ethanol

Hailey Tomashek

Hailey Tomashek

Numerade Educator

Problem 32

Why are uncompetitive and mixed inhibitors generally considered to be more effective in vivo than competitive inhibitors?

Rabeya Zahid

Numerade Educator