Chapter Questions
Consider the nonenzymatic elementary reaction $A \rightarrow B$. When the concentration of $A$ 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?
If there are 10 \mumol of the radioactive isotope $^{32} \mathrm{P}$ (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?
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 $10 \mathrm{mM} ?$
For each reaction below, determine whether the reaction is first order or second order and calculate the rate constant.$$\begin{array}{ccc}\hline & \text { Reaction A } & \text { Reaction B } \\\text { Time (s) } & \text { reactant (mM) } & \text { reactant (mM) } \\\hline 0 & 6.2 & 5.4 \\1 & 3.1 & 4.6 \\2 & 2.1 & 3.9 \\3 & 1.6 & 3.2 \\4 & 1.3 & 2.7 \\5 & 1.1 & 2.3 \\\hline\end{array}$$
For an enzymatic reaction, draw curves that show the appropriate relationships between the variables in each plot below.
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.
At what concentration of $\mathrm{S}\left(\text { expressed as a multiple of } K_{M}\right)$ will $v_{\mathrm{o}}=0.95 V_{\mathrm{max}} ?$
Identify the enzymes in Table $12-1$ whose catalytic efficiencies are near the diffusion-controlled limit.
Explain why each of the following data sets from a Lineweaver-Burk plot are not individually ideal for deter$\operatorname{mining} K_{M}$ for an enzyme-catalyzed reaction that follows Michaelis-Menten kinetics.
Calculate $K_{M}$ and $V_{\max }$ from the following data:$$\begin{array}{cc}\hline \text { [S] }(\mu \mathbf{M}) & v_{\mathbf{o}}\left(\mathbf{m M} \cdot \mathbf{s}^{-\mathbf{1}}\right) \\\hline 0.1 & 0.34 \\0.2 & 0.53 \\0.4 & 0.74 \\0.8 & 0.91 \\1.6 & 1.04 \\\hline\end{array}$$
You are trying to determine the $K_{M}$ for an enzyme. Due to a lab mishap, you have only two usable data points:$$\begin{array}{cc}\hline \text { Substrate } & \text { Reaction } \\\text { concentration ( } \boldsymbol{\mu} \mathbf{M} \text { ) } & \text { velocity }\left(\boldsymbol{\mu} \mathbf{M} \cdot \mathbf{s}^{-\mathbf{1}} \mathbf{~}\right) \\\hline 1 & 5 \\100 & 50 \\\hline\end{array}$$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.
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 $K_{M} ?$
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?
Is it necessary for measurements of reaction velocity to be expressed in units of concentration per time ( $\mathrm{M} \cdot \mathrm{s}^{-1},$ for example) in order to calculate an enzyme's $K_{M} ?$
Is it necessary to know $[\mathrm{E}]_{\mathrm{T}}$ in order to determine(a) $K_{M}$(b) $V_{\max },$ or $(\mathrm{c}) k_{\mathrm{cat}} ?$
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 $V_{\max } ?$
Enzyme A catalyzes the reaction $\mathrm{S} \rightarrow \mathrm{P}$ and has a $K_{M}$ of $50 \mu \mathrm{M}$ and a $V_{\max }$ of $100 \mathrm{nM} \cdot \mathrm{s}^{-1} .$ Enzyme $\mathrm{B}$ catalyzes the reaction $S \rightarrow Q$ 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 one minute which reaction product will be more abundant:$P$ or $Q ?$
In a bisubstrate reaction, a small amount of the first product $\mathrm{P}$ 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 (A*) if the reaction follows (a) a Ping Pong mechanism or (b) a Sequential mechanism?
Determine the type of inhibition of an enzymatic reaction from the following data collected in the presence and absence of the inhibitor.
Estimate $K_{1}$ 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.
For an enzyme-catalyzed reaction, the presence of $5 \mathrm{nM}$ 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.
How would diisopropylphosphofluoridate (DIPF; Section 11-5A) affect the apparent $K_{M}$ and $V_{\max }$ of a sample of chymotrypsin?
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 the inhibitor in the sample is (a) irreversible or (b) reversible?
Enzyme $\mathrm{X}$ and enzyme $\mathrm{Y}$ catalyze the same reaction and exhibit the $v_{\mathrm{o}}$ versus [S] curves shown below. Which enzyme is more efficient at low [S]? Which is more efficient at high [S]?
Sphingosine-1-phosphate (SPP) is important for cell survival. The synthesis of SPP 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. 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.