CHEM 3653: AC 4&5 Problems

Only questions 1-4 AC4

An exponentially growing population of some organism is determined to be 3.70 x 10⁴. This population grew by 239% over the preceding 10 years. Given this information, what was the population of this organism 10 years ago?

[This type of problem will help us when we study regulatory strategies of biochemical pathways later in the semester. In particular, we will want to know how the flux through a pathway changes in response to allosteric effectors that bind to and alter the activities of key enzymes involved in the pathway (or its “reverse” analog).]

1.09 × 10⁴

Given the information in the previous problem, what is the doubling time of the population (to the nearest tenth of a year)? Assume that the percent growth per year is a net percent growth and that it remains constant (i.e., provides exponential growth).

5.7 years

You are performing an assay that requires [y-³²P]-ATP (ATP with radioactive phosphorus at the y-phosphoryl group). The half-life of this isotope is 14.3 days. Approximately what percent of the initial radioactivity remains in a sample of [y-³²P]-ATP that is 43 days old?

12.5%

Assuming that the reaction shown below proceeds by an elementary step, what are the units of the rate constant k1? What is the reaction order? What is the rate equation (or expression) for this reaction? How do the instantaneous changes in the concentration of A (as a function of time) relate to the instantaneous changes in the concentration of B (also as a function of time)?

First-order reaction, units of k₁ = reciprocal time (e.g., s⁻¹)

Assuming that the reaction shown below proceeds by an elementary step (i.e., one A molecule collides with one B molecule to make one C molecule), what are the units of the rate constant k1? What is the reaction order with respect to A? With respect to B? Overall? What is the rate equation (or expression) for this reaction? How do the instantaneous changes in the concentration of A (as a function of time) relate to the instantaneous changes in the concentration of B (also as a function of time) and to the instantaneous changes in the concentration of C (also as a function of time)?

The reaction is first-order with respect to A and B, second order overall, and k₁ has units of M⁻¹s⁻¹; the rate equation is Rate = k₁[A][B], and A and B decrease at the same rate that C increases.

Assuming that the reaction shown below proceeds by an elementary step (i.e., one A productively collides with another A to make one B), what are the units of the rate constant k1? What is the reaction order with respect to A? Overall? What is the rate equation (or expression) for this reaction? How do the instantaneous changes in the concentration of A (as a function of time) relate to the instantaneous changes in the concentration of B (also as a function of time)?

The reaction is second-order with respect to A and overall, k₁ has units of M⁻¹s⁻¹, the rate equation is Rate = k₁[A]², and A decreases twice as fast as B increases.

Solutions of chymotrypsin prepared for experimental purposes are stored in a dilute solution of hydrochloric acid as a “preservative.” Explain.

HCl keeps His57 protonated, stopping it from activating Ser195 and preventing chymotrypsin from working.

Sulfhydryl groups can react with the alkylating reagent N-ethylmaleimide (NEM). When NEM is added to a solution of creatine kinase, Cys 278 is alkylated, but no other Cys residues in the protein are modified. What can you infer about the role of the Cys 278 residue based on this information?

Cys278 is unusually reactive and is likely involved in the enzyme's active site or catalysis.

Draw succinate and then draw the oxidized product of the reaction catalyzed by succinate dehydrogenase. (This is good practice for later in the semester.) To which class of enzymes does succinate dehydrogenase belong? Note that when we study the Krebs cycle, you will need to know the structure of succinate and the structure of the product of the succinate dehydrogenase reaction. So you're off to a good start learning this pathway. Do you see how thoughtful I am?

Malate dehydrogenase catalyzes a reaction in which C2 of L-malate is oxidized. Draw the structure of the product. To which class of enzymes does malate dehydrogenase belong? When we study the Krebs cycle, you will need to know the structure of L-malate and the product of the malate dehydrogenase reaction. So you're off to a good start on learning this pathway now. Again, I am so thoughtful.

An enzyme has a k_cat of 70 s⁻¹ and a Km of 5 x 10⁻⁶ M. Has this enzyme attained "catalytic perfection"?

No. Catalytic efficiency = 1.4 × 10⁷ M⁻¹s⁻¹, which is below catalytic perfection.

Consider an enzyme that obeys Michaelis-Menten kinetics. What fraction of V_max (expressed as a percent) would be obtained when the substrate concentration was one-third K_m?

25%

At what substrate concentration would an enzyme with a V_max of 50.0 µM min−1 and a Km of 0.0050 M operate at one-fifth of its maximum rate? Report your answer to three figures in terms of mM.

1.25 mM

An enzyme-catalyzed reaction was carried out with the substrate concentration initially a thousand times greater than the Km for that substrate. After 12 minutes, 1% of the substrate had been converted to product, and the reaction mixture contained 18 µmol of product. If, in a separate experiment, one-fourth as much enzyme and twice as much substrate were combined, how long (in minutes) would it take to form the same amount (18 µmol) of product?

48 mins

Consider the Michaelis-Menten equation. If the slowest, rate-limiting step in the enzyme-catalyzed reaction is k₂, then K_m approaches:

Km ≈ k₃/k₁

For a Michaelis-Menten reaction, k₁ = 8 x 10⁶ M⁻¹ s⁻¹; k₂ = 4 x 10³ s−¹; and k₃ = 9 x 10⁴ s⁻¹. Given this information, what is the value of Km, the Michaelis-Menten constant? Report your answer to the nearest 1 µM. Use the convention followed in class to characterize rate constants for forward and reverse steps in an enzyme-catalyzed reaction.

11,750 µM

For a Michaelis-Menten reaction, k₁ = 8 x 10⁶ M⁻¹ s−1; k₂ = 4 x 10³ s⁻¹; and k₃ = 9 x 10⁴ s⁻¹. Given this information, what is Kd, the dissociation constant for the enzyme-substrate complex? Report your answer to the nearest 1 µM.

500 µM

Given the information in the previous two problems, decide whether substrate binding for the enzyme in question approaches equilibrium (called rapid equilibrium by enzyme kinetics folks) or behaves more like a steady-state system. Hint: rapid equilibrium happens when k₂ >> k₃, and steady state occurs when k₃ > k₂ or even just comparable to k₂)

Steady-state system

Enzymes A, B, and C are isozymes, meaning they are different enzymes that catalyze the same reaction. When enzymes A and B are added to a reaction vessel containing a saturating amount of substrate S, it takes 2 minutes to produce the desired amount of product P. When enzymes A and C are added to a reaction vessel containing the same amount of S, it takes 3 minutes to produce the desired amount of P. When enzymes B and C are added to a reaction vessel containing the same amount of S, it takes 4 minutes to produce the desired amount of P. When enzymes A, B, and C are added to a reaction vessel that contains the same amount of S, how long will it take to produce the desired amount of P? Assume that enzymes A, B, and C all work at close to their respective V_max values, that the amounts of each enzyme used in the various experiments are consistent, that the amount of S is saturating (and remains so) for all enzymes in all combinations, and that the desired amount of product is the same in each case. Enter your answer in terms of minutes.

1.846 mins

The activation barrier for an uncatalyzed reaction is estimated to be 13 kcal/mol. The activation barrier for the catalyzed reaction is estimated to be 9 kcal/mol. How many times faster is the catalyzed rate versus the uncatalyzed rate? In other words, by what factor/coefficient do you have to multiply the uncatalyzed rate to equal the catalyzed rate? R is 1.987 cal/K mol and the temperature is 298 K.

859 times faster

An enzyme is known to enhance the rate of a reaction by a factor of 1 x 10¹⁰. If a given quantity of the enzyme catalyzes the conversion of a given quantity of substrate in 10.0 minutes, how long (in years) would it take for the same amount of the substrate to be converted to product under the same conditions but in the absence of the enzyme? Assume sterile conditions such that bacteria cannot affect the time.

190,259 years

Consider the two reactions shown below. Write what K_eq equals for each reaction in terms of the concentration(s) of products and reactants. Thought question: Why does the presence of a catalyst not affect K_eq?

S ⇌ P E + S ⇌ E + P

Both reactions have the same Keq because an enzyme does not change equilibrium.

The rate of an enzyme-catalyzed reaction is measured at several temperatures, generating the curve shown below. Explain why the enzyme activity increases with temperature and then drops off sharply.

Increasing temperature initially increases molecular movement and enzyme activity. At very high temperatures, the enzyme denatures and stops working.

Draw pairs of free energy diagrams that show the differences between the following reactions:

A fast reaction vs. a slow reaction

Draw pairs of free energy diagrams that show the differences between the following reactions:

A one-step reaction vs. a two-step reaction.

Draw pairs of free energy diagrams that show the differences between the following reactions:

An endergonic reaction vs. an exergonic reaction.

An enzyme has a V_max value of 540 nM s⁻¹ and a V_max/K_m value of 0.48 s⁻¹. When a series of experiments with an inhibitor is run the apparent value of V_max/K_m decreases to 0.08 s⁻¹ and the apparent V_max value decreases to 90 nM s⁻¹. Given this information, calculate the value of alpha (to one figure) for this inhibitor.

6

An enzyme has a V_max value of 540 nM s⁻¹ and a V_max/K_m value of 0.48 s⁻¹. When a series of experiments with an inhibitor is run the apparent value of V_max/K_m decreases to 0.08 s⁻¹ and the apparent V_max value decreases to 90 nM s⁻¹. Given this information, calculate the value of alpha’ (to one figure) for this inhibitor.

6

An enzyme has a V_max value of 540 nM s⁻¹ and a V_max/K_m value of 0.48 s⁻¹. When a series of experiments with an inhibitor is run the apparent value of V_max/K_m decreases to 0.08 s⁻¹ and the apparent V_max value decreases to 90 nM s⁻¹. Given this information, what type of inhibition is occurring? Write as your answer the best, most complete description of

the type of inhibition that is occurring.

Pure noncompetitive inhibition

The benefit of measuring the initial rate of a reaction v (or V_o) is that at the beginning of a reaction:

changes in [S] are negligible, so [S] can be treated as a constant.

An experiment is run to determine an enzyme's V_max and K_m. A second experiment is run, but this time with double the enzyme concentration. However, the data from the second experiment still appear to obey the steady-state assumption. What will the K_m value be in the second experiment relative to that in the first experiment?

None of the above - Km stays the same

An experiment is run to determine an enzyme's V_max and K_m. A second experiment is run, but this time with double the enzyme concentration. However, the data from the second experiment still appear to obey the steady-state assumption. What will the V_max value be in the second experiment relative to the first?

It will be double the original value

An experiment is run to determine an enzyme's k_cat and K_m. A second experiment is run, but this time with double the enzyme concentration. However, the data from the second experiment still appear to obey the steady-state assumption. What will the value of k_cat be in the second experiment relative to the value determined in the first experiment?

None of the above — kcat stays the same

A biochemist obtains the following data for an enzyme known to follow Michaelis-Menten kinetics. Given these data, what is a reasonable estimate of this enzyme's V_max? Report your answer in terms of µmol/min to the nearest whole number.

70-75 µmol/min

A biochemist obtains the set of data shown above for an enzyme that is known to follow Michaelis-Menten kinetics. Given these data, what is a reasonable estimate of K_m for this enzyme? Report your answer in terms of µM to the nearest one significant figure.

0.8 µM

Consider the adjacent kinetic mechanism. If one conducted a series of enzymatic assays at variable [A], fixed and saturating [B], and at different but fixed levels of [Q], what kind of inhibition would one likely see?

Competitive

An experimenter performs two sets of enzyme kinetics experiments. One set of experiments, when plotted as a double-reciprocal plot, yielded a y-intercept of 0.043 µM^-1 min and an x-intercept of -20.0 mM^-1. A second set of experiments, when similarly plotted, yielded a y-intercept of 0.043 µM^-1 min and an x-intercept of -6.67 mM^-1. The second set of experiments contained 84 nM of a competitive inhibitor. Given these data, what is the K_i (in nM to two figures) for this inhibitor? Hint: If you do not recall what the x-intercept represents, you can write the double-reciprocal equation and set 1/v equal to zero. Also, for this problem, you can assume that the enzyme exhibits Michaelis-Menten kinetics and that the estimates for V_max and K_m that are obtained from a Lineweaver-Burke (i.e., double-reciprocal) plot are satisfactory. (Recall that I advocated in class for the use of nonlinear fitting algorithms.)

42 nM

An enzyme is added to an aqueous solution of ATP, DNA, albumen, fat, and glycogen; the reaction mixture is incubated for 10 minutes. If an analysis of the mixture reveals the presence of all of the above compounds plus glucose, it can be concluded that the enzyme hydrolyzed some of the

Glycogen

Starch, cellulose and glycogen are all

Polymers of glucose

Which chiefly stimulates action of the respiratory center?

carbon dioxide in the blood

What cellular organelles would you expect to be absent from fungi?

chloroplasts

Which is the smallest organelle in the cell?

ribosome

Each of the following cell organelles have a membranous structure EXCEPT one. Which one is the EXCEPTION?

Centrioles

A 49-gram sample of sulfuric acid, H2 SO4 (98 g/mol) contains

2 moles of O atoms.

ATP inhibits phosphofructokinase even though ATP also is a substrate for the enzyme. Which of the following types of inhibition BEST explains this phenomenon?

Allosteric

The effectiveness of allosteric effectors in regulating metabolic pathways is based on their ability to ____.

change the conformation of the target enzyme(s).

Considering the adjacent scheme, which enzyme in the anabolic pathway that forms A₆ is likely to be allosterically regulated?

E₃

The data in the adjacent table were collected for an enzyme that is known to follow Michaelis-Menten kinetics. Given this information, which of the following best estimates the K_m for this enzyme?

2 × 10⁻⁵ mM

An enzyme has a V_max of 50 µmol product formed (min x mg protein)^-1 and a K_m of 10 µmol for the substrate. When a reaction mixture contains the enzyme and 5 µM substrate, which of the following percentages of the maximum velocity will be closest to the initial reaction rate?

33%

Hydrolysis

Cleavage of a peptide bond

Group transfer

Phosphorylation of a serine residue on a protein

Oxidation

Formation of a disulfide bond between tow cysteines

Reduction

Conversion of pyruvate to L-lactate

The following question is offered in anticipation of our chapters on metabolism:

Assuming that the average weight of an adult is 180 lbs, how many molecules of oxygen arrive each second at a mitochondrion of an average active person?

Assume that oxygen consumption is 43 mL per minute per kilogram of body weight, adults have about 1.0 x 10¹² cells, and there are 900 mitochondria per cell. Report your answer to seven figures.

1,749,427 O₂ molecules/mitochondrion/second

Glycine can be drawn with a net charge of zero in two forms, but at its pI, it is predominantly zwitterionic. Why is glycine predominantly zwitterionic rather than completely uncharged at its pI? What percent of glycine molecules would be in the completely uncharged form at the pI?

3.715 × 10^-8

Explain why gelatin, which is mostly collagen, is nutritionally inferior to other types of protein.

Has multiple G-P-HyP repeats; lacks many essential amino acids that we cannot make; and must get them from our diet.

Why is gelatin (collagen) nutritionally inferior to other proteins?

It is an incomplete protein because it lacks tryptophan, an essential amino acid

What determines the nutritional quality of a protein?

Its essential amino acid composition and digestibility

Radioactively labeled [¹⁴C]-proline is incorporated into collagen in cultured fibroblasts. The radioactivity is detected in the collagen protein. But collagen synthesized in the presence of [¹⁴C]-hydroxyproline is not radiolabeled. Explain why.

Proline is converted to hydroxyproline post-translationally; thus, [¹⁴C]-hydroxyproline would not be incorporated into collagen.