Problem 1
Differentiate between a first-order rate constant and a second-order rate constant.
Problem 2
What is a pseudo-first-order reaction?
Problem 4
What is the biochemical advantage of having a \(K_{\mathrm{M}}\) approximately equal to the substrate concentration normally available to an enzyme?
Problem 7
Penicillin is hydrolyzed and thereby rendered inactive by penicillinase (also known as \(\beta\) -lactamase), an enzyme present in some resistant bacteria. The mass of this enzyme in Staphylococcus aureus is \(29.6 \mathrm{kDa}\). The amount of penicillin hydrolyzed in 1 minute in a \(10-\mathrm{ml}\) solution containing \(10^{-9} \mathrm{g}\) of purified penicillinase was measured as a function of the concentration of penicillin. Assume that the concentration of penicillin does not change appreciably during the assay. $$\begin{array}{cc}\text { [Penicillin] } \mu \mathrm{M} & \text { Amount hydrolyzed (nanomoles) } \\\\\hline 1 & 0.11 \\\3 & 0.25 \\\5 & 0.34 \\\10 & 0.45 \\\30 & 0.58 \\\50 & 0.61 \\ \hline\end{array}$$ (a) Plot \(V_{0}\) versus \([\mathrm{S}]\) and \(1 / V_{0}\) versus \(1 /[\mathrm{S}]\) for these data. Does penicillinase appear to obey Michaelis- Menten kinetics? If so, what is the value of \(K_{\mathrm{M}} ?\) (b) What is the value of \(V_{\max } ?\) (c) What is the turnover number of penicillinase under these experimental conditions? Assume one active site per enzyme molecule.
Problem 8
The hydrolysis of pyrophosphate to orthophosphate is important in driving forward biosynthetic reactions such as the synthesis of DNA. This hydrolytic reaction is catalyzed in Escherichia coli by a pyrophosphatase that has a mass of \(120 \mathrm{kDa}\) and consists of six identical subunits. For this enzyme, a unit of activity is defined as the amount of enzyme that hydrolyzes \(10 \mu \mathrm{mol}\) of pyrophosphate in 15 minutes at \(37^{\circ} \mathrm{C}\) under standard assay conditions. The purified enzyme has a \(V_{\max }\) of 2800 units per milligram of enzyme. (a) How many moles of substrate are hydrolyzed per second per milligram of enzyme when the substrate concentration is much greater than \(K_{M} ?\) (b) How many moles of active sites are there in \(1 \mathrm{mg}\) of enzyme? Assume that each subunit has one active site. (c) What is the turnover number of the enzyme? Compare this value with others mentioned in this chapter.
Problem 13
Draw a double-reciprocal plot for a typical Michaelis-Menten enzyme and an allosteric enzyme that have the same $V_{\max },
Problem 15
What is feedback inhibition? Why is it a useful property?
Problem 16
An allosteric enzyme that follows the concerted mechanism has a T/R ratio of 300 in the absence of substrate. Suppose that a mutation reversed the ratio. How would this mutation affect the relation between the velocity of the reaction and the substrate concentration?
Problem 17
Differentiate between homotropic and heterotropic effectors.
Problem 19
You have isolated a dimeric enzyme that contains two identical active sites. The binding of substrate to one active site decreases the substrate affinity of the other active site. Can the concerted model account for this negative cooperativity?
