Problem 16
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 \(\mathrm{CO}_{2}\) : $$ \mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \rightleftharpoons \mathrm{H}_{2} \mathrm{CO}_{3} $$ 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 \(\min ^{-1}\) )?
Problem 18
Kinetic Inhibition Patterns Indicate how the observed \(K_{\mathrm{m}}\) of an enzyme would change in the presence of inhibitors having the given effect on \(a\) and \(\alpha^{\prime}\) : a. \(\alpha>\alpha^{\prime} ; \alpha^{\prime}=1.0\) b. \(\alpha^{\prime}>\alpha\) c. \(\alpha=\alpha^{\prime} ; \alpha^{\prime}>1.0\) d. \(\alpha=\alpha^{\prime} ; \alpha^{\prime}=1.0\)
Problem 20
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: $$ \text { Enz-SH }+\mathrm{Ag}^{+} \rightarrow \text { Enz-S-Ag }+\mathrm{H}^{+} $$ The affinity of \(\mathrm{Ag}^{+}\)for sulfhydryl groups is so great that \(\mathrm{Ag}^{+}\) can be used to titrate - SH groups quantitatively. An investigator added just enough \(\mathrm{AgNO}_{3}\) to completely inactivate a \(10.0 \mathrm{~mL}\) solution containing \(1.0 \mathrm{mg} / \mathrm{mL}\) 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?
Problem 21
Dlinical 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 \((\mathrm{pH} .0)\) : 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 prostatic acid phosphatase in human blood serum?
Problem 23
The Effects of Reversible Inhibitors The MichaelisMenten rate equation for reversible mixed inhibition is written as $$ V_{0}=\frac{V_{\max }[\mathrm{S}]}{\alpha K_{\mathrm{m}}+\alpha^{\prime}[\mathrm{S}]} $$ Apparent, or observed, \(K_{\mathrm{m}}\) is equivalent to the [S] at which $$ V_{0}=\frac{V_{\max }}{2 \alpha^{\prime}} $$ Derive an expression for the effect of a reversible inhibitor on apparent \(K_{\mathrm{m}}\) from the previous equation.
Problem 24
Perturbed \(\mathbf{p} \boldsymbol{K}_{\mathrm{a}}\) Values in Enzyme Active Sites Alanine racemase is a bacterial enzyme that converts \(\mathrm{L}\)-alanine to \(\mathrm{D}\) alanine, which is needed in small amounts to synthesize the bacterial cell wall. The active site of alanine racemase includes a Tyr residue with a p \(K_{\mathrm{a}}\) value of \(7.2\). The \(\mathrm{p} K_{\mathrm{a}}\) of free tyrosine is 10 . The altered \(\mathrm{p} K_{\mathrm{a}}\) of this residue is due largely to the presence of a nearby charged amino acid residue. Which amino acid(s) could lower the \(\mathrm{p} K_{\mathrm{a}}\) of the neighboring Tyr residue? Explain your reasoning.
