Lactose is a disaccharide sugar present in milk. Lactose is composed of two monosaccharides, galactose and glucose, that are joined together by a $\beta$ -glycosidic bond. The $\beta$ -glycosidic bond forms between the hydroxyl group on $\mathrm{C}-1$ of galactose and $\mathrm{C}-4$ of glucose.
When lactose is digested, the glycosidic bond between galactose and glucose is hydrolyzed. The enzyme responsible for hydrolyzing lactose is lactase, which is found in the small intestine. Millions of people lack sufficient levels of lactase, and as a result, they experience lactose intolerance. If lactose is not hydrolyzed, it remains in the intestines. Bacteria in the gut ferment the lactose, causing many unpleasant symptoms such as indigestion, cramping, and gas. Fortunately, commercial preparations can enable lactose-intolerant individuals to consume and digest milk products without discomfort.
Use the information provided to answer the following questions:
a. Draw the structure of lactose. (The structures of galactose and glucose are shown on page 1045 with their carbon numbering scheme.
b. Lactase enzyme activity, like most enzymes, is sensitive to $\mathrm{pH} .$ The figure above illustrates how lactase activity is affected by the $\mathrm{pH}$ of a solution. Based on the data in Figure a, what can you conclude about the $\mathrm{pH}$ of the small intestine?
c. A glutamic acid in the active site of lactase is suspected to be involved in the catalytic mechanism. Draw the structure of the glutamic acid side chain in the ionization state that likely exists when lactase is most catalytically active.