## Problems

Some problems related to the contents of the chapter follow. (In solving end-of-chapter problems, you may wish to refer to the tables on the inside of the back cover.) Each problem has a title for easy reference and discussion.

### 1. The Size of Cells and Their Components

(a) If you were to magnify a cell 10,000 fold (typical of the magnification achieved using an electron microscope), how big would it appear? Assume you are viewing a "typical" eukaryotic cell with a cellular diameter of 50 ^m.

(b) If this cell were a muscle cell (myocyte), how many molecules of actin could it hold? (Assume the cell is spherical and no other cellular components are present; actin molecules are spherical, with a diameter of 3.6 nm. The volume of a sphere is 4/3 kt3.)

(c) If this were a liver cell (hepatocyte) of the same dimensions, how many mitochondria could it hold? (Assume the cell is spherical; no other cellular components are present; and the mitochondria are spherical, with a diameter of 1.5 ^m.)

(d) Glucose is the major energy-yielding nutrient for most cells. Assuming a cellular concentration of 1 mM, calculate how many molecules of glucose would be present in our hypothetical (and spherical) eukaryotic cell. (Avogadro's number, the number of molecules in 1 mol of a nonionized substance, is 6.02 X 1023.)

(e) Hexokinase is an important enzyme in the metabolism of glucose. If the concentration of hexokinase in our eukaryotic cell is 20 ^m, how many glucose molecules are present per hexokinase molecule?

2. Components of E. coli E. coli cells are rod-shaped, about 2 ^m long and 0.8 ^m in diameter. The volume of a cylinder is wT2h, where h is the height of the cylinder.

(a) If the average density of E. coli (mostly water) is 1.1 X 103 g/L, what is the mass of a single cell?

(b) E. coli has a protective cell envelope 10 nm thick. What percentage of the total volume of the bacterium does the cell envelope occupy?

(c) E. coli is capable of growing and multiplying rapidly because it contains some 15,000 spherical ribosomes (diameter 18 nm), which carry out protein synthesis. What percentage of the cell volume do the ribosomes occupy?

3. Genetic Information in E. coli DNA The genetic information contained in DNA consists of a linear sequence of coding units, known as codons. Each codon is a specific sequence of three deoxyribonucleotides (three deoxyribonu-cleotide pairs in double-stranded DNA), and each codon codes for a single amino acid unit in a protein. The molecular weight of an E. coli DNA molecule is about 3.1 X 109 g/mol. The average molecular weight of a nucleotide pair is 660 g/mol, and each nucleotide pair contributes 0.34 nm to the length of DNA.

(a) Calculate the length of an E. coli DNA molecule. Compare the length of the DNA molecule with the cell dimensions (see Problem 2). How does the DNA molecule fit into the cell?

(b) Assume that the average protein in E. coli consists of a chain of 400 amino acids. What is the maximum number of proteins that can be coded by an E. coli DNA molecule?

4. The High Rate of Bacterial Metabolism Bacterial cells have a much higher rate of metabolism than animal cells. Under ideal conditions some bacteria double in size and divide every 20 min, whereas most animal cells under rapid growth conditions require 24 hours. The high rate of bacterial metabolism requires a high ratio of surface area to cell volume.

(a) Why does surface-to-volume ratio affect the maximum rate of metabolism?

(b) Calculate the surface-to-volume ratio for the spherical bacterium Neisseria gonorrhoeae (diameter 0.5 ^m), responsible for the disease gonorrhea. Compare it with the surface-to-volume ratio for a globular amoeba, a large eukaryotic cell (diameter 150 ^m). The surface area of a sphere is 4kt 2.

5. Fast Axonal Transport Neurons have long thin processes called axons, structures specialized for conducting signals throughout the organism's nervous system. Some ax-onal processes can be as long as 2 m—for example, the axons that originate in your spinal cord and terminate in the muscles of your toes. Small membrane-enclosed vesicles carrying materials essential to axonal function move along mi-crotubules of the cytoskeleton, from the cell body to the tips of the axons.

(a) If the average velocity of a vesicle is 1 ^m/s, how long does it take a vesicle to move from a cell body in the spinal cord to the axonal tip in the toes?

(b) Movement of large molecules by diffusion occurs relatively slowly in cells. (For example, hemoglobin diffuses at a rate of approximately 5 ^m/s.) However, the diffusion of sucrose in an aqueous solution occurs at a rate approaching that of fast cellular transport mechanisms (about 4 ^m/s). What are some advantages to a cell or an organism of fast, directed transport mechanisms, compared with diffusion alone?

6. Vitamin C: Is the Synthetic Vitamin as Good as the Natural One? A claim put forth by some purveyors of health foods is that vitamins obtained from natural sources are more healthful than those obtained by chemical synthesis. For example, pure l-ascorbic acid (vitamin C) extracted from rose hips is better than pure l-ascorbic acid manufactured in a chemical plant. Are the vitamins from the two sources different? Can the body distinguish a vitamin's source?

7. Identification of Functional Groups Figures 1-15 and 1-16 show some common functional groups of biomole-cules. Because the properties and biological activities of biomolecules are largely determined by their functional groups, it is important to be able to identify them. In each of the compounds below, circle and identify by name each functional group.

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