For all numerical problems, keep in mind that answers should be expressed with the correct number of significant figures. (In solving end-of-chapter problems, you may wish to refer to the tables on the inside of the back cover.) Brief solutions are provided in Appendix B; expanded solutions are published in the Absolute Ultimate Study Guide to Accompany Principles of Biochemistry.

• 1. The Size of Cells and Their Components A typical eukaryotic cell has a cellular diameter of 50 μm.

  1. If you used an electron microscope to magnify this cell 10,000-fold, how big would the cell appear?
  2. If this cell were a liver cell (hepatocyte) with the same cellular diameter, how many mitochondria could the cell contain? Assume the cell is spherical; that the cell contains no other cellular components; and that each mitochondrion is spherical, with a diameter of 1.5 μm. (The volume of a sphere is )
  3. Glucose is the major energy-yielding nutrient for most cells. Assuming a cellular concentration of 1 mm glucose (that is, 1 millimole/L), calculate how many molecules of glucose would be present in the spherical eukaryotic cell. (Avogadro’s number, the number of molecules in 1 mol of a nonionized substance, is )

• 2. Components of E. coli E. coli cells are rod-shaped, about 2 μm long, and 0.8 μm in diameter. E. coli has a protective envelope 10 nm thick. The volume of a cylinder is where h is the height of the cylinder.

  1. What percentage of the total volume of the bacterium does the cell envelope occupy?
  2. 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. The molecular weight of an E. coli DNA molecule is about 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. Calculate the length of an E. coli DNA molecule. Compare the length of the DNA molecule with the cell dimensions. Now, consider the photomicrograph showing the single DNA molecule of the bacterium E. coli leaking out of a disrupted cell (Fig. 1-31b). How does the DNA molecule fit into the cell?

• 3. Isolating Ribosomes through Differential Centrifugation Assume you have a crude lysate sample that you obtained from mechanically homogenizing E. coli cells. You centrifuged the supernatant from the sample at a medium speed (20,000 g) for 20 min, collected the supernatant, and then centrifuged the supernatant at high speed (80,000 g) for 1 h. What procedure should you follow to isolate the ribosomes from this sample?

• 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.

  1. How does the surface-to-volume ratio affect the maximum rate of metabolism?
  2. Calculate the surface-to-volume ratio for the spherical bacterium Neisseria gonorrhoeae (diameter 0.5 μm), responsible for the disease gonorrhea. The surface area of a sphere is
  3. How many times greater is the surface-to-volume ratio of Neisseria gonorrhoeae compared to that of a globular amoeba, a large eukaryotic cell (diameter 150 μm)?

• 5. Fast Axonal Transport Neurons have long thin processes called axons, structures specialized for conducting signals throughout the organism’s nervous system. The axons that originate in a person’s spinal cord and terminate in the muscles of the toes can be as long as 2 m. Small membrane-enclosed vesicles carrying materials essential to axonal function move along microtubules of the cytoskeleton, from the cell body to the tips of the axons. If the average velocity of a vesicle is 1 μm/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?

• 6. Comparing Synthetic versus Natural Vitamin C Some purveyors of health foods claim that vitamins obtained from natural sources are more healthful than those obtained by chemical synthesis. For example, some claim that 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? Explain your answer.

• 7. Fischer Projections of l- and d-threonine

  1. Identify the functional groups in the Fischer projection of l-threonine.

     

  2. Draw the Fischer projection structure of d-threonine.
  3. How many chiral centers does d-threonine have?

• 8. Drug Activity and Stereochemistry The quantitative differences in biological activity between the two enantiomers of a compound are sometimes quite large. For example, the d isomer of the drug isoproterenol, used to treat mild asthma, is 50 to 80 times more effective as a bronchodilator than the l isomer. Identify the chiral center in isoproterenol. Why do the two enantiomers have such radically different bioactivity?

  

• 9. Separating Biomolecules In studying a particular biomolecule (a protein, nucleic acid, carbohydrate, or lipid) in the laboratory, the biochemist first needs to separate it from other biomolecules in the sample — that is, to purify it. Specific purification techniques are described later in this book. However, by looking at the monomeric subunits of a biomolecule, you can determine the characteristics of the molecule that will allow you to separate it from other molecules. For example, how would you separate (a) amino acids from fatty acids and (b) nucleotides from glucose?

• 10. Possibility of Silicon-Based Life Carbon and silicon are in the same group on the periodic table, and both can form up to four single bonds. As such, many science fiction stories have been based on the premise of silicon-based life. Consider what you know about carbon’s bonding versatility (refer to a beginning inorganic chemistry resource for silicon’s bonding properties, if needed). What property of carbon makes it especially suitable for the chemistry of living organisms? What characteristics of silicon make it less well adapted than carbon as the central organizing element for life?

• 11. Stereochemistry and Drug Activity of Ibuprofen Ibuprofen is an over-the-counter drug that blocks the formation of a class of prostaglandins that cause inflammation and pain.

  

  Ibuprofen is available as a racemic mixture of (R)-ibuprofen and (S)-ibuprofen. In living organisms, an isomerase catalyzes the chiral inversion of the (R)-enantiomer to the (S)-enantiomer. The reverse reaction does not occur at an appreciable rate. The accompanying figure represents the two enantiomers relative to the binding sites a, b, and c in the isomerase enzyme that converts the (R)-enantiomer to the (S)-enantiomer. All three sites recognize the corresponding functional groups of the (R)-enantiomer of ibuprofen. However, sites a and c do not recognize the corresponding functional groups of the (S)-enantiomer of ibuprofen.

  1. What substituents represent A, B, and C in the (R)-enantiomer and in the (S)-enantiomer?

     

     The (S)-enantiomer of ibuprofen is 100 times more efficacious for pain relief than is the (R)-enantiomer. Drug companies sometimes make enantiomerically pure versions of drugs that were previously sold as racemic mixes, such as esomeprazole (Nexium) and escitalopram (Lexapro).

  2. Given that (S)-ibuprofen is more effective, why do drug companies not sell enantiomerically pure (S)-ibuprofen?

• 12. Components of Complex Biomolecules Three important biomolecules are depicted in their ionized forms at physiological pH. Identify the chemical constituents that are part of each molecule.

  1. Guanosine triphosphate (GTP), an energy-rich nucleotide that serves as a precursor to RNA:

     

  2. Methionine enkephalin, the brain’s own opiate:

     

  3. Phosphatidylcholine, a component of many membranes:

     

• 13. Experimental Determination of the Structure of a Biomolecule Researchers isolated an unknown substance, X, from rabbit muscle. They determined its structure from the following observations and experiments. Qualitative analysis showed that X was composed entirely of C, H, and O. A weighed sample of X was completely oxidized, and the and produced were measured; this quantitative analysis revealed that X contained 40.00% C, 6.71% H, and 53.29% O by weight. The molecular mass of X, determined by mass spectrometry, was 90.00 u (atomic mass units; see Box 1-1). Infrared spectroscopy showed that X contained one double bond. X dissolved readily in water to give an acidic solution that demonstrated optical activity when tested in a polarimeter.

  1. Determine the empirical and molecular formula of X.
  2. Draw the possible structures of X that fit the molecular formula and contain one double bond. Consider only linear or branched structures and disregard cyclic structures. Note that oxygen makes very poor bonds to itself.
  3. What is the structural significance of the observed optical activity? Which structures in (b) are consistent with the observation?
  4. What is the structural significance of the observation that a solution of X was acidic? Which structures in (b) are consistent with the observation?
  5. What is the structure of X? Is more than one structure consistent with all the data?

• 14. Naming Stereoisomers with One Chiral Carbon Using the RS System Propranolol is a chiral compound. (R)-Propranolol is used as a contraceptive; (S)-propranolol is used to treat hypertension. The structure of one of the propranolol isomers is shown.

  

  1. Identify the chiral carbon in propranolol.
  2. Does the structure show the (R) isomer or the (S) isomer?
  3. Draw the other isomer of propranolol.

• 15. Naming Stereoisomers with Two Chiral Carbons Using the RS System The (R,R) isomer of methylphenidate (Ritalin) is used to treat attention deficit hyperactivity disorder (ADHD). The (S,S) isomer is an antidepressant.

  1. Identify the two chiral carbons in the methylphenidate structure shown here.

     

  2. Does the structure show the (R,R) isomer or the (S,S) isomer?
  3. Draw the other isomer of methylphenidate.

• 16. State of Bacterial Spores A bacterial spore is metabolically inert and may remain so for years. Spores contain no measurable ATP, exclude water, and consume no oxygen. However, when a spore is transferred into an appropriate liquid medium, it germinates, makes ATP, and begins cell division within an hour. Is the spore dead, or is it alive? Explain your answer.

• 17. Activation Energy of a Combustion Reaction Firewood is chemically unstable compared with its oxidation products, and

  1. What can one say about the standard free-energy change for this reaction?
  2. Why doesn’t firewood stacked beside the fireplace undergo spontaneous combustion to its much more stable products?
  3. How can the activation energy be supplied to this reaction?
  4. Suppose you have an enzyme (firewoodase) that catalyzes the rapid conversion of firewood to and at room temperature. How does the enzyme accomplish that in thermodynamic terms?

• 18. Consequence of Nucleotide Substitutions Suppose deoxycytidine (C) in one strand of DNA is mistakenly replaced with deoxythymidine (T) during cell division. What is the consequence for the cell if the deoxynucleotide change is not repaired?

• 19. Mutation and Protein Function Suppose that the gene for a protein 500 amino acids in length undergoes a mutation. If the mutation causes the synthesis of a mutant protein in which just one of the 500 amino acids is incorrect, the protein may lose all of its biological function. How can this small change in a protein’s sequence inactivate it?

• 20. Gene Duplication and Evolution Suppose that a rare DNA replication error results in the duplication of a single gene, giving the daughter cell two copies of the same gene.

  1. How does this change favor the acquisition of a new function by the daughter cell?
  2. In the vascular plant Arabidopsis thaliana, 50% to 60% of the genome consists of duplicate content. How might this confer a selective advantage?

• 21. Cryptobiotic Tardigrades and Life Tardigrades, also called water bears or moss piglets, are small animals that can grow to about 0.5 mm in length. Terrestrial tardigrades (pictured here) typically live in the moist environments of mosses and lichens. Some of these species are capable of surviving extreme conditions. Some tardigrades can enter a reversible state called cryptobiosis, in which metabolism completely stops until conditions become hospitable. In this state, various tardigrade species have withstood dehydration, extreme temperatures from to pressures from 6,000 atm to a vacuum, anoxic conditions, and the radiation of space. Do tardigrades in cryptobiosis meet the definition of life? Why or why not?

  

• 22. Effects of Ionizing Radiation on Bacteria Treatment of a bacterial culture (E. coli) with ionizing radiation resulted in the survival of only a tiny fraction of the cells. The survivors proved to be more resistant to radiation than the starting cells were. When exposed to even higher levels of radiation, a tiny fraction of these resistant cells survived with even greater resistance to radiation. Repetition of this protocol with progressively higher levels of radiation yielded a strain of E. coli that was far more resistant to radiation than the starting strain. What changes might be occurring with each successive round of radiation and selection?

• 23. Data Analysis Problem In 1956, E. P. Kennedy and S. B. Weiss published their study of membrane lipid phosphatidylcholine (lecithin) synthesis in rat liver. Their hypothesis was that phosphocholine joined with some cellular component to yield lecithin. In an earlier experiment, incubating phosphocholine at physiological temperature with broken cells from rat liver yielded labeled lecithin. This became their assay for the enzymes involved in lecithin synthesis.

  

  The researchers centrifuged the broken cell preparation to separate the membranes from the soluble proteins. They tested three preparations: whole extract, membranes, and soluble proteins. Table 1 summarizes the results.

  TABLE 1 Cell Fraction Requirement for Incorporation of -Phosphocholine into Lecithin

  Tube number	Preparation	-Phosphocholine incorporated into lecithin
  1	Whole extract	6.3 μmol
  2	Membranes	18.5 μmol
  3	Soluble proteins	2.6 μmol

  1. Was the enzyme responsible for this reaction a soluble protein from the cytoplasm or a membrane-bound enzyme? Why?

     Having determined the location of the enzyme, the researchers investigated the effect of pH on enzyme activity. They carried out their standard assay in solutions buffered at different pH values between 6 and 9. The graph shows the results. The enzyme activity is the amount, in nanomoles per liter, of -phosphocholine incorporated into lecithin.

     

  2. What is the optimal pH for this enzyme?
  3. How much more active is the enzyme at pH 8 than at pH 6?

     Reactions with phosphorylated intermediates commonly require a divalent metal ion. The researchers tested and to determine if a divalent metal ion was important in this reaction. The graph shows the results.

     

  4. What is the metal ion dependence?

     The researchers reasoned that the reaction might require energy. To test the hypothesis, they incubated rat liver membranes and -phosphocholine with different nucleotides. Because the ATP sold in 1956 was not as highly purified as modern commercial preparations, the researchers used two different ATP sources, lot 116 and lot 122. Table 2 gives the results.

     TABLE 2 Requirement of Nucleotides for Lecithin Synthesis from Phosphocholine

     Tube number	Nucleotide added	incorporated into lecithin
     1	5 μmol ATP from lot 116	5.1 μmol
     2	5 μmol ATP from lot 122	0.2 μmol
     3	5 μmol ATP from lot 122 + 0.5 μmol GDP	0.4 μmol
     4	5 μmol ATP from lot 122 + 0.5 μmol CTP	15.0 μmol
     5	5 μmol ATP from lot 122 + 0.1 μmol CTP	10.0 μmol
     6	5 μmol ATP from lot 122 + 0.5 μmol UTP	0.4 μmol
     7	0.5 μmol CTP with no ATP	8.0 μmol

  5. What is your interpretation of the results in Table 2?
  6. Write the equation for the reaction the researchers studied. Include all required components, including the cell fraction, metal ion, and nucleotide cofactor.