1. 2.86 × 10⁶ molecules, because each leaflet of the bilayer contains 1.43 × 10⁶ molecules.

2. Essentially an “inside-out” membrane. The hydrophilic groups would come together on the interior of the structure, away from the solvent, whereas the hydrocarbon chains would interact with the solvent.

3. 2 × 10⁻⁷ cm, 6 × 10⁻⁶ cm, and 2 × 10⁻⁴ cm.

4. The radius of this molecule is 3.1 × 10⁻⁷cm, and its diffusion coefficient is 7.4 × 10−9 cm²s⁻¹. The average distances traversed are 1.7 × 10⁻⁷cm in 1 μs, 5.4 × 10⁻⁶cm in 1 ms, and 1.7 × 10⁻⁴cm in 1 s.

5. The membrane underwent a phase transition from a highly fluid to a nearly frozen state when the temperature was lowered. A carrier can shuttle ions across a membrane only when the bilayer is highly fluid. A channel, in contrast, allows ions to traverse its pore even when the bilayer is quite rigid.

6. The presence of a cis double bond introduces a kink in the fatty acid chain that prevents tight packing and reduces the number of atoms in van der Waals contact. The kink lowers the melting point compared with that of a saturated fatty acid. Trans fatty acids do not have the kink, and so their melting temperatures are higher, more similar to those of saturated fatty acids. Because trans fatty acids have no structural effect, they are rarely observed.

7. Palmitic acid is shorter than stearic acid. Thus, when the chains pack together, there is less opportunity for van der Waals interaction and the melting point is thus lower than that of the longer stearic acid.

8. Hibernators selectively feed on plants that have a high proportion of polyunsaturated fatty acids with lower melting temperature.

9. The initial decrease in fluorescence with the first addition of sodium dithionite results from the quenching of NBD-PS molecules in the outer leaflet of the bilayer. Sodium dithionite does not traverse the membrane under these experimental conditions; hence, it does not quench the labeled phospholipids in the inner leaflet. A second addition of sodium dithionite has no effect, as the NBD-PS molecules in the outer leaflet remain quenched. However, after a 6.5-hour incubation, about half the NBD-PS has flipped over to the outer leaflet of the bilayer, resulting in the 50% decrease in fluorescence when sodium dithionite is added.

10. The addition of the carbohydrate introduces a significant energy barrier to the flip-flop because a hydrophilic carbohydrate moiety would need to be moved through a hydrophobic environment. This energetic barrier enhances membrane asymmetry.

11. The C₁₆ alkyl chain is attached by an ether linkage. The C-2 carbon atom of glycerol has only an acetyl group attached by an ester linkage instead of a fatty acid, as is the case with most phospholipids.

12. In a hydrophobic environment, the formation of intrachain hydrogen bonds stabilizes the amide hydrogen atoms and carbonyl oxygen atoms of the polypeptide chain, and so an α helix forms. In an aqueous environment, these groups are stabilized by interaction with water, and so there is no energetic reason to form an α helix. Thus, the α helix would be more likely to form in a hydrophobic environment.

13. The protein may contain an α helix that passes through the hydrophobic core of the protein. This helix is likely to feature a stretch of hydrophobic amino acids similar to those observed in transmembrane helices.

14. The shift to the lower temperature would decrease fluidity by enhancing the packing of the hydrophobic chains by van der Waals interactions. To prevent this packing, new phospholipids having shorter chains and a greater number of cis double bonds would be synthesized. The shorter chains would reduce the number of van der Waals interactions, and the cis double bonds, which cause the kink in structure, would prevent the packing of the fatty acid tails of the phospholipids.

15. Each of the 21 v-SNARE proteins could interact with each of 7 t-SNARE partners. Multiplication gives the total number of different interacting pairs: 7 × 21 = 147 different v-SNARE–t-SNARE pairs.

16. (a) The graph shows that, as temperature increases, the phospholipid bilayer becomes more fluid. T_m is the temperature of the transition from the predominantly less fluid state to the predominantly more fluid state. Cholesterol broadens the transition from the less-fluid to the more-fluid state. In essence, cholesterol makes membrane fluidity less sensitive to temperature changes.

(b) This effect is important because the presence of cholesterol tends to stabilize membrane fluidity by preventing sharp transitions. Because protein function depends on the proper fluidity of the membrane, cholesterol maintains the proper environment for membrane-protein function.

17. The protein plotted in part c is a transmembrane protein from C. elegans. It spans the membrane with four α helices that are prominently displayed as hydrophobic peaks in the hydropathy plot. Interestingly, the protein plotted in part a also is a membrane protein, a porin. This protein is made primarily of β strands, which lack the prominent hydrophobic window of membrane helices. This example shows that, although hydropathy plots are useful, they are not infallible.

18. (a) Prostaglandin H₂ synthase-1 recovers its activity immediately after removal of ibuprofen, suggesting that this inhibitor dissociates rapidly from the enzyme. In contrast, the enzyme remains significantly inhibited 30 minutes after removal of indomethacin, suggesting that this inhibitor dissociates slowly from its active site.

(b) Aspirin covalently modifies prostaglandin H₂ synthase-1, indicating that it would dissociate very slowly (if at all). Hence, one would anticipate that very low activity would be evident in all conditions where inhibitor has been added (columns 2, 3, and 4).

19. To purify any protein, the protein must first be solubilized. For a membrane protein, solubilization usually requires a detergent—hydrophobic molecules that bind to the protein and thus replace the lipid environment of the membrane. If the detergent is removed, the protein aggregates and precipitates from solution. Often, the steps in purification, such as ion-exchange chromatography, are difficult to perform in the presence of sufficient detergent to solubilize the protein. Crystals of appropriate protein–detergent complexes must be generated.