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Berg JM, Tymoczko JL, Stryer L. Biochemistry. 5th edition. New York: W H Freeman; 2002.

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Biochemistry. 5th edition.

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Problems

1. Population density. How many phospholipid molecules are there in a 1-μm2 region of a phospholipid bilayer membrane? Assume that a phospholipid molecule occupies 70 Å2 of the surface area.

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

2. Lipid diffusion. What is the average distance traversed by a membrane lipid in 1 μs, 1 ms, and 1 s? Assume a diffusion coefficient of 10-8 cm2s-1.

2 × 10-7 cm, 6 × 10-6 cm, and 2 × 10-4 cm.

3. Protein diffusion. The diffusion coefficient, D, of a rigid spherical molecule is given by

Image ch12fb1.jpg

in which η is the viscosity of the solvent, r is the radius of the sphere, k is the Boltzman constant (1.38 × 10-16 erg/degree), and T is the absolute temperature. What is the diffusion coefficient at 37°C of a 100-kd protein in a membrane that has an effective viscosity of 1 poise (1 poise = 1 erg s-1/cm-3)? What is the average distance traversed by this protein in 1 μs, 1 ms, and 1 s? Assume that this protein is an unhydrated, rigid sphere of density 1.35 g cm-3.

The radius of this molecule is 3.1 × 10-7 cm, and its diffusion coefficient is 7.4 × 10-9 cm2 s-1. The average distances traversed are 1.7 × 10-7 cm in 1 μs, 5.4 × 10-6 in 1 ms, and 1.7 × 10-4 cm in 1 s.

4. Cold sensitivity. Some antibiotics act as carriers that bind an ion on one side of a membrane, diffuse through the membrane, and release the ion on the other side. The conductance of a lipid-bilayer membrane containing a carrier antibiotic decreased abruptly when the temperature was lowered from 40°C to 36°C. In contrast, there was little change in conductance of the same bilayer membrane when it contained a channel-forming antibiotic. Why?

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 former, in contrast, allows ions to traverse its pore even when the bilayer is quite rigid.

5. Flip-flop. The transverse diffusion of phospholipids in a bilayer membrane was investigated by using a paramagnetic analog of phosphatidyl choline, called spin-labeled phosphatidyl choline.

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The nitroxide (NO) group in spin-labeled phosphatidyl choline gives a distinctive paramagnetic resonance spectrum. This spectrum disappears when nitroxides are converted into amines by reducing agents such as ascorbate.

Lipid vesicles containing phosphatidyl choline (95%) and the spin-labeled analog (5%) were prepared by sonication and purified by gel-filtration chromatography. The outside diameter of these liposomes was about 25 nm. The amplitude of the paramagnetic resonance spectrum decreased to 35% of its initial value within a few minutes of the addition of ascorbate. There was no detectable change in the spectrum within a few minutes after the addition of a second aliquot of ascorbate. However, the amplitude of the residual spectrum decayed exponentially with a half-time of 6.5 hours. How would you interpret these changes in the amplitude of the paramagnetic spectrum?

The initial decrease in the amplitude of the paramagnetic resonance spectrum results from the reduction of spinlabeled phosphatidyl choline molecules in the outer leaflet of the bilayer. Ascorbate does not traverse the membrane under these experimental conditions; hence, it does not reduce the phospholipids in the inner leaflet. The slow decay of the residual spectrum is due to the reduction of phospholipids that have flipped over to the outer leaflet of the bilayer.

6. Flip-flop 2. Although proteins rarely if ever flip-flop across a membrane, distribution of membrane lipids between the membrane leaflets is not absolute except in the case of glycolipids. Why are glycosylated lipids less likely to flip-flop?

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.

7. Cis versus trans. Why are most unsaturated fatty acids found in phospholipids in the cis rather than the trans conformation? Draw the structure of a 16-carbon fatty acid as saturated, trans monounsaturated, and cis monounsaturated.

The presence of a cis double bond introduces a kink that prevents packing of the fatty acid chains. Cis double bonds maintain fluidity. Trans fatty acids have no structural effect, relative to saturated fatty acids, and so they are rare.

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8. A question of competition. Would a homopolymer of alanine be more likely to form an α helix in water or in a hydrophobic medium? Explain.

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

9. Maintaining fluidity. A culture of bacteria growing at 37°C was shifted to 25°C. How would you expect this shift to alter the fatty acid composition of the membrane phospholipids? Explain.

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

Data Interpretation Problems

10. Cholesterol effects. The red line on the following graph shows the fluidity of the fatty acids of a phospholipid bilayer as a function of temperature. The blue line shows the fluidity in the presence of cholesterol.

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(a) What is the effect of cholesterol?

(b) Why might this effect be biologically important?

(a) The graph shows that, as temperature increases, the phospholipid bilayer becomes more fluid. Tm 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.

11. Hydropathy plots. On the basis of the following hydropathy plots for three proteins, predict which would be membrane proteins. What are the ambiguities with respect to using such plots to determine if a protein is a membrane protein?

Image ch12fb4.jpg

(a)

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(b)

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(c)

Protein 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, protein 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.

Chapter Integration Problem

12. The proper environment. An understanding of the structure and function of membrane proteins has lagged behind that of other proteins. The primary reason is that membrane proteins are more difficult to purify and crystallize. Why might this be the case?

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, performing purification steps, such as ion-exchange chromatography, in the presence of sufficient detergent to solubilize the protein is difficult. Crystals must be generated of appropriate protein-detergent complexes.

By agreement with the publisher, this book is accessible by the search feature, but cannot be browsed.

Copyright © 2002, W. H. Freeman and Company.
Bookshelf ID: NBK22504

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