Chapter 9

The purple patches of the Halobacterium halobium membrane, which contain the protein bacteriorhodopsin, are approximately \(75 \%\) protein and \(25 \%\) lipid. If the protein molecular weight is 26,000 and an average phospholipid has a molecular weight of 800 , calculate the phospholipid-to-protein mole ratio.

Sucrose gradients for separation of membrane proteins must be able to separate proteins and protein-lipid complexes having a wide range of densities, typically 1.00 to \(1.35 \mathrm{g} / \mathrm{mL}\) a. Consult reference books (such as the CRC Handbook of Biochemistry \()\) and plot the density of sucrose solutions versus percent sucrose by weight (g sucrose per 100 g solution), and versus percent by volume (g sucrose per \(100 \mathrm{mL}\) solution). Why is one plot linear and the other plot curved? b. What would be a suitable range of sucrose concentrations for separation of three membrane-derived protein-lipid complexes with densities of \(1.03,1.07,\) and \(1.08 \mathrm{g} / \mathrm{mL} ?\)

Phospholipid lateral motion in membranes is characterized by a diffusion coefficient of about \(1 \times 10^{-8} \mathrm{cm}^{2} /\) sec. The distance traveled in two dimensions (across the membrane) in a given time is \(r=(4 D t)^{1 / 2},\) where \(r\) is the distance traveled in centimeters, \(D\) is the diffusion coefficient, and \(t\) is the time during which diffusion occurs. Calculate the distance traveled by a phospholipid across a bilayer in 10 msec (milliseconds).

Discuss the effects on the lipid phase transition of pure dimyristoyl phosphatidylcholine vesicles of added (a) divalent cations, (b) cholesterol, (c) distearoyl phosphatidylserine, (d) dioleoyl phosphatidylcholine, and (e) integral membrane proteins.

Consider a phospholipid vesicle containing \(10 \mathrm{m} M \mathrm{Na}^{+}\) ions. The vesicle is bathed in a solution that contains \(52 \mathrm{mM} \mathrm{Na}^{+}\) ions, and the electrical potential difference across the vesicle membrane \(\Delta \psi=\psi_{\text {outside }}-\psi_{\text {inside }}=-30 \mathrm{mV} .\) What is the electrochemical potential at \(25^{\circ} \mathrm{C}\) for \(\mathrm{Na}^{+}\) ions?

(Integrates with Chapter 3 .) Fructose is present outside a cell at \(1 \mu M\) concentration. An active transport system in the plasma membrane transports fructose into this cell, using the free energy of ATP hydrolysis to drive fructose uptake. What is the highest intracellular concentration of fructose that this transport system can generate? Assume that one fructose is transported per ATP hydrolyzed; that ATP is hydrolyzed on the intracellular surface of the membrane; and that the concentrations of ATP, ADP, and \(P_{i}\) are \(3 \mathrm{m} M, 1 \mathrm{m} M,\) and \(0.5 \mathrm{m} M,\) respectively. \(T=298 \mathrm{K}\). (Hint: Refer to Chapter 3 to recall the effects of concentration on free energy of ATP hydrolysis.)

In this chapter, we have examined coupled transport systems that rely on ATP hydrolysis, on primary gradients of \(\mathrm{Na}^{+}\) or \(\mathrm{H}^{+},\) and on phosphotransferase systems. Suppose you have just discovered an unusual strain of bacteria that transports rhamnose across its plasma membrane. Suggest experiments that would test whether it was linked to any of these other transport systems.

Proline residues are almost never found in short \(\alpha\) -helices; nearly all transmembrane \(\alpha\) -helices that contain proline are long ones (about \(20 \text { residues }) .\) Suggest a reason for this observation.

As described in this chapter, proline introduces kinks in transmembrane \(\alpha\) -helices. What are the molecular details of the kink, and why does it form? A good reference for this question is von Heijne, G. 1991\. Proline kinks in transmembrane \(\alpha\) -helices. Journal of Molecular Biology \(218: 499-503 .\) Another is Barlow, D. \(\mathrm{J}\)., and Thornton, J. M., \(1988 .\) Helix geometry in proteins. Journal of Molecular Biology \(201: 601-619\)

As described in the text, the \(\mathrm{pK}_{\mathrm{a}}\) values of Asp \(^{85}\) and \(\mathrm{Asp}^{96}\) of bacteriorhodopsin are shifted to high values (more than 11 ) because of the hydrophobic environment surrounding these residues. Why is this so? What would you expect the dissociation behavior of aspartate carboxyl groups to be in a hydrophobic environment?