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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. Concerted opening. Suppose that a channel obeys the concerted allosteric model (MWC model, Section 10.1.5). The binding of ligand to the R state (the open form) is 20 times as tight as to the T state (the closed form). In the absence of ligand, the ratio of closed to open channels is 105. If the channel is a tetramer, what is the fraction of open channels when 1, 2, 3, and 4 ligands are bound?

The ratio of closed to open forms of the channel is 105, 5000, 250, 12.5, and 0.625 when zero, one, two, three, and four ligands, respectively, are bound. Hence, the fraction of open channels is 10-5, 2.0 × 10-4, 4 × 10-4, 7.4 × 10-2, and 0.62.

2. Respiratory paralysis. Tabun and sarin have been used as chemical-warfare agents, and parathion has been employed as an insecticide. What is the molecular basis of their lethal actions?

Image ch13fb1.jpg

These organic phosphates inhibit acetylcholinesterase by reacting with the active-site serine residue to form a stable phosphorylated derivative. They cause respiratory paralysis by blocking synaptic transmission at cholinergic synapses.

3. Ligand-induced channel opening. The ratio of open to closed forms of the acetylcholine receptor channel containing zero, one, and two bound acetylcholine molecules is 5 × 10-6, 1.2 × 10-3, and 14, respectively.

(a) By what factor is the open/closed ratio increased by the binding of the first acetylcholine molecule? The second acetylcholine molecule?

(b) What are the corresponding free-energy contributions to channel opening at 25°C?

(c) Can the allosteric transition be accounted for by the MWC concerted model?

(a) The binding of the first acetylcholine molecule increases the open-to-closed ratio by a factor of 240, and binding of the second by a factor of 11,700.

(b) The free-energy contributions are 3.3 kcal mol-1 (14 kJ mol-1) and 5.6 kcal mol-1 (23 kJ mol-1) respectively.

(c) No. The MWC model predicts that the binding of each ligand will have the same effect on the open-to-closed ratio.

4. Voltage-induced channel opening. The fraction of open channels at 5 mV increments beginning at -45 mV and ending at +5 mV at 20°C is 0.02, 0.04, 0.09, 0.19, 0.37, 0.59, 0.78, 0.89, 0.95, 0.98, and 0.99.

(a) At what voltage are half the channels open?

(b) What is the value of the gating charge?

(c) How much free energy is contributed by the movement of the gating charge in the transition from -45 mV to +5 mV?

(a) -22 mV; (b) +4.5; (c) 5.2 kcal mol-1 (22 kJ mol-1).

5. Different directions. The potassium channel and the sodium channel have similar structures and are arranged in the same orientation in the cell membrane. Yet, the sodium channel allows sodium ions to flow into the cell and the potassium channel allows potassium ions to flow out of the cell. Explain.

An ion channel must transport ions in either direction at the same rate. The net flow of ions is determined only by the composition of the solutions on either side of the membrane.

6. Structure—activity relations. On the basis of the structure of tetrodotoxin, propose a mechanism by which the toxin inhibits sodium flow through the sodium channel.

The positively charge guanidinium group resembles sodium and binds to negatively charged carboxylate groups in the mouth of the channel.

7. A dangerous snail. Cone snails are carnivores that inject a powerful set of toxins into their prey, leading to rapid paralysis. Many of these toxins are found to bind to specific ion-channel proteins. Why are such molecules so toxic? How might such toxins be useful for biochemical studies?

The blockage of ion channels inhibits action potentials, leading to loss of nervous function. Like tetrodotoxin, these toxin molecules are useful for isolating and specifically inhibiting particular ion channels.

8. Only a few. Why do only a small number of sodium ions need to flow through the sodium channel to significantly change the membrane potential?

Because sodium ions are charged and because sodium channels carry only sodium ions (and not anions), the accumulation of excess positive charge on one side of the membrane dominates the chemical gradients.

9. Frog poison. Batrachotoxin (BTX) is a steroidal alkaloid from the skin of Phyllobates terribilis, a poisonous Colombian frog (source of the poison used on blowgun darts). In the presence of BTX, sodium channels in an excised patch stay persistently open when the membrane is depolarized. They close when the membrane is repolarized. Which transition is blocked by BTX?

Batrachotoxin blocks the transition from the open to the closed state.

10. Valium target. γ-Aminobutyric acid (GABA) opens channels that are specific for chloride ions. The GABAA receptor channel is pharmacologically important because it is the target of Valium, which is used to diminish anxiety.

(a) The extracellular concentration of Cl- is 123 mM and the intracellular concentration is 4 mM. In which direction does Cl- flow through an open channel when the membrane potential is in the -60 mV to +30 mV range?

(b) What is the effect of chloride-channel opening on the excitability of a neuron?

(c) The hydropathy profile of the GABAA receptor resembles that of the acetylcholine receptor. Predict the number of subunits in this chloride channel.

(a) Chloride ions flow into the cell. (b) Chloride flux is inhibitory because it hyperpolarizes the membrane. (c) The channel consists of five subunits.

11. The price of extrusion. What is the free-energy cost of pumping Ca2+ out of a cell when the cytosolic concentration is 0.4 μM, the extracellular concentration is 1.5 mM, and the membrane potential is -60 mV?

The free-energy cost is 7.6 kcal mol-1 (32 kJ mol-1). The chemical work performed is 4.9 kcal mol-1 (20.4 kJ mol-1) and the electrical work performed is 2.8 kcal mol-1 (11.5 kJ mol-1).

12. Rapid transit. A channel exhibits current increments of 5 pA at a membrane potential of -50 mV. The mean open time is 1 ms.

(a) What is the conductance of this channel?

(b) How many univalent ions flow through the channel during its mean open time?

(c) How long does it take an ion to pass through the channel?

(a) The conductance of the channel is 100 picosiemens (pS). (b) 3.1 × 104 ions flow through the channel during its mean open time of 1 ms. (c) The mean transit time for an ion is 32 ns.

13. Pumping protons. Design an experiment to show that lactose permease can be reversed in vitro to pump protons.

Membrane vesicles containing a high concentration of lactose are formed. The binding of lactose to the inner face of the permease is followed by the binding of a proton. Both sites then evert. Because the lactose concentration on the outside is low, lactose and the proton will dissociate from the permease. The downhill flux of lactose will drive the uphill flux of protons in this in vitro system.

Chapter Integration Problem

14. Speed and efficiency matter. Acetylcholine is rapidly destroyed by the enzyme acetylcholinesterase. This enzyme, which has a turnover number of 25,000 per second, has attained catalytic perfection with a kcat/KM of 2 × 108 M-1s-1. Why is it physiologically crucial that this enzyme be so efficient?

The catalytic prowess of acetylcholinesterase ensures that the duration of the nerve stimulus will be short.

Mechanism Problem

15. Remembrance of mechanisms past. Acetylcholinesterase converts acetylcholine into acetate and choline. Show the reaction as chemical structures :

Image ch13fb2.jpg

Like serine proteases, acetylcholinesterase is inhibited by DIPF. Propose a catalytic mechanism for acetylcholine digestion by acetylcholinesterase.

See equation below.

Data Interpretation Problem

16. Tarantula toxin. Acid sensing is associated with pain, tasting, and other biological activities (Chapter 32). Acid sensing is carried out by a ligand-gated channel that permits sodium influx in response to H+. This family of acid-sensitive ion channels (ASICs) comprises a number of members. Psalmotoxin 1 (PcTX1), a venom from the tarantula, inhibits some members of this family. Below are electrophysiological recordings of cells containing one of several members of the ASIC family made in the presence of the toxin at a concentration of 10 nM. The channels were opened by changing the pH from 7.4 to the indicated values. The PcTX1 was present for a short time (indicated by the black bar above the recordings) after which time it was rapidly washed from the system.

Image ch13fu9a.jpg

Image ch13fu9b.jpg

(A) Electrophysiological recordings of cells exposed to tarantula toxin. (B) Plot of peak current of a cell containing the ASIC1a protein versus the toxin concentration. [from P. Escoubas, et al., 2000, J. Biol. Chem. 275:25116-215121.]

(a) Which of the ASIC family members—ASIC1a, ASIC1b, ASIC2a, or ASIC3—is most sensitive to the toxin?

(b) Is the effect of the toxin reversible? Explain.

(c) What concentration of PcTX1 yields 50% inhibition of the sensitive channel?

(a) Only ASIC1a is inhibited by the toxin. (b) Yes, when the toxin was removed, the activity of the acid-sensing channel began to be restored. (c) 0.9 nM.

17. Channel problems 1. A number of pathological conditions result from mutations in the acetylcholine receptor channel. One such mutation in the β subunit, βV266M, causes muscle weakness and rapid fatigue. An investigation of the acetylcholine-generated currents through the acetylcholine receptor channel for both a control and a patient yielded the following results. What is the effect of the mutation on channel function? Suggest some possible biochemical explanations for the effect.

Image ch13fb3.jpg

This mutation is one of a class of mutations that result in slow channel syndrome (SCS). The results suggest that there is a defect in channel closing; so the channel remains open for prolonged periods. Alternatively, the channel may have a higher affinity for acetylcholine than does the control channel.

18. Channel problems 2. The acetylcholine receptor channel can also undergo mutation leading to fast channel syndrome (FCS), with clinical manifestations similar to those of slow channel syndrome (SCS). What would the recordings of ion movement look like in this syndrome? Again, suggest a biochemical explanation.

The mutation reduces the affinity of acetylcholine for the receptor. The recordings would show the channel opening only infrequently.

19. Transport differences. The rate of transport of two molecules, indole and glucose, across a cell membrane is shown in the right column. What are the differences between the transport mechanisms of the two molecules? Suppose that ouabain inhibited the transport of glucose. What would this inhibition suggest about the mechanism of transport?

Image ch13fb4.jpg

Glucose displays a transport curve that suggests the participation of a carrier, because the initial rate is high but then levels off at higher concentrations, consistent with saturation of the carrier, which is reminiscent of Michaelis-Menten enzymes (Section 8.4.1). Indole shows no such saturation phenomenon, which implies that the molecule is lipophilic and simply diffuses across the membrane. Ouabain is a specific inhibitor the Na+-K+ pump. If ouabain were to inhibit glucose transport, then a Na+-glucose cotransporter is assisting in transport.

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Media Problem

20. Image mouse.jpg The merits of inflexibility. The selectivity filter of potassium channels restricts passage of sodium ions even though sodium ions are smaller than potassium ions. Mutation of the tyrosine that is part of this filter to leucine has been shown to reduce selectivity against sodium in a channel homologous to the one whose structure has been determined [Chapman, M. L., Krovetz, H. S., and VanDongen, A. M. J., 2001. GYGD pore motifs in neighboring potassium channel subunits interact to determine ion selectivity. J. Physiol. 530:21–33]. Look at the three-dimensional structure in the Potassium Channel Structural Insights module and propose, in general terms, an explanation for the role of this tyrosine in the wild-type protein and the effect of its mutation to leucine.

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: NBK22491

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