A helping hand. Differentiate between simple diffusion and facilitated diffusion.

Powering movement. What are the two forms of energy that can power active transport?

Carriers. Name the three types of carrier proteins. Which of these can mediate secondary active transport?

The price of extrusion. What is the free-energy cost at 25°C of pumping Ca²⁺ out of a cell when the cytoplasmic concentration is 0.4 μM, the extracellular concentration is 1.5 mM, and the membrane potential is −60 mV?

Equilibrium potentials. For a typical mammalian cell, the intracellular and extracellular concentrations of the chloride ion (Cl⁻) are 4 mM and 150 mM, respectively. For the calcium ion (Ca²⁺), the intracellular and extracellular concentrations are 0.2 μM and 1.8 mM, respectively. Calculate the equilibrium potentials at 37°C for these two ions.

How sweet it is. Some animal cells take up glucose by a symporter powered by the simultaneous entry of Na⁺. The entry of Na⁺ provides a free-energy input of 10.8 kJ mol⁻¹ (2.6 kcal mol⁻¹) under typical cellular conditions (external [Na⁺] = 143 mM, internal [Na⁺] = 14 mM, and membrane potential = −50 mV). How large a concentration gradient of glucose at 37°C can be generated by this free-energy input?

Variations on a theme. Write a detailed mechanism for transport by the Na⁺–K⁺ ATPase based on analogy with the mechanism of the Ca²⁺ ATPase shown in Figure 13.5.

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

Opening channels. Differentiate between ligand-gated and voltage-gated channels.

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

Differing mechanisms. Distinguish the mechanisms by which uniporters and channels transport ions or molecules across the membrane.

Short circuit. Carbonyl cyanide 4-(trifluoromethoxy) phenylhydrazone (FCCP) is a proton ionophore: it enables protons to pass freely through membranes. Treatment of E. coli with FCCP prevents the accumulation of lactose in these cells. Explain.

Working together. The human genome contains more than 20 connexin-encoding genes. Several of these genes are expressed in high levels in the heart. Why are connexins so highly expressed in cardiac tissue?

Structure–activity relations. On the basis of the structure of tetrodotoxin, propose a mechanism by which the toxin inhibits Na⁺ flow through the Na⁺ channel.

Hot stuff. When SERCA is incubated with [γ-³²P]ATP (a form of ATP in which the terminal phosphate is labeled with radioactive ³²P) and calcium at 0°C for 20 seconds and analyzed by gel electrophoresis, a radioactive band is observed at the molecular weight corresponding to full-length SERCA. Why is a labeled band observed? Would you expect a similar band if you were performing a similar assay, with a suitable substrate, for the MDR protein?

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?

Pause for effect. Immediately after the repolarization phase of an action potential, the neuronal membrane is temporarily unable to respond to the stimulation of a second action potential, a phenomenon referred to as the refractory period. What is the mechanistic basis for the refractory period?

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

More than one mechanism. How might a mutation in a cardiac voltage-dependent sodium channel cause long QT syndrome?

Mechanosensitive channels. Many species contain ion channels that respond to mechanical stimuli. On the basis of the properties of other ion channels, would you expect the flow of ions through a single open mechanosensitive channel to increase in response to an appropriate stimulus? Why or why not?

Concerted opening. Suppose that a channel obeys the concerted allosteric model (MWC model, Section 7.2). The binding of ligand to the R state (the open form) is 20 times as tight as that 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?

Respiratory paralysis. The neurotransmitter acetylcholine is degraded by a specific enzyme that is inactivated by Tabun, sarin, and parathion. On the basis of the structures below, propose a possible basis for their lethal actions.

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.

Frog poison. Batrachotoxin (BTX) is a steroidal alkaloid from the skin of Phyllobates terribilis, a poisonous Colombian frog (the source of the poison used on blowgun darts). In the presence of BTX, Na⁺ 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?

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

Understanding SERCA. To study the mechanism of SERCA, you prepare membrane vesicles containing this protein oriented such that its ATP binding site is on the outer surface of the vesicle. To measure pump activity, you use an assay that detects the formation of inorganic phosphate in the medium. When you add calcium and ATP to the medium, you observe phosphate production for only a short period of time. Only after the addition of calcimycin, a molecule that makes membranes selectively permeable to calcium, do you observe sustained phosphate production. Explain.

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 k_cat/K_M of 2 × 10⁸ M⁻¹s⁻¹. Why is the efficiency of this enzyme physiologically crucial?

Remembrance of mechanisms past. Acetylcholinesterase converts acetylcholine into acetate and choline. Like serine proteases, acetylcholinesterase is inhibited by DIPF. Propose a catalytic mechanism for acetylcholine digestion by acetylcholinesterase. Show the reaction as chemical structures.

Tarantula toxin. Acid sensing is associated with pain, tasting, and other biological activities (Chapter 33). Acid sensing is carried out by a ligand -gated channel that permits Na⁺ influx in response to H⁺. This family of acid-sensitive ion channels (ASICs) includes a number of members. Psalmotoxin 1 (PcTX1), a venom from the tarantula, inhibits some members of this family. The following electrophysiological recordings of cells containing several members of the ASIC family were 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 below), after which time it was rapidly washed from the system.

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.

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What is the effect of the mutation on channel function? Suggest some possible biochemical explanations for the effect.

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 (Problem 30). What would the recordings of ion movement look like in this syndrome? Suggest a biochemical explanation.

Transport differences. The rate of transport of two molecules, indole and glucose, across a cell membrane is shown below. 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?