How would you need to change the diagram to convert the transporter into a pump that moves the solute up its concentration gradient by hydrolyzing ATP? Explain the need for each of the steps in your new illustration.

Using the Nernst equation and the ion concentrations given in Table 12-1 (p. 391), calculate the equilibrium membrane potential of $\mathrm{K}^{+}$and $\mathrm{Na}^{+}$- that is, the membrane potential where there would be no net movement of the ion across the plasma membrane (assume that the concentration of intracellular $\mathrm{Na}^{+}$is $10 \mathrm{mM}$ ). What membrane potential would you predict in a resting animal cell? Explain your answer. What would happen if a large number of $\mathrm{Na}^{+}$channels suddenly opened, making the membrane much more permeable to $\mathrm{Na}^{+}$than to $\mathrm{K}^{+}$? (Note that because few ions need to move across the membrane to change drastically the charge distribution across that membrane, you can safely assume that the ion concentrations on either side of the membrane do not change significantly.) What would you predict would happen next if the $\mathrm{Na}^{+}$channels closed again?

The previous figure shows a recording from a patch-clamp experiment in which the electrical current passing across a patch of membrane is measured as a function of time. The membrane patch was plucked from the plasma membrane of a muscle cell by the technique shown in Figure 12-25 and contains molecules of the acetylcholine receptor, which is a ligand-gated cation channel that is opened by the binding of acetylcholine to the extracellular face of the channel. To obtain a recording, acetylcholine was added to the solution inside the microelectrode. (A) Describe what you can learn about the channels from this recording. (B) How would the recording differ if acetylcholine were (i) omitted or (ii) added to the solution outside the microelectrode only?

A transmembrane protein has the following properties: it has two binding sites, one for solute A and one for solute B. The protein can undergo a conformational change to switch between two states: either both binding sites are exposed exclusively on one side of the membrane or both binding sites are exposed exclusively on the other side of the membrane. The protein can switch between the two conformational states only if both binding sites are occupied or if both binding sites are empty, but cannot switch if only one binding site is occupied.

A. What kind of protein do these properties define?

B. Do you need to specify any additional properties to turn this protein into a symport that couples the movement of solute A up its concentration gradient to the movement of solute B down its electrochemical gradient?

C. Write a set of rules that defines an antiport.

The ion channels that are regulated by binding of neurotransmitters, such as acetylcholine, glutamate, GABA, or glycine, have a similar overall structure. Yet each class of these channels consists of a very diverse set of subtypes with different transmitter affinities, different channel conductances, and different rates of opening and closing. Do you suppose that such extreme diversity is a good or a bad thing from the standpoint of the pharmaceutical industry?

Acetylcholine-gated cation channels do not discriminate between Na+, K+, and Ca2+ ions, allowing all to pass through them freely. So why is it that when acetylcholine binds to this protein in the plasma membrane of muscle cells, the channel opens and there is a large net influx of primarily Na+ ions?

Some bacterial cells can grow on either ethanol (CH3CH2OH) or acetate (CH3COO–) as their only carbon source. Dr. Schwips measured the rate at which the two compounds traverse the bacterial plasma membrane but, due to excessive inhalation of one of the compounds (which one?), failed to label his data accurately.

A. Plot the data from the table below.

$$\begin{array}{|c|c|c|} \hline \text{Carbon Source (mM)}&\text { Compound A } & \text { Compound B } \\ \hline 0.1 & 2.0 & 18 \\ \hline 0.3 & 6.0 & 46 \\ \hline 1.0 & 20 & 100 \\ \hline 3.0 & 60 & 150 \\ \hline 10.0 & 200 & 182 \\ \hline \end{array}$$

B. Determine from your graph whether the data describing compound A correspond to the uptake of ethanol or acetate.

Explain your answers.

We will see in Chapter 15 that endosomes, which are membrane-enclosed intracellular organelles, need an acidic lumen in order to function. Acidification is achieved by an H+ pump in the endosomal membrane, which also contains Cl– channels. If the channels do not function properly (e.g., because of a mutation in the genes encoding the channel proteins), acidification is also impaired.

A. Can you explain how Cl– channels might help acidification? B. According to your explanation, would the Cl– channels be absolutely required to lower the pH inside the endosome?

A rise in the intracellular $\mathrm{Ca}^{2+}$ concentration causes muscle cells to contract. In addition to an ATPdriven $\mathrm{Ca}^{2+}$ pump, muscle cells that contract quickly and regularly, such as those of the heart, have an additional type of $\mathrm{Ca}^{2+}$ pump-an antiport that exchanges $\mathrm{Ca}^{2+}$ for extracellular $\mathrm{Na}^{+}$across the plasma membrane. The majority of the $\mathrm{Ca}^{2+}$ ions that have entered the cell during contraction are rapidly pumped back out of the cell by this antiport, thus allowing the cell to relax. Ouabain and digitalis are used for treating patients with heart disease because they make heart muscle cells contract more strongly. Both drugs function by partially inhibiting the $\mathrm{Na}^{+}$pump in the plasma membrane of these cells. Can you propose an explanation for the effects of the drugs in the patients? What will happen if too much of either drug is taken?

Amino acids are taken up by animal cells using a symport in the plasma membrane. What is the most likely ion whose electrochemical gradient drives the import? Is ATP consumed in the process? If so, how?

One thousand Ca2+ channels open in the plasma membrane of a cell that is 1000 um3 in size and has a cytosolic Ca2+ concentration of 100 nM. For how long would the channels need to stay open in order for the cytosolic Ca2+ concentration to rise to 5 uM? There is virtually unlimited Ca2+ available in the outside medium (the extracellular Ca2+ concentration in which most animal cells live is a few millimolar), and each channel passes 106 Ca2+ ions per second.

Which of the following statements are correct? Explain your answers.

A. The plasma membrane is highly impermeable to all charged molecules.
B. Channels have specific binding pockets for the solute molecules they allow to pass.
C. Transporters allow solutes to cross a membrane at much faster rates than do channels.
D. Certain H+ pumps are fueled by light energy.
E. The plasma membrane of many animal cells contains open K+ channels, yet the K+ concentration in the cytosol is much higher than outside the cell.
F. A symport would function as an antiport if its orientation in the membrane were reversed (i.e., if the portion of the molecule normally exposed to the cytosol faced the outside of the cell instead).
G. The membrane potential of an axon temporarily becomes more negative when an action potential excites it.

Name the three ways in which an ion channel can be gated.

A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car’s motion, the eastward component of the car’s velocity is given by $v x ( t ) = \left( 0.860 m / s ^ { 3 } \right) t ^ { 2 }$. What is the acceleration of the car when $v _ { x } = 12.0 \mathrm { m } / \mathrm { s }$?