Active Transport

The carrier-mediated transport described above is always down electrochemical gradients, and so is identified with diffusion. Any process that works against gradients requires the expenditure of energy. Perhaps the most important example of active (energy-consuming) transport is the sodium-potassium pump. This pump acts as an antiport, actively pumping sodium ions out of the cell against its steep electrochemical gradient and pumping potassium ions in. As we will see later in this chapter, this pump is used to regulate the cell volume and to maintain a membrane potential. Indeed, almost a third of the energy requirement of a typical animal cell is consumed in fueling this pump; in electrically active nerve cells, this figure approaches two-thirds of the cell's energy requirement.

This pumping activity uses energy by the dephosphorylation of ATP into ADP through the overall reaction scheme

with subscript e or i denoting extracellular or intracellular concentrations respectively. The details of the sodium-potassium pump (or Na+-K+ ATPase) are thought to be as follows. In its dephosphorylated state, sodium binding sites are exposed to the intracellular space. When sodium ions are bound, the carrier protein is phosphorylated by the hydrolysis of ATP (step 1; see Fig. 2.9). This induces a change of conformation, exposing the sodium binding sites to the extracellular space and reducing the binding affinity of these sites, thereby causing the release of the bound sodium. Simultaneously, the potassium binding sites are exposed to the extracellular medium, so that potassium is bound (step 2). When potassium is bound, the carrier is dephosphorylated, inducing the reverse conformational change and exposing the potassium binding site to the cytosol (step 3). Potassium is released to the cytosol when the binding affinity for potassium decreases (step 4). Some estimates for the affinities are shown in Table 2.2.

To illustrate how to turn this verbal description into a mathematical model, we consider a simplified case in which there is a single binding site for sodium and potassium, leading to a one-for-one exchange, rather than the three-for-two exchange that actually occurs. We denote the carrier molecule by C, and assume the reactions k1 k2 Na+ + C Tl NaC NaCP ^ Na+ + CP, (2.49)

Table 2.2 Some estimated equilibrium constants for the sodium-potassium pump.

Ion

kd (mM)

Na+

1.3

Inside

K+

12

Inside

Na+

32

Outside

K+

0.14

Outside

Outside the cell K+ Na+

Step 2

ADP-

Step 1 Step 3

Step 4

Inside the cell

Figure 2.9 Schematic diagram of reactions for the sodium-potassium pump.

We apply the law of mass action to these kinetics, assume that intracellular sodium and extracellular potassium are supplied at the constant rate J and that intracellular potassium and extracellular sodium are also removed at the constant rate J, and then find that in steady state the flow of ions through the pump is given by

where K1 = k1k2kp,K-1 = k-1k-2k-p,K2 = k3k4k5,K-2 = k-3k-4k-5,Kn = k-1k-p + k2k-1 + k2kp, and Kk = k-3k-4[P] + k-3k5 + k4k5. The rate constants kp and k-p are the forward and backward rate constants for the hydrolysis of ATP. As before, the total concentration of carrier molecule is denoted by C0.

Because ATP is much more energetic than ADP, we expect the reverse reaction rate k-p to be small compared to the forward reaction rate kp. If we ignore the reverse reaction (take K-1 = 0), we find

which is independent of the extracellular sodium concentration. As expected, this flux exhibits the features of an enzymatic reaction, being nearly linear at small concentrations of intracellular sodium and saturating at large concentrations. However, if we include the effects of the reverse reactions, we see that it should be possible to run the pump backward by maintaining sufficiently high levels of extracellular sodium and in-

tracellular potassium, so that the energy stored in the electrochemical gradients can be extracted. Indeed, when this is the case experimentally, ATP is synthesized from ADP.

Other important pumps are Ca2+ ATPases and transporters that keep the intracellular concentration of Ca2+ low. Calcium is extremely important to the operation of cells (as will be discussed in Chapter 5). Internal free calcium is maintained at low concentrations (10-7 M) compared to high concentrations of extracellular calcium (10-3 M). The flow of Ca2+ down its steep concentration gradient in response to extracellular signals is one means of transmitting signals rapidly across the plasma membrane. The Ca2+ gradient is maintained in part by Ca2+ pumps in the membrane that actively transport Ca2+ out of the cell. One of these is an ATPase, while the other is a passive antiporter that is driven by the Na+ electrochemical gradient. The best-understood Ca2+ pump is an ATPase in the sarcoplasmic reticulum of muscle cells (Exercise 9). This Ca2+ pump has been found to function in a way similar to the sodium-potassium pump. In fact, the carriers for these two are known from DNA sequencing to be homologous proteins.

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