ATP-driven pumps and gradient-driven cotransport

Why some transport needs a power source

A channel or a facilitated carrier can only let a solute slide toward lower electrochemical potential. Cells nonetheless keep sodium low inside, potassium high inside, and cytosolic calcium thousands of times below its outside level. Each of those gradients is uphill for the solute being moved, so something must pay for it. Two payment schemes exist.

• Direct (primary) active transport. The protein couples movement of a solute to a chemical reaction, usually ATP hydrolysis.
• Indirect (secondary) active transport. The protein couples the uphill movement of one solute to the downhill movement of another. The downhill solute's gradient is a stored energy supply that was itself built by a primary pump.

This topic treats both, then does the bookkeeping that tells you whether a given coupling can work. How the resulting ion gradients generate a membrane voltage is a separate question; here the pump is a machine that moves ions, and we ask only what it moves, how, and at what energy price.

Notation for the energy bookkeeping

For a species of charge $z$ moving from outside to inside a cell whose interior is at membrane potential $V$ (inside relative to outside), the free-energy change per mole is

$$\Delta G_\text{in} = RT\ln\frac{[X]_\text{in}}{[X]_\text{out}} + zFV$$

The first term is the concentration (chemical) contribution and the second the electrical one. A negative value means inward movement is spontaneous. Moving the same species outward flips the sign. At 310 K, $RT \approx 2.577$ kJ/mol, and $F = 96{,}485$ C/mol. For an uncharged solute the electrical term vanishes. For a coupled step, add the free-energy changes of everything that moves together, weighted by how many of each move per cycle.

Pumps that spend ATP directly

P-type pumps

P-type pumps form a covalent phosphorylated intermediate: the terminal phosphate of ATP is transferred onto a conserved aspartate side chain of the pump itself. The name comes from this phosphate. The pump alternates between two broad shapes. In E1, the ion-binding sites face the cytosol and bind the exported ion tightly. In E2, the sites face the outside and bind that ion weakly. Phosphorylation and dephosphorylation drive the switch between them, which is how the energy of ATP becomes a change in affinity and access.

The Na+/K+ pump is the standard example. Each cycle exports 3 Na+ and imports 2 K+ at the cost of one ATP. The steps are:

1. In E1, three Na+ bind from the cytosol, where their affinity for the sites is high.
2. Bound Na+ promotes phosphorylation of the aspartate by ATP, giving E1-P with the ions occluded (trapped inside the protein).
3. The protein relaxes to E2-P. The sites now face outward and have low affinity for Na+, so 3 Na+ are released to the outside.
4. In E2-P, the sites have high affinity for K+. Two K+ bind from the outside, and that binding triggers hydrolysis of the aspartyl phosphate, giving E2 with K+ occluded.
5. ATP binding to the dephosphorylated enzyme speeds the return to E1. The sites again face the cytosol and affinity for K+ drops, so 2 K+ are released inside.

Because 3 positive charges leave and only 2 enter, each cycle moves one net positive charge out. The pump is therefore electrogenic. Whether that small imbalance matters for the membrane voltage belongs to the later topic on the resting potential; for now note only that the stoichiometry is not a charge-neutral exchange.

The same chemistry underlies the calcium pumps. One type sits in the plasma membrane and another in the membrane of the endoplasmic reticulum (the sarcoplasmic reticulum in muscle). Both are P-type, both phosphorylate an aspartate, and both lower cytosolic Ca2+ by exporting it to the outside or storing it in the lumen. This lets calcium serve as a signal: its resting level is so low that a modest influx raises the concentration several-fold.

V-type and F-type pumps

V-type pumps are proton pumps in the membranes of lysosomes, endosomes and secretory vesicles, where they acidify the lumen. They are large, multi-subunit rotary machines. ATP hydrolysis in one sector turns a ring in another, which carries protons across. Unlike P-type pumps, they form no phosphorylated intermediate, so a labeling experiment with radioactive phosphate does not produce a labeled pump. F-type ATP synthase has a similar architecture run in reverse: proton flow down its gradient turns the rotor and drives ATP formation. That reverse mode belongs to a later topic.

ABC transporters

ABC transporters contain two ATP-binding cassettes, each paired with a membrane-spanning domain. Binding of ATP brings the two cassettes together, which switches the membrane domain from an inward-facing to an outward-facing conformation; hydrolysis and release of products resets it. Different members export or import a very wide range of substrates, including lipids, peptides, sugars and ions. The unifying theme is the ATP-driven cassette dimer, not any specific cargo.

Letting one gradient pay for another

A secondary active transporter has no ATP site. Instead it has binding sites for two solutes and changes shape only in ways that keep their movements locked together. When both solutes travel in the same direction the protein is a symporter (cotransporter); when they travel in opposite directions it is an antiporter (exchanger). In both cases the downhill solute is usually Na+, because the Na+/K+ pump keeps its inward gradient steep.

Symport: sodium-glucose cotransport

The intestinal isoform of the sodium-glucose cotransporter couples 2 Na+ to each glucose. A kidney isoform couples only 1. Sodium moves in down its electrochemical gradient and drags glucose along even when glucose is already more concentrated inside. This differs from a glucose uniporter, which only allows downhill movement. The coupling is stoichiometric: if the transporter slips, energy is wasted and accumulation falls short.

Antiport: Na+/Ca2+ and Na+/H+ exchange

The Na+/Ca2+ exchanger lets 3 Na+ enter while 1 Ca2+ leaves. It moves one net positive charge in per cycle, so it is also electrogenic. The Na+/H+ exchanger swaps one Na+ in for one H+ out, so it is electroneutral, and it can raise cytosolic pH when the cell has become too acidic. Both exchangers depend on the sodium gradient and not on ATP directly.

The coupling ratio sets the ceiling

At equilibrium of the coupled step, the sum of the free-energy changes is zero. Any larger solute gradient would force the transporter to run backward. So the maximum gradient is set by the driving force and by the number of driver ions per cycle: more Na+ per solute means a higher ceiling.

Worked example: Na+ entry and the largest glucose gradient

Use model-cell values: Na+ at 145 mM outside and 12 mM inside, $V = -60$ mV, $T = 310$ K. Find the free energy for one mole of Na+ entering.

Concentration term: $RT\ln(12/145) = 2.577 \times (-2.492) \approx -6.42$ kJ/mol.

Electrical term: $zFV = (+1)(96{,}485)(-0.060) \approx -5.79$ kJ/mol.

Total: $\Delta G_\text{Na,in} \approx -12.2$ kJ/mol. Both terms favor entry, because Na+ is both more concentrated outside and drawn toward a negative interior.

For a symporter taking $n$ Na+ per glucose, glucose accumulation stops when

$$n\,\Delta G_\text{Na,in} + RT\ln\frac{[\text{glc}]_\text{in}}{[\text{glc}]_\text{out}} = 0$$

so the natural log of the ratio equals $-n\,\Delta G_\text{Na,in}/RT$.

• With $n = 2$: $2 \times 12.21 / 2.577 \approx 9.476$, and $e^{9.476} \approx 1.3 \times 10^4$.
• With $n = 1$: $12.21/2.577 \approx 4.738$, and $e^{4.738} \approx 114$.

Doubling the Na+ stoichiometry doubles the exponent, so it squares the ratio: $114^2 \approx 1.3 \times 10^4$. These are thermodynamic limits; real cells stay below them because glucose is also consumed or leaves by other routes.

Checking a calcium exchanger

With the same model Na+ values and a model Ca2+ of 1.2 mM outside and 100 nM inside, exporting a mole of Ca2+ costs $RT\ln(1.2\times 10^{-3}/10^{-7}) + 2F(0.060) \approx 24.2 + 11.6 \approx +35.8$ kJ/mol. Three Na+ entering supply $3 \times 12.21 \approx 36.6$ kJ/mol. The sum is only slightly negative, so the exchanger works but sits close to equilibrium. That is one reason ATP-driven calcium pumps share the work in many cells.

Can one ATP pay for one cycle of the Na+/K+ pump?

The pump moves three Na+ out and two K+ in, both against their gradients. Add up the costs and compare them with what ATP can supply.

Worked example: the energy budget of one pump cycle

Use the Na+ values above, plus K+ at 4 mM outside and 140 mM inside, $V = -60$ mV (model-cell values).

• Exporting 3 Na+ reverses the inward movement, so it costs $3 \times 12.21 \approx +36.6$ kJ/mol.
• Importing one K+: $RT\ln(140/4) + F(-0.060) = 2.577 \times 3.555 - 5.79 \approx 9.16 - 5.79 = +3.37$ kJ/mol. Two K+ cost about $+6.7$ kJ/mol.
• Total for one cycle: $36.6 + 6.7 \approx 43$ kJ/mol.

As an illustrative value, ATP hydrolysis under typical cell conditions can supply roughly 50 kJ/mol. One ATP therefore pays for the cycle with a small margin, consistent with the observed stoichiometry. A hypothetical pump exporting 4 Na+ per ATP would need about $48.8 + 6.7$ kJ/mol, more than the illustrative supply, and could not run at these gradients. The pump also slows and finally stalls if the gradients steepen or the ATP supply falls.

Estimating the current a pump population carries

Worked example: pump current

Suppose a cell has $10^6$ pumps, each completing 100 cycles per second, with one net charge moved outward per cycle.

Net charge transport rate: $10^6 \times 100 \times 1 = 10^8$ charges per second.

Multiply by the elementary charge: $10^8 \times 1.602 \times 10^{-19}$ C $\approx 1.6 \times 10^{-11}$ A, or about 16 pA.

The result is small, and it shows how a stoichiometric property (one net charge per cycle) turns into a current that can in principle be measured. It uses only turnover and count; it does not say what voltage the cell has.

Stopping the pump: why cotransport fades slowly

Suppose a pump-specific inhibitor is added, or ATP is depleted. Two kinds of transport behave differently.

• The pump itself stops almost at once, because it needs ATP at every cycle. Its dependence on ATP is direct.
• A Na+-driven cotransporter keeps working for a while, because the Na+ gradient it relies on is stored energy. Sodium leaks in through channels and other transporters, and the gradient decays gradually, over minutes in many cells, not instantly. As intracellular Na+ rises, the driving force falls, and the maximum glucose gradient shrinks with it. The dependence on ATP is indirect.

So a time course is diagnostic. If removing ATP abolishes a transport process within seconds, the process is probably directly ATP-driven. If it persists and then falls over minutes, in step with the sodium gradient, it is probably secondary. Adding a membrane-permeant agent that dissipates the Na+ gradient abolishes secondary transport immediately without lowering ATP, which separates the two cases further.

How pumps are studied

Several standard approaches build the case that a protein is an ATP-driven pump.

• Reconstitution. The purified protein is inserted into artificial vesicles (liposomes) that contain no other transport proteins. If ATP supplied to the correct side produces solute accumulation in the vesicle, the protein alone is sufficient. Orientation matters, since the ATP site must face the solution holding the ATP.
• ATP dependence. Transport must require ATP (and the magnesium it is normally bound to), and non-hydrolyzable analogs should not support it.
• Radioactive labeling. Supplying ATP with a radioactive terminal phosphate, then quickly stopping the reaction and separating proteins, labels a P-type pump through its phosphorylated aspartate. A V-type pump gives no such labeled intermediate. Brief reactions with Na+ alone favor the labeled state, and adding K+ makes the label disappear, matching the order of the cycle.
• Specific inhibitors. A pump-specific inhibitor that binds the extracellular face can lock the protein in an E2-like state. Applied to cells or vesicles, it confirms that a process depends on that pump and helps assign steps of the cycle.

Together, these experiments connect a molecular cycle to a measurable flux and justify the stoichiometries used throughout this topic.