Alkali-Metal Ions and Membrane Transport

Introduction

Sodium and potassium ions carry no unpaired electrons, form no covalent bonds with proteins and never change oxidation state in biology. Yet the difference between them is a matter of life and death: nerve impulses, kidney function and the uptake of nutrients all depend on keeping K⁺ inside cells and Na⁺ outside. This page explores how proteins tell apart two ions that differ by only about 36 pm in radius, and how cells spend energy to keep them separated.

Core explanation

The gradients. A typical animal cell contains about 140 mM K⁺ and 10–15 mM Na⁺, while blood plasma contains about 4–5 mM K⁺ and 140–145 mM Na⁺. These opposing gradients store energy, and together with channels that let K⁺ leak out they give a resting membrane potential of roughly −70 mV (inside negative).

Weak binders need precise sites. Na⁺ (ionic radius about 102 pm) and K⁺ (about 138 pm) are large, singly charged, closed-shell ions. They bind oxygen donors only weakly and exchange water extremely fast. With no ligand field effects to exploit, proteins must select them using size, coordination number and the cost of removing water .

The potassium channel filter. In potassium channels, four protein subunits line a narrow tunnel with backbone carbonyl oxygens from the sequence TVGYG. Each binding site in the filter surrounds the ion with eight oxygens in a square-antiprismatic cage — the same arrangement as the eight water molecules that surround a hydrated K⁺. A K⁺ ion can therefore shed its water shell and be "re-solvated" by the carbonyls at almost no energetic cost. Na⁺ is too small to touch all eight oxygens at once in this rigid cage; it would lose its strongly held water without being compensated. Because Na⁺ has a larger dehydration energy than K⁺ (smaller ion, higher charge density), entering the filter is unfavourable for Na⁺. The result is a selectivity for K⁺ over Na⁺ of more than 1000-fold, yet K⁺ still passes at up to about 10⁸ ions per second, because the ions repel one another along a single file of sites.

Sodium channels use a wider filter lined partly by carboxylate side chains; Na⁺ passes with some of its water still attached, and selectivity is lower (roughly 10- to 30-fold).

The Na⁺/K⁺-ATPase. Channels only let ions run down gradients. The gradients themselves are built by the sodium pump, which uses one ATP to move 3 Na⁺ out of and 2 K⁺ into the cell. The pump cycles between conformations that open alternately to the inside and outside, with ion-binding sites whose affinity changes as the protein is phosphorylated and dephosphorylated. Because it moves net positive charge out, it is electrogenic . This pump consumes a large share of the ATP made in resting animal cells, and a much larger share in nerve tissue.

Ionophores. Some microbial molecules, such as valinomycin, wrap K⁺ in a ring of carbonyl oxygens and carry it across membranes, mirroring the channel's chemistry in a small molecule.

Step-by-step reasoning

To explain why a given site prefers K⁺ or Na⁺:

1. Compare the dehydration energies: Na⁺ is harder to dehydrate than K⁺. 2. Ask whether the site's donors can replace the lost water at matching distances. 3. A rigid, larger cavity rewards K⁺ and penalises Na⁺. 4. A smaller or more flexible site with charged donors can favour Na⁺.

Visual explanation

Draw the potassium channel as four staves of a barrel with a narrow neck. In the neck, stack four rings of carbonyl oxygens pointing inwards. Place K⁺ ions in alternate cages separated by water molecules, and show a smaller Na⁺ ion rattling in a cage, touching only some of the oxygens.

Real-world analogy

The selectivity filter is like a glove designed for a particular hand. A hand of the right size slips out of its mitten (the water shell) and straight into the glove. A smaller hand can get in, but it does not fill the fingers, so it would rather keep its mitten on and stay outside.

Real-world example

Digoxin, a drug derived from foxglove, inhibits the Na⁺/K⁺-ATPase in heart muscle. Intracellular Na⁺ rises, which slows removal of Ca²⁺ by the Na⁺/Ca²⁺ exchanger, so more calcium is available for contraction. The narrow margin between useful and toxic doses reflects how central the pump is to every cell.

Why?

Why does K⁺ pass through a channel that rejects the smaller Na⁺? Selectivity is set by the balance between the energy lost on dehydration and the energy regained on binding. The filter matches K⁺'s hydration geometry, so the balance is near zero for K⁺ but unfavourable for Na⁺.

Common misconception

"Smaller ions always pass more easily through narrow pores." Hydrated Na⁺ is effectively larger than hydrated K⁺, and stripping its water is costly. Selectivity depends on energetics of dehydration and rebinding, not on a simple sieve.

Worked example

Question: A cell's Na⁺/K⁺-ATPase hydrolyses 1.0 × 10⁶ ATP molecules per second. How many Na⁺ and K⁺ ions are moved per second, and what is the net charge transferred?

Reasoning: Each cycle moves 3 Na⁺ out and 2 K⁺ in. Na⁺ out = 3.0 × 10⁶ s⁻¹; K⁺ in = 2.0 × 10⁶ s⁻¹. Net positive charge out = 3 − 2 = 1 per ATP.

Answer: 3.0 × 10⁶ Na⁺ out and 2.0 × 10⁶ K⁺ in per second, a net 1.0 × 10⁶ positive charges out per second.

Quick check

1. Which ion has the larger dehydration energy, Na⁺ or K⁺, and why? Answer: Na⁺, because it is smaller with a higher charge density, so it holds its water molecules more strongly.

Exam focus

Examiners reward answers that explain selectivity through dehydration energy and the eight-oxygen carbonyl cage, not through size alone. Learn the pump stoichiometry (3 Na⁺ out, 2 K⁺ in, 1 ATP) and the approximate intracellular and extracellular concentrations.

Advanced insight

Computer simulations suggest that the rigidity of the filter matters as much as cavity size: if the carbonyls were fully flexible they could close around Na⁺. Selectivity arises from the protein holding its donors at K⁺-appropriate distances, a principle also used when chemists design crown ethers and cryptands with matched cavities.

Summary

Cells keep K⁺ high inside and Na⁺ high outside. Potassium channels select K⁺ over Na⁺ by more than 1000-fold using a rigid ring of eight carbonyl oxygens that mimics K⁺'s water shell, making dehydration unfavourable only for Na⁺. The Na⁺/K⁺-ATPase builds the gradients, moving 3 Na⁺ out and 2 K⁺ in per ATP.

Practice questions

1. State the approximate intracellular and extracellular concentrations of K⁺. Answer: About 140 mM inside the cell and about 4–5 mM outside. 2. Explain why the Na⁺/K⁺-ATPase is described as electrogenic. Answer: Each cycle moves three positive charges out and two in, so it transfers one net positive charge out of the cell and contributes to the membrane potential. 3. Why can proteins not use ligand field effects to distinguish Na⁺ from K⁺? Answer: Both are closed-shell ions with no d electrons, so there is no ligand field stabilisation; only size, coordination number and hydration differ. 4. Valinomycin carries K⁺ across membranes far better than Na⁺. Suggest why. Answer: Its ring of carbonyl oxygens forms a rigid cavity that matches K⁺ and replaces its water shell, whereas Na⁺ is too small to be fully coordinated and loses more energy on dehydration.