Why does the K⁺ channel conduct K⁺ far better than the smaller Na⁺?

Its carbonyl-lined filter replaces the hydration shell of K⁺ exactly, but is too wide to solvate Na⁺ well

Na⁺ is too large to enter the pore

The channel binds Na⁺ covalently

K⁺ is transported with ATP hydrolysis

What happens to the iron of a haemoglobin subunit when O₂ binds?

High-spin Fe(II) out of the porphyrin plane becomes low-spin and moves into the plane

Low-spin Fe(II) becomes high-spin and moves out of the plane

Fe(II) is oxidised irreversibly to Fe(III) and released

The proximal histidine dissociates

Haemocyanin, the oxygen carrier of many molluscs and arthropods, contains

two copper ions per O₂, turning blue when oxygenated

In oxyhaemerythrin, dioxygen is bound

end-on to one iron of the di-iron pair, as a hydroperoxide hydrogen-bonded to the bridging oxo

side-on between two copper ions

to a haem iron trans to histidine

as a free superoxide radical in the protein

The intense blue colour of plastocyanin (ε ≈ 5000 L mol⁻¹ cm⁻¹ near 600 nm) arises from

cysteine thiolate → Cu(II) charge transfer

a d–d transition of octahedral Cu(II)

Cu(I) → ligand charge transfer

High-potential iron proteins (HiPIPs) and bacterial ferredoxins both contain [4Fe–4S] cubes, yet their potentials differ by about 0.7 V. The best explanation is that

HiPIPs use the [4Fe–4S]³⁺/²⁺ couple and ferredoxins the [4Fe–4S]²⁺/⁺ couple, the protein environment deciding which pair is accessible

HiPIPs contain copper in place of one iron

Ferredoxins have haem groups attached to the cube

The two clusters have different numbers of sulfur atoms

In carbonic anhydrase, the species that attacks CO₂ is

a zinc-bound hydroxide, formed because Zn²⁺ lowers the pKa of coordinated water to about 7

Bioinorganic Chemistry: Ion Transport, Oxygen Carriers, Electron Transfer, Nitrogen Fixation and Metalloenzymes

The Bioinorganic Chemistry sub-heading of Section 2 of the GATE Chemistry (CY) paper, in its own order: the transport of Na⁺ and K⁺; oxygen binding, transport and utilisation; electron-transfer reactions; nitrogen fixation; and the metalloenzymes containing magnesium, molybdenum, iron, cobalt, copper and zinc. The emphasis is on what the coordination chemistry of the earlier chapters explains — spin states, geometry, Lewis acidity, redox potentials and the choice of metal — rather than on the biology around it.

1. Na⁺ and K⁺ transport

Cells keep K⁺ high inside (about 140 mM) and Na⁺ high outside (about 145 mM), and this gradient drives nerve impulses and the uptake of nutrients. The Na⁺/K⁺-ATPase maintains it by active transport: each cycle hydrolyses one ATP and moves 3 Na⁺ out and 2 K⁺ in, so it is electrogenic, exporting one net positive charge. Passive movement down the gradient runs through ion channels. The K⁺ channel conducts K⁺ about 10⁴ times better than the smaller Na⁺ because its selectivity filter is lined with backbone carbonyl oxygens spaced to replace exactly the water molecules around a dehydrated K⁺; Na⁺ is too small to be solvated by all of them at once, so shedding its water costs more than the filter returns.

The same size-matching explains ionophores, small molecules that carry ions across membranes: valinomycin, a cyclic depsipeptide, wraps K⁺ in six carbonyl oxygens and is strongly K⁺-selective; synthetic crown ethers and cryptands select by cavity size — 18-crown-6 for K⁺, 15-crown-5 for Na⁺, 12-crown-4 for Li⁺ — and the three-dimensional cryptands bind more strongly still (the macrobicyclic effect).

2. Oxygen binding, transport and utilisation

Myoglobin (a monomer, storing O₂ in muscle) and haemoglobin (an α₂β₂ tetramer, transporting O₂ in blood) carry O₂ on a haem: Fe(II) in a porphyrin, bound below the ring to a proximal histidine, with the sixth site free for O₂. In deoxy-haemoglobin the iron is high-spin Fe(II), five-coordinate and too large for the porphyrin hole, so it sits about 40 pm out of the plane. On binding O₂ it becomes low-spin, shrinks, and moves into the plane, pulling the proximal histidine and the attached helix with it; the movement is transmitted across the subunit interfaces and raises the O₂ affinity of the remaining haems — cooperativity. So myoglobin gives a hyperbolic binding curve, Y = p/(p + P₅₀), and haemoglobin a sigmoidal one described by the Hill equation Y/(1 − Y) = (p/P₅₀)ⁿ with n ≈ 2.8. Oxyhaemoglobin is diamagnetic and is best described as Fe(III) bound to superoxide with the spins coupled; a distal histidine hydrogen-bonds the bound O₂, disfavours the linear binding that CO prefers, and so reduces CO’s natural advantage.

The three natural oxygen carriers
Carrier	Metal site	How O₂ binds	Colour change
Haemoglobin, myoglobin (vertebrates)	one Fe(II) haem with proximal His	end-on, bent, to one Fe (Fe(III)–O₂⁻ description)	dark red (deoxy) to bright red (oxy)
Haemocyanin (arthropods, molluscs)	two Cu(I), each bound to three His	side-on bridging peroxide μ-η²:η² between two Cu(II)	colourless (deoxy) to blue (oxy)
Haemerythrin (marine worms)	non-haem di-iron with a bridging oxo/hydroxo	end-on as hydroperoxide to one Fe(III) of the pair	colourless (deoxy) to violet-pink (oxy)

Utilisation. The O₂ carried to the tissues is reduced in the mitochondria by cytochrome c oxidase, whose haem a₃–Cu_B site takes four electrons and four protons to reduce O₂ to two water molecules without releasing partly reduced intermediates. Cytochrome P450 uses a haem with a cysteine thiolate ligand to insert one oxygen atom of O₂ into C–H bonds (monooxygenation, via a high-valent iron–oxo species), central to drug metabolism.

3. Electron-transfer proteins

Biological electron carriers cycle between two oxidation states with little structural change, which keeps the reorganisation energy small and electron transfer fast (outer-sphere, Marcus behaviour). Cytochromes use haem Fe(III)/Fe(II), with two axial protein ligands (His/Met in cytochrome c) so no site is left for O₂. Iron–sulfur proteins: rubredoxin (one Fe in four cysteine thiolates), plant-type ferredoxins ([2Fe–2S]), and cubane [4Fe–4S] clusters; the same cube works as [4Fe–4S]²⁺/⁺ at strongly negative potentials in bacterial ferredoxins and as [4Fe–4S]³⁺/²⁺ at positive potentials in high-potential iron proteins (HiPIPs), the protein environment choosing the pair. Blue (type 1) copper proteins — plastocyanin, azurin — bind Cu through two His, one Cys and a weak Met in a distorted tetrahedral geometry that sits between the preferences of Cu(II) and Cu(I) (the "entatic" state), minimising reorganisation; their intense blue colour (ε ≈ 5000 at about 600 nm) is S(Cys) → Cu(II) charge transfer, far stronger than any d–d band.

4. Nitrogen fixation

Nitrogenase reduces N₂, whose triple bond (945 kJ/mol) makes it one of the least reactive molecules, to ammonia at room temperature and 1 atm — the biological counterpart of the Haber process. It has two proteins. The Fe protein, carrying a [4Fe–4S] cluster, binds and hydrolyses MgATP and delivers electrons one at a time; the MoFe protein contains the P-cluster (Fe₈S₇), which relays electrons, and the FeMo-cofactor, MoFe₇S₉C with a central carbide and a homocitrate on molybdenum, where N₂ is bound and reduced. The limiting stoichiometry is N₂ + 8H⁺ + 8e⁻ + 16MgATP → 2NH₃ + H₂ + 16MgADP + 16Pᵢ: one H₂ is formed obligatorily for every N₂ reduced, so eight electrons, not six, are used. Vanadium and iron-only nitrogenases also exist.

5. Metalloenzymes of Mg, Mo, Fe, Co, Cu and Zn

Metalloenzymes the syllabus names
Metal	Examples	What the metal does
Mg	chlorophyll; kinases and ATPases (Mg–ATP); enolase; RuBisCO	Lewis acid that binds and orients phosphate; light harvesting in the chlorin ring
Mo	nitrogenase; xanthine oxidase, sulfite oxidase, nitrate reductase (molybdopterin enzymes)	oxygen-atom transfer cycling Mo(VI)/Mo(IV); N₂ reduction in FeMo-co
Fe	catalase, peroxidase, cytochrome P450, methane monooxygenase, ribonucleotide reductase	redox and O₂ activation through high-valent Fe=O species
Co	vitamin B₁₂ (cobalamin) enzymes: methionine synthase, methylmalonyl-CoA mutase	Co in a corrin ring; Co–C bond homolysis gives radicals for rearrangements; methyl transfer via Co(I)
Cu	Cu/Zn superoxide dismutase; tyrosinase; cytochrome c oxidase; ceruloplasmin	Cu(II)/Cu(I) redox; O₂ binding and activation
Zn	carbonic anhydrase; carboxypeptidase A; alcohol dehydrogenase; zinc fingers	redox-inert Lewis acid (d¹⁰): activates water or C=O; structural in zinc fingers

Carbonic anhydrase shows why zinc is chosen for hydrolytic chemistry. Zn²⁺, bound to three histidines, holds a water molecule whose pKa is lowered from about 15.7 to about 7, so at physiological pH it is largely Zn–OH⁻, a strong nucleophile held in place; it attacks CO₂ to give bound bicarbonate, which is displaced by water, and the cycle — among the fastest enzymes known, turnover about 10⁶ s⁻¹ — is limited by proton transfer. Zn²⁺ is ideal because as d¹⁰ it has no ligand-field preference (flexible geometry), is not redox-active (no unwanted radical chemistry), and is a strong enough Lewis acid. In carboxypeptidase A the same Zn²⁺ polarises the peptide C=O for attack by water. Vitamin B₁₂ chemistry turns on the weak Co–C bond: homolysis of adenosylcobalamin gives Co(II) and a 5′-deoxyadenosyl radical that abstracts hydrogen to start carbon-skeleton rearrangements, while methylcobalamin passes CH₃⁺ to homocysteine via Co(I), a supernucleophile.

Key takeaways

The Na⁺/K⁺-ATPase moves 3 Na⁺ out and 2 K⁺ in per ATP; K⁺ channels, valinomycin and crown ethers select by size and desolvation cost.
Deoxy-Hb has high-spin, out-of-plane Fe(II); O₂ binding makes it low-spin and in-plane, which drives cooperativity; haemocyanin binds O₂ as μ-η²:η² peroxide between two Cu, haemerythrin as hydroperoxide on one Fe.
Cytochromes, Fe–S proteins and blue copper proteins transfer electrons with minimal reorganisation; the blue colour is S(Cys) → Cu(II) LMCT.
Nitrogenase: N₂ + 8H⁺ + 8e⁻ + 16ATP → 2NH₃ + H₂; N₂ binds at the FeMo-cofactor, MoFe₇S₉C.
Zn²⁺ is the redox-inert Lewis acid of hydrolysis (carbonic anhydrase’s Zn–OH⁻); Co in B₁₂ works through Co–C homolysis; Mo enzymes transfer oxygen atoms; Mg handles phosphate.

Practice questions (16)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

How many Na⁺ ions does the Na⁺/K⁺-ATPase pump out of the cell for each ATP hydrolysed?
Numerical answer — type the value.
Show answer
Answer: 3
Each cycle exports 3 Na⁺ and imports 2 K⁺ per ATP. The unequal exchange is what makes the pump electrogenic; answering 2 confuses the Na⁺ count with the K⁺ count.
What net charge, in units of the elementary charge, does one cycle of the Na⁺/K⁺-ATPase move out of the cell?
Numerical answer — type the value.
Show answer
Answer: 1
3 Na⁺ out (+3) and 2 K⁺ in (−2 out) give a net +1 exported per ATP, which contributes directly to the negative resting potential inside the cell. Answering 5 adds the ions instead of subtracting.
Why does the K⁺ channel conduct K⁺ far better than the smaller Na⁺?
1. Its carbonyl-lined filter replaces the hydration shell of K⁺ exactly, but is too wide to solvate Na⁺ well
2. Na⁺ is too large to enter the pore
3. The channel binds Na⁺ covalently
4. K⁺ is transported with ATP hydrolysis
Show answer
Answer: A — Its carbonyl-lined filter replaces the hydration shell of K⁺ exactly, but is too wide to solvate Na⁺ well
Selection is by desolvation: K⁺ loses its water and is immediately solvated by the filter’s oxygens at the right distances, so the cost is repaid; Na⁺ is smaller, not larger, and cannot contact all the oxygens at once. Channels are passive; the pump uses ATP.
What happens to the iron of a haemoglobin subunit when O₂ binds?
1. High-spin Fe(II) out of the porphyrin plane becomes low-spin and moves into the plane
2. Low-spin Fe(II) becomes high-spin and moves out of the plane
3. Fe(II) is oxidised irreversibly to Fe(III) and released
4. The proximal histidine dissociates
Show answer
Answer: A — High-spin Fe(II) out of the porphyrin plane becomes low-spin and moves into the plane
Five-coordinate high-spin Fe(II) is too big for the ring hole and sits out of plane; the six-coordinate oxy form is low-spin, smaller and in plane. The move tugs the proximal His and triggers the conformational change behind cooperativity. Irreversible oxidation gives methaemoglobin, which cannot carry O₂.
Myoglobin binds O₂ with P₅₀ = 2.8 torr, following Y = p/(p + P₅₀). What fraction of myoglobin is oxygenated at an O₂ partial pressure of 8.4 torr, to two decimal places?
Numerical answer — type the value.
Show answer
Answer: 0.75
Y = 8.4/(8.4 + 2.8) = 8.4/11.2 = 0.75. The curve is hyperbolic because each myoglobin has one independent haem; doubling p from P₅₀ gives only 0.67, far short of the steep sigmoidal rise of haemoglobin.
An idealised cooperative O₂ carrier follows the Hill equation Y/(1 − Y) = (p/P₅₀)ⁿ with n = 3. What is its fractional saturation Y at p = 2P₅₀, to two decimal places?
Numerical answer — type the value.
Show answer
Answer: 0.89
Y/(1 − Y) = 2³ = 8, so Y = 8/9 = 0.889, i.e. 0.89. A non-cooperative carrier (n = 1) at the same pressure gives Y = 2/3 = 0.67: cooperativity is what lets haemoglobin load fully in the lungs and unload in the tissues over a narrow pressure range.
Haemocyanin, the oxygen carrier of many molluscs and arthropods, contains
1. two copper ions per O₂, turning blue when oxygenated
2. a haem iron like haemoglobin
3. a non-haem di-iron site
4. a single zinc ion
Show answer
Answer: A — two copper ions per O₂, turning blue when oxygenated
Despite the name, haemocyanin has no haem: two Cu(I) ions, each held by three histidines, bind O₂ as a side-on μ-η²:η² peroxide between two Cu(II), and the oxy form is blue from peroxide → Cu(II) charge transfer. The non-haem di-iron carrier is haemerythrin.
In oxyhaemerythrin, dioxygen is bound
1. end-on to one iron of the di-iron pair, as a hydroperoxide hydrogen-bonded to the bridging oxo
2. side-on between two copper ions
3. to a haem iron trans to histidine
4. as a free superoxide radical in the protein
Show answer
Answer: A — end-on to one iron of the di-iron pair, as a hydroperoxide hydrogen-bonded to the bridging oxo
In deoxyhaemerythrin one Fe(II) of the pair has a vacant site; O₂ binds there, both irons are oxidised to Fe(III), and the bridging hydroxide’s proton moves to give Fe–OOH hydrogen-bonded back to the μ-oxo. Side-on binding between two metals is haemocyanin’s mode.
Which of the following proteins function mainly as electron carriers?
1. Cytochrome c
2. Ferredoxin
3. Plastocyanin
4. Carbonic anhydrase
Show answer
Answer: A — Cytochrome c; B — Ferredoxin; C — Plastocyanin
Cytochrome c (haem Fe(III)/Fe(II)), ferredoxin (Fe–S clusters) and plastocyanin (type 1 Cu(II)/Cu(I)) shuttle electrons. Carbonic anhydrase uses redox-inert Zn²⁺ as a Lewis acid to hydrate CO₂, with no electron transfer at all.
The intense blue colour of plastocyanin (ε ≈ 5000 L mol⁻¹ cm⁻¹ near 600 nm) arises from
1. cysteine thiolate → Cu(II) charge transfer
2. a d–d transition of octahedral Cu(II)
3. Cu(I) → ligand charge transfer
4. a haem π → π* band
Show answer
Answer: A — cysteine thiolate → Cu(II) charge transfer
An ε of thousands is far beyond a Laporte-forbidden d–d band (ε below about 100); it is an allowed S(Cys) π → Cu(II) LMCT, favoured by the short Cu–S bond of the distorted tetrahedral site. Cu(I) is d¹⁰ and colourless, and there is no haem.
High-potential iron proteins (HiPIPs) and bacterial ferredoxins both contain [4Fe–4S] cubes, yet their potentials differ by about 0.7 V. The best explanation is that
1. HiPIPs use the [4Fe–4S]³⁺/²⁺ couple and ferredoxins the [4Fe–4S]²⁺/⁺ couple, the protein environment deciding which pair is accessible
2. HiPIPs contain copper in place of one iron
3. Ferredoxins have haem groups attached to the cube
4. The two clusters have different numbers of sulfur atoms
Show answer
Answer: A — HiPIPs use the [4Fe–4S]³⁺/²⁺ couple and ferredoxins the [4Fe–4S]²⁺/⁺ couple, the protein environment deciding which pair is accessible
The same Fe₄S₄ core has three accessible states, 3+, 2+ and 1+. A hydrophobic, weakly hydrogen-bonded pocket in HiPIPs stabilises the more oxidised pair (about +0.35 V), while ferredoxins cycle 2+/1+ (about −0.4 V). There is no copper or haem, and the core composition is identical.
In the limiting stoichiometry of nitrogenase, how many MgATP molecules are hydrolysed for each N₂ reduced?
Numerical answer — type the value.
Show answer
Answer: 16
N₂ + 8H⁺ + 8e⁻ + 16MgATP → 2NH₃ + H₂ + 16MgADP + 16Pᵢ: two ATP per electron transferred from the Fe protein, and eight electrons because one H₂ forms obligatorily. Counting six electrons for 2NH₃ alone gives 12.
How many electrons does nitrogenase use per N₂ molecule fixed, including the obligatory H₂ it produces?
Numerical answer — type the value.
Show answer
Answer: 8
Six electrons reduce N₂ to 2NH₃ and two more make the H₂ released with every turnover: 6 + 2 = 8. The chemical minimum of 6 is what the Haber process would suggest, but the enzyme always evolves H₂.
Which metal is at the centre of the corrin ring of vitamin B₁₂?
1. Cobalt
2. Iron
3. Nickel
4. Magnesium
Show answer
Answer: A — Cobalt
Cobalamin has cobalt in a corrin ring, cycling Co(III), Co(II) and Co(I); its weak Co–C bond is the source of the radicals used in mutase reactions. Iron is in haem, magnesium in chlorophyll and nickel in the related F430 cofactor.
In carbonic anhydrase, the species that attacks CO₂ is
1. a zinc-bound hydroxide, formed because Zn²⁺ lowers the pKa of coordinated water to about 7
2. a zinc-bound hydride
3. a Zn(III) oxo species
4. free OH⁻ from the solution
Show answer
Answer: A — a zinc-bound hydroxide, formed because Zn²⁺ lowers the pKa of coordinated water to about 7
Zn²⁺ held by three His acts as a Lewis acid, so the bound water ionises near neutral pH and Zn–OH⁻ is positioned next to the CO₂ binding pocket. Zn is d¹⁰ and redox-inert, so Zn(III) and hydride chemistry are not involved; free hydroxide is scarce at pH 7.
Which of the following enzymes contain molybdenum?
1. Nitrogenase (the common form)
2. Xanthine oxidase
3. Sulfite oxidase
4. Carboxypeptidase A
Show answer
Answer: A — Nitrogenase (the common form); B — Xanthine oxidase; C — Sulfite oxidase
The common nitrogenase has Mo in its FeMo-cofactor, and xanthine and sulfite oxidases carry Mo bound to a molybdopterin, doing oxygen-atom transfer through Mo(VI)/Mo(IV). Carboxypeptidase A is a zinc peptidase.