16.06.02 · inorgchem / bioinorganic

Oxygen transport and storage: hemoglobin, myoglobin, and cooperative binding

stub3 tiersLean: nonepending prereqs

Anchor (Master): Lippard & Berg — Principles of Bioinorganic Chemistry (1994)

Intuition Beginner

Hemoglobin carries oxygen in your blood. Myoglobin stores oxygen in your muscles. Both use an iron atom sitting inside a flat ring called a heme group. When oxygen lands on the iron, it binds reversibly — tight enough to grab O $_{2}$ in the lungs, loose enough to release it where the tissue needs it.

Hemoglobin is a tetramer: four protein subunits, each with its own heme. The remarkable property is cooperative binding. When the first O $_{2}$ molecule binds to one subunit, a shape change ripples through the protein that makes the next subunit bind O $_{2}$ more easily. Each successive binding event gets easier. The result is an S-shaped (sigmoidal) binding curve rather than a simple hyperbola.

Myoglobin is a monomer with a single heme. It binds O $_{2}$ with a hyperbolic curve — no cooperativity because there is only one site. Myoglobin's job is to hold onto O $_{2}$ in muscle until the tissue is truly hypoxic, then release it as a reserve supply.

Visual Beginner

The heme group is a flat porphyrin ring with Fe $^{2 +}$ at its centre, coordinated by four nitrogen atoms in the ring plane. Below the ring, a histidine residue from the protein backbone anchors the iron. Above the ring sits the O $_{2}$ binding site.

Worked example Beginner

Reading the hemoglobin oxygen dissociation curve.

Myoglobin binds O $_{2}$ with a hyperbolic curve: $Y = p O_{2} / (P_{50} + p O_{2})$ , where $P_{50}$ is the partial pressure at half-saturation. Myoglobin has a low $P_{50}$ (~2–3 mmHg), meaning it saturates at low O $_{2}$ pressure — it holds onto oxygen tightly.

Hemoglobin binds O $_{2}$ with a sigmoidal curve modelled by the Hill equation: $Y = p O_{2}^{n} / (P_{50}^{n} + p O_{2}^{n})$ . For hemoglobin, $n \approx 2.8$ (the Hill coefficient), reflecting positive cooperativity among the four subunits. Hemoglobin's $P_{50}$ is about 26 mmHg.

At lung $p O_{2}$ (~~100 mmHg), hemoglobin is nearly fully saturated (~~97%). At tissue $p O_{2}$ (~40 mmHg in resting muscle), the sigmoidal curve drops steeply — hemoglobin releases a large fraction of its O $_{2}$ . This steep region is the physiological sweet spot: small changes in tissue $p O_{2}$ produce large changes in O $_{2}$ delivery, precisely because of cooperativity.

Check your understanding Beginner

Exercise (easy, multiple choice).

In hemoglobin, cooperative binding means:

A. All four subunits bind O $_{2}$ at exactly the same instant B. Each subunit binds O $_{2}$ independently with no effect on the others C. Binding of O $_{2}$ to one subunit increases the O $_{2}$ affinity of the remaining subunits D. Binding of O $_{2}$ to one subunit decreases the O $_{2}$ affinity of the remaining subunits

Hint

"Positive cooperativity" = each binding event makes the next one easier. What does the sigmoidal shape of the curve tell you?

Answer

C. Each O $_{2}$ that binds shifts the protein from the T (tense, low-affinity) state toward the R (relaxed, high-affinity) state, making it progressively easier for the remaining subunits to bind their O $_{2}$ . This produces the characteristic sigmoidal curve. Option A describes all-or-nothing binding ( $n = 4$ ), which does not occur. Option D would be negative cooperativity.

Exercise (medium, short-answer).

Explain why carbon monoxide poisoning is deadly, using what you know about heme-oxygen binding.

Hint

CO is a much stronger-field ligand than O $_{2}$ . How does this affect binding to Fe $^{2 +}$ in heme?

Answer

CO binds to the Fe $^{2 +}$ in heme about 200–250 times more tightly than O $_{2}$ does, because CO is a strong pi-acceptor that forms an exceptionally stable Fe–CO bond through synergic sigma-donation and pi-back-bonding. When CO occupies the binding site, O $_{2}$ cannot bind. Worse, CO-bound subunits lock hemoglobin in the high-affinity R state, so even the remaining O $_{2}$ -carrying subunits refuse to release their oxygen to the tissues. At just 0.1% CO in inspired air, roughly half the heme sites are blocked, causing severe hypoxia despite normal blood O $_{2}$ content.

Formal definition Intermediate+

Hemoglobin is a tetrameric protein ( $α_{2} β_{2}$ in adults) with four heme groups, each containing Fe $^{2 +}$ in a protoporphyrin IX ring. It transports O $_{2}$ from the lungs to peripheral tissues. Myoglobin is a monomeric heme protein that stores O $_{2}$ in muscle cells and facilitates intracellular O $_{2}$ diffusion.

The Hill equation models fractional saturation $Y$ as a function of oxygen partial pressure:

Y = \frac{p O _{2}^{n_{H}}}{P _{50}^{n_{H}} + p O _{2}^{n_{H}}}

where $n_{H}$ is the Hill coefficient and $P_{50}$ is the $p O_{2}$ at half-saturation. For myoglobin, $n_{H} = 1$ (no cooperativity, hyperbolic curve). For human hemoglobin A, $n_{H} \approx 2.8$ , reflecting positive cooperativity among four subunits. The theoretical maximum is $n_{H} = 4$ (perfectly concerted all-or-nothing binding).

T-state and R-state. Hemoglobin exists in two quaternary conformations. The T (tense) state has low O $_{2}$ affinity, stabilised by salt bridges between and within subunits. The R (relaxed) state has high O $_{2}$ affinity. The allosteric equilibrium constant $L_{0} = [T_{0}] / [R_{0}] \approx 1 0^{4}$ for unliganded hemoglobin. O $_{2}$ binding shifts the equilibrium from T toward R.

The Bohr effect. Decreased pH (increased [H $^{+}$ ]) and increased [CO $_{2}$ ] lower hemoglobin's O $_{2}$ affinity, shifting the dissociation curve to the right. Mechanistically, protonation of specific residues (notably His146 on the beta chains) stabilises the T state through additional salt bridges. CO $_{2}$ forms carbamates with the N-terminal amino groups, also stabilising T. This ensures O $_{2}$ release in metabolically active tissues (low pH, high CO $_{2}$ ) and O $_{2}$ loading in the lungs (high pH, low CO $_{2}$ ).

2,3-Bisphosphoglycerate (2,3-BPG). This anion binds in the central cavity of deoxyhemoglobin, forming salt bridges with the beta chains and stabilising the T state. 2,3-BPG reduces O $_{2}$ affinity and is essential for efficient O $_{2}$ unloading. Fetal hemoglobin (HbF, $α_{2} γ_{2}$ ) has lower 2,3-BPG affinity than adult hemoglobin (HbA, $α_{2} β_{2}$ ), giving HbF higher O $_{2}$ affinity for efficient placental O $_{2}$ transfer from mother to fetus.

Heme structure. The heme group is iron(II) protoporphyrin IX: Fe $^{2 +}$ coordinated by four pyrrole nitrogen atoms in a planar tetradentate macrocycle. The proximal histidine (His F8) provides a fifth axial ligand. The sixth coordination site binds O $_{2}$ . In deoxyhemoglobin, Fe $^{2 +}$ is high-spin d $^{6}$ and sits ~0.4 A below the porphyrin plane. Upon O $_{2}$ binding, the iron shifts to low-spin d $^{6}$ and moves into the porphyrin plane, pulling the proximal histidine and triggering the T-to-R conformational change.

Counterexamples to common slips

Hemoglobin and myoglobin are not interchangeable. Hemoglobin is a tetramer with cooperative binding and a sigmoidal curve. Myoglobin is a monomer with hyperbolic binding. They have different physiological roles (transport vs. storage) and different $P_{50}$ values.
Iron does not change oxidation state upon O $_{2}$ binding. Fe $^{2 +}$ remains ferrous. The bonding is best described as Fe $^{2 +}$ coordinating singlet O $_{2}$ with partial electron transfer, not oxidation to Fe $^{3 +}$ . Oxidation to Fe $^{3 +}$ (methemoglobin) destroys O $_{2}$ binding capacity.
The Hill coefficient is not the number of binding sites. $n_{H} \approx 2.8$ for hemoglobin, not 4. The Hill model is an empirical approximation that ignores partially liganded intermediates. $n_{H}$ underestimates the true number of cooperative sites.

Key theorem with proof Intermediate+

Proposition (Hill equation from the two-state binding model). For a protein with $n$ cooperative binding sites, assuming only fully unliganded (P) and fully liganded (PL $_{n}$ ) states are populated, the fractional saturation is $Y = [L]^{n_{H}} / (K_{d}^{n_{H}} + [L]^{n_{H}})$ , where $1 \leq n_{H} \leq n$ .

Proof. The Hill model postulates the equilibrium:

P + n L ⇌ PL_{n}, K = \frac{[ PL _{n} ]}{[ P ] [ L ] ^{n}}

Fractional saturation:

Y = \frac{n [ PL _{n} ]}{[ P ] + [ PL _{n} ]} = \frac{K [ L ] ^{n}}{1 + K [ L ] ^{n}}

Setting $K_{d}^{n} = 1/ K$ gives $Y = [L]^{n} / (K_{d}^{n} + [L]^{n})$ . In practice, partially liganded species exist and contribute, so the fitted Hill coefficient $n_{H}$ is less than $n$ . For hemoglobin ( $n = 4$ ), $n_{H} \approx 2.8$ . $■$

Bridge. The Hill coefficient links the macroscopic cooperativity measured in a binding assay to the microscopic spin-state transition of Fe $^{2 +}$ in the heme pocket. The foundational mechanism is the high-spin-to-low-spin transition that moves the iron into the porphyrin plane and pulls the F-helix, producing the T-to-R structural switch. This connects the coordination chemistry of a single metal centre 16.04.01 to the emergent allosteric behaviour of the tetrameric protein.

Exercises Intermediate+

Exercise 2 (medium, short-answer).

Describe the molecular events that occur when O $_{2}$ binds to a single heme group in hemoglobin, and explain how this local event propagates to affect the other subunits.

Hint

Consider the spin-state change of Fe $^{2 +}$ and the resulting movement of the iron relative to the porphyrin plane. What does this movement pull on?

Answer

In deoxyhemoglobin, Fe $^{2 +}$ is high-spin d $^{6}$ with a relatively large ionic radius, causing it to sit ~0.4 A below the porphyrin plane. When O $_{2}$ binds as a strong-field ligand, the iron transitions to low-spin d $^{6}$ with a smaller ionic radius, allowing it to move into the porphyrin plane. This movement pulls the proximal histidine (His F8), which drags the entire F-helix of the subunit. The F-helix movement ruptures the salt bridges that stabilise the T-state quaternary structure. After two or more subunits bind O $_{2}$ , the accumulated strain overcomes the T-state constraints and the tetramer snaps to the R conformation, increasing the O $_{2}$ affinity of the remaining unliganded subunits.

Exercise 3 (medium, short-answer).

Explain the Bohr effect and its physiological significance. Why is it important that hemoglobin releases O $_{2}$ more readily at lower pH?

Hint

Which tissues have the lowest pH and highest CO $_{2}$ ? What do those tissues need most?

Answer

The Bohr effect is the decrease in hemoglobin's O $_{2}$ affinity with decreasing pH and increasing CO $_{2}$ . Protonation of His146 on the beta chains forms a salt bridge with Asp94, stabilising the T state. CO $_{2}$ forms carbamates with N-terminal amino groups, also stabilising T. Physiologically, metabolically active tissues produce both H $^{+}$ and CO $_{2}$ (via aerobic respiration), creating a local environment of lower pH. The Bohr effect ensures that hemoglobin releases O $_{2}$ preferentially in the tissues that need it most — a built-in feedback loop coupling O $_{2}$ demand to O $_{2}$ supply.

Exercise 4 (hard, short-answer).

Fetal hemoglobin (HbF) has higher O $_{2}$ affinity than adult hemoglobin (HbA). Explain the structural basis for this difference and why it is physiologically necessary.

Hint

The difference involves 2,3-BPG binding. What amino acid substitution distinguishes the $γ$ chain from the $β$ chain?

Answer

HbF has the subunit composition $α_{2} γ_{2}$ , while HbA is $α_{2} β_{2}$ . The $γ$ chain substitutes Ser for His143 (compared to the $β$ chain), eliminating a key positive charge in the central cavity that forms a salt bridge with 2,3-BPG. As a result, HbF binds 2,3-BPG less tightly than HbA. Since 2,3-BPG stabilises the T state and lowers O $_{2}$ affinity, reduced 2,3-BPG binding means HbF spends more time in the R state and has higher O $_{2}$ affinity ( $P_{50} \approx 19$ mmHg vs. ~26 mmHg for HbA).

This is physiologically essential for placental O $_{2}$ transfer: maternal HbA releases O $_{2}$ in the placenta, and fetal HbF picks it up at the same $p O_{2}$ because of its higher affinity. The ~7 mmHg difference in $P_{50}$ is sufficient to drive O $_{2}$ from mother to fetus across the placental barrier.

Exercise 5 (hard, short-answer).

At high altitude, the body adapts over days by increasing erythrocyte 2,3-BPG concentration. Analyse this adaptation using the T/R equilibrium framework and explain why it is beneficial.

Hint

At high altitude, arterial $p O_{2}$ is lower. What does this do to hemoglobin saturation? How does increased 2,3-BPG help?

Answer

At high altitude, reduced atmospheric pressure lowers arterial $p O_{2}$ , causing hemoglobin to be less saturated in the lungs. Increased 2,3-BPG concentration shifts the O $_{2}$ dissociation curve to the right by binding more tightly to deoxyhemoglobin in the central cavity, stabilising the T state and reducing O $_{2}$ affinity. This rightward shift means hemoglobin unloads O $_{2}$ more readily at the tissues, compensating for the reduced arterial O $_{2}$ content by extracting a larger fraction of the O $_{2}$ that is bound.

The trade-off is that the rightward shift also slightly reduces saturation in the lungs. However, at moderate altitude the gain in tissue O $_{2}$ extraction outweighs the small loss in arterial saturation. At extreme altitude (>5000 m), the adaptation becomes insufficient and supplemental O $_{2}$ or increased ventilation becomes necessary. The 2,3-BPG adaptation operates on a timescale of hours to days, mediated by changes in glycolytic flux through the Rapoport-Luebering shunt in erythrocytes.

Perutz mechanism, allosteric models, and synthetic oxygen carriers Master

The Perutz stereochemical mechanism provides the structural basis for cooperative O $_{2}$ binding. In the T state, the four subunits of hemoglobin are constrained by inter-subunit salt bridges: between His146 $β$ and Asp94 $β$ (intra-beta chain), between Lys40 $α$ and the C-terminal His146 $β$ (inter-chain), and between Val1 $α$ and Arg141 $α$ (inter-chain). The Fe $^{2 +}$ in each subunit is high-spin, displaced below the porphyrin plane, and the proximal His F8 bond to iron is strained and elongated.

Upon O $_{2}$ binding, the high-spin-to-low-spin transition moves iron into the porphyrin plane by ~0.4 A, pulling the proximal His and the F-helix. This shifts the FG corner of the subunit relative to the neighbouring subunit's C helix. The key structural event is the breakage of the salt bridges at the $α_{1} β_{2}$ interface. After the first O $_{2}$ binds, the protein remains largely in the T state (the salt bridges resist the strain). After the second O $_{2}$ binds, the accumulated strain overcomes the T-state restraints and the tetramer transitions to the R state. The R state has no inter-subunit salt bridges, a wider central cavity, and all four hemes in the high-affinity conformation. This is the molecular realisation of the MWC allosteric equilibrium constant $L_{0}$ .

The MWC model (Monod-Wyman-Changeux, 1965) treats hemoglobin as a symmetric allosteric oligomer in a pre-existing T/R equilibrium. The fractional saturation is:

Y = \frac{( 1 + c α ) ^{n}}{L _{0} ( 1 + α ) ^{n} + ( 1 + c α ) ^{n}}

where $α = p O_{2} / K_{R}$ , $c = K_{R} / K_{T} < 1$ , and $n = 4$ . The model is concerted: all subunits switch between T and R simultaneously; there are no hybrid conformations. The KNF (Koshland-Nemethy-Filmer, 1966) sequential model allows mixed conformations, with each binding event inducing a local conformational change in the neighbouring subunit. Experimental evidence from Fe/Co hybrid hemoglobins, in which selected subunits are rendered incapable of binding O $_{2}$ by substituting Co for Fe, favours the concerted MWC picture for the T-to-R transition, though the true mechanism contains elements of both models.

The Adair equation provides a model-independent description of stepwise binding:

Y = \frac{K _{1} [ L ] + 2 K _{1} K _{2} [ L ] ^{2} + 3 K _{1} K _{2} K _{3} [ L ] ^{3} + 4 K _{1} K _{2} K _{3} K _{4} [ L ] ^{4}}{4 ( 1 + K _{1} [ L ] + K _{1} K _{2} [ L ] ^{2} + K _{1} K _{2} K _{3} [ L ] ^{3} + K _{1} K _{2} K _{3} K _{4} [ L ] ^{4} )}

Positive cooperativity corresponds to $K_{1} < K_{2} < K_{3} < K_{4}$ . The measured Adair constants for human hemoglobin confirm that the first O $_{2}$ binds weakly and the fourth binds most tightly.

NO and CO binding to heme. CO binds ~~200–250 times more tightly than O $_{2}$ because it is a superior pi-acceptor. The Fe–C–O angle is bent (~~160 degrees in hemoglobin vs. 180 degrees in free heme models), imposed by steric interactions with the distal histidine. This bending weakens CO binding relative to free heme and is a protective mechanism: without the distal His constraint, CO would bind ~25,000 times more tightly than O $_{2}$ , making even trace CO lethal. Nitric oxide (NO) binds even more tightly than CO and plays a signalling role through soluble guanylate cyclase, a heme protein that detects NO at nanomolar concentrations. NO binding to the ferrous heme of soluble GC triggers a conformational change that activates cGMP production, mediating vasodilation. Hemoglobin also scavenges NO through two mechanisms: dioxygenation of NO by oxyhemoglobin (forming nitrate and metHb) and S-nitrosylation of Cys93 on the beta chain, which may contribute to hypoxic vasodilation (the Stamler hypothesis, though this remains debated).

Hemocyanin and non-iron oxygen carriers. Hemocyanins, found in arthropods and molluscs, use a dinuclear copper centre (Cu $^{+}$ /Cu $^{+}$ in deoxy form) to bind O $_{2}$ as a peroxide bridge (Cu $^{2 +}$ -O $_{2}^{2 -}$ -Cu $^{2 +}$ in oxy form). The binding is cooperative in many hemocyanins, with Hill coefficients up to ~5 for the hexahectameric molluscan forms. Hemerythrins, found in some marine invertebrates, use a diiron centre that binds O $_{2}$ as a hydroperoxide. These alternatives demonstrate that biology has evolved multiple structural solutions to the problem of reversible O $_{2}$ binding, with iron, copper, and diiron centres each providing distinct electronic strategies.

Synthetic oxygen carriers. The Collman picket-fence porphyrin (1970s) was the first synthetic model to achieve reversible O $_{2}$ binding at room temperature, using bulky tert-butyl groups on one face of the porphyrin to block bimolecular decomposition (the Fe–O $_{2}$ –Fe dimerisation pathway that produces mu-oxo dimers). The Baldwin capped porphyrin and the Busch lacunar cycliden complexes extended this approach. Modern synthetic blood substitutes have explored three strategies: (1) perfluorocarbon emulsions (physical O $_{2}$ solubility, no binding), (2) hemoglobin-based oxygen carriers (HBOCs) using cross-linked or polymerised hemoglobin (pyridoxal-5-prime-phosphate cross-linked Hb, recombinant Hb), and (3) totally synthetic porphyrinoid carriers. HBOCs have encountered clinical difficulties because cell-free hemoglobin scavenges NO, causing vasoconstriction and hypertension. The problem is that hemoglobin outside the red blood cell has access to the vascular endothelium and can deplete local NO concentrations, a side effect that erythrocyte encapsulation normally prevents.

Model complexes for reversible O $_{2}$ binding. The key design requirement is to achieve a binding constant in the narrow range that allows O $_{2}$ uptake at lung $p O_{2}$ and release at tissue $p O_{2}$ . Too strong and the carrier cannot unload; too weak and it cannot load. The mechanism of O $_{2}$ binding to heme involves end-on coordination of O $_{2}$ as a singlet, with Fe $^{2 +}$ donating sigma-electron density into the O $_{2}$ pi-star orbital and receiving pi-electron density back from a filled O $_{2}$ orbital (the synergic sigma/pi bonding model). The Fe–O–O angle is ~120 degrees, consistent with a bent end-on geometry. The O–O bond length increases from 1.21 A in free O $_{2}$ to ~1.2–1.3 A in oxyhemoglobin, indicating partial reduction of O $_{2}$ toward peroxide character without full electron transfer.

Connections Master

Bioinorganic metalloenzymes 16.06.01. This unit deepens the hemoglobin discussion from the introductory bioinorganic unit. The heme group is the same cofactor used by cytochromes, peroxidases, and catalases, but the protein environment tunes its function from O $_{2}$ transport to electron transfer to peroxide disproportionation.
Coordination chemistry 16.04.01. The octahedral geometry of the heme iron (four equatorial N from porphyrin, one axial His, one axial O $_{2}$ ), the trans-influence of the proximal histidine, and the spin-state transition are all direct applications of coordination chemistry principles. The spectrochemical series explains why O $_{2}$ acts as a strong-field ligand that triggers the high-spin-to-low-spin transition.
Crystal field theory 16.03.01. The spin-state change of Fe $^{2 +}$ (d $^{6}$ ) upon O $_{2}$ binding is a textbook application of crystal field theory. In the deoxy state, a weak-field ligand set produces high-spin d $^{6}$ with two unpaired electrons and a larger ionic radius. O $_{2}$ binding creates a strong-field environment, pairing all electrons in the t $_{2 g}$ level and shrinking the iron.
Organic chemistry: porphyrin synthesis and aromaticity. The protoporphyrin IX ring is a highly conjugated, planar aromatic macrocycle with 18 pi-electrons (4n+2, n=4). The aromaticity provides structural rigidity and tunes the electronic properties of the bound iron.
Protein structure and allostery 17.05.01. Hemoglobin is the paradigmatic allosteric protein. The T-to-R transition is a textbook case study in quaternary structure, domain movements, and the coupling between ligand binding and conformational equilibria.

Historical notes Master

Hemoglobin as a paradigm. Hoppe-Seyler crystallised hemoglobin in 1862. Hufner established that 1 g of hemoglobin binds 1.34 mL of O $_{2}$ (the Hufner constant) in the 1890s. Bohr, Hasselbalch, and Krogh discovered the Bohr effect (pH-dependent O $_{2}$ affinity) in 1904, establishing the concept of allosteric regulation decades before the term was coined.

Structural biology. Max Perutz began solving the hemoglobin structure by X-ray crystallography in 1937, a project that took 22 years. The 2.8 A resolution structure of horse oxyhemoglobin was published in 1960. Perutz proposed his stereochemical mechanism for cooperative binding in 1970 (Nature 228, 726), linking the X-ray structures of the T and R states to the cooperative binding thermodynamics. Perutz shared the 1962 Nobel Prize in Chemistry with John Kendrew (who solved myoglobin's structure at 2.0 A resolution in 1959).

Allosteric models. Monod, Wyman, and Changeux published the MWC concerted model in 1965 (J. Mol. Biol. 12, 88), treating hemoglobin as a symmetric allosteric oligomer. Koshland, Nemethy, and Filmer proposed the sequential KNF model in 1966 (Biochemistry 5, 365). The debate between concerted and sequential mechanisms has driven decades of biophysical research.

The Hill equation. Archibald Hill (1910) introduced his empirical equation to describe the sigmoidal O $_{2}$ binding curve of hemoglobin, well before the structure was known. Hill's approach was purely phenomenological — he fitted a power law to the binding data and interpreted the exponent as an effective interaction parameter. The Hill coefficient remains the standard first-pass measure of cooperativity in biochemistry.

Synthetic models. James Collman's picket-fence porphyrin (1975) was the breakthrough in modelling reversible O $_{2}$ binding with synthetic iron porphyrins. The design introduced the concept of steric protection of the O $_{2}$ binding site to prevent the bimolecular decomposition that had plagued earlier model systems.

Hemoglobin variants. The molecular basis of sickle cell disease (HbS, Glu6Val on the beta chain) was identified by Ingram in 1956 using fingerprinting (tryptic peptide mapping). This was the first demonstration that a single amino acid substitution causes a genetic disease, founding the field of molecular medicine. Over 1000 hemoglobin variants have been characterised, providing an unparalleled library of structure-function relationships in a single protein family.

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