⭐ Protein–Ligand Binding Theory — Full Educational Summary

🧩 What is macromolecule–ligand binding?

A macromolecule (protein, DNA, polysaccharide, receptor, enzyme, ribosome, etc.) can interact reversibly with a ligand to form a complex.

This interaction:

• is NOT covalent → equilibrium exists
• can go forward (binding) or backward (dissociation)
• is characterized by binding strength (affinity)

Affinity tells us how strongly ligand stays bound.

⚖️ Binding equilibrium and affinity

Reaction:

M + L ightleftharpoons ML

✔️ “Higher affinity → more to the right”

Correct idea.

This means:

• equilibrium favors complex formation
• more ML relative to free M and L

Mathematically:

• High affinity → low dissociation constant (Kd)
• Low affinity → high Kd

Because:

K_d = rac{[M]L}{ML}

If complex concentration is large → denominator large → Kd small → strong binding

🔥 ΔG and equilibrium (important correction)

You mentioned:

“something about ΔG = 0”

✔️ Correct but subtle

At equilibrium:

• the actual Gibbs free energy change (ΔG) is zero

But:

• the standard free energy (ΔG°) is usually NOT zero

Relation:

Delta G^circ = -RT ln K

So:

• if equilibrium constant favors binding → ΔG° negative
• if equilibrium constant favors dissociation → ΔG° positive

Thus:

• ΔG = 0 → system not changing anymore
• ΔG° tells how favorable binding is.

🔗 Number of binding sites (N) and saturation

✔️ N = maximum number of binding sites

Yes.

• If N = 4 → protein can bind 4 ligands
• When all sites occupied → saturation

📈 Binding curves and meaning of “n”

You asked:

“y-axis = n refers to average number of bonds or binding?”

✔️ It means:

Average number of ligands bound per macromolecule (n̄)

Not bonds.

Example:

• N = 4
• if average occupancy = 2 → n̄ = 2

At saturation:

ar{n} = N

🧪 Ligand concentration experiment design

Important theoretical idea:

• Increase ligand concentration
• Keep macromolecule concentration constant

Why?

So you can observe:

• progression from no binding → full saturation
• determine Kd from half-saturation point

Key relation:

ext{Fractional saturation} = rac{L}{K_d + L}

Thus:

✔️ Kd = ligand concentration at 50% saturation

Exactly analogous to:

• Km in enzyme kinetics.

🤝 Independent vs cooperative binding

✔️ Independent binding

• binding at one site does not influence other sites
• all sites have same Kd

✔️ Cooperativity

Binding at one site changes affinity at other sites

🟢 Positive cooperativity

• binding makes next binding easier
• curve becomes sigmoidal
• classic example: hemoglobin + oxygen

🔴 Negative cooperativity

• binding makes next binding harder

This is important biologically for regulation.

🧠 What does “allosteric” mean?

You asked:

“allosteric factor → hemoglobin?”

✔️ Yes — hemoglobin is an allosteric protein.

Allosteric means:

• binding at one site affects structure and affinity at another site

Example:

• oxygen binding shifts hemoglobin from T-state → R-state
• increases affinity of remaining sites.

Thus hemoglobin shows positive cooperativity.

🌡️ Thermodynamics of binding

Main equation:

Delta G = Delta H - TDelta S

Binding occurs spontaneously if:

Delta G < 0

🧊 Enthalpy-driven binding (ΔH negative)

Correct understanding:

Binding forces such as:

• hydrogen bonds
• ionic interactions
• van der Waals
• electrostatics

release heat → ΔH negative.

This stabilizes complex.

🌊 Entropy-driven binding

Example:

• ligand has ordered water shell
• water released upon binding → disorder increases → ΔS positive

Even if ΔH small, binding may still occur.

🔥 Why small energy changes give huge affinity changes

Very important theoretical point.

Only ~20 kJ/mol can shift equilibrium constant enormously.

Example from lecture:

• ΔG° ≈ −23 kJ/mol → binding essentially irreversible.

🔁 “Irreversible” binding — correction

You asked:

“irreversible reaction → ligand bound very strong?”

✔️ Yes — but technically still reversible.

In biochemistry:

• “irreversible” means Kd extremely small
• dissociation practically negligible.

Example:

• avidin–biotin binding.

📊 How do we measure binding? (Signals)

We monitor any property that changes upon binding.

Examples:

🌈 Absorption spectroscopy

Example:

• hemoglobin changes absorption when oxygen binds.

Note:

• oxygen itself does not change absorption — protein does.

✨ Fluorescence (tryptophan)

Correct idea.

If binding site contains tryptophan:

• empty site → certain fluorescence
• ligand binding → environment changes
• fluorescence intensity or wavelength shifts.

Thus binding detectable.

🔄 Structural methods

• Circular dichroism
• NMR

If binding induces conformational change.

⚖️ Mass-dependent methods

Example:

• ribosomal subunits binding.

Large mass change → detectable by:

• sedimentation or ultracentrifugation.

Yes — depends strongly on size.

🌡️ ITC — Isothermal titration calorimetry

You asked:

“binding ligand can absorb heat → enthalpy?”

Yes.

ITC measures:

• heat released or absorbed per binding step.

Gives:

• ΔH
• Kd
• stoichiometry
• entropy (calculated)

Very powerful.

🔥 DSC — Differential scanning calorimetry

Used mainly for:

• protein folding/unfolding

Measures:

• heat capacity change
• melting temperature
• unfolding enthalpy.

🌊 Surface Plasmon Resonance (BIAcore)

How it works (simplified):

• protein immobilized on metal surface (gold chip)
• ligand flows over surface
• binding changes refractive index near surface
• this alters resonance angle of surface plasmons.

Result:

• real-time binding kinetics
• kon, koff, Kd.

No labeling required.

⚙️ Enzyme inhibition assays

Correct idea.

If ligand binds enzyme:

• enzyme activity decreases
• rate measurement → binding strength inferred.

🧫 Solid-phase assays (ELISA)

Here:

• ligand or protein fixed to surface
• binding detected via antibody + enzyme color reaction.

⚗️ Methods requiring separation

Some techniques need separation of free vs bound ligand:

• equilibrium dialysis
• gel filtration chromatography.

🧪 Ionizable groups example (tyrosine protonation)

You asked:

“tyrosine hard to lose proton but at pH 14?”

✔️ Correct.

Tyrosine pKa ≈ 10.

Thus:

• at physiological pH → mostly protonated
• at pH 14 → extremely basic → almost no free protons → tyrosine becomes deprotonated.

Important idea:

• different groups bind protons with different affinity
• binding curve reflects multiple pKa values.

🌡️ Temperature dependence — van’t Hoff analysis

If Kd measured at different temperatures:

• plot ln(K) vs 1/T
• slope gives ΔH/R.

Thus thermodynamic parameters extracted.

📉 Why very strong binding makes Kd hard to measure

Important concept.

If affinity extremely high:

• almost no free ligand exists
• difficult to determine Kd experimentally.

Weak binding:

• easier Kd determination.

📊 Logarithmic ligand axis

Often ligand range spans:

• nanomolar → millimolar.

Thus:

• log scale used → curve appears hyperbolic or sigmoidal.

⭐ Key take-home concepts

• Binding strength described by Kd
• Half-saturation → Kd
• ΔG determines spontaneity
• Binding can be enthalpy- or entropy-driven
• Cooperativity regulates biological function
• Many spectroscopic / calorimetric / kinetic methods can detect binding
• Even small energy changes → huge affinity effects