Intrinsic Binding Energy and Connection Gibbs Energy
Jencks 1981 identified the core problem with comparing binding affinities of fragments vs the whole molecule: you can’t just add up observed ΔG° values. They don’t add. Binding constants don’t multiply. The math is meaningless.
The fix is to decompose binding of A-B into three terms:
ΔG°_AB = ΔG^i_A + ΔG^i_B + ΔG^s
- ΔG^i_A and ΔG^i_B: the intrinsic binding energies of each fragment — what they would contribute if binding didn’t cost any translational/rotational entropy. These are additive.
- ΔG^s: the connection Gibbs energy — the entropic cost of restricting a molecule’s translational and rotational freedom upon binding. Paid once per binding event, regardless of how many fragments are in the molecule.
ΔG^s is positive (unfavorable) and typically +4 to +10 kcal/mol for small molecule binding to proteins in water. For tight binding (like avidin-biotin: ΔG^s = +5.9 kcal/mol), this term is enormous — it’s the entropy tax that makes fragment binding look weak relative to the intact molecule.
The practical payoff: once you’ve paid ΔG^s once (the first fragment binds), the second fragment binds with its full intrinsic binding energy ΔG^i_B at no additional entropy cost. This is exactly why multivalent ligands are so potent: the entropy penalty that would be paid twice for two independent binders is paid only once for a bivalent molecule.
Real numbers from Jencks:
- Elastase peptide aldehyde: ΔG^s = +6.9 kcal/mol → 10⁵ M advantage
- Myosin ATPase: ΔG^s = +3.6 kcal/mol; individual fragment intrinsic energies -11.8 and -7.4 kcal/mol
- Typical small group intrinsic energies: CH₃ = 2-4, OH = 8, NH₂ = 4.5 kcal/mol
Warning about ΔH and TΔS: in aqueous solution, hydrophobic interactions release structured water (positive TΔS), which can make a purely enthalpic binding process look entropy-driven in the raw thermodynamic measurements. ΔH/TΔS attribution from ITC experiments is unreliable for understanding binding mechanisms. Use ΔG, not ΔH.
This framework is why Kramer & Karpen 1998 got 1000× potency from PEG-linked cGMP dimers, and why Mammen 1998 could quantitatively predict polyvalent inhibitor behavior.
Connections
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