STRC Research

On the Attribution and Additivity of Binding Energies — Jencks 1981

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On the Attribution and Additivity of Binding Energies — Jencks 1981

Citation: Jencks, W.P. (1981). On the attribution and additivity of binding energies. PNAS, 78(8), 4046-4050. DOI: 10.1073/pnas.78.8.4046

Authors: William P. Jencks, Graduate Department of Biochemistry, Brandeis University.

The Core Problem

When molecule A-B binds to a protein with Ka = 10³ M⁻¹, but A alone binds with Ka = 1 M⁻¹, it’s wrong to conclude that B moiety is “responsible for binding.” The same logic from B’s perspective would give the opposite conclusion. The sequence of experiments determines the apparent conclusion — which is meaningless.

Key Framework

Jencks introduces three terms to decompose binding of A-B:

ΔG°_AB = ΔG^i_A + ΔG^i_B + ΔG^s

  • ΔG^i_A: intrinsic binding energy of A — the Gibbs energy A would contribute in the absence of entropic penalty.
  • ΔG^i_B: intrinsic binding energy of B — same.
  • ΔG^s: connection Gibbs energy — the entropic cost paid once per binding event. Mostly translational + rotational entropy loss. Roughly +4-8 kcal/mol for typical small molecule binding.

Key insight: Observed binding energies of A and B are NOT additive in A-B. ΔG°_AB ≠ ΔG°_A + ΔG°_B. This is because the entropy penalty (ΔG^s) must be paid once for A-B but separately for A and B individually.

Numbers That Matter

  • ΔG^s range: +4 to +10 kcal/mol typically (equivalent to Ka/KaKb = <1 M to 10⁸ M)
  • Desthiobiotin binding to avidin: ΔG^s = +5.9 kcal/mol; ΔG°_AB = -16.9 kcal/mol; components give -6.1 and -4.9 separately
  • Myosin ATPase: ΔG^i_ADP = -11.8, ΔG^i_Pi = -7.4, ΔG^s = +3.6 kcal/mol
  • Typical intrinsic binding energies for small groups (kcal/mol): CH₃: 2-4; HS: 5-9; HO: 8; H₂N: 4.5; COO⁻: 4.3
  • Elastase peptide aldehyde: ΔG^s = 6.9 kcal/mol → factor of ~10⁵ M advantage from entropy restriction

Why Observed ΔH/TΔS Mislead

In aqueous systems, hydrophobic interactions release water (positive TΔS contribution) while an enthalpic process can show apparent entropy-driven binding due to solvent compensation. Observable thermodynamic parameters routinely misattribute binding forces. The ΔG^i / ΔG^s decomposition is more reliable than raw ΔH and TΔS.

Enzyme Catalysis Implications

  • ΔG^s advantage from substrate preorganization at enzyme active site can reach ~10⁸ M (rate acceleration of 10⁵-10⁸ × over bimolecular equivalent)
  • Strain/destabilization in enzyme-substrate complexes appears in ΔG^s or coupling term ΔG₁₂

Relevance to STRC Multivalent Ligand Design

This is the foundational paper for understanding why multivalent ligands (papers 4 and 5 in this series) are so much more potent than their monovalent components. The ΔG^s term is paid once for a bivalent ligand but would be paid twice for two independent ligands. When ΔG^s ≈ +6 kcal/mol, a properly designed bivalent ligand gets a ~10⁴ M effective concentration advantage — explaining the 1000× potency increases seen in Kramer & Karpen 1998.

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