On the attribution and additivity of binding energies
Jencks WP. Proc Natl Acad Sci USA 1981; 78(7):4046–4050. DOI: 10.1073/pnas.78.7.4046 PMID: 16593049 PMC: PMC319722
TL;DR
Introduces the decomposition of observed binding free energy for a bifunctional ligand A–B into: (i) intrinsic binding energy of fragment A, (ii) intrinsic binding energy of fragment B, and (iii) a “connection Gibbs energy” ΔG^s that represents the entropic cost of bringing both fragments into position. Establishes that simple additivity of observed ΔG values is not valid; the correct framework accounts for the entropy paid once (not twice) when A and B are covalently connected.
Key finding
The master equation (Eq. 6 in the paper):
ΔG_AB^0 = ΔG_A^i + ΔG_B^i + ΔG^s
where:
- ΔG_A^i = intrinsic binding energy of fragment A (the intramolecular binding step after one end is anchored)
- ΔG_B^i = intrinsic binding energy of fragment B
- ΔG^s = connection Gibbs energy (largely −RT × translational/rotational entropy penalty paid on first binding event; released for second binding event in A–B)
Because A–B pays the translational/rotational entropy only once rather than twice, the observed binding of A–B is more favorable than ΔG_A^0 + ΔG_B^0 by ΔG^s.
The ΔG^s term equals RT ln(K_AB / K_A K_B) — equivalently, K_AB / K_A K_B has units of M and represents the effective concentration (Ceff). Jencks explicitly states this ratio can range from <1 M to 10^8 M depending on tightness of fit.
Numbers that matter
| Quantity | Value | Conditions/Notes |
|---|---|---|
| Example: K_AB/K_A × K_B (Ceff upper bound) | up to ~10^8 M | Tight enzymic active-site geometry; theoretical maximum from translation/rotation entropy |
| Example: ΔG^s for desthiobiotin binding to avidin | +5.9 kcal/mol | K_AB/K_A K_B = 2×10^4 M (favorable Ceff) |
| Example: ΔG^s for heavy meromyosin bivalent actin binding | −5.3 kcal/mol | K_AB/K_A K_B ≈ 10^−4 M (unfavorable; second head constrained incorrectly) |
| Entropy loss on combining A+B: | −40 cal mol^-1 K^-1 (molar) or −32 cal mol^-1 K^-1 (mole fraction) | Upper bound from gas-phase translation+rotation |
| Intrinsic binding energy −ΔG^i for CH3 group | 2.0–3.9 kcal/mol | From enzyme active-site substitution data |
| Intrinsic binding energy −ΔG^i for SH group | 5.4–9.1 kcal/mol | |
| Intrinsic binding energy −ΔG^i for OH group | ~8 kcal/mol | |
| ΔG^s for elastase peptide-aldehyde complex | +6.9 kcal/mol | Corresponds to ~10^5 M Ceff advantage; transition-state stabilisation |
| ΔG^s for myosin ATPase (ATP vs ADP+Pi) | +3.6 kcal/mol | Plus coupling term ΔG_12 = 2.8 kcal/mol; interaction energy ΔG_I = 6.4 kcal/mol |
Critical statement (verbatim from paper): “Values of ΔG^s can, in principle, correspond to values of K_AB/K_A K_B = <1 M to 10^8 M, depending on the tightness of binding in a complex, whereas the mole fraction standard state corresponds to the single value of 55 M.”
Limitations
- Framework is empirical, not predictive: ΔG^s must be measured, not computed from structure alone.
- Does not provide a formula to calculate Ceff from tether geometry; Ceff/ΔG^s values require experimental K data.
- Intrinsic binding energy values are lower limits (Jencks notes conditions for tight binding are rarely optimal in ground-state complexes).
Connections
[source]STRC Engineered Homodimer Avidity — foundational theory for h26 avidity claim[source]avidity-and-dimers — parameter table that cites this work[applies]STRC Engineered Homodimer Avidity — ΔG_AB = ΔG_A^i + ΔG_B^i + ΔG^s applies to homodimer avidity calculation[see-also]1998-mammen-polyvalent-interactions-angew — Mammen 1998 extends Jencks framework to polyvalent systems[see-also]1998-kramer-karpen-polymer-ligand-dimers-nature — empirical Ceff measurement validating this framework