STRC Research

Fragment Additivity Assumption and Superadditivity

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Fragment Additivity Assumption and Superadditivity

P2 concept — distilled from 2014-schneider-de-novo-molecular-design-book §1.5 (Schneider & Baringhaus, Fig. 1.22) and §6.5 (Mazanetz et al.). The cornerstone assumption underlying all fragment-based design — and its principal failure mode.

The additivity assumption

“A general assumption of fragment-based compound assembly is that fragment contributions to the ligand binding energy are additive.” — Schneider 2014 §1.5

For two fragments A and B linked into product AB:

ΔG_bind(AB) ≈ ΔG_bind(A) + ΔG_bind(B) + ΔG_linker

This holds approximately when:

  • Binding mode and orientation of A and B in AB are unchanged from their fragment-binding modes.
  • The linker contributes only a small ΔG_linker (entropy cost of linker rotational freedom + zero or modest interaction).
  • No water reorganization.

Superadditivity (Fig. 1.22, factor Xa example)

Schneider 2014 documents non-additivity to −14 kJ/mol for a factor Xa inhibitor (PDB 4a7i):

QuantityValue
K_i of product AB (factor Xa inhibitor)2 nM
Linkersingle bond
Excess binding energy beyond ΔG(A) + ΔG(B)−14 kJ/mol (≈ −3.3 kcal/mol superadditive)

Reference: Schneider 2014 §1.5 [101]; Klebe lab water-rearrangement work [42 in Ch.1].

Why superadditivity happens

  1. Loss of one rotational + translational entropy when two fragments → one molecule. Moving from a 6-DOF + 6-DOF system to a 6-DOF + internal-DOF system frees ~5 kcal/mol of binding energy that was paid for entropy reduction in fragments A and B individually.
  2. Water displacement. A rigid AB molecule may displace ordered water that A and B couldn’t displace alone — large favorable ΔS contribution (Klebe lab’s “water rearrangement” mechanism, Schneider 2014 §1.5 [42]).
  3. Cooperative pre-organization. AB enforces the binding-competent conformation of one fragment that was in equilibrium between binding and non-binding states.

Why subadditivity also happens

Per Schneider 2014 §5.3.4 [64]:

“linking frequently disturbs the binding modes of the original fragments, and the linker itself often forms suboptimal interactions.”

Mechanisms:

  • Linker geometry forces one fragment off its anchor.
  • New steric clash between linker atoms and pocket walls.
  • Linker rigidification absorbs entropy beyond the rotational/translational savings.
  • Linker-water network destabilizes.

Implications for STRC

h01 fragment-grow strategy

  • Track Group Efficiency (GE) — never trust ΔΔG_b ≈ Σ ΔG_i_added.
    • GE = −ΔΔG_b / ΔHAC (per Ligand Efficiency Metrics Catalog).
    • If GE drops below 0.2 kcal/mol per added HA, the addition is dead weight — either revert or accept that the additivity assumption has failed for this scaffold.
  • Phase 4 docking pose stability: when scoring an elaborated fragment, re-dock from scratch (don’t extend in place). If the binding mode shifts, the parent-fragment ΔG cannot be summed in.
  • MM-PBSA / MM-GBSA gates exist precisely because additivity breaks. The 2.6–3.3 kcal/mol error band of MM-PBSA (Genheden & Ryde 2015, see free-energy-methods) is comparable to the −3.3 kcal/mol superadditivity in the factor Xa example — the gate is set wide enough to catch superadditive and subadditive cases.

h09 peptide self-assembly

Peptide-fragment additivity is especially unreliable:

  • Self-assembly is by definition cooperative — adding one residue can flip a peptide from disordered to β-sheet.
  • The Shannon-entropy / sequence-diversity framework (Hiss & Schneider §18.2.1, Eqs. 18.2–18.4) implicitly accepts that the fitness landscape is non-additive.
  • Conclusion: ACO / SME / PSO algorithms test full sequences by full fitness — they do not assume residue-by-residue additivity. This is a feature, not a bug.

h26 disulfide engineering

The dimer-stabilization energy of an engineered disulfide bond is strongly non-additive with the underlying protein-protein interface energy:

  • A disulfide constrains backbone conformation, which cooperatively re-shapes the entire interface.
  • FEP point-mutation must be done on the fully assembled dimer, not by scoring single Cys-vs-Ser mutations in monomers and summing.

Decision rule

When designing or scoring a multi-fragment / multi-residue / multi-substituent compound:

  1. First-principles question: is the binding mode preserved? If yes, additivity is a usable approximation. If no, abandon additivity and rescore the full compound.
  2. Always validate with the full compound before claiming a binding-energy estimate.
  3. For lead optimization: never trust ΔG_calc to better than 1.5 kcal/mol from any additive method. Use FEP/TI for the last sub-kcal — see Recipe — Receptor-Based Scoring Function Selection.

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