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Single-Topology vs Dual-Topology Alchemical Paradigms

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Single-Topology vs Dual-Topology Alchemical Paradigms

P2 concept — synthesised from 2007-chipot-free-energy-calculations-book §2.8.4 and §2.8.5 (Chipot), pp. 56–60. The two ways to encode an alchemical mutation in an FEP run; deciding which one to use governs the choice of soft-core handling, the cancellation of bonded terms, and the achievable accuracy. STRC h01 and h26 both default to dual-topology for the reasons below.

Single-topology paradigm (§2.8.4)

A single common topology describes both the reference (state 0) and target (state 1) of the mutation. The most complex topology serves as the common denominator; “missing” atoms are kept and turned into noninteracting ghost particles by progressively zeroing their nonbonded parameters as λ varies. Linear scaling on the parameters:

q_i(λ)     = λ q_i^(1) + (1 − λ) q_i^(0)
R_ij*(λ)   = λ R_ij*^(1) + (1 − λ) R_ij*^(0)
ε_ij(λ)    = λ ε_ij^(1) + (1 − λ) ε_ij^(0)

— [Chipot & Pohorille 2007, p. 57, Eq. 2.47]

Pros

  • Simple bookkeeping for atom-count-conserving mutations (e.g., charge-only changes like Asp → Asn).
  • Natural fit for protonation-state changes.

Cons (book §2.8.4)

  • Numerical instability when atoms vanish: residual partial charges on shrinking atoms can come arbitrarily close to others, producing exploding nonbonded energies. Mitigated by decoupling the electrostatic and vdW transformations into two stages, doubling the simulation cost.
  • Bond-length artefacts: shrinking atoms have shrinking bonds; the bonded-term contributions to ΔA from bond-length and bond-angle changes are usually neglected on the assumption they cancel in bound vs. free states. The book flags this as an assumption, not a guarantee — failure mode if the bound geometry is sterically constrained.

Dual-topology paradigm (§2.8.5)

The reference and target topologies coexist throughout the transformation. An exclusion list ensures atoms that are not common to states 0 and 1 never interact with each other. The Hamiltonian is the simple linear interpolation:

U(x; λ) = λ U_1(x) + (1 − λ) U_0(x)        [Eq. 2.48]

— [Chipot & Pohorille 2007, p. 58, §2.8.5]

In the initial state (λ=0) only topology 0 sees the rest of the system; in the final state (λ=1) only topology 1 does. Both side-chain candidates are present at all times; only their interaction strength with the environment scales.

Pros

  • No shrinking-bond problem: bonded interactions inside each topology never change as a function of λ.
  • Decoupling of electrostatics and vdW is no longer mandatory: the topologies don’t share atoms, so charges and vdW can be scaled together without singularities (still better to decouple them when possible).
  • Natural for atom-count-changing mutations like Ser → Cys, Ala → Cys, or any docked-ligand creation/annihilation.

Cons (book §2.8.5)

  • End-point catastrophes at λ → 0 or 1: at the endpoints the appearing or vanishing topology has near-zero but nonzero interaction strength, allowing solvent atoms to clash arbitrarily close. Numerical fluctuations in ⟨ΔU⟩ become enormous. This is the failure mode of dual-topology.
  • Mitigation: the soft-core potential Recipe — Soft-Core Potential for Alchemical End Points. Without it, even windows as narrow as δλ ≃ 10⁻⁵ still suffer the catastrophe. With it, the potential derivative stays bounded as λ → 0 or 1.
  • Flexible-side-chain artefacts: if either topology has multiple low-energy conformations, additional sampling (replica exchange, longer windows) is required.

Decision matrix for STRC

SituationUseReason
E1659E → E1659A (h01 phase5)dual-topology + soft-coreatom counts differ (CH₂COO⁻ vs CH₃)
Charge-only protonation shift (h01 LRA)LRA, not alchemical at allrun Recipe — LRA Method for pKa Shift Calculation instead
S1080C disulfide design (h26)dual-topology + soft-coreSer → Cys gains S, ε differs
A1078C (h26)dual-topology + soft-coreAla → Cys gains S and CH₂
Ligand-A → ligand-B in pocket (relative h01 binding ΔΔA)dual-topology + soft-coreatom counts differ between candidates
Annihilating one ligand in solvent vs pocket (absolute h01 binding)dual-topology + soft-core, double-decouplingend-point catastrophes mandatory to avoid

The book’s ultimate recommendation: dual-topology + soft-core for almost every non-trivial mutation in modern engines (NAMD, GROMACS, AMBER). The single-topology paradigm survives mostly for legacy charge-only perturbations.

How to use this in STRC

  • All h01 phase5 scripts: docstring should specify # alchemical paradigm: dual-topology with soft-core λ-scaling (Chipot & Pohorille 2007 §2.8.5; engine = NAMD).
  • h26 phase 1d: same; AF3 baseline → engineered Cys requires dual-topology because cysteine adds atoms to alanine/serine.
  • Avoid mixing paradigms within one thermodynamic cycle — comparing a single-topology mutation to a dual-topology mutation introduces uncontrolled bias.

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