2007 Chipot & Pohorille — Free Energy Calculations: Theory and Applications in Chemistry and Biology
Edited monograph, 14 chapters, Springer Series in Chemical Physics 86. Provides the load-bearing methods reference for h01 (E1659A pharmacochaperone) MD/FEP/MM-PBSA/LRA work and for any binding-free-energy or PMF computation in the STRC program.
Citation
Chipot, C.; Pohorille, A. (Eds.). Free Energy Calculations: Theory and Applications in Chemistry and Biology. Springer Series in Chemical Physics, vol. 86. Springer, Berlin Heidelberg, 2007. ISBN-13 978-3-540-38447-2. xviii + 519 pp.
TL;DR
A unified treatment of free energy methods in MD/MC: FEP, thermodynamic integration (TI), histogram methods (WHAM, Wang–Landau, multicanonical), nonequilibrium work (Jarzynski/Crooks), enhanced sampling (replica exchange), the Potential Distribution Theorem, quantum corrections, and approximate methods for drug design (LIE, PBFE, MM/PBSA, LRA pKa). The book’s thesis: most modern methods reduce to a small set of foundational ideas (Kirkwood, Zwanzig, Widom, Bennett, Torrie–Valleau) — they differ in how the ensemble is sampled and how estimators are constructed. Two tables in the entire book; the value is in the algorithms and pseudocodes.
Numbers that matter
The book is methodological — most “numbers” are illustrative, not parameters to lift. The two tabulated and one calibrated quantity worth preserving:
| Parameter | Value | Units | Source (page/fig/table) | Uncertainty |
|---|---|---|---|---|
| Argon hydration ΔA, FEP creation, TIP3P, NAMD, 300 K, 1 atm, 21 windows | +2.11 | kcal/mol | Fig. 2.7 caption (Ch. 2) | hysteresis vs. annihilation 0.03 |
| Argon hydration ΔA, FEP annihilation, same protocol | −2.08 | kcal/mol | Fig. 2.7 caption (Ch. 2) | — |
| Argon hydration, experimental, 298 K | 2.002 | kcal/mol | Fig. 2.7 caption (Ch. 2) | — |
| Total simulation time for argon hydration calibration | 9.24 | ns | Fig. 2.7 caption (Ch. 2) | — |
| Per-window equilibration / data collection | 40 / 400 | ps | Fig. 2.7 caption (Ch. 2) | — |
| MD time step | 2 | fs | Fig. 2.7 caption (Ch. 2) | — |
| van der Waals cutoff | 10 | Å | Fig. 2.7 caption (Ch. 2) | — |
| ABF illustrative force std-dev (polyalanine, ξ=19 Å) | σ ≈ 13 vs. mean −1 | (force units) | Fig. 4.4 caption / §4.6.5 | n≈14,000 samples to reach 10% error |
| AspRS Asp/Asn binding ΔΔA, MDFE benchmark used to fit PBFE protein dielectric | ~15 | kcal/mol | §12.6.3 (Archontis et al.) | reproduced with ε≈4 |
| Thioredoxin Asp26 ionization relaxation free energy (MDFE) | −56 | kcal/mol | §12.6.4 | requires ε=3 in continuum to reproduce |
| Dielectric constant range: protein interior (continuum models) | 1–4 | — | §12.6.3, §12.6.4 | 1–2 if explicit MD already samples relaxation; 4 fits mutant data |
| Water dielectric (high-dielectric medium, continuum) | ~78 | — | §12.6 (standard) | physical |
| Aqueous LIE Coulomb coefficient β (linear-response prediction) | 1/2 | — | §12.5 | empirical adjustment common |
| Jorgensen extended-LIE inhibitor RMS error (factor Xa, 60 ligands) | <1.0 | kcal/mol | §12.5 (citation 102) | reported result |
Verbatim table contents are in Flat-Histogram Reweighting Reference Table (Table 3.1) and MFEP Two-Stage Strategies Table (Table 6.1).
Method essentials
The book is a method anthology. Per-chapter takeaways for STRC:
- Ch. 2 (FEP): dual-topology alchemical mutation with soft-core λ-scaling avoids end-point catastrophes; SOS (simple overlap sampling) and BAR are strictly preferred over forward exponential averaging. Pseudocode (a)–(g) at §2.8.6 is verbatim canonical for h01 phase5.
- Ch. 4 (TI, ABF): ABF accumulates the running-average mean force in bins of ξ and applies the negative as a bias; once converged the system is effectively diffusive on a flat surface. Algorithm 1 (Velocity-Verlet outer loop) and Algorithm 2 (ABF subroutine) are extracted verbatim.
- Ch. 5 (NEW): Jarzynski identity and Crooks fluctuation theorem; BAR estimator (5.50) needs forward + reverse work distributions and a Newton–Raphson iteration. Strongly outperforms exponential and cumulant estimators except in symmetric toy systems.
- Ch. 6 (errors): the operative diagnostic is whether
Γ*₁ ⊆ Γ*₀— the target’s important phase space must be a subset of (or coincide with) the reference’s. If not, stage with an intermediate M whoseΓ*_Mcovers the union or sits in the overlap. - Ch. 12 (approximate methods): LIE = α(⟨V_vdW⟩_prot − ⟨V_vdW⟩_solv) + β(⟨V_elec⟩_prot − ⟨V_elec⟩_solv) + γ. PBFE/MM-PBSA decompose ΔA_bind into direct interaction + ligand desolvation + protein desolvation. LRA: ΔA = (q/2)(⟨V⟩_reactant + ⟨V⟩_product) — gives pKa with one MD per endpoint instead of full alchemical λ scan.
Limitations
- Two tables in 519 pages — almost no parameter values to lift; cite the book for methods and equations, not for force-field constants.
- Force-field parameters (TIP3P partial charges, AMBER, CHARMM) are not tabulated; cite the original force-field papers for those.
- No quantitative benchmark on protein–ligand binding free energy accuracy beyond illustrative examples; for h01 MM-PBSA error bands cite Genheden & Ryde 2015 instead (already in pharmacochaperone).
- Dual-topology + soft-core is described qualitatively; specific α_vdW values used in NAMD/GROMACS soft-core defaults must come from those manuals.
Relevance to STRC
- index: phase5 alchemical scoring of E1659A pharmacochaperone candidates uses exactly the FEP point-mutation framework (§2.8.6) with dual-topology + soft-core (§2.8.5). MM-PBSA gate already in
phase5script (pharmacochaperone_phase5_mmpbsa.py) decomposes per Eq. (12.65)–(12.67). LRA (§12.3.2) is the right tool to estimate the E1659A pKa shift quantitatively from existing 100 ns MD trajectories without re-running alchemical λ. - index: Phase 1d AF3 designs A1078C/S1080C/S1579C disulfide cysteines need ΔΔG_dimer scoring; FEP point-mutation in dual-topology paradigm is the canonical recipe. Soft-core λ schedule mandatory because cys side chains differ in atom count from native ser/ala.
- index: ABF (§4.6) is the recommended PMF method for the h09 self-assembly reaction coordinate (e.g., RADA16 monomer → β-sheet); replica exchange (Ch. 8) handles configurational sampling.
- STRC Electrostatic Analysis E1659A: the LRA framework at §12.3.2 — particularly Eq. (12.40) summing per-atom charge increments times the average potential — provides a defensible literature citation for the multi-method PAE-corrected ΔΔG approach already in the electrostatics note.
Connections
[part-of]free-energy-methods[source]2007-chipot-pohorille-free-energy-calculations-book[applies]index[applies]index[applies]index[see-also]Recipe — FEP Point-Mutation Algorithm[see-also]Recipe — Soft-Core Potential for Alchemical End Points[see-also]Recipe — ABF Adaptive Biasing Force Algorithm[see-also]Recipe — Bennett Acceptance Ratio Estimator[see-also]Recipe — LRA Method for pKa Shift Calculation[see-also]Phase Space Overlap and FEP Sampling[see-also]Single-Topology vs Dual-Topology Alchemical Paradigms[see-also]Flat-Histogram Reweighting Reference Table[see-also]MFEP Two-Stage Strategies Table