GB(OBC) Model: Implicit-Solvent ABFE Method

• GB(OBC) Model is a generalized Born implicit-solvent model in Amber designed for absolute binding free energy calculations using a modified double decoupling method.
• It integrates conformational and orientational restraints along with dielectric scaling to efficiently manage solvent coupling and eliminate the need for soft-core potentials.
• Benchmark results show pooled performance with R² = 0.86 but also reveal significant host-wise variations and systematic charge-dependent biases.

GB(OBC) denotes the Onufriev–Bashford–Case generalized Born implicit-solvent model as implemented in Amber with igb=2, and in current automated absolute binding free-energy workflows it is used as the solvent model within a double decoupling method that combines Boresch orientational restraints, additional conformational restraints, and MBAR-based free-energy estimation (Ayoub et al., 26 Sep 2025). In that setting, GB(OBC) is not merely a drop-in replacement for explicit solvent. It changes the structure of the alchemical protocol itself: solvent coupling is represented through external-dielectric scaling, receptor–ligand Lennard-Jones interactions can be toggled without soft-core potentials, and periodic-boundary electrostatic finite-size corrections and net-charge correction schemes are avoided (Ayoub et al., 26 Sep 2025). On pooled host–guest benchmarks, GB(OBC) was reported to correlate well with experiment with $R^2 = 0.86$, but this aggregate result obscured substantially weaker host-wise correlations and large systematic errors associated with charged functional groups, especially ammonium and carboxylates (Ayoub et al., 26 Sep 2025).

1. Definition and thermodynamic role

Within the workflow described in “Automated Workflow for Absolute Binding Free Energy Calculations with Implicit Solvent and Double Decoupling” (Ayoub et al., 26 Sep 2025), GB(OBC) is the principal generalized Born model used for absolute binding free energy calculations under implicit solvent. The implementation is specified operationally rather than through a printed GB energy functional: the model is Amber GB with igb=2, radii set to mbondi2, ionic strength saltcon=0.3 M for all systems except OAH, which uses saltcon=0.15 M, and no surface-area nonpolar term, gbsa=0 (Ayoub et al., 26 Sep 2025).

The model is embedded in a modified double decoupling thermodynamic cycle. The binding free energy is written as

$\Delta G_{\text{bind}} = \Delta G_{1,8}$

and decomposed as

$$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$

The major states are defined explicitly. State 1 is the unbound end state. State 2 adds conformational restraints to host and ligand. State 3 is the restrained host and ligand in vacuum. State 4 is the restrained host and ligand in vacuum with ligand partial charges set to zero. State 5 introduces Boresch orientational restraints analytically. State 6-LJ is the restrained receptor–ligand system in vacuum with ligand charges zero and no receptor–ligand interactions except LJ. State 6-GB is the restrained receptor–ligand system in GB solvent with ligand charges zero and receptor and ligand fully interacting. State 7 is the restrained receptor–ligand system in GB solvent with full ligand charges. State 7-restraints removes conformational and orientational restraints through MD windows. State 8 is the bound end state with only flat-bottom harmonic host–guest restraints (Ayoub et al., 26 Sep 2025).

A crucial methodological consequence is that solvent itself becomes an alchemical degree of freedom. In this workflow, GB solvent is removed and reintroduced through dielectric scaling rather than through coupling to explicit water molecules. This suggests that GB(OBC) is functioning simultaneously as a solvation model and as a device that restructures the alchemical path.

2. Restraints and alchemical pathway

A distinctive feature of the GB(OBC) workflow is the simultaneous use of conformational restraints and Boresch orientational restraints (Ayoub et al., 26 Sep 2025). The conformational restraints are harmonic distance restraints applied separately within receptor and ligand for every atom pair separated by less than 6 Å, with reference distances taken from the last frame of the state 8 trajectory, and they are active in states 2 through 7 (Ayoub et al., 26 Sep 2025). Their role is twofold: they account for the free-energy cost of selecting a particular conformation from the bound and unbound ensembles, and they collapse conformational freedom in the intermediate states.

The orientational restraint component follows the standard six-coordinate Boresch construction, with one distance $r_{\text{aA}}$, two angles $\theta_{\text{A}}$ and $\theta_{\text{a}}$, and three torsions $$\phi_{\text{AB}}, \phi_{\text{aA}}, \phi_{\text{ba}}$$ (Ayoub et al., 26 Sep 2025). The anchor atoms are selected automatically from heavy atoms by one of three user-selectable strategies: nearest heavy atom to each molecule’s center of mass, nearest receptor heavy atom to the ligand heavy atom nearest the ligand center of mass, or shortest heavy-atom receptor–ligand contact (Ayoub et al., 26 Sep 2025). The remaining anchor atoms are then chosen iteratively to keep key angles between $80^\circ$ and $100^\circ$, relaxing this range in $1^\circ$ steps down to $\Delta G_{\text{bind}} = \Delta G_{1,8}$0 if necessary (Ayoub et al., 26 Sep 2025).

The actual computational path is described as follows: add conformational restraints, reduce GB dielectric to vacuum, discharge ligand, add Boresch restraints analytically, turn on or off receptor–ligand LJ in vacuum, reintroduce GB solvent, reintroduce ligand charges, and remove orientational and conformational restraints (Ayoub et al., 26 Sep 2025). The paper states that the use of conformational restraints with implicit solvent models allows ligand van der Waals, Coulomb, and solvent interactions to each be turned on or off in a single step, eliminating the need for soft-core LJ potentials (Ayoub et al., 26 Sep 2025).

This is one of the most consequential properties of the GB(OBC) model in this context. In explicit-solvent DDM, soft-core LJ is usually required to avoid steric catastrophes during decoupling. Here the absence of explicit solvent, together with conformational and orientational restraints, changes that requirement.

3. Solvent scaling, charge scaling, and numerical protocol

For GB(OBC), solvent coupling is realized by scaling the external dielectric. In the state-7 reintroduction stage, the external dielectric windows are

$\Delta G_{\text{bind}} = \Delta G_{1,8}$1

(Ayoub et al., 26 Sep 2025). Ligand charges are scaled to zero and back using parmed, and charge reintroduction uses

$\Delta G_{\text{bind}} = \Delta G_{1,8}$2

so that one intermediate half-charge state is inserted before the full-charge state (Ayoub et al., 26 Sep 2025).

The workflow uses pmemd.mpi from Amber 21, a 4 fs timestep with hydrogen mass repartitioning by factor 4, SHAKE on hydrogens, and effectively infinite cutoffs with

$\Delta G_{\text{bind}} = \Delta G_{1,8}$3

(Ayoub et al., 26 Sep 2025). End states are sampled with TREMD using 8 replicas at temperatures

$\Delta G_{\text{bind}} = \Delta G_{1,8}$4

and numexchg=2500000, with exchange attempted every step and 10,000 target-temperature frames saved (Ayoub et al., 26 Sep 2025).

Intermediate restraint strengths are distributed over 33 lambda windows on a $\Delta G_{\text{bind}} = \Delta G_{1,8}$5 scale. Conformational and distance restraint force constants range from

$\Delta G_{\text{bind}} = \Delta G_{1,8}$6

while orientational restraint force constants range from

$\Delta G_{\text{bind}} = \Delta G_{1,8}$7

(Ayoub et al., 26 Sep 2025). The paper reports that for CB7 guests, stiff and weak restraint protocols gave negligibly different OBC ABFEs, which it interprets as evidence of path independence (Ayoub et al., 26 Sep 2025).

Free energies are estimated with PyMBAR 4.0. Energies from each state’s trajectory are reevaluated in all other states using sander with imin=5, and time-correlated frames are pruned with the PyMBAR timeseries module (Ayoub et al., 26 Sep 2025). The manuscript notes, however, that MBAR uncertainties are much smaller than the variability across independent replicas, likely because TREMD target-temperature samples retain hidden time correlation (Ayoub et al., 26 Sep 2025).

4. Benchmark systems and reported performance

The benchmark comprises 93 host–guest complexes from the TapRoom repository, spanning five host families: ACD with 22 guests, BCD with 22 guests, CB7 with 14 guests, OAH with 25 guests, and WP6 with 13 guests (Ayoub et al., 26 Sep 2025). Host and guest parameters use GAFFv2 and AM1-BCC charges, and complexes are initialized from AutoDock Vina docking with a rigid host and flexible ligand (Ayoub et al., 26 Sep 2025).

For pooled data across all systems, the OBC model gave the following reported metrics (Ayoub et al., 26 Sep 2025):

Metric	OBC value
RMSE	6.12 kcal/mol
MAE	3.96 kcal/mol
$\Delta G_{\text{bind}} = \Delta G_{1,8}$8	0.86
Slope	0.33
$\Delta G_{\text{bind}} = \Delta G_{1,8}$9	0.65

The paper emphasizes that this pooled $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$0 is misleading because host-wise performance is substantially weaker. The host-wise OBC results are reported as follows (Ayoub et al., 26 Sep 2025):

Host	RMSE	MAE	$$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$1
ACD	1.79	1.45	0.40
BCD	1.62	1.41	0.80
CB7	13.84	13.28	0.44
OAH	2.61	1.90	0.31
WP6	6.32	5.98	0.68

These data show that GB(OBC) performs well on pooled ranking but much less reliably within individual host families. BCD is the strongest host-wise case, while CB7 is the clearest failure mode, with RMSE $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$2 kcal/mol and MAE $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$3 kcal/mol (Ayoub et al., 26 Sep 2025).

The paper also reports numerical reproducibility across five independent OBC runs. The standard deviation of mean ABFE and mean MBAR uncertainty, both in kcal/mol, were 2.19 and 0.08 for CB7, 0.64 and 0.33 for WP6, 0.46 and 0.11 for ACD, 0.43 and 0.003 for BCD, and 0.41 and 0.14 for OAH (Ayoub et al., 26 Sep 2025). This supports a distinction between numerical convergence and chemical accuracy: the workflow can be reproducible while still being systematically biased.

5. Systematic errors and chemical interpretation

The dominant limitation of GB(OBC) in the study is systematic charge-dependent bias (Ayoub et al., 26 Sep 2025). The paper states that positively charged ammonium groups tend to have ABFE underestimated, while negatively charged carboxylate groups are overestimated (Ayoub et al., 26 Sep 2025). The strongest examples are CB7 and WP6, whose guest sets are dominated by cationic ligands. For CB7, all 14 guests are cationic, with charges from $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$4 to $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$5, and the model fails badly (Ayoub et al., 26 Sep 2025). WP6 shows a similar trend; if the zwitterionic guest G8 is omitted, the OBC correlation improves to $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$6 with $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$7 kcal/mol (Ayoub et al., 26 Sep 2025).

For ACD and BCD, the pattern is more subtle. The paper reports that all negatively charged ligands are overbound, all positively charged ligands are underbound, and neutral ligands are near experiment (Ayoub et al., 26 Sep 2025). Yet BCD performs markedly better than ACD in correlation, which the authors attribute to a larger dynamic range and the presence of an ACD outlier, nmb, whose calculated value is $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$8 kcal/mol versus an experimental $$\begin{aligned} \Delta G_{\text{bind}} &=\Delta G_{1,8}\ &=\Delta G_{1,2}+\Delta G_{2,3}+\Delta G_{3,4}\ &\phantom{=}+\Delta G_{4,5}+\Delta G_{5,6}+\Delta G_{7,8}. \end{aligned}$$9 kcal/mol (Ayoub et al., 26 Sep 2025).

OAH is an instructive case because the host itself carries $r_{\text{aA}}$0 with solvent-exposed carboxylates. Under OBC, the positively charged ligands are large outliers; omitting those ligands raises OBC’s host-wise correlation to $r_{\text{aA}}$1 (Ayoub et al., 26 Sep 2025). The authors therefore argue that the dominant bias is associated with guest charge class rather than simply with the presence of host carboxylates.

The physical diagnosis given in the paper is that GB cavity radii fail to correctly balance direct Coulomb interactions with dielectric effects (Ayoub et al., 26 Sep 2025). The authors further state that GB accuracy depends critically on cavity radii and atomic partial charges, and they present a small comparison showing that, for four CB7 ligands under OBC2, changing the charge model can shift predicted ABFE by up to 18 kcal/mol (Ayoub et al., 26 Sep 2025). A plausible implication is that the limitations of GB(OBC) in this benchmark are driven less by sampling or restraint design than by the electrostatic balance built into the implicit-solvent model itself.

6. Correction models, use cases, and methodological significance

To compensate for systematic charge-dependent bias, the paper introduces an empirical linear correction

$r_{\text{aA}}$2

with coefficients fit separately by guest charge class through five-fold cross-validation (Ayoub et al., 26 Sep 2025). For OBC, the reported parameters are $r_{\text{aA}}$3 for charge $r_{\text{aA}}$4; $r_{\text{aA}}$5 for charge $r_{\text{aA}}$6; $r_{\text{aA}}$7 for charge $r_{\text{aA}}$8; and $r_{\text{aA}}$9 for charge $\theta_{\text{A}}$0 (Ayoub et al., 26 Sep 2025).

After this correction, the pooled OBC metrics become RMSE $\theta_{\text{A}}$1 kcal/mol, MAE $\theta_{\text{A}}$2 kcal/mol, $\theta_{\text{A}}$3, slope $\theta_{\text{A}}$4, and $\theta_{\text{A}}$5 (Ayoub et al., 26 Sep 2025). The correction substantially improves absolute error and slope, but slightly reduces $\theta_{\text{A}}$6. The paper interprets this as reduced dynamic range rather than a loss of chemical fidelity (Ayoub et al., 26 Sep 2025).

Methodologically, the significance of GB(OBC) extends beyond its raw benchmark numbers. The paper attributes to the GB-based workflow several structural advantages over explicit-solvent DDM: no explicit waters, no periodic electrostatic corrections, simpler handling of net-charge changes, no soft-core LJ, and near-perfect scaling of predefined intermediate windows with processor count (Ayoub et al., 26 Sep 2025). The authors estimate that the number of intermediate states is likely about half of what explicit-solvent DDM would require, although they do not provide a direct wall-clock comparison (Ayoub et al., 26 Sep 2025).

The practical conclusion of the study is restrained. GB(OBC) is described as the best-performing Amber GB variant tested on the pooled benchmark, but not as a universally reliable ABFE model (Ayoub et al., 26 Sep 2025). The most favorable use case appears to be chemically homogeneous ligand series, where functional-group-specific biases cancel more effectively. Future improvement directions proposed in the paper include reoptimizing GB cavity radii, improving charge models, and combining fast GB sampling with more physical endpoint solvation models such as GBNSR6, AGBNP2, or 3D-RISM through a “bookending” strategy (Ayoub et al., 26 Sep 2025). This suggests that GB(OBC), in its present form, is best understood as a computationally efficient but electrostatically imbalanced implicit-solvent model whose strengths lie in workflow simplification and sampling efficiency rather than in uniformly transferable physical accuracy.