Towards Reconciling the Standard Binding Free Energy of Lenacapavir to HIV-1 Capsid with Experiment: Thermodynamic Effects of Solvent Buffer and Ligand Reorganization

Abstract

We report a large thermodynamic effect of solvent buffer on the standard binding free energy for a large hydrophobic ligand and show that realistic comparison with the experimental binding affinity requires correctly accounting for the solvent reference state and ligand reorganization. We focus on lenacapavir (LEN; MW ≈ 1 kDa), a HIV-1 capsid inhibitor with very low aqueous solubility. Using several absolute binding free energy (ABFE) protocols including double-decoupling method (DDM), potential-of-mean-force (PMF) approaches, and the Alchemical Transfer Method (ATM) we obtained standard binding free energy values in neat water of $\Delta {\text{G}}_{\text{bind}}^0$= −26.4 to −30.0 kcal/mol for LEN binding to the HIV-1 capsid CA dimer, much stronger than the SPR-derived affinity measured in 5% DMSO buffer (≈–13.4 kcal/mol). We analyze the discrepancy and identify two dominant contributors to the calculated overbinding. (i) Solvent reference state: A thermodynamic cycle analysis and solvation free energy calculations reveal that the 5% DMSO buffer stabilizes the free ligand by ~−4 kcal/mol relative to neat water. Additionally, we propose that the enrichment of the hydrophobic cosolvent in the apo binding pocket makes it more energetically costly to displace DMSO upon ligand binding. (ii) Ligand reorganization: incomplete treatment of LEN’s internal conformational reorganization in the ABFE protocols leads to overbinding; a DDM variant with explicit ligand reorganization reduces the overestimate by ~6 kcal/mol. Together, considerations of these effects significantly reduce the discrepancy between ABFE calculations and experiments. Our results suggest that for large, hydrophobic ligands, quantitative agreement between ABFEs and experiments requires (a) reporting $\Delta {\text{G}}_{\text{bind}}^0$ in the appropriate assay buffer (not simply in water) and (b) explicit treatment of ligand reorganization.

Introduction

Accurately predicting absolute binding free energies (ABFEs) is essential for understanding the thermodynamics that drive molecular recognition and for guiding rational drug design.^1–7 Contemporary ABFE workflows can achieve mean unsigned errors of ~1–3 kcal/mol for compounds that satisfy Lipinski’s Rule of Five (≤500 Da; modest flexibility)^{4, 8–16} (although in some challenging cases protein reorganization can lead to errors of up to ~10 kcal/mol⁴). While most approved small-molecule drugs fall in this range of size and flexibility, a small but growing subset of approved drugs and clinical candidates extends to larger sizes, sometimes 600–1000 Da with ≈10 or more rotatable bonds.^17–18 For such large and flexible ligands, achieving adequate sampling of ligand and protein reorganization and binding-site water exchange within practical simulation times can be very challenging. A further experimental complication is that, for hydrophobic ligands, very low aqueous solubility often necessitates cosolvents (e.g., a few percent DMSO, sometimes with a trace surfactant) to prevent precipitation during affinity measurements; this changes the solvent reference state and can shift the observed binding equilibrium relative to neat water, an important consideration that is often overlooked in absolute binding free energy calculations.¹⁹

Here we focus on lenacapavir (LEN), an HIV-1 capsid inhibitor, to assess how current ABFE methods perform for a large hydrophobic ligand. LEN is a long-acting antiretroviral drug in HIV/AIDS treatment and prevention.²⁰ It targets the HIV-1 capsid protein (CA) and interferes with processes such as nuclear import, reverse transcription, and uncoating.^20–21 With 968 Da molecular weight and 13 rotatable bonds, it ranks among the largest FDA-approved small-molecule drugs, both in terms of molecular weight and structural complexity (Fig. 1). LEN has very low solubility in water, and its reported experimental binding affinity was measured by surface plasmon resonance (SPR) in 5% (v/v) DMSO buffer.²²

Figure 1.

Left: chemical structures of lenacapavir. Right: X-ray structure of lenacapavir (blue) bound at the dimeric interface of two CA monomers.

We applied several ABFE methods, implemented across different simulation packages, to compute the standard binding free energy of LEN binding to the HIV-1 capsid dimer in water. The ABFE methods used include the standard double decoupling method (DDM)^23–24, the recently developed Alchemical Transfer Method (ATM),^25–29 and a hybrid of the alchemical and potential of mean force method (Alchem-PMF)³⁰. To improve the sampling of water equilibration when decoupling a ligand of this size, we also test a fragment-wise, progressive double decoupling scheme

These ABFE protocols produced $\Delta G_{\mathit{\text{bind}}}^0$ values much more favorable than the experimental estimate from SPR in 5% (v/v) DMSO. The overestimation persisted across methods, software platforms and structural models and protein oligomeric forms. Performing the alchemical calculation in fragments (progressive/fragment-wise decoupling) or changing force-field parameters had only modest impact on $\Delta G_{\mathit{\text{bind}}}^0$. Alternative ligand protonation states and protein reorganization also produced only small changes. We therefore examined two effects for the binding of this large hydrophobic ligand, one often treated inadequately and the other largely neglected in ABFE calculations: (i) the ligand-reorganization free energy cost, and (ii) the assay solvent composition. As shown below, considering both effects helps reconcile the ABFE calculations with the experiment.

Methods

System Preparation

Starting structures of HIV-1 capsid (CA) in complex with LEN were taken from the experimental holo (PDB: 6v2f) and apo (PDB: 4xfx) capsid hexamer. The dimer was the standard oligomeric form used in this work for all ABFE calculations across all methods (Schrödinger ABFEP, GROMACS DDM, ATM, Progressive-DDM, DDM with ligand reorganization, and Alchem-PMF). The hexameric form was investigated exclusively using Schrödinger ABFEP to assess potential structural stability or allosteric effects on the calculated binding free energy. LEN was modeled in both the protonated and deprotonated forms. All systems were solvated in explicit water, neutralized, and brought to experimental ionic strength (150 mM NaCl). Unless otherwise noted, TIP3P water was used across ABFE protocols. Equilibration comprised restrained minimization (protein heavy atoms and ligand), gradual heating to 300 K, and NPT relaxation. All simulations used particle-mesh Ewald electrostatics and standard long-range dispersion settings from the respective engines.

ABFEP from Schrödinger Inc.

We employed the Absolute Binding Free Energy Perturbation (ABFEP) approach in the Schrödinger Suite (release 2024–2)⁴, which is based on the double decoupling scheme²⁴. In this method, the calculation begins with the ligand in pure solvent, where the van der Waals and electrostatic interactions within the ligand, as well as between the ligand and water molecules, are gradually turned off, creating a “dummy” ligand molecule. This dummy ligand is then restrained to the protein binding site using the Boresch-Karplus cross-link restraints.²⁴ Subsequently, the van der Waals and electrostatic interactions within the ligand, and between the ligand and the protein and surrounding water, are gradually restored, after which the cross-link restraints are released.

The ABFEP runs were initiated from the holo and apo capsid hexamers. Apo-based complexes were generated by superimposing apo and holo structures, transferring the ligand to apo structures (Maestro, Schrödinger 2024–2), where no clashes were observed between the apo protein and Lenacapavir. The CA dimer was extracted from either the apo or holo hexamer structures. The simulations employed the OPLS4 force field³¹. The default Schrödinger ABFEP protocol was followed: complexes were solvated in an SPC water box (8 Å buffer for charged LEN, 5 Å for neutral LEN), neutralized with counterions, and supplemented with 0.15 M salt. An MD relaxation protocol was first performed, followed by 1 ns of Grand Canonical Monte Carlo³² μVT simulations at 300 K with protein backbone heavy-atom restraints. This step was necessary to identify the atoms for cross-link restraints. Subsequently, 15–30 ns ABFEP simulations per lambda window were carried out with 108 lambda windows for charged LEN and 68 lambda windows for neutral LEN. The replica exchange production simulation was carried out in the NPT ensemble with solute tempering (REST)³³. The free energy of the transformation was calculated using multistate Bennett’s acceptance ratio method (MBAR)³⁴. This workflow is automated within the FEP+ module of Schrödinger 2024–2.

GROMACS DDM

A GROMACS implementation of DDM¹⁰ (Fig. 5) was run using Amber ff99SB-ILDN³⁵ for protein and GAFF2³⁶ for LEN with AM1-BCC³⁷ partial charges. Electrostatics were decoupled first over 11 linear Coulomb lambda-windows (λ = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0), followed by van der Waals decoupling with 17 LJ lambda-windows (λ = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.94, 0.985, 1.0) using soft-core potential. Each window was equilibrated for 5 ns and followed by 70 ns of simulation to monitor convergence. The last 35 ns were used to compute $\Delta G_{\mathit{\text{bind}}}^0$. The same lambda-schedules were used in both the solvent and complex decoupling legs. We have examined the conformational ensembles of the decoupled ligand in both the solvent leg and the complex leg by comparing the sampled distributions of selected dihedral angles: see Supporting Information Fig. S7. As expected, these distributions are very similar between the two decoupling legs.

Figure 5.

Left: the experimental structure of the bound LEN in the complex; Right: a representative MD structure of the free LEN in solution. Red dash lines indicate pi-pi stacking interactions. Green broken lines indicate VDW interactions.

The Boresch-Karplus translation/rotation restraint²⁴ of the ligand was applied in the complex leg using 17 bonded-lambda windows (λ = 0.0, 0.01, 0.025, 0.05, 0.075, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0). At each window $dH/d\lambda$ data were collected from 2 ns simulation and the free energy of application of the Boresch-Karplus restraints was estimated through multistate Bennett’s acceptance ratio method (MBAR).³⁴ The free energy of releasing the same set of ligand translational/rotational restraints in bulk solution at 1 M standard state was calculated analytically.^{24, 38}

DDM with Explicit Ligand Reorganization

To address LEN’s many internal torsion degrees of freedom and substantial internal flexibility, we employed a ligand restrain-and-release variant of DDM, following earlier treatment of conformational free energy schemes.^{15, 39}

In standard DDM, i.e.

$$\Delta G_{\mathit{\text{bind}}}^{°}=-\Delta G_{\mathit{\text{trans}}\_\mathit{\text{rot}}}^{\mathit{\text{site}}}-{\Delta G}_{\mathit{\text{decoupl}}}^{\mathit{\text{site}}}+\Delta G_{\mathit{\text{trans}}\_\mathit{\text{rot}}}^{\mathit{\text{ghost}}}+{\Delta G}_{\mathit{\text{decoupl}}}^{\mathit{\text{bulk}}}$$ (1)

the accurate calculation of the two decoupling free energies ${\Delta G}_{\mathit{\text{decoupl}}}^{\mathit{\text{site}}}$ and ${\Delta G}_{\mathit{\text{decoupl}}}^{\mathit{\text{bulk}}}$ which have the largest magnitudes among all the terms in the DDM cycle, are quite challenging because during decoupling the ligand samples an increasingly larger conformational space as the ligand-environment interactions are slowly turned off.

In the DDM variant with ligand reorganization,

$$\Delta G_{\mathit{\text{bind}}}^{°}=-\Delta G_{\mathit{\text{trans}}\_\mathit{\text{rot}}}^{\mathit{\text{site}}}-\Delta G_{\mathit{\text{restr}}\_\mathit{\text{torsion}}}^{\mathit{\text{site}}}-{\Delta G}_{\mathit{\text{decoupl}}}^{\mathit{\text{site}}}+\Delta G_{\mathit{\text{trans}}\_\mathit{\text{rot}}}^{\mathit{\text{ghost}}}+{\Delta G}_{\mathit{\text{decoupl}}}^{\mathit{\text{bulk}}}+\Delta G_{\mathit{\text{restr}}\_\mathit{\text{torsion}}}^{\mathit{\text{bulk}}}$$ (2)

harmonic torsional restraints were applied to ligand rotatable bonds in both the complex and solution environments before decoupling, resulting in a more restricted conformational search space which reduces the difficulty of sampling: see Fig. 2. By avoiding the need to sample the large conformational change during the decoupling simulations in the bulk solution and in the complex, the DDM variant facilitates more accurate calculations of ${\Delta G}_{\mathit{\text{decoupl}}}^{\mathit{\text{site}}}$ and ${\Delta G}_{\mathit{\text{decoupl}}}^{\mathit{\text{bulk}}}$, the two most crucial terms in DDM and improves the ABFE estimate.

Figure 2.

Thermodynamic cycles of (upper) standard DDM and (lower) the DDM with ligand reorganization.

To calculate the free energy of applying/releasing the torsional restraints in the bound and unbound ligands (i.e. $\Delta G_{\mathit{\text{restr}}\_\mathit{\text{torsion}}}^{\mathit{\text{site}}}$ and $\Delta G_{\mathit{\text{restr}}\_\mathit{\text{torsion}}}^{\mathit{\text{bulk}}}$), harmonic torsional restraints were applied to all the rotatable bonds of LEN using 17 restraint-lambda windows (λ = 0.0, 0.01, 0.025, 0.05, 0.075, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0). While 2 ns of the $dH/d\lambda$ data per lambda were sufficient for converging the bound state leg, more than 50 ns per lambda were needed to converge the free energy of the unbound state leg to within 0.6 kcal/mol. All other setups are the same as the standard GROMACS DDM described above.

Progressive DDM (Schrödinger RBFEP, OPLS4)

In this DDM variant designed to overcoming any bottleneck from sampling the solvent exchange during the decoupling of large ligand,⁴⁰ LEN is divided into a core (L) and three functional groups (A, B, C). The RBFEP module was used to calculate relative binding free energies in a stepwise manner, progressing from L*ABC → L, as illustrated in Figure S4 (Supporting Information). The absolute binding free energy of the core was then determined using the Schrödinger ABFEP module, following the methodology described above, which includes the use of the Boresch-Karplus restraints on the ligand translation and rotation.

Force Field Builder³¹ (Schrödinger Suite, release 2024–2) was used to parameterize any missing torsions in the LEN-related ligands studied here. The default RBFEP protocol, as implemented in the FEP+ module^20,41, was employed: 24 lambda windows and an 8 Å SPC water buffer were used for charged ligands, whereas 16 lambda windows and a 5 Å SPC water buffer were applied for neutral ligands. Following a relaxation stage, 20-ns production simulations were performed in the NPT ensemble with REST³³, and relative free energies were computed via multistate Bennett’s acceptance ratio method (MBAR).^{34, 42} To evaluate the consistency of the FEP+ predictions, cycle closure correction⁴³ was applied, and the resulting ΔΔG^pred values were converted to ΔG^pred using the absolute binding free energy of the core ligand obtained from the ABFEP protocol.

ATM

The Alchemical Transfer Method (ATM)^29,28,44 implements ABFE and RBFE protocols formally equivalent to DDM and FEP+, except that the alchemical transformation is achieved by a direct coordinate transformation rather than a series of decoupling or mutating steps of the ligand atoms by modifications of the force field parameters. In the ATM-ABFE protocol, for example, the ligand coordinates are displaced by a fixed amount from the binding site region to a corresponding area in the solvent bulk. In the ATM-RBFE protocol, the two ligands are displaced in opposite directions to switch places in the binding site and the solvent bulk. Because the displacement involves the whole ligand, the ATM-ABFE protocol cannot handle ligands as big as LEN. Hence, in this application, we adopted a progressive ABFE unbinding protocol similar to the progressive DDM approach described above. We used a sequence of nine RBFE steps starting with LEN (lenacapavir in Figure S2, Supporting Information) and ending with fragment l9. Fragment l9 was then transferred to solution using the ATM-ABFE protocol (Fig. S2). The sum of the free energies of these ten steps is the excess binding free energy of LEN with a negative sign. For each step, we employed the standard ATM setup workflow, alchemical potential, and λ-schedule (https://github.com/Gallicchio-Lab/AToM-OpenMM/blob/master/examples/RBFE/cdk2/scripts/asyncre_template.cntl). The center of the binding site was defined as the centroid of the C-alpha atoms of residues 37, 38, 41, 135, 169, 172, 173, 179, 182, 183, 270, 273, 274, 276, 277, 283, 286, 287, 289, 290, 293, 294, 325, 326, 327, and 350 of capsid (PDB ID: 6VKV). The center of LEN was defined as the atom labeled “1” in Figure S2. To define the binding site region, the distance between the center of the binding site and the center of the ligand was restrained with a tolerance of 2 Angstroms based on the observed fluctuations of the position of LEN during a 20 ns preparatory MD simulation. The alignment atoms employed during the ATM-RBFE steps are labeled “1”, “2”, and “3” in Figure S2. The length of the ATM displacement vector was set to 43 Å.

Alchem-PMF (Physical Pathway with Alchemical Softening)

ABFE was also computed with Alchem-PMF,³⁰ which combines a physical extraction pathway (PMF) with alchemical softening/recoupling of sterically hindering groups. In brief, the standard PMF defines a pulling coordinate r = |r(P1–L1)| between a receptor anchor atom (P1) and a ligand anchor atom (L1), together with five angular restraints (θ, φ, Θ, Φ, Ψ) that fix ligand orientation and the linear pulling direction relative to the receptor; umbrella sampling along r yields the one-dimensional PMF w(r) under these orientational restraints. The ABFE is assembled from: (i) the reversible work to apply orientational restraints in the bound complex; (ii) the reversible work of moving the restrained ligand from the binding site to a bulk location along r (from the PMF w(r)); and (iii) the free energy of analytic release of restraints to the 1 M standard state in bulk.

For enclosed sites or ligands with buried substituents, direct pulling can encounter high, poorly sampled steric barriers and impede water exchange into the vacated pocket. Alchem-PMF circumvents this by alchemically removing (or softening) non-bonded interactions for the minimal set of sterically obstructing atoms (typically a localized ligand moiety and, if needed, nearby receptor side chains) before the PMF pulling, then restoring those interactions after the ligand reaches bulk. The resulting thermodynamic cycle adds two alchemical terms to the standard PMF expression: a bound-state decoupling free energy (${\Delta G}_{\mathit{\text{decouple}}\_\mathit{\text{bound}}}$) and a bulk-state recoupling free energy (${\Delta G}_{\mathit{\text{decouple}}\_\mathit{\text{bulk}}}$). Thirty umbrella windows spanned bound to bulk with a single radial force constant; each window was equilibrated before production and analyzed by WHAM. In the case of the LEN-CA complex, the ligand atoms that are deeply buried in the binding pocket (Fig. S3) are alchemically decoupled before pulling.

Calculation of Solvation Free Energy of LEN in DMSO buffers

The solvation free energies of LEN in DMSO/water buffers were performed using GROMACS at two DMSO concentrations: 5% and 10% v/v. Both LEN and DMSO were parameterized using the General AMBER Force Field GAFF2³⁶ with the AM1-BCC³⁷ partial charge model. The LEN was solvated in a box of mixed solvent containing DMSO/water. The mixed solvent box was prepared using the gmx insert-molecules command in GROMACS. To achieve 5% and 10% v/v DMSO concentrations, 20 and 40 DMSO molecules were added respectively, to a box of 1450 TIP3P water molecules at random positions.

To calculate the solvation free energy, the LEN was first decoupled electrostatically from the solvent by using 11 Coulomb lambda-windows (${\lambda }_{\mathit{\text{Coul}}}$ = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0), and then the van der Waals solute-solvent interactions were turned off by using 17 LJ lambda-windows (${\lambda }_{LJ}$ = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.94, 0.985, 1.0). Soft-core potential was applied during the latter stage to avoid singularities. In each $\lambda$ window the system was equilibrated for 10 ns and followed by 20 ns of production run to collect $〈\frac{dH}{d\lambda }〉$ in each lambda windows. The results of $〈\frac{dH}{d\lambda }〉$ were then used to compute the solvation free energy using thermodynamic integration (TI).

Results

Table 1 shows the ABFE of Lenacapavir with HIV-1 capsid dimer calculated using different methods. The protocols span both alchemical and physical pathway approaches:

• Schrödinger ABFEP and GROMACS DDM follow the standard double-decoupling method (DDM).^23–24 The DDM with ligand reorganization uses the same GROMACS DDM protocol but adds ligand torsion-restrain/release legs to better account for the ligand reorganization cost.

• Alchem-PMF combines a physical pathway PMF extraction with alchemical decoupling to aid removal of a bulky ligand from a buried pocket.³⁰

• ATM^{25, 27–28} and Progressive DDM⁴⁰ apply fragment-based strategies that transfer or alchemically decouple ligand fragments in stages, which facilitates water equilibration during solute cavity annihilation and recreation.

Table 1.

Absolute binding free energy of LEN calculated using different ABFE methods.

Method (Code, force field)	$\Delta G_{\mathit{\text{bind}}}^0$ (kcal/mol)
ABFEP (Schrödinger Inc., OPLS4)4	−26.4 ±1.1
DDM (GROMACS, Amber ff99SB-ILDN/GAFF2)10	−28.7 ± 0.5
DDM with ligand reorganization (GROMACS, Amber ff99SB-ILDN/GAFF2)10	−22.5 ± 1.0
Alchem-PMF (GROMACS, Amber ff99SB-ILDN/GAFF2)30	−27.5 ± 0.3
ATM ABFE Protocol (OpenMM, Amber ff14SB/GAFF2)29, 44–45	−27.2 ± 1.1
Progressive DDM (Schrödinger, OPLS4)4	−30.1 ± 1.2
Experiment (SPR, in 5% DMSO)22	−13.4

The error bars in Table 1 are estimated from variations in $\Delta G_{\mathit{\text{bind}}}^0$ obtained from multiple independent runs, each initialized using either different LEN–CA dimer starting structures selected from the 6 LENs in the CA hexamer structure (for ABFEP, DDM/GROMACS, and Progressive DDM) or from different thermalized starting structures with different initial velocities (for Alchem-PMF and ATM).

Apparent convergence of the calculated $\Delta G_{\mathit{\text{bind}}}^0$ was assessed by computing $\Delta G_{\mathit{\text{bind}}}^0$ on non-overlapping time blocks (see the convergence plots Fig. S5 in the Supporting Information). For ABFEP, Alchem-PMF, and Progressive DDM the block-wise estimates plateau within ~15–30 ns (for ABFEP and Progressive DDM, this refers to the simulation time per λ window; for Alchem-PMF, to simulation time per umbrella sampling window), with late-time variation ≤ 0.5–0.8 kcal/mol. For ATM-ABFE the plateau is reached between 35 ns and 40 ns. Both GROMACS DDM and DDM with ligand reorganization showed a small late-time drift of ~0.9–1.0 kcal/mol between 45 and 80 ns (Fig. S5).

Several observations follow from Table 1.

First, all methods significantly overestimate the experimental binding free energy of −13.4 kcal/mol, predicting values that are 9–16 kcal/mol more favorable. DDM with ligand reorganization produced a smaller but still substantial overestimate of ~9 kcal/mol. This suggests that inadequate treatment of ligand reorganization is one source of the discrepancy; we return to this in a later section.

Second, consistent results are obtained for the five methods, ABFEP (Schrödinger), DDM (GROMACS), Alchem-PMF (GROMACS), ATM ABFE Protocol (OpenMM) and Progressive DDM (implemented using ABFEP and FEP+ from Schrödinger) across different thermodynamic pathways, software package and force fields. The two standard DDM implementations, Schrödinger ABFEP and GROMACS DDM which use different force field and sampling protocols (e.g. use of REST2 or not), produce similar standard binding free energies (–26 to −29 kcal/mol). The results from the hybrid Alchem-PMF (–27.5 kcal/mol) and the ATM ABFE Protocol (−27.2 kcal/mol) falls within the same range as the standard DDM, indicating that switching between a purely alchemical pathway, a hybrid physical-plus-alchemical scheme, and an alchemical-transfer pathway does not affect the final affinity estimate for this system.

Third, both fragment-based protocols, ATM-ABFEP and Progressive DDM, gave $\Delta G_{\mathit{\text{bind}}}^0$ values in a narrow range of −27 to −30 kcal/mol, closely matching the results from the other protocols. Like ATM-ABFEP, Progressive DDM was designed to improve water equilibration during cavity creation, yet it gave a slightly more favorable value (~3.7 kcal/mol) than regular ABFEP that used the same OPLS4 force field. This indicates that, for this system, insufficient sampling of ligand-cavity annihilation/creation is unlikely to explain the much larger ~13 kcal/mol overestimation relative to the SPR measurement.

Because the overestimation is large across very different ABFE engines and pathways, we next examined common sources of ABFE error to see whether any of them could plausibly account for the large gap of 9–16 kcal/mol between the computation and experiments.

Conventional suspects do not explain the overestimation in $\Delta G_{\mathit{\text{bind}}}^0$

Ligand protonation state

Lenacapavir’s sulfonamide nitrogen can be either protonated or deprotonated near physiological pH. A relative binding free energy (FEP+ from Schrödinger Inc.) calculation between the two protonation states gave $\Delta G_{\mathit{\text{bind}}}^{\text{LEN}->\text{LEN}-}$ = −1.1 kcal/mol impact on affinity. This minor shift confirms that protonation state is not a significant contributor to the large overestimation.

Protein oligomeric form

Because mature HIV-1 capsid is primarily composed of CA hexamers, we compared ABFEP results for the dimer and hexamer. The two receptors yielded nearly identical affinities (–27.4 ± 1.1 vs −27.1 ± 1.0 kcal/mol), differing by < 0.5 kcal/mol. Thus, receptor oligomeric state can be ruled out as a source of systematic error.

Protein reorganization

When receptor reorganization induced by ligand binding is not adequately sampled within the finite trajectories used in ABFE, the calculated $\Delta G_{\mathit{\text{bind}}}^0$ can be biased. In holo-initiated DDM runs, insufficient sampling of the apo-like conformations in the fully decoupled λ window tends to overestimate affinity; in apo-initiated runs, insufficient sampling of holo-like conformations in the fully coupled λ window tends to underestimate affinity. Accordingly, the difference between holo- and apo-initiated ABFEs ($\Delta \Delta G_{\mathit{\text{bind}}}^0$) provides a practical upper-bound diagnostic for the free energy cost of receptor reorganization.^{46–49, 4} To this end we have computed $\Delta G_{\mathit{\text{bind}}}^0$ starting from both holo and apo capsid models in dimer and hexamer contexts. Complexes based on the apo structures were prepared by superimposing apo and holo capsids and transferring the bound LEN and deleting the holo protein from the complex. Across all setups, $\Delta G_{\mathit{\text{bind}}}^0$ values vary between −25.7 and −26.4 kcal/mol, with a ≤1 kcal/mol difference between holo- and apo-initiated calculations (holo slightly more favorable for both dimer and hexamer cases). If we believe that $\Delta \Delta G_{\mathit{\text{bind}}}^0$ computed from the experimental holo and apo structures reflects the protein reorganization cost, then this small shift suggests that protein conformational reorganization does not contribute substantially to the ~9–16 kcal/mol gap between computed ABFEs and the SPR measurement.

When we superimposed capsid dimers from the holo and apo experimental structures on the N-terminal domain (NTD) of the monomer that makes the most extensive contact with LEN, we observed distal allosteric differences, particularly in the NTD of the other monomer (Figure 3A). In our DDM runs, the decoupled complex-leg end state, which should correspond to the apo protein if well converged, relaxed to an intermediate between the holo and apo structures, especially in regions exhibiting allostery (Figure 3B). Moreover, in MD-relaxed apo+LEN starting structures, the allosteric pattern did not fully match that of the holo state (Figure 3C).

Figure 3.

(A) Experimental dimer structures from PDB 4XFX (apo, gray) and 6V2F (holo, green).(B) Experimental dimer structures from PDB 4XFX (apo, gray) and 6V2F (holo, green), along with the capsid dimer conformation in the decoupled state initiated from the experimental holo complex (red).(C) Experimental dimer structures from PDB 4XFX (apo, gray) and 6V2F (holo, green), together with the capsid dimer conformation in the MD-relaxed complex initiated from the apo structure with docked LEN (red)..

Taken together, these observations indicate that distal allosteric reorganization is not fully sampled and may contribute modestly to the difference between calculated $\Delta G_{\mathit{\text{bind}}}^0$ and the SPR result, even though the small calculated $\Delta \Delta G_{\mathit{\text{bind}}}^0$ between the results obtained using the apo and holo structures indicates that reorganization is unlikely to be a dominant source of the ~9–16 kcal/mol discrepancy. This suggests that HIV-1 capsid differs from more flexible targets (e.g., kinases), where protein reorganization penalties was shown to reach ~5 kcal/mol and significantly impact binding free energy calculations.⁴⁹

No fitting artifacts in the SPR kinetics

To test whether the long dissociation tail in the SPR sensorgrams (Fig. 1A of Ref. 6) could reflect an overestimated k_off (and thus an artificially weak affinity), we regenerated association/dissociation curves using the reported global-fit parameters (Fig. S1; Equations S1–S4) and then overlaid dissociation traces computed with a 10-fold smaller k_off while keeping k_on fixed. The reduced k_off curves decay markedly more slowly and no longer match the measured traces (Fig. 4A); when the time axis is extended by 10×, the mismatch is even more pronounced (Fig. 4B). Thus, the original global fit does not appear to overestimate k_off.

Figure 4.

A: The binding fit curves using the originally reported k_on and k_off (1.5 × 10⁻⁵) are shown in orange, while the fit curves using the same k_on but a 10-fold smaller k_off (1.5 × 10⁻⁶) is shown in blue. B: The time scale here is 10 times longer than in panel A.

Taken together, these control calculations show that none of the factors considered explain the ~9 – 16 kcal/mol gap between computation and experiment. We now focus on two effects: ligand reorganization free energy cost for which DDM with ligand reorganization provides better account (Table 1) and the effects from the experimental solvent (5% DMSO) used in the SPR affinity measurements.

The DDM variant with ligand reorganization reduces the LEN overbinding

Applying the modified DDM variant with the ligand torsion restrain/release cycle gave a standard binding free energy of −22.5 ± 1.0 kcal/mol, i.e. ≈ 6 kcal weaker than $\Delta G_{\mathit{\text{bind}}}^0$ = −28.7 ± 0.5 kcal/mol from the standard DDM using the same GROMACS DDM setup (Table 1). LEN is a large molecule with 13 rotatable bonds which makes the sampling of the ligand degrees of freedom challenging for standard ABFE protocols employing tens of nanoseconds of simulation time to capture the ligand reorganization free energy. As shown in Fig. 5, LEN undergoes very large reorganization between its structure in solution and that in the bound complex. While the free LEN in solution is stabilized by multiple nonbonded intramolecular interactions, such favorable intramolecular interactions are completely absent in the bound LEN (Fig. 5), which is stabilized by favorable interactions with the protein (not shown in Fig. 5).

By restraining ligand torsions in the bound, fully coupled state and releases them in a separate step, when the ligand is fully coupled in solution (see Fig. 2 and Eq. (2)), the DDM variant better accounted for such extensive ligand reorganization in ABFE calculation. In contrast, the limited simulation times per λ window used in the standard ABFE protocols were insufficient to fully explore the unbound conformational ensemble of LEN and hence underestimated the reorganization free energy penalty. This conclusion is supported by the convergence analysis (see Fig. S5, Supporting Information) generally indicating a slow upward drift of the ABFE binding free energy estimates towards less negative values as the simulations with the standard protocols are extended to longer times.

Remaining error of ~ 9 kcal/mol: Impact of solvent reference states

Even with the improvement in accounting for the ligand reorganization effect using the DDM variant of Fig. 2, the $\Delta G_{\mathit{\text{bind}}}^{°}$ is still about −9 kcal/mol too favorable compared with that obtained from experiment, i.e. −22.5 kcal/mol vs. −13.4 kcal/mol (Table 1). In this section we provide quantitative evidence and a thermodynamic framework to show that this remaining error is likely attributable to the different solvent conditions used in the SPR measurements (5% v/v DMSO buffer) and ABFE calculations (neat water). LEN is practically insoluble in water (solubility S ≈ 0.31 μg/mL) but highly soluble in DMSO (S ≈ 100 to 195 mg/mL). The addition of less polar DMSO to the solution has two principal effects on the binding affinity of LEN to the protein pocket. First, the presence of DMSO increases the solubility of free LEN in the buffer solution, which as shown below leads to a weakening of binding by a factor equivalent to the free energy cost of transferring LEN from the buffer solution to neat water. Second, it is reasonable to expect that the preferential absorption (enrichment) of DMSO by the nonpolar protein binding pocket in the buffer solution increases the free energy cost of displacing the DMSO molecules by LEN relative to that in water. Since absolute binding free energy is determined by the difference between the transfer free energy of the ligand into the binding pocket and that into solution (Fig. 5), each of the above effects contributes to a weaker standard binding free energy of the LEN with the capsid protein, as shown below in a detailed semiquantitative thermodynamic analysis.

Estimate of the difference of insertion free energy of LEN in pure water and DMSO/water solution using experimental solubilities and solvation free energy calculations

Consider saturated solutions of LEN in pure water (LEN(aq)) and in 5% DMSO water mixture (LEN(aq,DMSO)) in equilibrium with solid LEN (LEN(s)) (Figure 6A). By definition, the concentration of LEN in each solution is the corresponding solubility. Assuming ideal solutions, the chemical potential μ(L(aq)) of LEN can be written as

$$\mu \left(L\left(aq\right)\right)=\mu °\left(L\left(aq\right)\right)+k_{B}T\text{ln}\frac{S\left(L\left(aq\right)\right)}{C°}$$ (3)

where μ◦(L(aq)) is the standard chemical potential and S(L(aq)) is the solubility of LEN in water. The standard state is an ideal solution at $C°$ = 1 M concentration. The expression of the chemical potential of LEN in the DMSO/water mixture is written analogously to Eq. (3), i.e.

$$\mu \left(L\left(aq,\mathit{\text{DMSO}}\right)\right)=\mu °\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)+k_{B}T\text{ln}\frac{S\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)}{C°}$$ (3’)

Figure 6.

A. Diagram that illustrates the derivation of Eq. (4). Solid LEN (LEN(s)) is at bottom and saturated LEN solutions in pure water (left) and a mixture of 5% DMSO and water (right) are in equilibrium with the solid. The chemical potential of LEN is the same in these three environments. B. Diagrams illustrating the transfer free energy of LEN from the gas phase to a pure water solution (left) and a 5% DMSO/water mixture (right) at their standard states denoted by a superscript circle.

Because the chemical potential of LEN in each saturated solution is equal to the chemical potential of solid LEN, the chemical potentials of LEN in the two saturated solutions in Fig. 6A are the same. Equating the two expressions Eq. (3) and Eq. (3’), we arrive at the following expression for the difference of standard chemical potentials of LEN in the DMSO/water mixture and in pure water in terms of the respective solubilities:

$$\Delta \mu °=\mu °\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(L\left(aq\right)\right)={-k}_{B}T\text{ln}\frac{S\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)}{S\left(L\left(aq\right)\right)}$$ (4)

The aqueous solubility of LEN has been reported as $S\left(L\left(aq\right)\right)=$ 0.31 μg/mL at room temperature.⁵⁰ Using the reported 320 μM LEN in 4.3% DMSO buffer²¹ as a proxy for solubility, i.e. ≈10³-fold over water, Eq. (4) implies $\Delta \mu °={-k}_{B}T\text{ln}\frac{S\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)}{S\left(L\left(aq\right)\right)}=-4.1$ kcal/mol at 300 K.

Now consider the standard molar transfer free energy of LEN from the gas phase to water, ${\Delta G°}_t\left(L\left(aq\right)\right)=\mu °\left(L\left(aq\right)\right)-\mu °\left(L\left(g\right)\right)$, and to the DMSO/water mixture (Figure 6B). The difference between the transfer free energies is:

$${\Delta \Delta G°}_t\left(L\left(aq\right)\to L\left(aq,\mathit{\text{DMSO}}\right)\right)={\Delta G°}_t\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)-{\Delta G°}_t\left(L\left(aq\right)\right)$$

$$=\mu °\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(L\left(aq\right)\right)$$ (5)

which is exactly Eq. (4). Hence this analysis shows that the transfer free energy of LEN from the gas phase to the DMSO/water solution is predicted to be approximately −4.1 kcal/mol more favorable than the transfer to water.

In addition to estimating the ${\Delta \Delta G°}_t\left(L\left(ag\right)\to L\left(aq,\mathit{\text{DMSO}}\right)\right)$ using experimental solubilities, we also calculated this quantity using free energy simulations by alchemically annihilating a ligand in DMSO/water and pure water and taking the difference of the free energy changes. Using GROMACS with GAFF parameters for DMSO and TIP3P for water, we found that the calculated solvation free energy shifts relative to water are ${\Delta \Delta G°}_t\left(L\left(aq\right)\to L\left(aq,\mathit{\text{DMSO}}\right)\right)={\Delta G°}_t\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)-{\Delta G°}_t\left(L\left(aq\right)\right)=-3.35\pm 1.03$ kcal/mol at 5% DMSO, and −4.43 ± 0.87 kcal/mol at 10% DMSO. These results are consistent with the estimate from Eq. (4) using experimental solubilities at 5% DMSO (≈ −4.1 kcal/mol) and show the expected concentration dependence (stronger stabilization at 10% than at 5%). The general agreement between the calculation and the solubility-based thermodynamic estimates provide quantitative evidence that solvation free energy of LEN in DMSO/water is substantially more favorable than that in pure water, which as shown below contributes to the weaker binding affinity in the DMSO/water buffer.

Effect of DMSO on the binding affinity of LEN for the receptor

The standard molar binding free energy ${\Delta G°}_{\mathit{\text{bind}}}$ of a ligand L to a receptor R to form the complex RL in water:

$$\text{L}\left(\text{aq}\right)+\text{R}\left(\text{aq}\right)\to \text{RL}\left(\text{aq}\right)$$

is the difference between the standard chemical potentials of the complex and the free receptor and ligand

$${\Delta G°}_{\mathit{\text{bind}}}\left(aq\right)=\mu °\left(RL\left(aq\right)\right)-\mu °\left(R\left(aq\right)\right)-\mu °\left(L\left(aq\right)\right)$$ (6)

Motivated by the DDM thermodynamic cycle (Figure 5), ${\Delta G°}_{\mathit{\text{bind}}}$ can be expressed in terms of the free energies of transfer of the ligand to water and to the receptor binding site in water by adding and subtracting the chemical potential of the ligand in vacuum $\mu °\left(L\left(g\right)\right)$

$${\Delta G°}_{\mathit{\text{bind}}}\left(aq\right)=\left[\mu °\left(RL\left(aq\right)\right)-\mu °\left(R\left(aq\right)\right)-\mu °\left(L\left(g\right)\right)\right]-\left[\mu °\left(L\left(aq\right)\right)-\mu °\left(L\left(g\right)\right)\right]$$ (7)

$$={\Delta G°}_t\left(RL\left(aq\right)\right)-{\Delta G°}_t\left(L\left(aq\right)\right)$$ (8)

where ${\Delta G°}_t\left(RL\left(aq\right)\right)$ is the free energy of transfer of the ligand from the gas phase to the receptor binding site in water:

$$\text{L}\left(\text{g}\right)+\text{R}\left(\text{aq}\right)\to \text{RL}\left(\text{aq}\right)$$

i.e.

$${\Delta G°}_t\left(RL\left(aq\right)\right)=\mu °\left(RL\left(aq\right)\right)-\mu °\left(R\left(aq\right)\right)-\mu °\left(L\left(g\right)\right)$$

And ${\Delta G°}_t\left(L\left(aq\right)\right)$ is the free energy of transfer of the ligand from the gas phase to water:

$$\text{L}\left(\text{g}\right)\to \text{L}\left(\text{aq}\right)$$

with

$${\Delta G°}_t\left(L\left(aq\right)\right)=\mu °\left(L\left(aq\right)\right)-\mu °\left(L\left(g\right)\right)$$

Analogously, we can write the equation for the binding free energy for the DMSO/water mixture as

$${\Delta G°}_{\mathit{\text{bind}}}\left(aq,\mathit{\text{DMSO}}\right)=\left[\mu °\left(RL\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(R\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(L\left(g\right)\right)\right]-\left[\mu °\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(L\left(g\right)\right)\right]$$ (7’)

$$={\Delta G°}_t\left(RL\left(aq,\mathit{\text{DMSO}}\right)\right)-{\Delta G°}_t\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)$$ (8’)

where ${\Delta G°}_t\left(RL\left(aq,\mathit{\text{DMSO}}\right)\right)$ is the free energy of transfer of the ligand from the gas phase to the receptor binding site in DMSO/water mixture:

$$\text{L}\left(\text{g}\right)+\text{R}\left(\text{aq},\text{DMSO}\right)\to \text{RL}\left(\text{aq},\text{DMSO}\right)$$

with

$${\Delta G°}_t\left(RL\left(aq,\mathit{\text{DMSO}}\right)\right)=\mu °\left(RL\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(R\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(L\left(g\right)\right)$$

And ${\Delta G°}_t\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)$ is the free energy of transfer of the ligand from the gas phase to DMSO/water mixture:

$$\text{L}\left(\text{g}\right)\to \text{L}\left(\text{aq,DMSO}\right)$$

with

$${\Delta G°}_t\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)=\mu °\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(L\left(g\right)\right)$$

Taking the difference between Eq. (8’) and Eq. (8), we arrive at an expression for the difference between the standard binding free energy in DMSO/water mixture and pure water:

$${\Delta \Delta G°}_{\mathit{\text{bind}}}\left(aq\to \left(aq,\mathit{\text{DMSO}}\right)\right)={\Delta G°}_{\mathit{\text{bind}}}\left(aq,\mathit{\text{DMSO}}\right)-{\Delta G°}_{\mathit{\text{bind}}}\left(aq\right)$$ (9)

$$={\Delta \Delta G°}_t\left(RL\left(aq\right)\to RL\left(aq,\mathit{\text{DMSO}}\right)\right)-{\Delta \Delta G°}_t\left(L\left(aq\right)\to L\left(aq,\mathit{\text{DMSO}}\right)\right)$$ (10)

Eq. (10) is the central equation for understanding the effects of adding DMSO on the binding affinity. The first term in Eq. (10), ${\Delta \Delta G°}_t\left(RL\left(aq\right)\to RL\left(aq,\mathit{\text{DMSO}}\right)\right)$, i.e. the “pocket leg” contribution in the thermodynamic cycle in Fig. 7, is the difference between the free energy of transferring a gas-phase ligand into the protein pocket in the DMSO/water mixture and that in pure water, i.e.

$${\Delta \Delta G°}_t\left(RL\left(aq\right)\to RL\left(aq,\mathit{\text{DMSO}}\right)\right)={\Delta G°}_t\left(RL\left(aq,\mathit{\text{DMSO}}\right)\right)-{\Delta G°}_t\left(RL\left(aq\right)\right)$$ (10-1)

$$=\left[\mu °\left(RL\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(R\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(L\left(g\right)\right)\right]-\left[\mu °\left(RL\left(aq\right)\right)-\mu °\left(R\left(aq\right)\right)-\mu °\left(L\left(g\right)\right)\right]$$ (10-2)

The second term in Eq. (10), ${\Delta \Delta G°}_t\left(L\left(aq\right)\to L\left(aq,\mathit{\text{DMSO}}\right)\right)$, i.e. the “solvent leg” contribution in Fig. 7, is the difference between the free energy of transferring a gas-phase ligand into the DMSO/water and that into pure water,

$${\Delta \Delta G°}_t\left(L\left(aq\right)\to L\left(aq,\mathit{\text{DMSO}}\right)\right)=\left[\mu °\left(L\left(aq,\mathit{\text{DMSO}}\right)\right)-\mu °\left(L\left(g\right)\right)\right]-\left[\mu °\left(L\left(aq\right)\right)-\mu °\left(L\left(g\right)\right)\right]$$ (10-3)

We have already shown that, in the case of LEN, the second term (“solvent-leg term”) in Eq. (10) ${\Delta \Delta G°}_t\left(L\left(aq\right)\to L\left(aq,\mathit{\text{DMSO}}\right)\right)$ is negative (≈ −4.1 kcal/mol using the experimental solubilities, or ≈ −3.35 kcal/mol using calculated solvation free energy difference; see Eqs. (4) and (5) and the discussions given there), which according to Eq. (10) contributes to making the binding free energy in DMSO about 3–4 kcal/mol less favorable than in pure water.

Figure 7.

Thermodynamic Cycle that connects ABFEs in aqueous solution and DMSO/water mixture.

We next consider the first term (“pocket-leg term”) in Eq. (10), ${\Delta \Delta G°}_t\left(RL\left(aq\right)\to RL\left(aq,\mathit{\text{DMSO}}\right)\right)$. We propose that, for a hydrophobic receptor pocket, this term also likely makes the binding free energy in DMSO less favorable than in water. A thermodynamic-cycle analysis, presented in the Supporting Information, suggests that this pocket-leg contribution to ${\Delta \Delta G°}_{\mathit{\text{bind}}}\left(aq\to \left(aq,\mathit{\text{DMSO}}\right)\right)$ can be decomposed into a cavity-formation term, associated with displacing DMSO preferentially bound in the hydrophobic pocket, and a ligand–pocket interaction term that largely cancels between water and DMSO buffer. We hypothesize that the cavity term dominates and is positive, thereby disfavoring binding in the DMSO buffer relative to water and reinforcing the trend inferred from the solvent-leg contribution (see Supporting Information, Eqs. S5–S8 and Fig. S6).

Our analysis on the plausible mechanisms by which DMSO affects binding affinity is consistent with previous reports that addition of DMSO weakens apparent binding relative to DMSO-free aqueous buffer, even though those studies did not resolve the underlying physical origin. Senac et al.¹⁹ examined the effect of adding DMSO to the binding affinity in host–guest complexes of 1-adamantane carboxylic acid (ADA) with β- and γ-cyclodextrin and found that 5% DMSO reduced the affinity of ADA for β-cyclodextrin by ~2.1 kcal/mol, whereas the effect on the looser γ-cyclodextrin complex was smaller (~0.7 kcal/mol), indicating that DMSO weakens tight, hydrophobic cavities more strongly. Cubrilovic and Zenobi⁵¹ compared three protein–ligand complexes in 0–8% DMSO and observed that the largest affinity loss (≈10.5-fold or 1.4 kcal/mol shift in ${\Delta G°}_{\mathit{\text{bind}}}$) occurred for carbonic anhydrase binding chlorothiazide, which is the least water-soluble ligand in their set, while the more water-soluble ligands (Pefabloc and NAG3) showed smaller decreases. This trend of solubility dependence is consistent with one of the mechanisms we propose here: when a ligand is poorly soluble in neat water, adding a few percent DMSO stabilizes the free ligand in the bulk solvent and shifts the binding equilibrium (see Eq. (10)). LEN is an extreme case with a molar mass 3–5 times the ligands in those studies, and the LEN binding pocket is also significantly more extensive. In addition, the SPR buffer employed in the measurement of LEN-CA binding affinity also contains 0.05% Tween-20 surfactant which further increases the LEN solubility, so it is reasonable to expect a much larger buffer-induced binding affinity decrease relative to neat water.

Discussion

This work evaluates the performance of current absolute binding free energy (ABFE) protocols on a large hydrophobic ligand (lenacapavir, LEN) and substantially accounts for an initially very large discrepancy with experiment through two physically distinct effects: ligand reorganization and the solvent reference state. Across diverse thermodynamic pathways and software code (standard DDM, Alchem-PMF, ATM, progressive DDM), the calculated values in neat water converge to ${\Delta G°}_{\mathit{\text{bind}}}$ ≈ −26.4 to −30.0 kcal/mol, while SPR in 5% (v/v) DMSO reports ≈ −13.4 kcal·mol−¹ (Table 1). Control calculations indicate that changes in ligand protonation, receptor oligomeric form, and force field each shift ${\Delta G°}_{\mathit{\text{bind}}}$ by only ~ 1 kcal/mol, and SPR fitting artifacts were ruled out by explicit sensitivity analyses of k_off (Fig. 4). These observations focus our attention on: (i) the ligand reorganization, since LEN undergoes extensive structural rearrangement upon binding that is challenging to sample in standard ABFE calculations due to its many torsional degrees of freedom, and (ii) the effect of buffer composition, as the experiments were carried out in a mixed solvent while the simulations used neat water.

Ligand reorganization indeed turns out to be an important contributor to the overbinding of LEN. With 13 rotatable bonds, LEN has substantial internal flexibility. A DDM variant that explicitly restrains and releases ligand torsions, following earlier work such as BAT2,¹⁵ reduces the overbinding by ~6 kcal/mol relative to standard DDM by avoiding the need to sample the large ligand conformational change during decoupling (Fig. 2).

On the other hand, several ABFE protocols take a different approach by applying enhanced sampling during ligand decoupling while keeping the ligand conformation unrestrained. For example, Schrödinger’s ABFEP⁴ and the recently developed protocol by Wu et al.14 employ REST or Hamiltonian replica exchange in λ space to accelerate exploration of the ligand’s conformational ensemble across all λ windows, instead of applying torsional restraints. In principle, such enhanced-sampling schemes should improve convergence, but in practice their impact is system dependent: enlarging the accessible conformational space can also increase correlation times and, in some systems, even slow convergence.⁵² For LEN–CA, the restraint/release DDM variant yields a better estimate of ${\Delta G°}_{\mathit{\text{bind}}}$ than the current implementation of Schrödinger ABFEP, which relies on enhanced sampling to flatten the unrestrained ligand’s conformational landscape (Table 1). However, it is difficult to draw firm conclusions from a single large ligand, particularly because the two protocols also use different force fields. It would therefore be informative in future work to compare these restrained versus enhanced-sampling strategies more systematically, using a common force field and a set of ligands spanning a range of sizes and flexibilities, to assess their relative ability to capture ligand–reorganization penalties.

Even with this improvement from the DDM with ligand reorganization, a ~9 kcal/mol gap to the SPR value remains, indicating that ligand reorganization alone cannot reconcile computation and experiment. Our thermodynamic analysis and solvation free energy calculations suggest that the solvent reference state provides the dominant missing term. SPR was executed in 5% DMSO buffer. In such a buffer, two effects can systematically weaken binding relative to pure water: (1) bulk stabilization of free LEN in the DMSO/water buffer (higher solubility, lower chemical potential),^53–54 and (2) the proposed cosolvent occupancy of the hydrophobic pocket, which likely raises the work to form the complex by displacing DMSO. A buffer-transfer analysis using experimental solubilities yields a bulk shift of about +4.1 kcal/mol at 300 K (Eqs. 4–5), consistent with the expected direction. We also calculated the solvation free energy of LEN in the 5% DMSO buffer and that in pure water using standard alchemical decoupling simulations, which gave ${\Delta \Delta G°}_t\left(L\left(aq\right)\to L\left(aq,\mathit{\text{DMSO}}\right)\right)$ ≈ −3.35 kcal/mol, confirming the thermodynamic analysis based on experimental solubilities. The binding pocket contribution is also hypothesized to disfavor binding in the DMSO buffer because DMSO likely enriches hydrophobic pockets and is expected to be more costly to displace on binding than bound water. Together, the quantitative estimate of the bulk stabilization and qualitatively hypothesized pocket effects help rationalize the residual ~9 kcal/mol overbinding after DDM with ligand reorganization and explain why water-reference ABFEs are not directly comparable to K_d measured in DMSO-containing buffers, and fully buffer-matched ABFE calculations would be required for rigorous validation.

Protein reorganization appears secondary for this system. Holo- versus apo-initiated calculations in both dimeric and hexameric capsid contexts differ by ~1 kcal/mol, suggesting limited net protein reorganization cost along the simulated pathway (Fig. 3). Some distal allosteric shifts are still visible upon decoupling; they may contribute to the remaining discrepancy.

Lastly, the possibility that force field limitations also contribute to the remaining discrepancy still exists. As seen from Fig. 5, the unbound ligand in solution features extensive intramolecular π−π interactions, whereas such interactions are not involved in the intermolecular recognition between LEN and binding pocket (structure not shown). It was reported that classical force fields tend to underestimate the strengths of π−π interactions (Sherrill et al.⁵⁵). It is therefore conceivable that our ABFE simulations using the standard force fields underestimated the thermodynamic stability of the unbound state, thereby shifting the binding equilibrium to favor the bound state and contribute to the remaining overestimation.

Implications for ligand screening in drug discovery

Although we find that adding only 5% DMSO can shift the apparent binding free energy of LEN by many kcal/mol, we do not conclude that the widespread use of DMSO-containing buffers in high-throughput screening is inherently problematic. In most ligand screening and SAR campaigns, the main goal is to obtain relative affinities or activities across a series of chemically related compounds under the same assay conditions. In that context, a substantial part of the DMSO effect (bulk solubility enhancement plus preferential pocket adsorption) is expected to be similar across analogs within a congeneric series, so that much of the cosolvent contribution cancels when considering binding free energy differences among ligands. Our work highlighted that cosolvents can strongly perturb absolute binding free energies, particularly for very hydrophobic ligands like LEN, and that this must be taken into account when one aims at quantitative comparison between computation and experiment.

In addition, we do not regard 5% DMSO as a realistic model of the physiological environment experienced by a drug molecule. The intracellular milieu is a crowded, compositionally complex mixture of proteins, nucleic acids, lipids, metabolites, and other components, and does not contain DMSO at appreciable concentrations. Instead, DMSO is introduced into in vitro assays primarily as a technical cosolvent to increase solubility and enable reliable measurements. Our results therefore do not argue that DMSO is more “physiological” than water, but rather use DMSO as a concrete example to demonstrate that any cosolvent or molecular crowder can have a large thermodynamic impact on binding, and that the effective in vivo recognition landscape can differ substantially from that inferred from simple aqueous or DMSO-based in vitro conditions.

Limitations and future work.

In this study we estimated the buffer effect semi-quantitatively using solubility-based thermodynamic arguments, solvation free energy calculations, and qualitative pocket-solvation reasoning. A rigorous treatment mimicking experimental buffer conditions requires running ABFE calculations in a DMSO/water buffer for a system with a large, topologically complex binding site: the LEN pocket comprises three connected sub-pockets, two of which are deeply buried. Mixed solvents can exhibit slow exchange between pocket and bulk (DMSO has a larger excluded volume than water), so achieving convergence will likely require advanced sampling techniques^56–57 through insertion–deletion of water and DMSO cosolvent targeting pocket solvent to accelerate equilibration. In addition, the presence of surfactants (e.g., 0.05% Tween-20 in the SPR buffer) above its critical micelle concentration (CMC) further complicates the bulk reference state through potential micelle-assisted solvation of LEN. A rigorous treatment of these multicomponent equilibria is challenging and beyond the scope of the present work. Such binding free energy calculations that mimic the experimental buffer conditions could be an important direction for future studies.

Supplementary Material

Supporting Information Available

1. Procedure for SPR Curve Fitting

2. Figure S2. The sequence of RBFE (relative binding free energy) steps used in the ATM calculation of the ABFE for LEN.

3. Figure S3. Buried ligand atoms of LEN that are alchemically decoupled from the environment in Alchem-PMF for computing the ABFE of LEN.

4. Figure S4. The sequence of stepwise alchemical removal of functional groups from LEN in the Progressive DDM calculation of the ABFE of LEN.

5. Figure S5. Convergence in the ${\Delta G°}_{\mathit{\text{bind}}}$ calculated using different ABFE methods employed in this study.

6. Thermodynamic cycle analysis of the sign of the first term in Eq. (10), ${\Delta \Delta G°}_t\left(RL\left(aq\right)\to RL\left(aq,\mathit{\text{DMSO}}\right)\right)$, i.e. the “pocket-leg” contribution to binding free energy difference in the two buffers.

7. Figure S7. Conformational ensembles of the decoupled ligand in both the solvent leg and the complex leg in the standard GROMACS DDM simulation: comparisons of the sampled distributions of selected dihedral angles.