Computational modeling of PROTAC ternary complexes as ensembles using SILCS-xTAC

Abstract

Proteolysis targeting chimeras, or PROTACs, are an emerging class of drugs that offer the potential to develop therapeutics targeting “undruggable” proteins by stabilizing protein-protein interactions (PPI). This involves leveraging the physiological protein degradation mechanism based on ubiquitination through stabilization of target protein-E3 ubiquitin ligase PPI mediated by the PROTAC. Existing computational methods for ligand design are not typically designed for the ternary complex problem and may have limited accuracy or efficiency, due to the use of either rigid docking or full molecular dynamics (MD) simulations. Here we present a method which uses SILCS (site identification by ligand competitive saturation) to address the challenge of designing ligands which stabilize PPI by using of precomputed ensembles of 1) functional group affinity patterns, termed FragMaps, for efficient and accurate ligand docking and of 2) a collection of putative PPI dimer 3D structures as docking targets. SILCS simulations involving aqueous, multi-solute grand canonical Monte Carlo (GCMC)/MD calculations generate the FragMaps for both the target and ligase proteins. An ensemble of PPI dimer conformations are generated using the FragMaps and then dimer FragMaps are generated by merging the two sets of FragMaps. PROTAC molecules are docked into the ensemble of dimer FragMaps, and final scoring metrics are extracted from the most favorable ternary complex. The scoring metrics, including energetics, binding site geometry and physicochemical terms, are weighted together to construct an activity score. The method is benchmarked on a diverse set of ternary crystal structures of different proteins and PROTACs, and the derived activity score shows modest correlation with DC₅₀ values in cells for a wide variety of systems. The SILCS-xTAC method is a powerful tool to facilitate PROTAC optimization by predicting binding geometries and energetics of ternary complexes.

Graphical Abstract

Introduction

Accurate modeling of ternary complexes involving two proteins mediated by a ligand is a critical, outstanding challenge in computational chemistry. One important and highly discussed class of ligands which facilitate protein-ligand-protein complexes are targeted protein degrader (TPD) molecules like PROTACs, or Proteolysis Targeting Chimeras.^1,2 PROTACs facilitate the degradation of a target protein of interest (POI) by stabilizing an interaction with an E3 ligase substrate-recognition protein,³ most often Cereblon,⁴ VHL (von Hippel-Lindau),^5,6 MDM2 (mouse double mutant 2),⁷ or cIAP (cellular inhibitor of apoptosis protein). The E3 ligase complex catalyzes the ubiquitination of the target protein, which ultimately causes recognition by the 26S proteasome for degradation.⁸ Throughout this article, the E3 ligase substrate-recognition protein and the target POI are referred to simply as the ligase and target, respectively. Similarly, the ligase warhead or target warhead refers to the known ligands which bind to those proteins.

PROTACs have numerous critical therapeutic advantages over conventional occupancy-driven therapeutic molecules.^2,9 Since ubiquitination is a chemical modification, it is effectively irreversible on the drug-binding timescale, reducing the susceptibility to resistance-conferring mutations that reduce binding occupancy. Additionally, removing high occupancy requirements means proteins which lack conventional druggable pockets can be targeted.¹⁰ PROTACs act catalytically, since they can unbind from the ternary complex while the target protein remains ubiquitinated. These advantages suggest that PROTACs require lower therapeutic doses than occupancy-driven drugs with similar binding affinity, and that degradation of the target results in complete ablation of all of the target’s functions.

Due to their desirable properties PROTACs have been designed for many systems,^11,12 but the design process is largely empirical, generating interest in computational design methods.¹³ In general, there is a need for improved accuracy and efficiency in computational modeling of ternary complexes, particularly since some PROTAC ternary complexes are known to be ensembles in solution.^14,15 To address the dynamics of PROTAC ternary complexes, MD simulations are a natural choice at the cost of significant computational time. Coarse-grain alchemical MD simulations have been used to study PROTAC cooperativity,¹⁶ and non-Markovian dynamics models used to connect local MD simulations to characterize diverse, including non-native, PPIs.¹⁷ Recently, MD simulations and quantum mechanics/density functional theory (QM/DFT) calculations of complexes with PROTACs of various degradation efficiencies indicated that more potent PROTACs tended to result in more stable, less dynamic complexes, and that the ligase warhead interaction energy correlates with overall efficiency as well.¹⁸ A variety of computational PROTAC design approaches have been developed, based on machine learning (ML),^19–22 conventional docking,^23–26 or MD,^27,16,17 listed in order of decreasing computational efficiency. ML approaches leverage available databases,^28,29 focusing primarily on linker design and highly efficient virtual screening.^19,21,22,30 Physics-based PROTAC modeling methods employ conventional docking both for the protein-protein and protein-ligand aspects.^23–26,31 Both AlphaFold3 and Boltz-1 have been integrated into a computational workflow (PROTACfold) to predict ternary complexes, with reasonable results on proteins not in the respective training sets.³² Most notable are methods which connect the structural modeling to cellular activities. One such approach correlated a statistical count of favorable complexes to degradation efficiency in several systems.²⁴ Another, DegraderTCM based on Molecular Operating Environment (MOE, Chemical Computing Group), predicts PROTAC interaction energy score which separates high and low degrader efficiency in among PROTACs of various activities.³³ In general, a major challenge to the development of computational methods for PROTAC development is the availability of adequate experimental data, either for training of ML models and for validation of physics-based models otherwise benchmarked against experimental ternary structures.

Here, we demonstrate the use of the computer-aided drug design (CADD) method SILCS (site-identification by ligand competitive saturation) in ternary complex prediction and PROTAC design. SILCS is designed to provide the accuracy of atomistic, explicit solvent MD and the computational efficiency of conventional docking. The method is based on precomputed ensembles extracted from oscillating excess chemical potential grand canonical Monte Carlo/MD (μ_ex-GCMC/MD) simulations of a protein in an aqueous solution containing eight solutes representing different classes of functional groups.^34,35 The simulations result in grid free energy (GFE) distributions of each functional group, the FragMaps, that are the basis for all subsequent SILCS calculations. In addition, the μ_ex-GCMC/MD simulations define Exclusion maps, or the regions where the water and solutes do not sample, and protein side chain and backbone probability distributions (protein probability grids, PPGs).³⁶ Critically, the use of explicit solvent μ_ex-GCMC/MD simulations means that the FragMaps and PPGs include contributions from solvation and protein flexibility. The FragMaps and PPGs are also leveraged in a fast Fourier transform (FFT) driven PPI docking method (SILCS-PPI) from which an ensemble of PPI dimer conformations are generated.³⁶

By combining these capabilities, the SILCS methodology uses the precomputed ensemble approach to effectively address the ternary complex design challenge central to PROTAC development.³⁷ Following initial calculation of the SILCS FragMaps for the ligase and target SILCS-PPI docking is used to generate an ensemble of protein dimer conformations. The PROTACs are then efficiently docked using the SILCS-Monte Carlo (MC) approach, which has previously been shown to rapidly dock and rank ligands with accuracy approaching that of computationally-demanding free energy perturbation methods.^38,39 This allows for independent selection of the best ternary complex for each PROTAC under consideration during ligand design from which the PROTAC predicted binding affinity to the protein dimer is obtained. In addition, the atom-based scoring approach in the SILCS method allows for partitioning of the overall predicted binding affinity into different moieties of a PROTAC, namely ligase warhead, target warhead and linker, offering higher resolution information to further the PROTAC design process. The SILCS-xTAC complex prediction and activity score, a weighted sum of mostly energetic terms describing the ternary complex, are benchmarked against a diversity of experimental PROTAC ternary complexes and cell-based activity experiments.

Methods

Experimental data curation

A diverse set of eleven experimental structures of PROTAC ternary complexes were used to benchmark the SILCS-xTAC method for PPIs (Table 1) and PROTAC conformations (Table 2). The target and ligase proteins were extracted from the PDB record, along with the PROTAC itself. The individual proteins used for the SILCS simulation were then aligned to the ternary complex using TMalign.⁴⁰ For VHL-SMARCA2 (6hax, 6hay) and CRBN-BRD4-BD1 (6bn7, 6boy), two complexes exist for the same system with different PROTACs. Since the protein RMSD of both complexes are < 1 Å, only one complex was selected to represent both as noted in Table 1 (6hay and 6bn7, respectively). However, for the PROTAC docking benchmark both PROTACs were used (Table 2). For DCAF-WDR5 and CIAP-BTK, the pairs of complexes selected are significantly different.

Table 1:

Benchmarking the SILCS-PPI and the top 20 predicted PPI complexes against experimental structures.

System	PDB ID	RMSD			iRMSD
		All	Clust.	T20	All	Clust.	T20	Rank
CIAP BTK	6w7o	13.5	15.1	18.1	2.0	3.0	11.7	1541
CIAP BTK	6w8i	1.9	5.4	15.9	0.0	0.5	1.3	2
CRBN BRD4-BD1	6bn7	6.1	8.4	12.4	1.1	1.5	1.9	16
DCAF WDR5	9dlw	13.4	13.4	15.9	2.0	2.0	2.0	1
DCAF WDR5	9b9h	20.0	28.8	29.9	1.1	3.1	3.1	14
VHL BCL-xL	6zhc	10.3	10.9	10.9	0.0	3.6	5.1	50
VHL BRD4-BD2	5t35	3.5	5.3	5.3	0.9	1.1	1.1	1
VHL FAK1	7pi4	23.1	24.1	25.2	9.6	9.6	9.6	6*
VHL SMARCA2	6hay	19.4	19.7	20.1	2.6	2.8	2.9	3
VHL SMARCA4	6hr2	14.5	16.2	16.6	1.7	2.1	2.2	4
VHL WDR5	7jtp	17.2	17.2	22.7	4.7	4.7	4.7	4*

The minimum values of RMSD and iRMSD are reported. The threshold for a hit was set at iRMSD < 4.0. The hit rates overall and specifically in the T(op) 20 were 9 (82%) and 7 (64%) out of 11, respectively. The distance cutoff used to define iRMSD for each complex is listed in Table S4. The final column “Rank” is based on the PGFE score of the first PPI with iRMSD < 4 among those clustered. Where a PPI with iRMSD < 4 is not present, the rank of the PPI of minimum iRMSD is given and denoted with an asterisk (*).

Table 2:

Benchmarking the PROTAC 2-step SILCS-MC docking protocol.

System	PDB ID	Ligand Code	RMSD	Ligase RMSD	Target RMSD	Ligase COM	Target COM
CRBN BRD4-BD1	6bn7*	rn6	3.4 ± 0.7	1.5 ± 0.2	3.6 ± 0.7	1.9 ± 0.2	1.1 ± 0.1
CRBN BRD4-BD1	6boy	rn3	4.8 ± 0.4	2.2 ± 0.1	4.3 ± 0.4	2.5 ± 0.5	1.2 ± 0.1
VHL BCL-xL	6zhc	ql8	9.1 ± 0.6	6.9 ± 1.0	6.2 ± 0.8	4.4 ± 1.2	5.5 ± 1.0
VHL BRD4-BD2	5t35	759	4.2 ± 0.7	3.5 ± 0.4	2.9 ± 1.3	1.3 ± 0.8	2.2 ± 0.6
VHL FAK1	7pi4	7qb	2.7 ± 0.1	2.0 ± 0.2	1.8 ± 0.4	0.9 ± 0.2	1.4 ± 0.2
VHL SMARCA2	6hax	fwz	3.3 ± 0.4	3.2 ± 0.2	2.4 ± 0.5	1.6 ± 0.2	1.7 ± 0.3
VHL SMARCA2	6hay*	fx8	4.1 ± 0.4	3.6 ± 0.3	2.7 ± 0.3	1.6 ± 0.2	2.1 ± 0.3
VHL SMARCA4	6hr2	fwz	2.2 ± 0.3	2.3 ± 0.3	1.5 ± 0.2	1.1 ± 0.1	1.2 ± 0.1
VHL WDR5	7jtp	x6m	2.9 ± 0.3	3.0 ± 0.1	2.6 ± 0.6	1.4 ± 0.2	1.5 ± 0.1
CIAP BTK	6w7o	tl7	4.1 ± 0.1	4.2 ± 0.2	4.0 ± 0.3	2.0 ± 0.2	2.6 ± 0.2
CIAP BTK	6w8i	tky	4.1 ± 0.4	4.7 ± 0.4	2.7 ± 0.8	1.7 ± 0.5	2.3 ± 0.7
DCAF WDR5	9b9h	a1am2	4.3 ± 0.4	4.7 ± 0.5	4.1 ± 1.1	1.0 ± 0.4	3.3 ± 0.3
DCAF WDR5	9dlw	a1baf	5.9 ± 0.6	5.2 ± 0.5	5.4 ± 0.4	1.6 ± 0.1	3.3 ± 0.3
Mean			4.0 ± 0.0	3.4 ± 0.1	3.1 ± 0.1	1.7 ± 0.1	2.1 ± 0.1

The asterisk (*) indicates entry used to generate the alignment. The values are the mean ± standard error of the mean from three runs with different random seeds and initial coordinates. 2D images of the PROTACs used are shown in Figure S3. The final row is the mean and standard error of the means from that column.

To benchmark the ability of SILCS-xTAC to predict the activity of PROTACs, fifteen experimental activity data sets were obtained. The systems, activity assays, and literature sources are described in Table S1, and include a total of 118 unique DC₅₀ measurements for 89 unique PROTACs.^14,41–50 The systems include three ligases: VHL, CRBN, and MDM2, and ten targets: BCL2, BCL-xL, BRD4-BD1, BRD4-BD2, CDK9, EGFR, FAK1, HDAC8, SMARCA2, SMARCA4, and WDR5. DC₅₀ is the concentration at which 50% of target protein levels have been degraded, and the value depends sensitively on assay-specific details such as protein concentration, PROTAC concentration, cell line, and assay duration, so that pooling the data together would not be advisable. The majority of the data sets were obtained from the PROTAC-DB,^28,51,52 after significant parsing. The selected PROTAC activity data sets were required to include at least four PROTACs with measured DC₅₀ values, and in two systems additional entries were appended.^14,41 The data was reorganized so that each unique assay has a single column, and the details describing the experiment (assay, cell line, concentrations, duration, etc.) are in the column header. Furthermore, when a single column contains values corresponding to multiple different experimental conditions, these were separated into multiple columns appropriately. Maximal or minimal flags such as “not detected” were replaced with 1.2 or 0.8 times the largest or smallest numerical value in column, respectively.

SILCS-xTAC Workflow

The SILCS-xTAC method models an ensemble of target-ligase dimers which are stabilized by the PROTAC binding at the interfaces (Figure 1). In the approach, following generation of the SILCS FragMaps for both the target and the ligase, a set of dimers are generated using SILCS-PPI. FragMaps and an Exclusion map are generated for each dimer by merging the two separate sets of maps for each protein, avoiding the need to perform SILCS simulations on each full dimer. Subsequently, the PROTACs are docked using SILCS-MC into the dimer FragMaps and Exclusion map. The ternary complex with the most favorable PROTAC predicted binding affinity, termed the ligand grid free energy (LGFE), is selected. Notably, since the SILCS FragMaps are precomputed each PROTAC docking run requires only minutes allowing for large numbers, N, of protein dimers as well as different modifications of the PROTACs to be tested.

Figure 1: SILCS-xTAC workflow.

The default protocol uses the number of top complexes, N = 20, and the total inter-site distance cutoff = 30 Å.

Oscillating μ_ex-GCMC/MD simulations and FragMaps Calculation.

Experimental structures were obtained from the wwPDB⁵³ of each target and ligase individually. Where possible, apo structures were used; regardless, any ligands were removed prior to the simulations. Table S2 describes which experimental structures were used to initiate each SILCS simulation. Note that throughout this article, the protein kinase EGFR refers to the double-mutant L858R/T790M, which was generated using the CHARMM-GUI.⁵⁴ All proteins were represented with the CHARMM36m force field and CHARMM-specific TIP3P water,⁵⁵ and the cosolutes and PROTACS were represented using the CGenFF force field.^56,57 The input molecular structures were prepared with the CHARMM-GUI,⁵⁴ and appropriate protonation states at pH = 7 for residues were determined with PropKa3.⁵⁸ Generally, short chain breaks were connected using the CHARMM-GUI, and large missing loops were omitted with the associated N- and C-termini surrounding the missing residues acetylated and methylaminated, respectively. Prior to simulations, the χ1 values of sidechains of solvent exposed residues were randomly assigned values between 0 and 324° in increments of 36°. Molecular dynamics simulations were performed with Gromacs version 2023^59,60 and SILCS software version 2024 (SilcsBio LLC).

The SILCS simulation to generate the FragMaps consists of multiple simulations of alternating cycles of μ_ex-GCMC and MD simulations, as previously described.^34,35 A single cycle consists of 200,000 moves of μ_ex-GCMC, followed by 5,000 steps of steepest descent minimization, 100 ps equilibration NVT MD, and then 1 ns of production NPT MD. Example Gromacs MD input files for the minimization, equilibration, and NPT production simulations are included in the supplementary data on GitHub. The standard protocol consists of 10 individual simulations of 100 cycles of μ_ex-GCMC/MD each, resulting in a cumulative total MD NPT production simulation time of 1 μs. The eight solutes, benzene, propane, methanol, dimethyl ether, imidazole, formamide, acetate, methylammonium, are inserted into the water box simultaneously at 0.25 M. The μ_ex-GCMC solute and water moves consist of insertions, deletions, rigid translations, and rigid rotations, during which the protein conformation is fixed. While the μ_ex of each solute is constant during a given GCMC cycle, the solute’s chemical potentials are oscillated from cycle to cycle to help drive insertions and deletions in the simulation system to maintain the 0.25 M concentration while continually performing insertions and deletions throughout the GCMC sampling. Following the GCMC sampling in the subsequent MD simulations the protein Cα atoms are harmonically restrained with a force constant of 0.12 kcal/(mol•Å²), which allows for sufficient backbone flexibility to sample the local conformational distribution while maintaining the overall conformation of the protein. The μ_ex-GCMC/MD protocol encompasses the full 3D structure of the proteins.

Once the full simulations are complete, the trajectories from the ten individual simulations are pooled and the occupancy of the relevant non-hydrogen atoms defining the functional group of the solute molecules are calculated on a grid of 1 ų voxels. The occupancy is normalized with respect to the concentration of each solute based on the concentration relevant to water (55 M) and converted into grid free energy (GFE) FragMaps based on a Boltzmann transformation, so that in solution GFE = 0 kcal/mol. The set of voxels with zero solute or water non-hydrogen atom occupancy are defined as the Exclusion map. The occupancy of each protein side chain atom is also calculated in the 1 ų voxels over the cumulative MD simulation, creating protein side chain probability grids (PPGs).

Convergence of the ten replicas is assessed by calculating an overlap coefficient (OC) between the maps from two independent sets of five replicas (Equation 1). In Equation 1, $Q$ is the occupancy function and the superscripts $A,B$ distinguish the two sets of maps. It was previously determined that an OC > 0.6 defines reasonable convergence³⁴ and the values are typically between 0.7 and 0.9 for various maps. The OCs for the FragMaps of VHL, SMARCA2, CRBN, and BRD4-BD1 are shown in Table S3.

$$OC\left({\text{Q}}^{\text{A}},{\text{Q}}^{\text{B}}\right)=\sum _{\text{x},\text{y},\text{z}}min\left(\frac{{\text{Q}}_{\text{x},\text{y},\text{z}}^{\text{A}}}{{\sum }_{\text{x},\text{y},\text{z}}{\text{Q}}_{\text{x},\text{y},\text{z}}^{\text{A}}},\frac{{\text{Q}}_{\text{x},\text{y},\text{z}}^{\text{B}}}{{\sum }_{\text{x},\text{y},\text{z}}{\text{Q}}_{\text{x},\text{y},\text{z}}^{\text{B}}}\right)$$ #(1)

Protein-protein docking with SILCS-PPI and FragMap merge

The ensemble of PPI poses was generated using the SILCS-PPI method (SilcsBio LLC).³⁶ In brief, the ligase was used as the static receptor and the target protein is moved through various translations and rotations to determine favorable dimer conformations. A set of rotations of the target protein are computed, and then for each rotation, a FFT algorithm is used to evaluate the grid-based energy function of all translations of the target with respect to the ligase. The step size of the rotations is 10° and ten solutions were saved per rotation such that the protocol generates a set of 149,040 PPIs for a single system. The PPIs are scored using a protein GFE function (PGFE) which is based on the overlap of complementary FragMap-PPG pairs along with a penalty associated with the overlap of the Exclusion maps.³⁶ The PGFE is defined in Equations 2–4 below:

$$\mathit{\text{PGFE}}\left(dx,dy,dz\right)=E^{A,B}\left(dx,dy,dz\right)+E^{B,A}\left(dx,dy,dz\right)+E_{\mathit{\text{excl}}}\left(dx,dy,dz\right)$$ #(2)

$$E^{A,B}\left(dx,dy,dz\right)=\sum _{\text{x},\text{y},\text{z}}\sum _{\text{i}}^{\text{Maps}}{GFE}_i^A\left(x,y,z\right)\bullet {PPG}_i^B\left(x+dx,y+dy,z+dz\right)$$ #(3)

$$E_{\mathit{\text{excl}}}\left(dx,dy,dz\right)=\sum _{x,y,z}EXC{L}^A\left(x,y,z\right)\bullet EXC{L}^B\left(x+dx,y+dy,z+dz\right)$$ #(4)

$\mathit{\text{EXCL}},GFE$, and $PPG$ refer to the Exclusion maps, the FragMaps, and the PPGs, respectively. The superscripts $A,B$ refer to the maps from the two separate proteins, the two summations are over Cartesian dimensions $x,y,z$ and complementary map types $i$. The $dx,dy,dz$ indicate the range of translations. Each Exclusion map voxel carries the value 1. The protein atoms are then assigned to one of the five generic complementary SILCS FragMap types, namely apolar, hydrogen-bond donor, hydrogen-bond acceptor, negatively charged, positively charged, as previously described.³⁴ For example, for the apolar GFE FragMap, the complementary PPG atom type includes carbons from apolar sidechains including phenylalanine and leucine.

For the total set of PPIs, the distance between the two warhead binding sites is calculated. For the set of experimental ternary complexes, the distances varied between 10–28 Å, as shown in Table S4. For each protein, the binding site was defined as the center-of-mass (COM) of the ligand bound in the appropriate site in a corresponding experimental protein-ligand structure (Table S2).

This total set of PPIs are clustered using a 2-pass scheme described previously, first clustering by COM then by Euler angles used to describe the rotational orientation of the second protein with respect to the first.³⁶ This clustering has several key user-tunable parameters, namely the number of Cα contacts to be excluded automatically (10 used), the root mean square deviation (RMSD) cutoff to define clusters (10 Å used), and the rotational cutoff to define clusters (0.5° used).⁶¹ The dimer with the most favorable PGFE score is selected to represent each cluster. By default, a set of 2000 dimers are then selected as ranked by PGFE.

The clustered set of PPIs is sorted iteratively by the distance between the known ligand binding sites and PGFE as follows. All dimers with an inter-site distance less than a cutoff are sorted by PGFE and appended to the final sorted list. The initial cutoff is set to 1 Å for simplicity. The distance cutoff is incremented by 1 Å, and this procedure is repeated until all PPIs have been moved to the final sorted list. This results in a list which is sorted both by inter-site distance and PGFE, which works well in our benchmark systems. For this study, the top 20 PPIs were selected as representing the solution ensemble.

The FragMaps, or Exclusion map, for each dimer are generated by merging the FragMaps of each separate protein as described in Equation 5. The target protein FragMaps are translated ($\text{dx},\text{dy},\text{dz}$) and rotated to align with the ternary complex orientation using the SciPy function affine_transform ($T^{-1}$) with second-order spline interpolation (${\text{GFE}}^{B^{*}}$). Although the default third order interpolation is standard in conventional image transformation, it gave a distortion on the scale of approximately 1 Å. The two sets of maps are zero-padded to the final dimension of the combined FragMaps before summing GFEs for each voxel and FragMap $i$. The accuracy of the Map Merge was assessed by calculating the OCs (Equation 1) of those derived from SILCS simulations of experimental target-ligase dimers and merged maps for two systems.

$${GFE}_{\text{i}}^{\text{AB}}(x,y,z)={GF\text{E}}_{\text{i}}^{\text{A}}\left(\text{x},\text{y},\text{z}\right)+{\text{GFE}}_{\text{i}}^{{\text{B}}^{*}}\left(T^{-1}\left(\text{x}-\text{dx},\text{y}-\text{dy},\text{z}-\text{dz}\right)\right)$$ #(5)

For benchmarking, the structural agreement between experimental and predicted dimer structures was measured using RMSD and interface RMSD (iRMSD) of Cα atoms, as previously performed to evaluate PPI docking methods.³⁶ In order to apply a consistent definition across all complexes, the interface cutoff distance was selected for each system such that at least four contacts in the experimental structure within the cutoff were present; these cutoffs are listed in Table S4.

PROTAC docking with SILCS-MC

PROTAC docking is performed in the field of the FragMaps and Exclusion map using the SILCS-MC program (SilcsBio LLC).⁶² The program first converts each CGenFF atom type in the PROTACs to a corresponding FragMap atom type using the SILCS Atom Classification Scheme as described by Ustach, et al.³⁸ For any ligand pose, the corresponding LGFE is the sum of the atomic GFEs over the classified atoms $n$ in the ligand and their respective FragMap types $i$ (Equation 6). The atomic GFEs are based on the GFE of the voxel corresponding to its FragMap type. The MC docking proceeds using the Metropolis criteria based on the LGFE plus the CGenFF intramolecular energy using the dielectric constant of 4 times the interatomic distance. Each docking run involves many parallel Monte Carlo simulations, then the most favorable PROTAC conformations are selected from among the parallel runs, based only on the LGFE without the CGenFF intramolecular energy. Omitting the CGenFF intramolecular energy avoids the need to account for that energy in the unbound state, while the LGFE of any unbound state in solution is zero due to the definition of the GFE normalization.

$$\mathit{\text{LGFE}}=\sum _{\text{i}}^{\text{Maps}}\sum _{\text{n}}^{\text{Atoms}}{\text{GFE}}_{\text{i}}\left(x_n,y_n,z_n\right)$$ #(6)

The general PROTAC docking workflow follows two successive rounds of SILCS-MC sampling: one to relax the linker during which each warhead is restrained to their respective binding sites determined from experimental binary protein-ligand structures, and a second where the PROTAC is unrestrained. Prior to SILCS-MC, all ligand coordinates were minimized and assigned a protonation state for pH 7 using MOE (Chemical Computing Group). In the case of the HDAC8-binding compounds, the zinc-binding group (e.g. hydroxamate) were deprotonated to reflect their protonation while coordinating zinc. In the first round of SILCS-MC, selected atoms in each warhead are harmonically restrained in the known ligand binding site according to $\frac{k}{2}{\left(r-r_0\right)}^2$ with a force constant $k=10\text{kcal}/(\text{mol}•{\AA }^2)$. Multiple atomic restraint functionality was implemented in SILCS-MC to allow each warhead to be restrained separately. By default, a total of four atoms are restrained. For each warhead, two atoms are selected which lie nearest to the points at COM ± 40% of the molecules extent along the 1^st principal component analysis (PCA) axis. In practice, the user may supply any number of atom restraints. The RDKit v2024.03.05 implementation of Maximum Common Substructure (MCS) was used to identify the atoms corresponding to the warheads.^63,64 The reference warheads used for the SILCS-xTAC alignment via determination of site and PCA orientation are indicated in Table S2.

The first round of SILCS-MC initiates from a PROTAC configuration which has been rigidly aligned to minimize the RMSD between the corresponding set of atoms and coordinates specified in the restraint file. This alignment is performed in RDKit in three steps: first, a rigid alignment to minimize RMSD to the restraints, then a brief relaxation MC simulation using the Merck Molecular Force Field^65–69 with the atoms harmonically restrained with 10 kcal/(mol•Å²), and then a final unrestrained minimization. This final pose is used as the initial input pose for SILCS-MC. Each SILCS-MC run consists of a cycle of MC sampling with 10,000 moves followed by 40,000 moves of simulated annealing (SA). The moves are distributed between rigid translations of up to 0.1 Å, rigid rotations of up to 9°, and dihedral rotations of up to 9°. Each ligand is subjected to 1,250 parallel SILCS-MC runs, and the conformation with the lowest LGFE is selected as the initial pose for the next round. The second round of SILCS-MC without restraints is the same as the first except that it consists of 1,000 moves MC and 4,000 moves of SA.

Each PROTAC is individually docked to all of the selected PPI dimer conformers, which was 20 in the present study, and the lowest LGFE conformation among all the dimers selected. Several SILCS-xTAC features are extracted from the selected ternary complex. In addition to the overall LGFE, the sum of the GFEs of a substructure (sGFE) including the two warhead and the linker are calculated. RDKit MCS is used to extract the sGFE for the target and ligase warheads, and the linker contribution is calculated as the remaining portion of the total LGFE.^63,64 Distance metrics, including the distance between the warhead COMs and known ligand binding sites, and RMSD between the restrained atoms and their target coordinates, are also calculated. If the inter-site distance is greater than the PROTAC’s linker length, this will be reflected in the final energetic and geometric metrics. Each warhead is docked separately into the FragMap of the respective protein and its LGFE obtained as reference values as described below. The SILCS-MC parameters for the Warhead docking protocol follows the same as the PROTAC docking protocol, with the two atom restraints applied in the first round then removed in the second.

Machine learning activity model: Ridge regression and cross-validation

Linear regression with Ridge regularization was performed on each data set containing only a single study, target, ligase, and assay. The result of Ridge regression is a model such as described in Equation 7. DC₅₀ values were transformed into an energy-scale, RTlnDC₅₀.

$${\mathit{\text{RTlnDC}}50}_{\mathit{\text{pred}}}=\sum _m^{\mathit{\text{Metrics}}}{w}_m\bullet m$$ #(7)

Ten metrics were considered per PROTAC, including eight directly from the final SILCS-xTAC conformation: target warhead sGFE and final ΔCOM, ligase warhead sGFE and final ΔCOM, linker sGFE, final RMSD of the restrained PROTAC atoms with respect to final positions. Two additional external metrics were added, namely the Wildman-Crippen calculated logP (ClogP)⁷⁰ and number of rotatable bonds (N_rot) of the PROTAC, calculated by RDKit.⁶³ Model performance is evaluated using Pearson correlation coefficient (r), and RMSE. When r or RMSE are reported as a weighted average, the weights are the number of PROTACs in each separate data set.

To robustly estimate model performance and weights despite the small size of the training data sets (average size of ~7.9 PROTACs per data set), Ridge regression was performed with leave-one-out cross-validation (LOO-CV), with the Ridge regularization strength parameter $\alpha$ = 1. In LOO-CV a model is trained on all data less one sample, then predicts the left-out sample. The process repeats for each sample in the data. Model performance metrics are estimated using the predicted values each made by a model trained without the corresponding sample. LOO-CV was performed for each data set corresponding to a single target-ligase pair and assay, coming from a single study (Table S1). Recursive Feature Elimination (RFE) was used to determine which combination of the ten SILCS-xTAC metrics is most optimal across all data sets, by running LOO-CV using successively fewer SILCS-xTAC metrics as input. The metrics were ranked over all the data sets by weighting each metric by the number of PROTACs in each data set, and a weight of zero if the metric was dropped for that data set. The consensus set of N metrics is then the top N metrics in this weighting. Where the Pearson correlation coefficient r is reported in figures, a confidence interval (CI) was calculated using bootstrapping. The uncertainty value was calculated as half the magnitude of the CI, although the CI may be asymmetric. Where the uncertainty value is 1.00, the CI could not be estimated due to too many points being identical.

Molecular rendering of proteins and protein-ligand complexes was done with VMD version 1.9.3,⁷¹ and 2D images of PROTACs were generated using RDKit.⁶³ Plots were made with matplotlib⁷² and the Petroff accessible color sequence,⁷³ and Ridge regression and LOO-CV were performed using scikit-learn version 1.6.1.⁷⁴ Additional supporting information including SDF and SMILES strings for all PROTACs and warheads, as well as the SILCS-xTAC data derived in this article, are freely available on GitHub at https://github.com/mackerell-lab/silcs-xtac-si.

Results

The SILCS-xTAC workflow shown on Figure 1 was developed to allow ternary complex ligand design projects to be initiated on novel systems without any knowledge of the structure of the PPI complex of the ligase-target or of any known PROTAC lead compound. The workflow requires the structures of both proteins, as well as bound conformations of at least one warhead-like ligand for each of the ligase and the target, which is generally known, to demonstrate a rough ligand orientation. If the protein structure or site information is not available, developments in computational protein structure prediction,^75–78 binding site identification^79–82 and ligand screening^83,84 can be utilized. Once the prerequisite information is available, the SILCS FragMaps are calculated, a process typically requiring about 1–3 days on 10 GPUs for each protein. The FragMaps are then used in SILCS-PPI from which a collection of dimer structures are selected, and the PPI calculation itself typically requires about 30 minutes to 4 hours on 32 CPUs or a single GPU. SILCS FragMaps of each of the dimer structures are then rapidly generated via the merging procedure. PROTAC optimization then proceeds by determining the optimal PROTAC conformation in the dimer using the multi-step docking protocol, a process which typically requires about 3–5 minutes per PROTAC on a GPU. All computing was performed at the University of Maryland Computer-Aided Drug Design Center on various Nvidia GPU cards, e.g. Nvidia GTX 1080Ti, RTX 2080Ti, RTX A4500 and AMD CPUs, e.g. Opteron 6276, Ryzen 7 1700, EPYC 7551P.

In the remainder of this article the SILCS-xTAC workflow is validated against a variety of experimental data following which the information content obtained from the SILCS approach is presented. Validation is performed against experimental 3D structural information on PROTAC-ligase-target ternary complexes as well as biological data. However, as discussed below the available experimental data is sparse with multiple confounding aspects making direct comparison of the calculated and experimental data challenging (Table S5). Furthermore, it is demonstrated that PROTAC design can be facilitated by relating the energetic contributions of different components of the PROTAC to binding and biological activity.

SILCS-PPI ensembles contain members similar to experimental ternary complex structures

The SILCS-xTAC method initially generates an ensemble of PPIs, and this protocol was benchmarked on a diverse set of experimental PROTAC ternary complexes (Table 1) to assess whether the generated ensembles contain members similar to the experimental structures. While some of the experimental PPIs may be relatively stable and unique, many are not. PROTAC ternary complexes can be flexible and dynamic in solution^15,27,85,86 and have multiple significantly different PPI structures.^15,87 In addition, the complex structures may have crystallographic packing artifacts that artificially bias towards a specific conformation.¹⁴ The limited total number of complexes, along with the diversity and complexity in treating them as representative of PPIs in solution, suggest that validating the method based solely on available structural data may not be optimal. However, we have undertaken comparison of a diverse set of eleven known structures with the ensemble of 20 PPI complexes calculated with SILCS-PPI and subsequent structure selection for each of the eleven systems. The Rank in Table 1 gives the rank order of either the first PPI with iRMSD < 4 Å or the rank of minimum iRMSD. We note that the hit rate reached a threshold of diminishing returns at approximately 20 PPI, after which the next lowest Rank is 50. Global RMSD values are quite a bit larger than the iRMSD and are included to give a sense of the overall similarity of the final structures to the experimental structures.

The minimum RMSD and iRMSD are reported in Table 1 for all PPIs generated, for the 2,000 clustered structures, and for the top 20 selected based on warhead inter-site distance cutoff of 30 Å. Among all PPIs generated, nine out of eleven or 82% of systems have a corresponding structure with iRMSD < 4 Å, a threshold used previously to define a PPI hit.⁸⁸ Among the two misses, VHL-WDR5 is a near-hit with iRMSD = 4.7 Å, only slightly above the cutoff, while VHL-FAK1 is a significant miss with iRMSD = 9.6 Å. Analysis of the number of contacts and the interaction energy between the ligase and target proteins in the experimental structure (Table S4) show both values to indicate a minimal interactions between the proteins, suggesting an important role of the PROTAC in stabilizing the ternary complex. While additional studies would be required to verify this hypothesis, in such cases the present protocol would not be effective. However, across the majority of cases the SILCS-PPI method generates crystal-like PPIs, and those with low iRMSD are collected by the distance cutoff and clustering then applied.

In the top 20 complexes selected by our ranking scheme, seven of eleven or ~64% of the systems contain a dimer with iRMSD < 4 Å. Thus, for a reasonable number of cases the default ensemble captures structure(s) close to the experimental structure. Representative examples of the generated ensemble of 20 PPIs and the corresponding experimental structure for 4 systems are shown in Figure 2, including systems with hits (Figure 2A, 2C, 2D) and one system with both a hit and a miss (Figure 2B). In all cases, significant conformational diversity is observed in the predicted PPI dimer structures, with some poses highly similar to the crystallographic pose as indicated in Table 1.

Figure 2: Representative examples of PPI ensembles and experimental structures.

Modelled ensembles are silver NewCartoon representation, while experimental structures are blue (ligase) and red/magenta (target). A) VHL and SMARCA4 (PDB ID: 6hr2) B) CIAP and BTK (PDB ID: 6w8i, red; 6w7o, magenta). C) CRBN and BRD4-BD1 (PDB ID: 6bn7). D) DCAF and WDR5 (PDB ID: 9b9h, red; 9dlw, magenta).

There were four systems for which successful predictions were not made in the 20 structures, namely VHL-FAK1, VHL-WDR5, VHL-BCL-xL, and CIAP-BTK (PDB ID: 6w7o), with minimum iRMSD values of 9.6, 4.7, 5.1 and 11.7 Å, respectively. Figure S1 depicts the PPI of minimum iRMSD in comparison to the experimentally-aligned pose for these systems. Given the cutoff of 4 Å, VHL-WDR5 and VHL-BCL-xL (Figure S1A and B) might be viewed as near-hits since they have comparatively low iRMSD values of 4.7 and 5.1 Å. Both VHL-WDR5 and VHL-FAK1 are missed by the overall SILCS-PPI protocol, so the miss in the top 20 is not an issue with the clustering and ranking approach, and we note that the minimum iRMSD structure is retained in the top 20 in both cases (Table 1). Finally, for the CIAP-BTK case, the protocol misses 6w7o but captures 6w8i. Schiemer, et al. observed that significant dynamics are present in these complexes in solution,¹⁵ and so it is possible that our method captures a plausible conformational ensemble. We note that DegraderTCM achieves remarkably superior performance on the systems they report, near crystallographic resolution, possibly achieved by modeling the PPI and PROTAC concurrently.³³ PROTACfold also boasts near crystallographic resolution, but only on complexes in the AF3/Boltz-1 training sets.³²

In some cases, there are intramolecular conformational differences between the structure used in the SILCS FragMaps (Table S2) and the conformation in the experimental complex. Two such cases are depicted in Figure S2, namely CRBN-BRD4-BD1 and VHL-BCL-xL. Both involve small loops at the interface. The conformational difference in the CRBN at the loop (F150-GI-E153) is relatively minor (backbone RMSD = 3.1 Å) and may be partially captured by the inherent flexibility encoded in the FragMaps and PPGs associated with the default harmonic restraint of 0.12 kcal/(mol•Å²) on the Cα atoms in the SILCS simulations. However, in the VHL-BCL-xL case the backbone RMSD in the loop in BCL-xL (Y101-RRAF-S106) is 6.4 Å, which is too large to be captured using the default restraint and may contribute to the miss. In principle, both differences might be captured in the SILCS method by removing the harmonic restraints on loops in the initial the GCMC/MD simulations in the interface region of the proteins.

SILCS-MC protocol can capture experimental PROTAC conformations in ternary complexes

The SILCS-MC protocol for docking PROTACs into merged dimer FragMaps was validated in two ways. First, by comparing the dimer FragMaps calculated from direct SILCS GCMC/MD simulations of the experimental dimer complex (Expt-FragMaps) to those calculated from merged FragMaps based on alignment to the experimental structure (M-FragMaps). Second, by docking PROTACs with into the M-FragMaps and comparing to the experimental PROTAC conformation. The map merge initial assessment was done using a calculation of the OC (Equation 1) between the M-FragMaps and the Expt-FragMaps for two systems, VHL-SMARCA2 and CRBN-BRD4-BD1. The OCs are given in Table S6 in the M columns. For comparison the OC values for the FragMaps from the first 5 and second 5 SILCS simulations on the experimental dimer structures are shown (Table S6). As is evident the OC values for the merged maps (M) are similar to those for the SILCS simulations on the two experimental dimers (Expt). In addition, the OC values are similar to those calculated for the monomer proteins listed in Table S2. These results indicate that the quality of M-FragMaps is similar to that of the explicitly calculated Expt-FragMaps on the experimental dimers. The ability to merge maps allows for the ensemble of PPI complexes to readily be increased beyond the 20 used in the present study.

The second validation was performed by docking the PROTACs into the experimentally-aligned M-FragMaps and comparing the SILCS-MC docked PROTAC conformations to the experimental conformations. This should be viewed as a benchmark of the SILCS-xTAC docking method in the best-case scenario, since the RMSD to experimental crystal structures will likely be higher across the ensemble of PPIs. To ensure that the PROTACs are relaxed in both the placement of the warheads and flexible linkers, a two-step SILCS-MC protocol was developed using the benchmark set of experimental structures and corresponding M-FragMaps. The results were quantified using PROTAC RMSD as well as the RMSD of the two warheads (Table 2). The protocol was replicated three times using different randomized initial PROTAC conformations generated using RDKit. For reference, the warhead RMSDs and LGFEs were calculated from docking the warhead to the separate FragMaps of each of the two proteins with the results included in Table 3. Figure 3 shows the agreement between the experimental and SILCS predicted PROTAC structures in four cases, namely CRBN-BRD4-BD1, VHL-SMARCA2, CIAP-BTK, and VHL-FAK1. This includes three cases where the results are reasonable and one with modest performance, CIAP-BTK. Notably, in CRBN-BRD4-BD1, the agreement is substantially better for the PROTAC in 6bn7 than 6boy, because both predicted PROTAC linker conformations are similar to 6bn7. The small, systematic upward deviation of the VHL warheads (Figure 3B, Figure 3D) relative to the crystallographic binding pose is a feature of the VHL FragMaps, rather than our sampling protocol. The reference warhead sampling obtains similar or somewhat improved RMSD values for the VHL ligands (Table 3). This deviation may reflect a resolution artifact of the 1 Å voxels or the binding position at 300 K rather than crystallographic conditions.

Table 3: Reference values for SILCS-MC docking of warheads.

The warhead sampling protocol follows the same two-step protocol with restraints as the PROTAC sampling protocol (Table S4). LW and TW stand for ligase and target warheads, respectively.

System	LW RMSD	TW RMSD	LW LGFE	TW LGFE
CRBN BRD4-BD1	1.1	1.2	−9.1	−11.0
VHL BCL-xL	2.2	3.0	−8.6	−4.6
VHL BRD4-BD2	2.5	0.8	−8.4	−9.4
VHL FAK1	1.8	0.9	−9.3	−13.5
VHL SMARCA2	2.8	2.3	−9.8	−6.1
VHL SMARCA4	1.8	1.2	−9.0	−7.2
VHL WDR5	3.6	2.9	−8.0	−9.9
CIAP BTK	2.0	1.0	−11.3	−11.0
DCAF WDR5	1.6	3.0	−4.4	−11.9

Figure 3: Representative examples of 2-step PROTAC docking compared to experimental structures.

A) CRBN-BRD4-BD1 (blue: 6bn7, red: 6boy). B) VHL-SMARCA2; (blue: 6hay, red: 6hax). C) CIAP-BTK (6w7o). D) VHL-FAK1 (7pi4). The apolar FragMaps are shown as green mesh contoured at −1.2 kcal/mol. The docked PROTAC conformations are shown with Licorice representation and colored with carbon as teal, oxygen as red, nitrogen as blue, sulfur as yellow, and halogens as pink. The experimental PROTAC conformations are shown in a thinner Licorice representation and colored blue unless denoted above.

Generally, the PROTAC sampling method is able to identify a pose with RMSD < 4 Å for one (8 of 13) or both (6 of 13) warheads, with total average warhead RMSD of ~3.4 Å (Table 3). Furthermore, the total average PROTAC RMSD is ~4 Å, and is less than 5 Å in 10 of 13 cases. This performance is commensurate with state-of-the-art methods DegraderTCM and PROTACfold,^33,32 although we note that we are using the M-FragMaps based on the known experimental PPI structures. The overall RMSD includes the linker which is expected to be quite flexible and solvent-exposed. In some cases, the position of the linker is modelled in the experimental structures without substantial electron density, making its precise conformation somewhat ambiguous.¹⁵ Note that the standard error across the three replicas is reasonably predictive of RMSD in the overall PROTAC RMSD and ligase warhead RMSD, with r values of 0.5 and 0.8, respectively (Figure S4). This suggests that by repeating the sampling protocol with different initial conformations, the variance in RMSD among the predicted poses can be used to estimate the reliability of the SILCS-predicted PROTAC conformation.

Notably there are two large misses where the PROTAC RMSD is > 5 Å and both warhead RMSDs > 4 Å, namely DCAF-WDR5 (9dlw) and VHL-BCL-xL (Figure S5). For DCAF-WDR5 one challenge is that the warheads are large and branching, so the two-point restraints are somewhat inadequate. Furthermore, the PROTAC in 9dlw has a comparatively long linker with many rotatable bonds (Figure S3). For BCL-xL the issue may be the comparatively long linker as well as the length of the BCL-xL warhead. The initial configurations could be tangled, making overall convergence impossible, and the two site restraints may again not be adequate to capture the binding conformation. Such cases may require intervention to generate an adequate initial PROTAC conformation or apply additional restraints. For example, the performance could be improved by greater precision in the restraint protocol, including defining an accurate binding conformation of the ligand. The SILCS-xTAC protocol can be readily extended to apply these as well as other variations in the protocols, but here we demonstrate the strengths and limitations of the default protocol.

SILCS-xTAC provides metrics useful for ligand optimization

After generating the ensemble of 20 PPIs and merging their FragMaps, a set of PROTACs can be docked into all predicted M-FragMaps, generating an ensemble of ternary complexes. Representative output is given in Figure 4, illustrating the final PROTAC conformations for 18 PROTACs⁴¹ in two representative dimers of VHL and SMARCA4. The information extracted from these dimers is given in Table 4 and includes the sGFE contributions from the warheads and linker, the reference LGFE values of the warheads, and metrics relating to the position of the warheads with respect to the known pockets. These metrics are extracted from the complex with the most-favorable LGFE.

Figure 4: SILCS-xTAC ligand optimization in VHL-SMARCA4.

The dimer complexes depicted are the A) first- and B) tenth- ranked, respectively, and are shown in silver NewCartoon. The PROTACs are drawn in Licorice representation without hydrogens, and the colors representing each atom are the same as in Figure 3. These PROTACs are identical to those in Table 4 and Figure S6.⁴¹

Table 4: Summary of metrics extracted from SILCS-xTAC docking run.

Results are based on the VHL-SMARCA4 system (Figure S6).⁴¹ All metrics for each PROTAC were extracted from the ternary complex with the most-favorable LGFE. LW stands for Linker Warhead, TW stands for Target Warhead. ΔGFE stands for the difference between the final sGFE and the reference LGFE value of the ligand, and ΔCOM for the distance between the warhead COM and binding site. The unit of the sGFE values is kcal/mol, the unit of COM and RMSD values is Å, and the unit of the experimental DC₅₀ values is nM. The DC₅₀ experiment measured the degradation of SMARCA4 in A549 cells.⁵⁵

ID	LW sGFE	TW sGFE	Linker sGFE	LW ΔsGFE	TW ΔsGFE	LW ΔCOM	TW ΔCOM	Restr. RMSD	ClogP	Nrot	DC50
1	−9.5	−4.8	−2.4	1.2	3.6	2.7	1.1	1.6	4.2	18	1245
2	−10.0	−6.1	−0.4	0.7	2.3	1.4	5.3	2.6	4.0	15	117
3	−8.3	−4.7	−2.8	2.4	3.7	1.9	2.2	1.7	2.7	17	2044
4	−8.7	−5.2	−2.4	2.0	3.2	2.3	1.3	1.5	3.1	18	735
5	−6.1	−6.5	−3.0	4.6	1.9	2.7	1.8	1.9	2.3	19	1927
6	−6.8	−4.9	−4.2	3.9	3.5	2.9	1.4	2.0	4.2	21	219
7	−9.4	−5.7	−0.5	1.4	2.7	2.3	2.0	2.0	3.8	16	16
8	−9.5	−5.0	−0.9	1.2	3.4	1.4	1.9	1.5	4.0	14	168
9	−9.2	−6.5	−1.4	1.5	2.0	2.3	1.4	1.8	4.6	18	170
10	−6.6	−6.7	−3.1	4.2	1.7	0.6	1.8	1.5	3.9	17	26
11	−7.2	−6.1	−2.5	3.5	2.3	1.6	2.3	1.8	4.2	17	16
12	−9.4	−5.2	−1.0	1.3	3.2	2.4	1.9	1.7	4.0	15	5000
13	−8.2	−5.7	−1.1	2.6	2.7	3.7	6.2	3.6	4.0	15	634
14	−7.7	−5.7	−1.7	3.0	2.7	2.6	5.5	3.0	4.4	16	25
15	−7.4	−5.3	−2.7	3.4	3.2	0.9	2.4	1.6	4.1	15	168
16	−6.5	−7.9	−1.9	4.3	0.5	1.6	2.6	2.0	5.6	15	33
17	−7.8	−5.3	−2.3	2.9	3.1	1.8	1.0	1.4	4.6	15	78
18	−7.3	−6.5	−1.6	3.4	1.9	2.9	1.2	1.7	5.1	14	118

The LGFE is the predicted binding free energy of the PROTAC to the PPI dimer (Table 4). SILCS uses only the LGFE for final scoring. Given the size and conformational flexibility of PROTACs we consider the N_rot to account for the missing chain entropy term ($S_{\mathit{\text{conf}}}\propto {N_{rot}k}_{B}l{nN}_{\mathit{\text{states}}}$). The LGFE score is then partitioned into the contributions of the ligase and target warheads (denoted LW and TW, respectively) and the linker based on their sGFE scores: LW sGFE, TW sGFE, and Linker sGFE. In addition, we define LW ΔsGFE and TW ΔsGFE scores as the difference of the final sGFE value and the LGFE of the LW and TW alone. For example, for PROTAC 1 in Table 4, those values are 1.2 and 3.6 kcal/mol. These difference values directly indicate the binding energy lost by each warhead due to the presence of the linker and the PPI dimer conformation. Ideally, the difference value would be 0, indicating that linker does not impact the interaction of the warheads with their respect proteins. Three metrics describe how the PROTAC shifts from the ideal orientation that maximizes interactions of the warheads with the ligase and target. The LW and TW ΔCOM metrics report how each warhead COM shifts with respect to the known binding sites, and the Restr. RMSD captures the shift in the final PROTAC conformation relative to the four warhead orientation coordinates used during the restrained initial SILCS-MC sampling. In addition, ClogP is considered as it captures some solubility effects that may be predictive of cellular permeability.

SILCS-xTAC model provides limited prediction of cellular DC₅₀ data

DC₅₀ values were used to examine how the information content in the SILCS-xTAC metrics relates to PROTAC activity. DC₅₀ is defined as the assay-specific concentration of a PROTAC molecule at which 50% of the target protein is degraded, typically measured in cells. On the other hand, SILCS-xTAC LGFE is an estimate of the cell-free ternary binding affinity RTlnK_D, where K_D is the dissociation constant of the PROTAC to the PPI dimer in the ternary complex. LGFE is the simple sum of individual atomic GFEs (Equation 6), which neglects non-trivial chain entropy contributions in flexible molecules such as PROTACs. Furthermore, there are a number of confounding variables in relating cellular DC₅₀ measures to SILCS-xTAC metrics, including the so-called hook effect, cooperativity or non-cooperativity, off-target binding, various cellular solubility and permeability effects, and other factors listed in Table S5. It has been shown for example that PROTACs may exhibit higher cellular activity without positive cooperativity or forming stable ternary complexes.⁸⁹ There can also be significant variability in the activity exhibited between different cellular contexts.⁹⁰ Due to these confounding factors, direct correlation between LGFE and DC₅₀ is negligible as expected. However, a simple machine learning model may be able to improve this correlation by reweighting the individual metrics presented in Table 4. Note that the fitting and subsequent RMSE and correlation coefficient calculations are done using log-scale DC₅₀ values, RTlnDC₅₀, with RT = 0.6 kcal/mol. We note that in our model development, the features do not include information on the chemical structures but on the energetic properties from SILCS, the chain entropy term and the solvation energies in the form of ClogP. This approach has been applied in previous studies in which SILCS physics-based properties were used as features for ML development^79,91,92 and may improve transferability by avoiding the use of specific chemical structures.

Ridge regression with LOO-CV/RFE was performed to determine optimal set of SILCS-xTAC metrics. For each separate system, a different set of weights (Equation 8) was obtained using LOO-CV. The r and RMSE over the RFE procedure are reported in Figure S7, and indicate that the performance is relatively stable, although the overall signal is low. Based on a balance of r and RMSE, the consensus set containing nine SILCS-xTAC metrics was selected as optimal, with weighted average r = 0.22 and RMSE = 1.2 kcal/mol values. The nine SILCS-xTAC metrics are the warhead sGFE values, the change in the warhead COMs, the difference in the final warhead sGFE and reference warhead LGFEs, ClogP and N_rot. The overall performance of LOO-CV fitting on each data set separately using these nine metrics is reported in Figure 5, including uncertainty in the Pearson correlation coefficients, which indicate that the fitting of each small dataset is poor. The model weights for each system are reported in Table S7, along with their standard errors. Notably the small standard errors provide evidence of stable fitting for each system using only a few data points (Table S7). The negative correlation obtained by LOO-CV fitting in some systems is partially attributable to the confounding variables listed in Table S5. Overall, the weighted average r = 0.22 and RMSE = 1.2 kcal/mol values, and the confidence intervals on each dataset, reflect at best modest and system-dependent signal.

Figure 5: Performance of LOO-CV regression models on SILCS-xTAC metrics.

The model weights for each system and nine optimal SILCS-xTAC metrics are listed in Table S7. The dashed line indicates y=x, and the grayed region indicates y=x±1. The Pearson r and uncertainty for each system were calculated using bootstrapping. Additional information describing the experimental assays performed and the original references are reported in Table S1. The superscripted (a) and (b) denote distinct data sets involving VHL-FAK1 as described in Table S1.

The performance of the LOO-CV fitting is variable among the systems considered, indicated by the individual r values in the legend of Figure 5. The performance is reasonable for some systems, namely VHL-SMARCA4 (r = 0.45±0.22), and CRBN-BRD4BD2 (r = 0.75±0.10), while poor for others: VHL-BCL2 (r = −0.43±0.53) CRBN-BRD4BD1 (r = −0.27±0.61), CRBN-HDAC8 (r = −0.39±0.56). We also report uncertainty in the correlation, which tends to be large particularly when the correlation is low or the number of points in the subset is small. When the uncertainty overlaps with zero, such as VHL-FAK1^(b) where r = 0 to 0.8, there is no evidence to distinguish between zero, or relatively strong positive correlation. While this is somewhat as-expected, it will be possible to generate specific models for each individual system by performing the full LOO-CV/RFE procedure individually. However, this poses a significant risk of over-fitting since the number of SILCS-xTAC metrics is roughly the same as the number of PROTACs in most data sets.

To test whether the correlation signal is coming from the LOO-CV/RFE training protocol or the SILCS-xTAC metrics themselves, the same LOO-CV protocol was applied using randomized SILCS-xTAC metrics with RFE to drop one metric as above. Across ten randomized replicas, the performance was degraded with the weighted average r = 0.00±0.04 and RMSE = 2.4±0.1 kcal/mol. In comparison to with unrandomized data, this result suggests that the LOO-CV/RFE protocol does not overfit the metrics. While the performance is modest across the full dataset, there is some correlation signal coming from the SILCS-xTAC metrics. Furthermore, very reasonable and stable performance is obtained using any number of metrics (Figure S7). It is to be expected that the signal is stronger for certain systems than for others, due to various confounding variables as noted in Table S5.

To apply SILCS-xTAC at the beginning of a project when no activity data is available a single, general, first-guess model would be of utility. A general model was obtained by a weighted average of the model weights from each data set (Table S7), where the weighted average was done using the number of PROTACs in each system. The performance of the resulting general model is shown in Figure 6. As expected, there is a clear degradation of the performance of the general model as compared to the individual LOO-CV fitted models, as demonstrated by RMSE increase from 1.2 to 2.1 kcal/mol. However, while the average correlation is still only modest, there is not a substantial degradation in average correlation per system r = 0.18 as compared to 0.22. This general model may provide the basis for a preliminary prediction of PROTAC activity during early stages of ligand design when no prior activity data is available, although our validation indicates that the information content is minimal. Thus, SILCS-xTAC provides a solid basis for early-stage PROTAC discovery and optimization by predicting ensembles of ternary complexes, generating a set of metrics describing the optimal complex that may be used to predict cellular activity as well as supply information in the form of the various GFE terms that can be used to guide ligand design.

Figure 6: Performance of the general model.

The model weights are listed in Table S7 and were obtained by weighted average of the model weights obtained by LOO-CV for each data set. The dashed line indicates y=x, and the grayed region indicates y=x±1. The Pearson r and uncertainty reported for each system were calculated with bootstrapping. Additional information describing the experimental assays performed and the original references are reported in Table S1. The superscripted (a) and (b) denote distinct data sets involving VHL-FAK1 as described in Table S1.

Conclusions

We have presented a physics-based drug design workflow, SILCS-xTAC, capable of modelling PROTAC-target-ligase ternary complexes and to a limited degree predict cellular PROTAC activity. Following initial generation of the SILCS FragMaps for the ligase and target, the SILCS-PPI workflow generates an ensemble of PPIs that reflect the conformational heterogeneity in target-ligase-PROTAC complexes in cells. A subset of these is selected based on ranking the binding site-binding site distances and the PGFE values. FragMaps describing the complex are generated by merging the FragMaps of the two independent proteins. Next, SILCS-xTAC employs a two-step MC sampling protocol to relax the PROTAC linker with the warheads restrained by two atoms to binding sites followed by relaxation of the overall molecule. The docking is performed for each PROTAC to the ensemble of PPIs and extracts the final complex based on the most favorable LGFE overall. Individual sGFE contributions corresponding to the warheads and linkers, the LGFEs of the individual warheads bound to their respective proteins, metrics describing warhead orientation in the pocket, as well as PROTAC features N_rot and ClogP were then reweighted to fit to DC₅₀ values from cellular assays.

Experimental structures of PROTAC-mediated ternary complexes were used to validate both the PPIs and the PROTAC docking. Overall, we found reasonable agreement between members of the ensemble of PPIs and experimental structures. Similarly, we found overall good agreement between final PROTAC warhead conformations and the conformations in experimental structures, as well as reasonable agreement to the overall PROTAC conformation in some cases. Note that this docking was done in the context of a merged FragMap aligned to the experimental PPI orientation. In both cases, SILCS-xTAC may be able to capture PPI poses and PROTAC conformations which reflect conformational dynamics in solution but are not present in the crystal structure. Finally, we demonstrate the use of a group-based LOO-CV/RFE fitting protocol to select a set of SILCS-xTAC metrics and general linear model for use in predicting DC₅₀ in cellular assays.

This work represents an efficient physics-based method which accounts for the dynamics and heterogeneity in PROTAC ternary complexes, and which can provide information related to the prediction of binding affinity and protein degradation activity in cells. This is important for improving physics-based modeling of ternary ensembles with the aim of expediting the rational design of xTAC molecules and similar event-driven therapeutics, including AUTOTACs,⁹³ LYTACs,⁹⁴ DUBTACs,⁹⁵ AbTACs,⁹⁶ ByeTACs,⁹⁷ etc. In particular, the design of molecular glues may be facilitated by application of this technology, as their efficacy may not be impacted as much by the confounding effects discussed as compared to PROTACs. The SILCS-xTAC methodology is anticipated to generalize well to the design of other ternary complex or event-driven therapeutic molecules, as the fundamental intermolecular interactions described in the FragMaps is the basis of biophysical interactions in a range of scenarios.

Supplementary Material

SI

Table S1: PROTAC activity (DC₅₀) data sets.

Table S2: Proteins used in the SILCS simulations.

Table S3: Overlap coefficients quantifying convergence of SILCS μ_ex-GCMC/MD simulations.

Table S4: Experimental complex inter-site distances, Cα-Cα cutoffs, contacts, and interaction energies.

Table S5: Confounding variables complicating the prediction of PROTAC DC50 activity.

Table S6: Overlap coefficients of merged FragMaps using experimental alignment (M) against FragMaps from SILCS simulations of full experimental dimer structures (Expt).

Table S7: Regression weights determined by LOO-CV for each system.

Figure S1: Experimental complex and SILCS-PPI of minimum iRMSD among those clustered.

Figure S2: Experimental complexes overlaid with structures used to generate the merged FragMaps.

Figure S3: PROTACs and highlighted warheads from experimental structures.

Figure S4: Correlation of RMSD and Standard Error of RMSD of the full PROTACs and of the ligase and target warheads across 3 replicas of SILCS-MC docking.

Figure S5: Examples of 2-step PROTAC docking wide-miss cases.

Figure S6: PROTACs and highlighted warheads from VHL-SMARCA4 system.

Figure S7: Performance of LOO-CV and average models for different numbers of SILCS-XTAC metrics.

Data and Software Availability

Information about the compounds described in the article, including SDF and SMILES strings for all PROTACs and warheads, MD simulation input and parameter files, as well as the SILCS-xTAC data derived in this article and their experimental DC₅₀ values from the literature and corresponding DOIs, are available on GitHub at https://github.com/mackerell-lab/silcs-xtac-si.