Predicting Collision Cross Sections with GRACE: Geometric Residual Adduct Conditioning via Early-fusion

1 Introduction

• Accurate CCS predictions can filter candidate structures outside experimental tolerance, reducing the annotation search space; values within approximately 3% are often indistinguishable.CCS reflects the effective size and shape of a charged gas-phase species and is sensitive to molecular structure and adduct type.Source: §1 · p. 2
• Physics-based CCS workflows combine conformer ensembles, electronic-structure calculations, and CCS evaluation, but their computational cost scales poorly for large, flexible, high-throughput libraries.Conformer quality and diversity particularly affect predictions for flexible metabolites.Source: §1 · p. 2
• Published CCS models typically use random held-out splits, while adduct identity is often appended at the prediction head rather than used to condition a 3D encoder.The introduction also notes limited incorporation of physicochemical descriptors or chemical inductive biases in learned CCS regressors.Source: §1 · p. 2
• CCSBench contains 9,209 experimental CCS values across three adducts, with random, scaffold, and adduct-sensitive splits designed to probe standard, structural, and adduct-driven generalization.The adduct-sensitive split places the most adduct-responsive molecules exclusively in the test set.Source: §1 · p. 2
• GRACE combines 3D molecular geometry with chemically motivated inductive biases, and its reported improvements extend across four external test sets and a prospective 20-molecule comparison.On the prospective set, the reported error is less than half that of the best quantum mechanical workflow, at a fraction of its computational cost.Source: §1 · p. 3

Descriptor- and sequence-based models

• Descriptor- and sequence-based predictors include MetCCS, AllCCS, CCSBase, CCS-Predictor 2.0, and DeepCCS, but the described approaches do not explicitly model conformers or geometry's response to ionization.DeepCCS uses SMILES with adduct information, while the cited descriptor approaches use hand-crafted or SMILES-derived features.Source: §2 · p. 3

Adduct-aware graph models

• GraphCCS encodes adduct identity through adduct-graph topology, but does not generate or relax an adduct-specific 3D conformer.The paper distinguishes this heuristic adduct-aware representation from conformer-based 3D modeling.Source: §2 · p. 3
• Other graph models add topological, physicochemical, or geometric descriptors, whose form varies across methods.The paper notes variation in whether geometry enters as derived descriptors, explicit conformer coordinates, or invariant quantities.Source: §2 · p. 3

Explicit geometric and conformer-based models

• SigmaCCS and SigmaCCS2 encode explicit conformer information but append adduct identity after geometric or graph-level encoding; IMPACT-4CCS combines ab initio calculations with learned potentials at greater expense.SigmaCCS2 represents conformer bond lengths and dihedral angles as fixed features rather than passing Cartesian positions directly to the encoder.Source: §2 · p. 3
• GraphCCS [73] and SigmaCCS [74] are re-evaluated as complementary baselines: adduct-aware graph construction without conditioned conformer geometry versus explicit conformer encoding with late adduct fusion.Both are evaluated on the curated dataset using the same splits and random seeds as GRACE.Source: §2 · pp. 3–4

3.1 Dataset Curation

• Records without SMILES were reconstructed from compound identifiers and checked against molecular formula information, including hydrogen counts.Samples with unresolved atom-count discrepancies were discarded.Source: §3.1 · p. 4
• Duplicate canonical-SMILES/adduct records were resolved using a 3% agreement rule, with discordant measurements discarded or assessed for bimodality and outliers.One sample per pair was retained after duplicate resolution; distinct chiral markings remained distinct molecules.Source: §3.1 · p. 5
• 9,209 CCSBench measurements cover protonated, deprotonated, and sodiated adducts, compiled from prior modeling datasets and experimental sources.The sources include GraphCCS, SigmaCCS, the Unified CCS Compendium, and MetlinCCS.Source: §3.1 · pp. 4–5, Figure 1 · p. 4
• Approximately 8% of molecules could not be processed into 3D conformers and were excluded; these molecules tend to be larger and outside the benchmark's typical metabolite mass range.The resulting benchmark contains 9,209 measurements.Source: §3.1 · p. 5

3.2 Evaluation Splits

• The random split uses an 80/10/10 sample partition, while the scaffold split assigns Bemis–Murcko scaffolds wholly to train or test to probe chemically novel scaffolds.About 3,300 molecules without a Murcko scaffold are distributed randomly between train and test.Source: §3.2 · p. 5
• The adduct-sensitive split reserves molecules whose cross-adduct CCS range exceeds 7.8 Å2 for validation and test, targeting cases with larger adduct-dependent variation.The selected subset has a mean range of 14.2 Å2; this is a targeted stress test rather than an i.i.d. deployment estimate.Source: §3.2 · p. 5

4.1 Problem Formulation

• CCS prediction is framed as supervised regression from a neutral molecule and its adduct label to the measured adducted ion’s CCS.CCS reflects an ion’s effective rotationally averaged size and shape, influenced by its 3D geometry, compactness, and ionization-related charge distribution.Source: §4.1 · p. 6

4.2 Conformer Generation

• GRACE generates 10 neutral-molecule conformers with ETKDG and MMFF94 optimization, matching the geometry protocol used to pretrain its encoder.Neutral conformers avoid ambiguity about charged-group placement and reduce geometry distribution shift during fine-tuning.Source: §4.2 · p. 7

4.3 Encoder

• The model uses UniMol, a pretrained 15-layer transformer that encodes pairwise distances as attention biases for global geometric reasoning.Its 512-dimensional CLS token provides the global molecular representation.Source: §4.3 · p. 7

4.4 Conformer Pooling

• Four pooling strategies combine conformer CLS embeddings: single-conformer selection, uniform averaging, Boltzmann-weighted averaging, and learned attention pooling.Single-conformer selection is random during training and uses the lowest-MMFF94-energy conformer at inference.Source: §4.4 · p. 7

4.5 Adduct Conditioning

• Early fusion injects adduct information into the encoder through a learned CLS-token embedding and low-rank query/value attention adapters.Both components are zero-initialized; GRACE conditions neutral-conformer representations on adduct identity but does not generate adduct-specific conformers or simulate ion-induced rearrangement.Source: §4.5 · pp. 7–8

4.6 Residual Learning

• GRACE predicts the residual to an adduct-aware Ridge baseline, whose 2D descriptors capture much of the mass-dominated CCS signal.The full descriptor baseline reaches RMSE 7.82 Å2; the neural component learns the remaining adduct- and geometry-dependent signal.Source: §4.6 · pp. 8–9, Table 2 · p. 9

4.7 Training Details

• Training uses AdamW, validation-MSE early stopping, five random seeds, and best-validation checkpoints, with MPD as the primary evaluation metric.The reported metrics also include RMSE, Pearson r, Spearman ρ, and the train–test RMSE generalization gap.Source: §4.7 · p. 9

5.2 CCSBench Evaluation

• GRACE posts MPD (1.670 ± 0.023)% on random, (2.113 ± 0.042)% on scaffold, and (2.363 ± 0.032)% on adduct-sensitive splits, beating GraphCCS on each.The best-MPD GRACE pooling mode is selected separately for each split.Source: Table 3 · p. 10, §5.2 · p. 11

5.1 Conformer Pooling and Fusion Strategy

• Early fusion improves over late fusion across splits; single-conformer pooling outperforms multi-conformer pooling on the adduct-sensitive split, while learned attention pooling performs worst across splits.On random and scaffold splits, pooling-mode RMSE differences are within one standard deviation across seeds.Source: §5.1 · p. 10
• Figure 3 compares train and test RMSE across epochs for GRACE and GraphCCS under random, scaffold, and adduct-sensitive splits; GRACE’s generalization gap is substantially smaller throughout training.Shaded bands represent ±1 standard deviation across five seeds.Source: Figure 3 · p. 11

5.2 CCSBench Evaluation

• GRACE’s random-split generalization gap is (0.081 ± 0.085) Å2 versus GraphCCS’s (1.571 ± 0.494) Å2, a 19-fold reduction.The authors associate the reduction with residual learning and zero-initialized residual prediction, while noting model capacity and training dynamics may also contribute.Source: §5.2 · p. 11

5.3 Evaluation on External Datasets

• Across 12 external testset–training-split combinations, GRACE has the lowest RMSE and MPD in 11; SigmaCCS is marginally best on TS2 under the random split.These are best-configuration results, with training split and, for GRACE, pooling mode jointly selected.Source: §5.3 · p. 12, Table 4 · p. 12

5.4 Prospective Experimental Validation

• On the 20-molecule GPCL set, GRACE reaches RMSE 2.68 Å2 and MPD 1.74%, with lower RMSE than each of four published physics-based estimates.The authors caution that the small sample limits generalization of the observed error pattern.Source: §5.4 · p. 13, Table 5 · p. 13

6.2 Stereoisomer Leakage

• Removing stereoisomeric test cases changes GRACE RMSE by at most +0.19 Å2 and GraphCCS RMSE by at most +0.24 Å2, so leakage did not materially inflate reported accuracy.Leakage rates were 20.1%, 14.1%, and 6.9% for the random, scaffold, and adduct-sensitive splits, respectively.Source: §6.2 · p. 14

6.1 Generalization Gains from Residual Learning and Early Fusion

• GRACE matches or outperforms GraphCCS across all three training splits; on the random split, its generalization gap is 0.08 Å2 versus 1.57 Å2 for GraphCCS.The discussion attributes the smaller gap partly to removing the mass–CCS trend with residual learning, while noting that capacity or regularization differences cannot be ruled out.Source: §6.1 · p. 14, Table 6 · p. 15

6.3 Effect of Multi-Conformer Pooling on the Adduct-Sensitive Split

• On the adduct-sensitive split, single-conformer pooling has the lowest RMSE (6.34 Å2), while Boltzmann pooling has the highest (6.58 Å2).The discussion links the disadvantage of neutral-molecule Boltzmann weighting to its mismatch with the ion’s conformer population; on the scaffold split, uniform pooling slightly outperforms single-conformer pooling (MPD 2.11% vs. 2.21%).Source: §6.3 · p. 15, Table 6 · p. 15

6.4 Adduct Conditioning Using Late Fusion

• On the adduct-sensitive split, the best late-fusion RMSE is 7.96 Å2 versus 6.34 Å2 for GRACE; on the random split, it is 5.30 Å2 versus 4.64 Å2.Late fusion appends adduct information after geometric encoding, whereas GRACE conditions the encoder; the advantage is widest on the adduct-sensitive split.Source: §6.4 · p. 15

6.5 Geometry-Stratified Performance Analysis

• 29.7 ± 3.8% versus 8.9 ± 4.3%: GRACE’s overall improvement over the Ridge baseline exceeds late fusion’s, with a four-fold smaller relative geometry-dependence.The HIGH–LOW gap is +3.9% for GRACE and +5.4% for late fusion; the authors treat the descriptor-stratified analysis as diagnostic, not a formal independent hypothesis test.Source: §6.5 · p. 16, Figure 6 · p. 16

6.6 Counterfactual Adduct Swap Analysis

• For [M+H]+↔[M−H]− swaps, directional accuracy is 75–80% and rank correlation is ρ = 0.65; sodium-swap directional accuracy is 44–56%, near chance, despite positive rank correlations.The counterfactual holds the conformer fixed and changes the adduct token; the Ridge baseline’s fixed sodium offset leaves residual predictions centered near zero, making their signs uninformative.Source: Figure 7 · p. 17, Figure 8 · p. 17, §6.6 · p. 18

6.7 Limitations and Future Directions

• The current approach generates and weights conformers for neutral molecules, and its evaluation covers only [M+H]+, [M−H]−, and [M+Na]+.The discussion identifies ionic-state conformer optimization and weighting as a possible future direction and notes the need for additional curation to extend adduct coverage.Source: §6.7 · p. 18

• GRACE uses encoder-level adduct conditioning with LoRA adapters and residual learning against a physical descriptor baseline.The residual target removes the dominant size-driven CCS component, while early fusion lets the geometry encoder learn adduct-dependent residual structure.Source: §7 · p. 18
• MPD was 1.67% versus 1.77% on random, 2.11% versus 2.28% on scaffold, and 2.36% versus 2.51% on adduct-sensitive splits, favoring GRACE.The comparisons are against the best competing model on random and the reported comparator values on the other splits.Source: §7 · p. 18
• The generalization gap is consistently smaller than GraphCCS across all three splits, with the largest reduction on the random split.Source: §7 · p. 18
• Neutral-molecule MMFF energy-based Boltzmann pooling degrades adduct-sensitive performance because the neutral thermal ensemble does not represent charged-ion conformer populations.The paper identifies ion-specific conformer weighting as a future direction.Source: §7 · p. 18
• Charge-sign adduct swaps achieve 75% directional accuracy, while sodium-containing swaps are near chance and retain positive rank correlations.The Ridge baseline absorbs the mean sodium-adduct offset, leaving no net directional signal in the residual output.Source: §7 · pp. 18–19
• On a held-out experimental set, GRACE outperforms the previously reported physics-based workflows under their published settings.Source: §7 · p. 19
• The authors expect residual learning to transfer to properties where a physics-based prior explains substantial variance and propose the adduct-sensitive split as a challenge set.They frame encoding domain knowledge as reducing the effective complexity of what the network must learn.Source: §7 · p. 19

• Excluded molecules had a median of 41 rotatable bonds, versus 6 for retained molecules, and 94% met the lipid-like criterion versus 32%.The criterion was at least 10 rotatable bonds and no more than one ring.Source: Figure 9 · p. 25
• Excluded molecules averaged 857 Da, nearly twice the retained molecules’ 438 Da, but flexibility was the sharper distinction.Source: Figure 9 · p. 25
• ETKDG search cost rises combinatorially with torsional degrees of freedom, while MMFF94 struggles with long, largely acyclic lipid-like chains.These factors are given as reasons the conformer-generation pipeline failed for the excluded molecules.Source: Figure 9 · p. 25

• For TS4 (GPCL), results use all 20 molecules, and the model is retrained after duplicates are removed from training.Source: §A.2 · p. 25, Table 7 · p. 25
• Table 7 reports each external test set’s source, original size, and de-duplicated size used in the study.Source: Table 7 · p. 25, §A.2 · p. 25

• Table 8 covers 12 configurations spanning three pooling modes, two token representations, and two fusion strategies across all three evaluation splits.Source: §A.3 · p. 25
• The pooling comparison includes single-conformer, uniform ensemble, Boltzmann energy-weighted, and learned attention-weighted strategies, with mean and standard deviation across five seeds.Source: Table 8 · p. 26

A.4 Full CCSBench Results Across All Configurations and Splits

• Table 9 compares four GRACE conformer-pooling modes with GraphCCS and SigmaCCS across splits, reporting train and test MPD, RMSE, rank correlations, and generalization gaps.The caption does not provide individual metric values.Source: Table 9 · p. 26
• GRACE achieves the lowest MPD for [M+H]+ and [M+Na]+ across all splits, while GraphCCS is competitive on [M−H]−.Per-adduct training metrics for GraphCCS are unavailable.Source: Table 10 · p. 27
• Table 10 reports per-adduct CCS accuracy for the best configuration per split, and Table 11 extends per-adduct reporting to all GRACE pooling modes and competitors.Table 11 includes test Spearman ρ and Kendall τ for GraphCCS, but not its per-adduct training metrics.Source: Table 10 · p. 27, Table 11 · p. 28

A.5 External Benchmark Results Across All Configurations and Splits

• Across four external test sets, GRACE achieves lower RMSE than GraphCCS and SigmaCCS in the majority of configurations.GRACE shows consistent gains over competitors on [M+H]+ and [M+Na]+ across all test sets.Source: Table 13 · p. 30, Table 14 · p. 31

A.7 Early vs. Late Fusion: Effect of Residual Learning

• On the random split, late fusion with residual learning had a +3.0 Å2 generalization gap, while early fusion with residual learning had a +0.08 Å2 gap.The authors interpret the contrast as suggesting that adduct-in-encoder conditioning is necessary for residual learning to generalize.Source: §A.7 · p. 32, Table 16 · p. 32

A.6 Late Fusion Results Across All Pooling Modes and Token Representations

• Late fusion reached 7.96 Å2 on the adduct-sensitive split versus GraphCCS at 6.53 Å2, a 1.4 Å2 deficit that motivated encoder-level conditioning.Table 15 compares late-fusion configurations using three pooling strategies and two token representations under each split.Source: Table 15 · p. 32, §A.8 · p. 33

A.8 From Late Fusion to GRACE

• Replacing the pretrained CLS token failed to converge, while additive-delta early fusion with mismatched learning rates showed periodic validation spikes.The co-trained-delta variant without residual learning had healthy but incomplete training; resource constraints stopped it during warmup, so the residual contribution to stability could not be isolated from the learning-rate change.Source: §A.8 · p. 33, Figure 10 · p. 34
• The final early-fusion candidate started at 7.45 Å2 and converged smoothly to 5.08 Å2 over 128 epochs using a residual target anchored to the Ridge baseline.The Ridge model explained R2=0.961 of random-split variance; the residual target reduced loss scale and stabilized early warmup. Figure 10 shows the candidate crossing below GraphCCS.Source: §A.8 · p. 33, Figure 10 · p. 34

A.9 Stereoisomer Leakage Robustness

• Removing test molecules whose stereoisomers appeared in training yielded performance comparable to the full test set, indicating that leakage does not drive GRACE’s gains.The reported comparison uses the clean subset after leaked molecules are removed.Source: Table 17 · p. 34, Table 18 · p. 35