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. 2026 Sep 7;66(18):11619–11630. doi: 10.1021/acs.jcim.6c00371

Deep3DCCS: Geometry-Driven Collision Cross Section Prediction from Multi-View Molecular Projection Tensors

Pattipong Wisanpitayakorn †,‡,§, Vivek Bhakta Mathema †,‡,§, Kwanjeera Wanichthanarak †,‡,§, Thanyanatthamon Keawhawong ‡,§, Narumol Jariyasopit †,‡,§, Pairash Saiviroonporn ∥, Trongtum Tongdee ∥, Yongyut Sirivatanauksorn ‡,§, Sakda Khoomrung †,‡,§,⊥,#,*
PMCID: PMC13625951  PMID: 42906041

Abstract

Collision cross section (CCS) measurements from ion mobility–mass spectrometry improve confidence in molecular identification in metabolomics and lipidomics and reduce false-positive annotations in untargeted analyses. However, experimental CCS coverage remains incomplete, and accurate computational prediction remains needed. Here, we present Deep3DCCS, a geometry-driven deep learning framework that predicts CCS from stacked multi-angle molecular projection tensors using a three-dimensional convolutional neural network operating across the projection-view and two spatial image dimensions. Three-dimensional molecular structures generated from SMILES strings were rotated around the x, y, and z-axes, converted into binary two-dimensional projections, and assembled into standardized multi-view tensors for CCS regression. Deep3DCCS was developed and evaluated using curated AllCCS and METLIN lipid CCS datasets containing 3948 molecule–adduct entries across [M – H]−, [M + H]+, and [M + Na]+ ions, and input optimization identified 32 × 32 pixel projections with five rotations per axis as a practical balance between prediction accuracy, model stability, and computational feasibility. In independent true-validation experiments, AllCCS-trained models achieved MRPE values of 3.27–3.79% on AllCCS validation data and 2.93–3.72% on METLIN validation data, whereas METLIN-trained models transferred less effectively to the broader AllCCS chemical space. Overall, these results support multi-view molecular projection tensors as a viable geometry-driven representation for CCS prediction and demonstrate that substantial CCS-relevant information can be learned directly from three-dimensional molecular morphology using a 3DCNN architecture, with low single-digit prediction errors across independent and cross-dataset validation experiments.

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Introduction

Ion mobility-mass spectrometry (IM-MS) has emerged as a valuable tool for distinguishing structurally similar species, such as isomers and isobars, in complex biological samples by providing separation based on collision cross-section (CCS) values. CCS is a physicochemical property that reflects the size, shape, polarizability, and gas-phase structure of ions, serving as a unique molecular descriptor for differentiating closely related compounds. − CCS, when integrated with retention time, accurate mass-to-charge ratios (m/z), and tandem mass spectrometry (MS/MS) data, significantly enhances confidence in molecular identification and reduces false-positive metabolite annotations. Despite its potential, the experimental determination of CCS values remains incomplete, with current datasets representing only a fraction of the diversity of molecules encountered in metabolomics, lipidomics, and related chemical annotation workflows. −

To address this challenge, several computational approaches have been developed for CCS prediction. Traditional tools such as MobCal and IMoS , rely on molecular mechanics and dynamics to calculate CCS values based on physical principles. Our recent work highlights hybrid approaches that use first-principles calculations to derive a small set of physically meaningful descriptors, for example adduct polarizability and m/z, enabling accurate prediction even with limited training data. For high-throughput CCS predictions, machine learning (ML) and deep learning (DL) methods have gained prominence. Models such as AllCCS, , CCSbase, CCSP 2.0, and DeepCCS leverage molecular descriptors, fingerprints, or other predefined chemical representations to predict CCS values. These methods are computationally efficient and often highly accurate within their training domains; however, many do not explicitly encode three-dimensional molecular shape as an image-like representation that can be directly learned by convolutional neural networks.

Recent studies − have emphasized the importance of integrating structural information, particularly three dimensional (3D) molecular features, into CCS prediction models. SigmaCCS2 , employs graph neural networks (GNNs) that utilize 3D conformer data to encode molecular topology and connectivity. Although graph-based approaches incorporate structural information, they primarily represent molecules through atoms, bonds, and learned graph embeddings rather than through direct image-based molecular shape representations. The hybrid approach by Bouwmeester et al. combines molecular mechanics-based features with machine learning, leveraging Projection Approximation (PA) to incorporate 3D geometrical information. PA estimates CCS values by averaging 2D projections of a molecule’s 3D structure across orientations, capturing features like size and shape. More recently, PACCS was introduced as a projected-area-based CCS prediction approach that calculates voxel-projected area from molecular conformers and combines this geometry-derived information with deep learning. Together, these studies demonstrate that three-dimensional molecular geometry and projection-derived structural information can improve CCS prediction. However, many existing approaches still compress molecular geometry into graph embeddings, predefined projected-area descriptors, scalar features, or orientation-averaged representations. Therefore, image-based molecular projection strategies that preserve orientation-dependent silhouette, compactness, anisotropy, and spatial shape patterns may provide an alternative route for learning CCS-relevant structural information.

In this study, we introduce Deep3DCCS, a geometry-driven deep learning framework for CCS prediction that represents SMILES-derived three-dimensional molecular structures as stacked multi-angle projection tensors. Rather than relying on predefined molecular descriptors, Deep3DCCS encodes molecular geometry through a multi-view image representation and learns CCS-relevant features using a three-dimensional convolutional neural network (3DCNN) applied across the rotational-view and spatial image dimensions. By integrating structural information across multiple molecular orientations, this approach provides a projection-tensor-based framework for molecular CCS prediction. We evaluate Deep3DCCS using AllCCS-derived and METLIN lipid datasets, including independent true-validation and cross-dataset experiments, to assess model stability, chemical-space effects, and generalization beyond lipid-only training.

Experimental Section

CCS Dataset Preparation and Independent Validation Design

Two CCS datasets were used in this study: AllCCS records retrieved from the publicly accessible AllCCS web interface in January 2020 and a METLIN lipid CCS dataset obtained from the METLIN Lipids repository. The AllCCS dataset was used to represent broader chemical-space coverage, whereas the METLIN dataset was used to evaluate performance in lipid-enriched chemical space. Simplified Molecular-Input Line-Entry System (SMILES) representations corresponding to three adduct types, [M – H]−, [M + H]+, and [M + Na]+, were used as the primary inputs to the Deep3DCCS pipeline. To reduce overlap between database sources, overlapping molecule–adduct records between AllCCS and METLIN were identified using normalized structural and database identifiers, including InChIKey, SMILES, LMSD ID, PubChem CID, and CAS number, together with matched adduct type. These overlapping records were removed before model development and validation. For molecule–adduct entries with multiple reported experimental CCS measurements from different sources, CCS values were averaged and represented as a single entry before dataset splitting. After curation, the final model-input dataset contained 3948 useable CCS entries for the three adduct types used for model development and evaluation, [M – H]−, [M + H]+, and [M + Na]+, including 2507 AllCCS entries and 1441 METLIN entries. For AllCCS, the curated dataset contained 1240 [M + H]+ entries, 722 [M – H]− entries, and 545 [M + Na]+ entries. For METLIN, the curated dataset contained 540 [M + H]+ entries, 325 [M – H]− entries, and 576 [M + Na]+ entries. Each METLIN lipid was classified using LIPID MAPS nomenclature, with lipid category manually verified for accuracy. AllCCS compounds were classified using available chemical-class metadata and grouped at the superclass level for downstream error analysis.

For model development and independent evaluation, curated entries were divided into an 80% model-development set and a 20% independent true-validation set. The independent true-validation set was held out from model training, model-parameter assessment, and internal performance assessment. The model-development set was used for training, internal validation, internal testing, model-parameter assessment, and data-saturation analysis, whereas the independent true-validation set was used only for final performance evaluation.

Molecular Structure Optimization and Projection Image Generation

For each molecule, three-dimensional molecular structures were generated and optimized using an automated Python pipeline built on RDKit. SMILES strings for each molecule were first converted to neutral three-dimensional molecular structures, and implicit hydrogens were made explicit using RDKit. A single conformer was embedded using the ETKDGv3 algorithm with randomized initial coordinates to generate a low-energy three-dimensional geometry, followed by energy minimization using the Universal Force Field (UFF) with a maximum of 2000 optimization iterations. The final optimized geometries were saved in SDF format and exported as Cartesian coordinates for subsequent processing. For molecules represented by multiple adduct entries, projection images were generated from the same neutral optimized geometry, while the corresponding adduct-specific experimental CCS values were retained as prediction targets. Thus, the baseline Deep3DCCS model-development workflow uses a neutral single-conformer baseline and does not perform ion-specific conformer or gas-phase ensemble generation, including adduct-site assignment, charge localization, metal coordination, conformer sampling, or conformer ranking.

To generate multi-angle two-dimensional projections, atomic coordinates were recentered to the mass-weighted molecular center of mass. Atomic marker sizes were scaled according to van der Waals radii obtained from a curated element-specific radius table. Each structure was independently rotated about the x, y, and z axes using rotation matrices with an angular increment θ = π/N, where N denotes the number of rotations per axis. This parameterization allows flexible control over angular sampling density. For each rotational orientation, two-dimensional point-based projections were rendered using Matplotlib without axes or grid lines. Images were organized into axis-specific subdirectories (x, y, z) and saved in PNG format. All projection images were resized to a user-defined square resolution and binarized using an intensity threshold to generate binary representations.

Adduct-Aware Gas-Phase Structure Optimization

To evaluate the influence of ion-specific molecular structures on CCS prediction, adduct-aware conformers were generated using CREST (v3.0.2) with the GFN2-xTB method on a Linux compute server equipped with dual AMD EPYC 9454 processors. For each molecule, candidate ionization or coordination sites appropriate to the corresponding adduct ([M + H]+, [M – H]‑, or [M + Na]+) were screened, and the lowest-energy site was retained for subsequent conformational sampling. CREST conformer searches were performed using an energy window of 6.0 kcal mol–1. Redundant conformers were subsequently removed, and the lowest-energy unique conformer was selected as the representative adduct-specific ion structure.

The adduct-aware control experiment was performed using AllCCS entries for which ion-optimized structures were successfully generated. Separate adduct-aware Deep3DCCS models were developed for each adduct using matched ion-optimized model-development sets comprising 500 [M – H]−, 920 [M + H]+, and 411 [M + Na]+ molecule–adduct entries. Ion-optimized structures were converted to projection tensors using the same projection settings, model architecture, and training procedure used in the neutral-structure baseline workflow. The resulting models were then evaluated on corresponding independent ion-optimized true-validation sets comprising 126 [M – H]−, 212 [M + H]+, and 107 [M + Na]+ entries, respectively.

To assess whether the single-conformer representation introduced flexibility-dependent prediction error, molecular flexibility and size were evaluated in the AllCCS independent true-validation set using the number of rotatable bonds and molecular weight, respectively, calculated from SMILES representations using RDKit. Because the same neutral molecular structure could correspond to multiple adduct entries, prediction errors were averaged across available adducts for each unique molecule in the primary analysis (n = 469). Associations of rotatable-bond count and molecular weight with absolute RPE and signed percentage error were evaluated using Spearman rank correlation. Signed percentage error was calculated as (predicted CCS – experimental CCS)/experimental CCS × 100, such that positive values indicate CCS overprediction and negative values indicate underprediction. Ninety-five percent confidence intervals for Spearman ρ were estimated using 5000 bootstrap resamples, and P values were adjusted using the Benjamini–Hochberg procedure across the four primary tests. Adduct-specific correlations were additionally evaluated as secondary sensitivity analyses, with Benjamini–Hochberg correction applied for multiple testing.

3D Convolutional Modeling of Multi-View Projection Tensors

Binary two-dimensional projection images generated from SMILES-derived, geometry-optimized molecular structures were used as structural inputs, whereas the corresponding experimental CCS values were used as regression targets for model training. A three-dimensional convolutional neural network (3DCNN) was constructed to perform CCS regression on multi-view stacks of two-dimensional molecular projection images generated at defined rotational increments for each molecule. Keras (TensorFlow backend) was used for model construction and training, and scikit-learn was used for performance evaluation. The baseline Deep3DCCS workflow, including molecular structure generation, projection-image generation, model training, evaluation, and inference, was performed on a Windows 10 Enterprise workstation equipped with an Intel Core i9-10900X CPU, 64 GB RAM, and an NVIDIA GeForce RTX 3090 Ti GPU with 24 GB GPU memory. Runtime values should therefore be interpreted in the context of this hardware configuration. Binarized projection images generated from the x, y, and z-axis rotation series were concatenated to form a multi-view molecular projection tensor. In this tensor, the stacked projection images define the projection-view dimension, whereas the height and width dimensions define the spatial shape of each two-dimensional molecular projection. The 3DCNN was therefore used to learn CCS-relevant patterns across both molecular orientation and projected spatial shape. Here, 3DCNN refers to convolution across the stacked projection-view and spatial image dimensions, not to a voxelized three-dimensional molecular volume.

As described above, curated entries were first assigned to an 80% model-development set and a 20% independent true-validation set. Within the 80% model-development set, entries were further partitioned into training, internal validation, and internal test subsets using a 60:20:20 split. The internal validation subset was used to monitor model training, whereas the internal test subset was used for post-training performance assessment during model development.

The network architecture comprised four sequential 3D convolutional blocks with 32, 64, 128, and 256 filters, respectively, each employing 3 × 3 × 3 kernels, ReLU activation, and same padding. MaxPooling3D layers were applied after the first three convolutional blocks, with anisotropic pooling in the early layers to preserve angular resolution along the projection-view dimension. Batch normalization was applied after the first convolutional block to stabilize feature learning. A GlobalAveragePooling3D layer was used in place of flattening to condense projection-tensor feature representations while retaining global structural information. The resulting features were passed to fully connected layers with 128 and 64 units using LeakyReLU activation. The final CCS prediction was produced by a single neuron with linear activation.

Optimization of Image Resolution and Rotational Sampling

To optimize the input representation for CCS prediction, the effects of projection image resolution and rotational sampling density were systematically evaluated using the AllCCS model-development dataset. Projection image resolutions of 8 × 8, 16 × 16, 32 × 32, 64 × 64, 128 × 128, 160 × 160, and 200 × 200 pixels were examined in combination with rotational sampling densities of 1, 3, 5, and 10 rotations per axis, where computationally feasible. For each resolution–rotation combination, 40 independent 3DCNN training replicates were conducted to assess prediction robustness. Model performance was quantified using the mean relative percentage error (MRPE) across replicates. Some high-resolution and high-rotation combinations were not evaluated because the resulting input tensors exceeded the available graphics processing unit (GPU) memory. The optimized input condition was selected by considering prediction accuracy, model stability, and computational feasibility. Based on this assessment, 32 × 32 pixel projection images with five rotations per axis were selected for subsequent Deep3DCCS model development and independent true-validation analyses.

Benchmarking Against CCS Prediction Tools

The predictive performance of the optimized 3DCNN model was benchmarked against established CCS prediction tools: CCSbase2, , AllCCS2, , and SigmaCCS2. , For AllCCS2 and CCSbase2, predictions were obtained using the publicly available online interfaces, with SMILES representations and adduct information submitted according to the input requirements of each platform. For SigmaCCS2, predictions were generated locally using the publicly released general pretrained model weights (model.pt). Predicted CCS values from each comparator were compiled with the corresponding experimental CCS values and Deep3DCCS predictions. Performance was evaluated using relative percentage error (RPE) and mean relative percentage error (MRPE).

To determine whether molecule-level differences represented systematic performance advantages, ΔRPE was calculated as comparator RPE minus Deep3DCCS RPE, such that positive values indicated lower error for Deep3DCCS. Within predefined AllCCS superclasses and METLIN lipid categories, paired ΔRPE distributions were evaluated against zero using two-sided Wilcoxon signed-rank tests, while the proportion of positive ΔRPE values was evaluated using exact binomial tests against an expected proportion of 0.5. P values from these class-level analyses were adjusted using the Benjamini–Hochberg false discovery rate procedure. To investigate whether relative performance was associated with orientation-dependent molecular geometry, projected-area variability was calculated as the coefficient of variation of occupied molecular area across the 15 binary projections generated from five rotations around each of the x, y, and z-axes. Because the same neutral molecular geometry could correspond to multiple adduct entries, ΔRPE values were averaged across adducts for each unique molecule in the primary analysis. Associations between projected-area variability and ΔRPE were evaluated using Spearman rank correlation, with 95% confidence intervals estimated from 5000 bootstrap resamples and P values adjusted using the Benjamini–Hochberg procedure across the six dataset–comparator comparisons.

Results and Discussion

Effect of Image Resolution and Rotational Sampling on CCS Prediction Performance

Figure illustrates the Deep3DCCS framework developed in this study for structure-driven CCS prediction and independent model evaluation. SMILES representations are first converted into geometry-optimized three-dimensional molecular structures, which are systematically rotated about the x, y, and z-axes to generate multi-angle two-dimensional projection images. These binarized projections are assembled into ordered multi-view image stacks that preserve spatial relationships across molecular orientations and serve as input to a 3DCNN. The resulting input tensor is represented as 3n × R × R × 1, where n denotes the number of rotations per axis, R denotes the projection image resolution, and the factor of three corresponds to the x, y, and z-axis rotation series. By performing convolution across both spatial and rotational-view dimensions, the 3DCNN captures cross-view geometric dependencies and learns hierarchical structural features associated with experimental CCS values. Figure also summarizes the model-development and independent true-validation workflow, in which input-condition optimization and feature learning were performed before final evaluation on held-out molecule–adduct entries.

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Overview of the Deep3DCCS workflow and independent validation design. (a) Input representation generation. SMILES representations from the curated AllCCS and METLIN lipid CCS datasets were converted into optimized three-dimensional molecular structures. Each structure was rotated around the x-, y-, and z-axes to generate multi-angle binary projection images, which were resized and stacked into a molecular projection tensor with dimensions 3n × R × R × 1, where n is the number of rotations per axis and R is the projection image resolution. (b) Model optimization and feature learning were performed within the 80% model-development set using training, internal validation, and internal test subsets. (c) Final model performance was evaluated using the held-out 20% independent true-validation set by comparing predicted and experimental CCS values using RPE and R2.

Because CCS reflects the overall size, shape, and orientationally averaged geometry of gas-phase ions, both the spatial resolution of molecular projections and the density of rotational sampling directly influence how effectively molecular geometry is encoded for learning. As shown in Figure A, CCS prediction accuracy exhibited a clear dependence on representational complexity across the AllCCS model-development dataset. The lowest-resolution condition, 8 × 8 pixels, produced consistently higher MRPE values, indicating that excessive spatial compression reduced CCS-relevant molecular shape information. Increasing projection resolution from 8 × 8 to intermediate resolutions improved prediction accuracy, with 32 × 32 pixel projections and five rotations per axis providing a favorable balance of low MRPE, stable error variation, and computational efficiency. Consistent behavior was observed when performance was evaluated using the coefficient of determination (R2; Figure B), where correlation improved with increasing image resolution and rotational sampling but plateaued at higher levels of complexity. Notably, further increases in spatial resolution or rotational sampling beyond intermediate-resolution and moderate-rotation conditions did not translate into consistently improved accuracy and instead increased error variability in some conditions. This behavior suggests that while additional geometric detail can improve the model’s ability to capture global CCS trends, excessive representational complexity introduces redundancy and reduces sample efficiency given the available training data. Together, these results indicate that effective CCS prediction requires a balance between geometric detail and dataset scale, motivating the use of 32 × 32 pixel projection images with five rotations per axis in subsequent analyses. The numerical mean and standard deviation values corresponding to Figure are provided in Supporting Information Table S1.

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Optimization of Deep3DCCS projection-tensor input conditions. (A) Average MRPE and (B) average R2 across combinations of image dimension and number of molecular rotations. Bars represent mean performance, and error bars indicate standard deviation across evaluated runs. Missing bars indicate rotation–resolution combinations that were not evaluated because the tensor size exceeded available GPU memory. Optimization was performed using the AllCCS model-development dataset.

Data Saturation and Training-Condition Assessment

To evaluate whether Deep3DCCS performance was constrained by training-set size and to determine an appropriate final training condition, model performance was assessed as a function of training dataset size, batch size, and training duration using the optimized projection-tensor representation. As shown in Figure A, average MRPE decreased sharply as the training dataset size increased from 1% to 5–10%, indicating that very small training subsets were insufficient to capture the relationship between molecular projection features and experimental CCS values. Beyond approximately 10–20% of the training dataset, the reduction in MRPE became more gradual and approached a plateau after 30% training-data inclusion across all three adduct types. A similar trend was observed for R2 values (Figure B), where model correlation improved rapidly with increasing training-set size and then stabilized at higher training fractions. These results indicate that the available training data were sufficient to support stable Deep3DCCS performance within the evaluated chemical space, with diminishing improvements as additional training data were included. This saturation should therefore be interpreted in the context of the present dataset, input representation, and model capacity rather than as a fundamental performance limit. As larger and more chemically diverse CCS datasets become available, future development can jointly scale training data, model capacity, projection complexity, and computational resources.

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Data saturation and training-condition assessment of Deep3DCCS. (A) Average MRPE and (B) average R2 as a function of training dataset size for [M – H]−, [M + H]+, and [M + Na]+ adducts. Prediction error decreased rapidly and R2 increased as the training fraction increased from very small subsets, followed by performance stabilization at larger training-set sizes. (C) Final internal validation MRPE across batch-size and epoch combinations. BS denotes batch size. Batch size 8 with 250 epochs provided a balanced training condition with low validation error across adduct types while avoiding unnecessary additional training. (D) Internal validation mean squared error (MSE) loss curves for the selected 250-epoch training condition, showing rapid early convergence followed by stabilization of validation loss. Error bars represent standard deviation across independent runs.

The effects of batch size and training duration were then evaluated using final internal validation MRPE across six training conditions: batch sizes of 4, 8, and 16 combined with 250 or 500 epochs, with five independent replicates performed for each condition (Figure C). Validation MRPE remained similar across conditions, and extending training to 500 epochs did not consistently reduce error. Batch size 8 with 250 epochs provided low validation error across adduct types while avoiding unnecessary training time, and was therefore selected for final model development and independent true-validation analyses. Internal validation loss curves supported this choice, with MSE decreasing rapidly during early epochs and approaching a stable plateau before the end of 250-epoch training (Figure D). Together, these results indicate stable learning behavior and support batch size 8 with 250 epochs as a practical final training condition.

To assess the practical scalability of Deep3DCCS, the runtime of the optimized workflow was summarized for each major processing step (Supporting Information Table S2). Model training required approximately 87–182 s per trained model. The end-to-end prediction workflow, including SMILES-to-optimized 3D structure generation, projection-image generation, and 3DCNN inference, required 471–486 s per 1000 molecules, corresponding to approximately 5.5 days per 1 million molecules under similar hardware, batching, and molecule-complexity conditions. For a fixed projection configuration, model architecture, hardware, and inference batch size, the computational cost of the prediction workflow is expected to scale approximately linearly with the number of input molecules. Structure generation and projection rendering are performed independently for each molecule, whereas 3DCNN inference is performed in batches. Thus, the measured million-molecule runtime provides an order-of-magnitude estimate of the computational scale required for large-library prediction. This runtime is practical for offline large-library CCS prediction and reference-library construction. Because structure generation and projection-image generation are molecule-independent, these preprocessing steps are also well suited to parallel computing across CPU cores or compute nodes, which can further reduce wall-clock time. Expanded computational resources could improve prediction throughput, support training as larger experimental CCS datasets become available, and enable evaluation of larger projection tensors or model architectures for both model development and large-scale prediction.

Independent True Validation and CCS-Range Dependence of Cross-Dataset Generalization

After optimizing the input representation and training condition, Deep3DCCS was evaluated using independent true-validation sets to assess within-dataset performance and cross-dataset transferability. AllCCS-trained models achieved MRPEs of 3.27%, 3.79%, and 3.57% for [M – H]−, [M + H]+, and [M + Na]+, respectively, on the AllCCS validation set (Figure A,B), and retained similar performance on the METLIN validation set, with MRPEs of 3.03%, 2.93%, and 3.72% (Figure A,C). These results indicate that training on the broader AllCCS chemical space supported transfer to the lipid-enriched METLIN dataset.

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Independent true-validation performance and CCS-range dependence of cross-dataset generalization. (A) Adduct-specific MRPE for AllCCS-trained models evaluated on AllCCS and METLIN independent true-validation sets. (B,C) Predicted versus experimental CCS values for AllCCS-trained models evaluated on (B) AllCCS and (C) METLIN validation data. (D) Adduct-specific MRPE for METLIN-trained models evaluated on AllCCS and METLIN independent true-validation sets. (E,F) Predicted versus experimental CCS values for METLIN-trained models evaluated on (E) METLIN and (F) AllCCS validation data. Points are colored and shaped by adduct type, and the red dashed line indicates y = x. R2, MRPE, and the number of evaluated molecule–adduct entries are shown for each adduct type. (G) MRPE by experimental CCS range for AllCCS-trained and METLIN-trained models evaluated on the AllCCS validation set. (H) Adduct-specific MRPE by experimental CCS range for the METLIN-trained model evaluated on the AllCCS validation set. Error bars indicate variability in prediction error within each CCS bin.

In contrast, METLIN-trained models performed well on METLIN validation data, with MRPEs of 3.15%, 2.32%, and 3.05% for [M – H]−, [M + H]+, and [M + Na]+, respectively (Figure D,E), but transferred less effectively to AllCCS, where MRPEs increased to 5.27%, 5.95%, and 5.62% (Figure D,F). The METLIN-to-AllCCS scatter plot showed greater deviation at lower CCS values, suggesting reduced coverage of smaller and more chemically diverse AllCCS molecules by the lipid-enriched METLIN training space.

This interpretation was supported by CCS distribution and CCS-range analyses. METLIN was shifted toward higher CCS values than AllCCS in both model-development and validation datasets (Supporting Information Figure S1). On the AllCCS validation set, the METLIN-trained model showed the largest error increase below 150 Å2, whereas the difference between AllCCS- and METLIN-trained models decreased at higher CCS ranges (Figure G). Adduct-specific binning of the METLIN-trained model on AllCCS validation data showed elevated low-CCS error across adduct types, particularly for [M + H]+ and [M + Na]+ (Figure H).

Together, these results show that transferable Deep3DCCS performance depends on representative coverage of the target CCS range and chemical space. The broader AllCCS dataset produced more transferable models, whereas METLIN-only training was more specialized toward higher-CCS lipid-like structures. The adduct-dependent low-CCS error further motivated us to directly evaluate whether replacing the original neutral molecular representation with adduct-aware gas-phase structures could improve prediction accuracy.

Impact of Ion-Specific Structure and Molecular Flexibility on Prediction Error

To evaluate the influence of the neutral-structure approximation, an additional control experiment was performed using CREST-derived adduct-aware structures for the AllCCS dataset. Separate Deep3DCCS models were trained and evaluated using the ion-optimized structures following the same projection and modeling workflow as the neutral-structure baseline. The adduct-aware models achieved independent true-validation MRPE values of 3.36% for [M – H]− (n = 126), 3.11% for [M + H]+ (n = 212), and 3.61% for [M + Na]+ (n = 107). These values were similar in magnitude to the corresponding MRPE values of 3.27%, 3.79%, and 3.57% obtained with the original neutral-structure workflow on the full AllCCS true-validation sets. The lack of consistent improvement indicates that replacing the neutral geometry with a single optimized ion structure is not, by itself, sufficient to account for the remaining prediction error. This may reflect several aspects of the current representation. Experimental CCS can reflect contributions from an ensemble of gas-phase conformations, whereas the present control uses only the lowest-energy unique CREST conformer. The 15 projection images sample different orientations of this single optimized geometry rather than different molecular conformers. A single-conformer representation may nevertheless approximate experimental CCS when one gas-phase conformer predominates or when accessible conformers have similar overall molecular dimensions and compactness, but may be less representative when flexible ions populate substantially different folded or extended structures. In addition, alternative protonation, deprotonation, or metal-coordination sites may coexist and produce different gas-phase structures. Finally, the binary projection tensors primarily encode molecular shape and size and do not explicitly represent charge localization or other electronic properties introduced by ionization. These factors may help explain why the [M – H]− error was not selectively reduced by adduct-aware structure optimization.

To further assess the effect of the single-conformer approximation, we examined whether prediction error increased systematically with molecular flexibility in the AllCCS independent true-validation set. At the unique-molecule level (n = 469), rotatable-bond count was not associated with absolute RPE (Spearman ρ = −0.012, 95% CI = −0.105 to 0.080, BH-adjusted q = 0.889). Molecular weight was likewise not associated with absolute RPE (ρ = 0.019, 95% CI = −0.072 to 0.109, q = 0.889). Thus, the present analysis did not identify a systematic increase in prediction-error magnitude with either molecular flexibility or molecular size. However, rotatable-bond count showed a weak positive association with signed percentage error (ρ = 0.150, 95% CI = 0.061 to 0.238, q = 0.004), indicating a modest tendency toward CCS overprediction as molecular flexibility increased. Molecular weight was not associated with signed percentage error (ρ = −0.006, 95% CI = −0.097 to 0.086, q = 0.889). Adduct-specific sensitivity analyses showed that the positive association between rotatable-bond count and signed error was most evident for [M–H]− (ρ = 0.294, q = 0.0016) and [M + Na]+ (ρ = 0.474, q < 0.001), whereas rotatable-bond count was not significantly associated with absolute RPE for any individual adduct (Supporting Information Table S3). Overall, these results indicate that molecular flexibility was not associated with greater prediction-error magnitude, but was associated with a modest directional bias toward CCS overprediction, particularly for [M – H]– and [M + Na]+ ions.

Chemical-Class and Lipid-Category Dependence of Prediction Error

To evaluate chemical-class dependence, prediction error was examined by AllCCS superclass and METLIN lipid category (Figure ). In the AllCCS true-validation set, the largest superclass groups were organoheterocyclic compounds, lipids and lipid-like molecules, organic oxygen compounds, organic acids and derivatives, and benzenoids (Figure A). Across the major superclass groups shown in Figure B, organic oxygen compounds and nucleosides, nucleotides, and analogues showed the lowest MRPE values, whereas benzenoids, lipids and lipid-like molecules, phenylpropanoids and polyketides, and organic acids and derivatives showed higher MRPE values. The “Other” group, which combines categories with fewer than five validation entries, and organic nitrogen compounds both contained few entries, so their larger uncertainty should be interpreted cautiously rather than as clear class-specific underperformance.

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Class composition and class-specific prediction error in the independent true-validation datasets. (A) Superclass composition of the AllCCS true-validation set based on available chemical-class metadata. (B) Superclass-specific MRPE for AllCCS true-validation molecules. (C) Lipid category composition of the METLIN true-validation set. The n values indicate the number of evaluated molecule–adduct entries in each class or category. (D) Lipid category-specific MRPE for METLIN true-validation molecules based on LIPID MAPS classification. Error bars indicate variability in prediction error within each class or category.

For the METLIN validation set, glycerophospholipids and sphingolipids represented the largest lipid categories, followed by sterol lipids and unannotated lipids (Figure C). Category-specific MRPE values were generally low for most lipid groups, including fatty acyls, glycerophospholipids, sphingolipids, and unannotated lipids (Figure D). Sterol lipids showed the highest MRPE among METLIN lipid categories, which may reflect the sensitivity of compact fused-ring structures to ionization-induced reorientation or adduct-dependent coordination effects that are not explicitly represented by neutral-geometry projection tensors. Glycerolipids and other minor categories showed larger uncertainty, which may reflect their smaller validation sample sizes. Overall, the METLIN category analysis suggests that Deep3DCCS performs consistently across major lipid categories, while higher error or uncertainty in specific groups may reflect class-specific ion behavior and limited sample representation.

Benchmarking Against Established CCS Prediction Tools

After evaluating independent validation performance and class-specific error patterns, the optimized Deep3DCCS models were benchmarked against AllCCS2, CCSbase2, and SigmaCCS2 using the same independent true-validation molecule–adduct entries (Figure ). Comparator tools generally produced lower MRPE values on both the AllCCS and METLIN validation sets (Figure A,B), whereas Deep3DCCS achieved MRPE values of approximately 3–4% across adduct types. Thus, the present implementation does not show an overall predictive-accuracy advantage over these established tools. However, the low single-digit errors achieved using the projection-tensor representation demonstrate that substantial CCS-relevant information can be learned directly from three-dimensional molecular morphology using a 3DCNN architecture.

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Benchmarking of Deep3DCCS against established CCS prediction tools. Adduct-specific MRPE values for Deep3DCCS, AllCCS2, CCSbase2, and SigmaCCS2 on the (A) AllCCS and (B) METLIN independent true-validation sets. Bars show MRPE for each adduct type, and error bars indicate standard error across molecule–adduct entries. (C) Entry-level difference in RPE between each comparator model and Deep3DCCS, calculated as comparator RPE minus Deep3DCCS RPE for matched molecule–adduct entries. Values below zero indicate lower error for the comparator model, whereas values above zero indicate lower error for Deep3DCCS. Box plots summarize the median and interquartile range, with overlaid points representing individual molecule–adduct entries. (D,E) Descriptive class-level mapping of entries for which Deep3DCCS produced lower RPE than each comparator model, summarized as the percentage of matched molecule–adduct entries with positive ΔRPE in (D) AllCCS superclass groups and (E) METLIN lipid categories. These percentages describe the distribution of individual lower-error predictions and do not indicate statistically significant class-level superiority. The n values indicate the number of molecule–adduct entries in each superclass or lipid category. Categories with fewer than five entries were combined as “Other.”

Entry-level ΔRPE analysis was then used to assess molecule-specific performance differences between Deep3DCCS and the comparator tools (Figure C). ΔRPE was calculated as comparator RPE minus Deep3DCCS RPE, so negative values indicate lower error for the comparator model and positive values indicate lower error for Deep3DCCS. Although the ΔRPE distributions were centered mostly below zero, positive values were observed for all comparator models, indicating that Deep3DCCS outperformed individual tools for a subset of molecule–adduct entries. However, the occurrence of positive ΔRPE values alone does not establish a systematic domain of improved performance.

Class-level mapping of positive ΔRPE entries showed that individual lower-error Deep3DCCS predictions occurred across multiple chemical groups (Figure D,E). In the AllCCS validation set, individual molecule–adduct entries with lower Deep3DCCS RPE were observed across multiple superclass groups (Figure D); however, paired statistical testing did not identify any superclass with a statistically supported systematic Deep3DCCS advantage after correction for multiple testing (Supporting Information Table S4). In the METLIN validation set, individual lower-error Deep3DCCS predictions were also observed across several lipid categories, including fatty acyls and glycerolipids, although these categories contained relatively few matched entries (Figure E). Statistical testing did not identify any lipid category with a systematic Deep3DCCS advantage after correction for multiple testing (Supporting Information Table S4). Thus, Figure D,E should be interpreted as a descriptive mapping of individual lower-error predictions rather than evidence of class-dependent superiority.

We additionally examined whether relative Deep3DCCS performance was associated with orientation-dependent molecular geometry, providing a direct test of whether the multi-view projection representation preferentially benefits molecules whose projected shape varies across orientations. Projected-area variability across the 15 molecular views was compared with ΔRPE for each comparator. No positive association remained significant after correction for multiple testing (Spearman ρ = −0.131 to 0.061; Benjamini–Hochberg-adjusted q ≥ 0.273) (Supporting Information Table S5). Therefore, the present analysis did not identify orientation-dependent projected-area variability as a structural explanation for the individual cases in which Deep3DCCS produced lower prediction error.

Overall, these results position Deep3DCCS as a distinct geometry-driven CCS prediction framework rather than a replacement for established tools. Its present utility lies in providing a spatially explicit representation for investigating geometry-driven structure–CCS relationships and a quantitative baseline for the development of projection-based molecular learning approaches. The adduct-aware control experiment showed that use of a single representative ion-optimized conformer did not uniformly improve prediction accuracy. Future development should therefore extend beyond single adduct-aware structures toward gas-phase conformer-ensemble modeling, consideration of alternative ionization and coordination sites, and ion-specific structural representations. Although the present flexibility analysis did not identify increasing absolute prediction error with increasing rotatable-bond count, conformer-ensemble modeling remains relevant for flexible molecules because multiple gas-phase conformations with different compactness may not be represented by a single minimized structure. Future implementations could extend the present CREST-based approach by retaining multiple low-energy ion conformers and alternative protonation, deprotonation, and metal-coordination states for ensemble-based prediction. Importantly, the projection-tensor representation is not mutually exclusive with descriptor- or graph-based approaches. Future hybrid implementations could combine the learned projection-tensor representation with molecular descriptors or graph-derived features, thereby retaining explicit three-dimensional morphological information while incorporating physicochemical and topological information not encoded by the present binary projections. Chemically informative tensor channels encoding properties such as atom type, partial atomic charge, polarizability, or projection density provide an additional direction for extending the representation.

Conclusion

We present Deep3DCCS, a geometry-driven deep learning framework that predicts collision cross sections directly from multi-view molecular projection tensors using a 3DCNN. Without relying on predefined molecular descriptors, Deep3DCCS learns CCS-relevant features from SMILES-derived molecular geometry and provides a projection-tensor-based strategy for CCS prediction. Independent true-validation and cross-dataset analyses showed that model performance depends strongly on the chemical-space and CCS-range coverage of the training data, with broader AllCCS training providing better transferability to the lipid-enriched METLIN dataset than METLIN-only training to the broader AllCCS chemical space. Benchmarking against AllCCS2, CCSbase2, and SigmaCCS2 showed that Deep3DCCS did not uniformly outperform these established CCS prediction tools, although lower prediction errors were observed for individual molecule–adduct entries across multiple chemical classes and lipid categories. Additional statistical analyses did not identify a chemical subgroup or orientation-dependent projection characteristic in which Deep3DCCS showed a systematic performance advantage. A key limitation of the original Deep3DCCS implementation is the use of neutral, single-conformer geometries, which do not explicitly capture adduct-specific ion structures or gas-phase conformational heterogeneity. A CREST-based adduct-aware control yielded MRPE values of 3.36%, 3.11%, and 3.61% for [M – H]–, [M + H]+, and [M + Na]+, respectively, without a consistent improvement over the neutral-structure workflow. Analysis of the original AllCCS validation data further showed no systematic increase in absolute RPE with rotatable-bond count, although a weak positive association with signed prediction error indicated a modest tendency toward overprediction as molecular flexibility increased. Future development may extend the present framework through conformer-aware and ion-specific representations, chemically informative tensor channels, or hybrid integration of projection-derived features with molecular descriptors or graph-based representations. Such approaches could incorporate physicochemical and topological information that is not explicitly encoded by the present binary projections while retaining the spatial molecular representation introduced here. Taken together, the present results establish multi-view molecular projection tensors as a viable geometry-driven representation for CCS prediction and provide a quantitative baseline for continued development of this approach.

Supplementary Material

ci6c00371_si_001.pdf (153.6KB, pdf)

Acknowledgments

This research received funding from the National Science, Research, and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research, and Innovation, Grant no. B05F650015. The authors acknowledge the Center of Excellence for Innovation in Chemistry (PERCH–CIC) and Ministry of Higher Education, Science, Research, and Innovation, Thailand. This project is partially supported by the Research Excellence Development (RED) program at the Faculty of Medicine Siriraj Hospital, Mahidol University, Thailand. This research project is supported by Siriraj research development fund, Grant number (IO) R016737002, Faculty of Medicine Siriraj Hospital, Mahidol University. This research project has been supported by Mahidol University (Fundamental Fund: fiscal year 2025 by National Science Research and Innovation Fund (NSRF), to S.K.), Bangkok, Thailand.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.6c00371.

  • Supporting Information tables and figures summarizing the numerical input-condition optimization results, runtime analysis, molecular-flexibility and prediction-error analysis, class- and category-specific ΔRPE statistical analyses, orientation-dependent projection-geometry analysis, and CCS distribution comparisons (PDF)

¶.

P.W. and V.B.M. contributed equally to this work and are considered co-first authors. P.W. and V.B.M. developed and validated the deep learning models. P.W. visualized the data and prepared the original manuscript draft. T.K. annotated lipid categories using the LIPID MAPS classification system. P.S. and T.T. provided computational resources, critical scientific discussion, and infrastructure supporting the CREST-based adduct-aware conformer calculations. Y.S. and S.K. acquired funding and resources. P.W., V.B.M., K.W., N.J., P.S., T.T., Y.S., and S.K. interpreted results, reviewed and edited the manuscript. PW, VBM, KW, and SK conceptualized the study. SK designed and supervised the study.

The authors declare no competing financial interest.

Deep3DCCS is released as a fully open-source software package, enabling transparency, reproducibility, and collaborative development within the scientific community. It includes an intuitive graphical user interface (GUI) built with PyQt5 and associated datasets, allowing users to run the full CCS prediction pipelinefrom SMILES input and 3D structure generation to image projection and model inferencewithout requiring programming expertise. Full software and associated datasets can be downloaded from https://github.com/vivekmathema/Deep3DCCS.

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Supplementary Materials

ci6c00371_si_001.pdf (153.6KB, pdf)

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