UniKineG: Unified-Coordinate Geometric Graphs Enable Robust Enzyme Kinetic Prediction

Abstract

Enzyme kinetic parameters $(k_{\mathit{cat}}, K_m, \mathrm{and} k_{\mathit{cat}}/K_m)$ are fundamental for quantifying catalytic efficiency and substrate specificity in biochemistry and drug discovery. However, experimental determination is resource intensive, and accurate prediction remains a persistent challenge due to the complex spatial nature of catalysis. In this paper, we present UniKineG, a novel deep learning framework that redefines kinetic prediction by modeling the explicit spatial state of enzyme–substrate complexes. Unlike conventional methods that treat proteins and ligands as isolated modalities, UniKineG employs molecular docking to embed both entities into a unified 3D coordinate system. Within this shared geometric context, we utilize a heterogeneous graph neural network integrated with geometric vector perceptrons (GVPs) to capture intricate vector-based interactions, such as directional hydrogen bonds, hydrophobic contacts, and electrostatic complementarity. This structure-based approach confers exceptional robustness: UniKineG effectively overcomes the dependency on high-sequence homology, demonstrating superior generalization on out-of-distribution (OOD) datasets encompassing both unseen enzyme sequences and diverse substrate scaffolds. Consistently outperforming state-of-the-art predictors, UniKineG achieves high-precision predictions. This work establishes a solid foundation for understanding enzyme–small molecule interactions in 3D space and offers a transformative tool for computational enzymology.

1. Introduction

Enzymes serve as the catalytic engines of life, orchestrating biological processes ranging from metabolic flux regulation to signal transduction and drug metabolism [1]. The directionality and rate of these biochemical reactions are governed by fundamental kinetic parameters: the turnover number ($k_{\mathit{cat}}$), the Michaelis constant ($K_m$), and the catalytic efficiency ($k_{\mathit{cat}}/K_m$) [2]. The correct identification of such parameters plays important roles in elucidating reaction mechanisms as well as in guiding rational enzyme design and rebuilding genome-scale metabolic models [3]. Thus, the Michaelis–Menten framework that is created can form a mathematical basis to measure substrate affinity and catalytic capacity, both having an impact on physiological homeostasis [4]. However, experimental determination using in vitro assays is labor intensive, time consuming, and often constrained by substrate availability and assay sensitivity. Therefore, databases as comprehensive as BRENDA and SABIO-RK only cover a portion of the known enzymatic space [5,6]. Such terrible data poverty amidst the rapidly expanding numbers of sequenced genomes is a problem for computational enzymology [7,8,9].

Artificial intelligence (AI) has emerged as a powerful tool to bridge this gap. Early machine-learning attempts combined structural active site information with flux balance analysis to predict $k_{\mathit{cat}}$ in specific organisms but had low transferability [10]. Next came deep learning. Li et al. were the ones who started this movement with DLKcat, which uses deep convolutional neural networks (CNNs) and graph neural networks (GNNs) to pull features from protein sequences and substrate graphs, respectively, in the first large-scale $k_{\mathit{cat}}$ prediction [11]. TurNup and UniKP also used integrated pretrained protein language models (pLMs), such as ESM-1b, to encode the rich evolutionary semantics of amino acid sequences and conduct multitask prediction [12,13]. In more recent years, efforts have increasingly focused on improving dataset curation, reliability, and out-of-distribution (OOD) evaluation. CataPro and CatPred emphasize more rigorous data standardization and benchmarking [14,15]; notably, CatPred provides prediction-specific uncertainty quantification and explicitly evaluates OOD enzymes using rich sequence and structure representations. In parallel, DEKP [16] integrates pretrained sequence encoders with structure-aware graph modules to mitigate performance degradation under low-sequence similarity and reports sensitivity to mutation-induced changes in catalytic efficiency. Beyond enzyme kinetics, graph neural networks have also been applied to other biochemical prediction settings, such as classifying whether small molecules are depleted by the human gut microbiome [17]. Related studies in drug metabolism/toxicology (e.g., P-gp inhibition prediction) further suggest that model performance can depend strongly on the representation choice and data regime [18].

Although there are architectural innovations, there is still an important limit: Most of the existing frameworks consider enzymes and substrates to be topologically isolated modalities. Even when pretrained representations, structure-aware encoders, or uncertainty modeling are introduced, the enzyme and substrate are often still encoded separately and fused late, leaving the interfacial 3D interaction geometry underutilized.

To represent 1D sequences and 2D molecular graphs by themselves and to concatenate them at the late stage, which cannot properly model the spatial state of the catalytic microenvironment [19], it is very hard to obtain all those hard and important geometry-dependent interactions that help things, like the precise alignment of catalytic residues and substrate functional groups, that govern the reaction turnover number ($k_{\mathit{cat}}$) [20,21].

This shortcoming is the most severe when predicting $k_{\mathit{cat}}$. Biochemical mechanisms suggest that while $K_m$ is mostly governed by the binding affinity, a property mostly driven by the static geometric fit and surface interactions, like electrostatics and hydrophobicity, $k_{\mathit{cat}}$ reflects the maximal reaction rate, which is governed by the stabilization of the transition state, electron transfer, and dynamic conformational fluctuations [22,23]. These processes are strictly regulated by vector-based geometric constraints, such as the directional alignment of hydrogen bonds and the precise orientation of dipoles. These small vector-level features are usually omitted from the scalar representation or sequence-based embedding used by the previous methods [24]. For this, this sort of a predictive framework needs to have knowledge that it is geometry aware and that it can use different multimodal information within a physically rigorous spatial context.

And now for our UniKineG, which is another deep learning framework, but this is to be able to predict enzymes’ kinetic parameters on the basis of the current atom-level interaction state. Unlike conventional methods that handle proteins and ligands separately, UniKineG integrates both into a unified 3D Euclidean coordinate system via molecular docking. This representation is then constructed into a multimodal heterogeneous graph to preserve the relative spatial orientation of the complex [25]. Crucially, we add a geometric vector perceptron (GVP) module [24] that adds rotation-equivariant processing to be consistent with the complex, no matter the orientation, and captures the directional geometric patterns at the interface. Based on the explicit 3D geometry of the enzyme–substrate complex, UniKineG can greatly reduce the heavy dependency on sequence homology. From our comprehensive benchmarking, UniKineG always outperformed all the current best of the most advanced method, with excellent generalization to out-of-distribution (OOD) datasets, which is an excellent basis for designing an enzyme to catalyze novel substrate specificity.

2. Results

2.1. Overview of the UniKineG Deep Learning Framework

UniKineG creates a geometry-aware prediction pipeline, which is created to be able to predict enzymes’ kinetics through geometry-aware message passing. The pipeline starts by aligning isolated enzyme and substrate structures into a unified 3D Euclidean coordinate system via molecular docking, providing a possible 3D pose for interaction modeling, even if no co-crystal structure is available (Figure 1). Within this unified geometric context, the architecture comprises two tightly coupled subsystems (Figure 2):

Figure 1.

Docked enzyme–substrate complex used to construct 3D interaction graphs. The overall structure of enzyme Q9Y223 with UDP-N-acetyl-α-D-glucosamine docked in the catalytic cleft (protein, ribbon; ligand, sticks), highlighting key contacts between the ligand and surrounding residues.

Figure 2.

Architecture of UniKineG for predicting enzyme kinetic parameters from docked complexes. (a) Protein branch: residue embeddings from ESM-2 are combined with residue-level geometric features derived from the protein structure and encoded by stacked GVPConv layers. (b) Ligand branch: atomic features from the molecular graph and 3D coordinates from the docked pose are encoded by GVPConv layers. (c) Cross-modal fusion: a protein–ligand interaction graph is constructed from spatial contacts and processed by GVP-CrossConv for bidirectional message passing, followed by pooling and an MLP regressor. (d) GVPConv updates scalar and vector channels while preserving SE(3) equivariance.

Multimodal representation and intramolecular modeling (Figure 2a,b,d). UniKineG builds a dual branch input enriched with semantics and physics priors. The enzyme branch is based on ESM-2 evolutionary embeddings, which are concatenated with 30-dimensional physicochemical features (e.g., charge and hydrophobicity), and the substrate branch encodes SMILES using NovoMolGen, which encodes SMILES-derived semantic features as well as 45-dimensional atomic features. The local geometric context is encoded using GVPConv layers in both branches. This module uses coordinate-derived directional vectors to update representations in a direction that can capture directional geometric patterns at the interface. Intermolecular geometric interaction and readout (Figure 2c). For modeling cross-molecular interactions in the docked complex, a heterogeneous graph is built to enable bidirectional geometric message passing with GVPCrossConv. By incorporating relative distances and directional vectors, the model tightly couples the active pocket environment with the substrate’s physicochemical characteristics. Finally, we obtain global scalar and vector representations using weighted pooling and fuse them via an MLP to regress the target kinetic parameters $(k_{\mathit{cat}},{ K}_m, \mathrm{and} k_{\mathit{cat}}/K_m)$.

2.2. Predictive Performance of UniKineG for Enzyme Kinetic Parameters

To verify that UniKineG generalizes beyond mere sequence and scaffold similarities and avoids learning spurious correlations, we adopted the partitioning protocol from CatPred, with minor modifications. Specifically, we established a benchmark setup with a rigorous OOD constraint based on sequence gradients. We constructed two additional OOD scenarios to mimic real-world discovery challenges beyond standard held-out tests. In enzyme generalization, multilevel sequence clustering by CD-HIT was carried out at a gradient of thresholds, and the stringent 40% identity threshold (CD-HIT-40) was chosen as the main reference. At the same time, in order to perform substrate generalization, we added a constraint according to the ECFP4 fingerprint similarity, making the strict Tanimoto coefficient cutoff threshold as the main metric to block information leakage from chemical neighbors (Figure 3).

Figure 3.

Performances of UniKineG and ablated variants under in-distribution and OOD splits. Coefficient of determination (R², computed based on log-transformed targets) for predicting kcat (a), Km (b), and kcat/Km (c) in held-out (in-distribution), enzyme-unseen (maximum sequence identity ≤ 40%; CD-HIT-40), and substrate-unseen (maximum ECFP4 Tanimoto similarity ≤ 0.2) test sets.

Compared against this full evaluation framework, the full UniKineG model achieved strong results for all three prediction tasks on both the held-out split as well as the strict OOD splits (Figure 4d–f). When the held-out testing was performed for UniKineG, the values were all above 0.65, demonstrating exceptional precision. Crucially, the performance was still decent under the harshest enzyme-unseen split (CD-HIT-40), with respectable $R^2$ values of 0.538 for $k_{\mathit{cat}}$ and 0.567 for $K_m$, outperforming standard sequence-based baselines. Similarly, in the strict substrate-unseen setting, stable performance was also observed, indicating that the model is also generalizable to novel unexplored biochemical spaces (Supplementary Table S1).

Figure 4.

Predictive accuracy and ablation analysis of UniKineG. (a–c) Density scatter plots comparing predicted versus experimental values in the test set for (a) $k_{\mathit{cat}}$, (b) ${ K}_m$, and (c) $k_{\mathit{cat}}/K_m$. The color gradient represents the data point density, and Pearson correlation coefficients (PCCs) are annotated in the top left corner. (d–f) Ablation study results illustrating the contributions of geometric components across varying enzyme sequence identity thresholds (CD-HIT) and substrate similarity constraints (Tanimoto). The line charts compare the $R^{2 }$ performance of the full UniKineG model against those of four ablated variants: scalar only (without vector features), distance only (without directional vectors), no cross-graph (without intermolecular message passing), and no geometry (sequence-only baseline) for (d) $k_{\mathit{cat}}$, (e)${ K}_m$, and (f) $k_{\mathit{cat}}/K_m$.

UniKineG consistently secured the highest $R^2$ value and Pearson correlation coefficient (PCC) in challenging OOD settings (Figure 4). For instance, on the CD-HIT-40 split, UniKineG outperformed the top-performing baseline by substantial margins, achieving relative improvements of about 7–10% in correlation metrics for both $k_{\mathit{cat}}$ and $K_m$. A similar trend was observed on the substrate-unseen split, where UniKineG demonstrated superior robustness against structural divergence compared to those of models relying on 1D descriptors.

Finally, ablation studies on the CD-HIT-40 split revealed a distinct hierarchy of geometric contributions (Figure 3). First, structural guidance proved to be foundational: Removing the geometry completely (“no geometry”) caused a performance collapse, with $R^2$ dropping by over 50%, confirming that sequence semantics alone cannot reconstruct the catalytic microenvironment. Second, cross-molecular message passing is essential: The “no cross-graph” variant, which lacks explicit enzyme–substrate interaction modeling, suffered significant degradation, demonstrating that independent molecular encoding (“late fusion”) is insufficient for capturing interfacial dynamics. Most critically, a profound gap persisted between the “distance-only” variant and the full model. The inclusion of vector features yielded a substantial performance boost (raising $R^2$ from 0.398 to 0.538). This gain of approximately 35% underscores the pivotal role of “vector perception”: Unlike scalar distances, which merely define the atomic proximity, the directional vectors within UniKineG capture spatial orientation and angular constraints. This geometric completeness empowers the model to recognize precise orientation-dependent interaction patterns, driving the breakthrough performance in OOD scenarios.

2.3. UniKineG Outperforms Existing Deep Learning Frameworks in Benchmark Assessments

To position UniKineG within the current landscape of computational enzymology, we conducted a systematic benchmarking analysis against four representative models, retraining and evaluating all the frameworks under unified data-splitting protocols to ensure rigorous comparability. The baselines represent distinct evolutionary stages of the field: DLKcat, the pioneer in cross-species deep learning; UniKP, a multitask-learning framework; and the recent CataPro and CatPred, which integrate protein language models with graph neural networks.

UniKineG established a clear performance lead across all three tasks ($k_{\mathit{cat}}$, $K_m$, and $k_{\mathit{cat}}/K_m$), despite the generally high fidelity of all the baselines (Figure 5a–c). For $k_{\mathit{cat}}$ prediction, UniKineG achieved high precision ($R^2 \approx 0.681$), significantly outperforming the strongest baseline, CataPro ($R^2 \approx 0.645$), while earlier models (like DLKcat and UniKP) plateaued at 0.525 and 0.603, respectively. Furthermore, UniKineG reduced the RMSE to 0.972, significantly surpassing the baseline average ($\mathit{RMSE} \approx 1.14$) (Supplementary Table S2). These results suggest that introducing a docking-driven coordinate system can improve accuracy without degrading the distribution performance.

Figure 5.

Model performances across different tasks and data splits. (a,d) $k_{\mathit{cat}}$ prediction. Performance evaluations on enzyme sequence identity splits (CD-HIT) and substrate structural similarity splits (Tanimoto). (b,e) $K_m$ prediction; (c,f) $k_{\mathit{cat}}/K_m$ prediction.

The most distinguishing advantages emerged in rigorous OOD settings. Whether traversing the CD-HIT sequence identity gradient $(\mathrm{from} 99\% \mathrm{to} 40\%)$ or the Tanimoto chemical similarity gradient $(\mathrm{from} 0.4 \mathrm{to} 0.2)$, the trend of the fading heatmap intensity reveals a consistent fact: As the distance from the training distribution increases, baseline models suffer from a pronounced stepwise degradation (Figure 6). Specifically, under the stringent CD-HIT-40 condition, DLKcat experienced a sharp degradation, with its $k_{\mathit{cat}}{R}^2$ value plummeting to 0.151, and even structure-informed models (like CatPred) struggled to maintain fidelity ($R^2 \approx 0.348$). In contrast, UniKineG remained robust, maintaining an $R^2$ value of 0.538, significantly outperforming the runner-up CataPro ($R^2 \approx 0.499$) (Figure 5a). This robustness extends to chemical space: in the $\mathrm{Tanimoto} \tau \le 0.2$ setting for novel substrates, UniKineG maintained $R^2$ scores of 0.495 and 0.563 for $k_{\mathit{cat}}$ and $K_m$, respectively, whereas CataPro dropped to 0.283 and 0.431, and DLKcat fell as low as 0.149 and 0.272 (Figure 5d–f). This consistent ${\mathrm{R}}^2$ value superiority across dual OOD scenarios is visualized by the high-intensity bottom row in (Figure 6). It confirms that UniKineG’s generalization stems not from memorizing outliers but from learning geometry-aware interaction patterns that extend beyond sequence and scaffold similarities.

Figure 6.

Summary of generalization boundaries across different partitions and tasks. The PCC heatmaps demonstrate the evaluation results of five models in retention sets and OOD partitions, covering three modes: retention dataset (CD-HIT consistency from 99% to 40%), enzyme unseen (ECFP4 Tanimoto from 0.4 to 0.2), and substrate unseen. Rows represent partition/task combinations, and columns indicate models.

This systematic superiority can be attributed to fundamental differences in inductive bias. While baselines, like DLKcat and UniKP, rely on “late-stage fusion” to learn statistical correlations, and even CataPro and CatPred integrate structures only implicitly, UniKineG leverages GVP modules to execute geometric vector message passing within a unified coordinate system. By encoding orientation-dependent geometric interaction patterns directly into the representation, UniKineG ensures that predictions are driven by physically rational 3D representations. This marks a shift toward geometry-grounded representations, ensuring robustness, even when sequence homology and scaffold similarity fail.

2.4. Robust Generalization of UniKineG in Independent External Datasets

To assess the model’s generalization beyond our curated benchmark, we evaluated the frozen model in three task-specific external datasets derived from DLKcat (kcat) [11], CatPred-DB (Km) [15], and IECata (kcat/Km) [26].

To ensure the integrity of the evaluation, we implemented a multistage-filtering pipeline to prevent data leakage. Enzyme–substrate pairs overlapping with our benchmark (training/validation/test) were identified and excluded. Specifically, enzymes were matched using sequence hashes (MD5) generated after sequence normalization (whitespace removal and uppercasing). Simultaneously, substrates were standardized using RDKit identifiers, primarily InChIKey, or canonical SMILES, when unavailable, to ensure consistent chemical matching. After filtering and within-set deduplication (median aggregation for repeated pairs), the resulting external benchmarks contained 10,630 kcat, 5023 Km, and 4386 kcat/Km samples.

As summarized in Table 1, the model retains stable predictive performance under expected dataset shifts. For Km prediction, the model achieved PCC = 0.825, R² = 0.608, and RMSE = 1.106, indicating that the learned representations remain consistent with kinetic trends across unseen data. For kcat and kcat/Km, the model achieved R² = 0.545 and 0.523, respectively, and PCC remained robust (>0.78 across all the tasks). A modest attenuation relative to the internal benchmark is expected, likely reflecting heterogeneous experimental conditions (e.g., the pH, temperature, cofactors, and buffer composition) that are not explicitly modeled. Overall, these external results support the model’s utility for ranking enzyme candidates in silico; comparisons with prior work are provided in the discussion.

Table 1.

Predictive performances of UniKineG in independent external validation sets.

Parameter	Dataset Source	Nsamples	R2	RMSE	PCC
Kcat	DLKcat	10,630	0.545	1.188	0.796
Km	CatPred-DB	5023	0.608	1.106	0.825
Kcat/Km	IECata	4386	0.523	1.217	0.783

3. Discussion

Predicting enzyme kinetics is also another part of knowing biocatalytic mechanisms, as well as developing other novel synthesis routes, discovering metabolic routes, and even finding new types of enzymes [27,28]. The UniKineG framework shown in this paper has integrated molecular-docking-derived 3D structural information with GVP neural networks [24] to improve the accuracy and generalization of $k_{\mathit{cat}}$, $K_m$, and $k_{\mathit{cat}}/K_m$. The success of UniKineG signifies more than a performance increment: It shows the value of structure-aware modeling over that of descriptor engineering based on sequences or simple features by explicitly representing enzyme–substrate interaction geometries [29,30]. It could reduce our dependence on sequence homology and improve generalization to less-represented regions of the enzyme–substrate space. Importantly, the use of GVP-based vector features enables orientation-sensitive message passing, and the resulting representations are equivariant to rigid-body rotations and translations of the complex, making the predictor less sensitive to arbitrary coordinate-frame choices and pose orientations. This geometric equivariance improves robustness to coordinate perturbations, but it does not, by itself, constitute the explicit modeling of time-dependent conformational dynamics.

UniKineG’s slightly better results correspond to the 3D interaction context’s importance for kinetic predictions. The strong Km performance $({\mathrm{R}}^2 = 0.724)$ indicates that we may have learned something useful about the interfacial geometry and physicochemical context, which is informative for predicting the correct Km value for us in our benchmark setting. More significantly, for $k_{\mathit{cat}}/K_m$, a frequently used measure of catalytic efficiency [22], UniKineG achieves an $R^2$ value of 0.655, which is better than the strongest baseline on the held-out split. This result suggests that to predict catalytic efficiency, one needs to capture not just that atoms are near each other but also the precise spatial orientation. It also shows that directions of directional geometric features can add information beyond distances alone, possibly even orientation-sensitive interactions [31]. At the same time, we note that kcat is often more coupled to transition-state stabilization and dynamic catalytic events than Km, so a single static conformation may only partially capture the factors governing turnover. UniKineG can be used to prioritize candidates, with small structural differences resulting in large changes in predicted kinetics, and reduce experimental effort. On the contrary, multitask frameworks, such as UniKP, are mostly based on 1D sequence representations [13], whereas CataPro [14], which, although has structural information, does not have any explicit cross-molecular modeling, strengthens our idea that including some kind of explicit cross-molecular message passing is good for our model to be able to model enzyme–substrate interactions.

UniKineG has some new developments, but its limitations cannot be ignored as well. This structure-first approach is a model, so its performance ceiling is naturally limited by the fidelity of the antecedent molecular docking. For docking that is not accurate, especially with very flexible or complex substrates, it may introduce structural noise [32]. In particular, we expect the framework to be more challenged using metalloenzymes and cofactor-dependent enzymes (where catalysis depends on metal ions/cofactors that may be missing or simplified in the docked complex), as well as using enzymes with highly flexible active-site loops or pronounced induced-fit behaviors. But it also means that UniKineG is a model that might be improved upon by advancements in complex structure prediction (such as next-generation approaches, like AlphaFold3 [29]) that can produce better-quality complex geometries and, hence, reduce pose-related noise.

Another important limitation of the current structure-first pipeline is the absence of explicit solvent molecules in docked enzyme–substrate complexes. In many enzymes, structured water molecules are not merely a background solvent but can form conserved hydrogen bond networks and even participate directly in catalytic proton transfers (e.g., “water wires”). Notably, a recent large-scale survey of 1013 high-resolution enzyme crystal structures (<1.5 Å) reported that >99% contain continuous chains of water molecules linking active-site residues to the bulk solvent, highlighting the prevalence of active-site water networks in enzymatic systems. In contrast, standard AutoDock Vina (v1.2.6) docking typically treats solvation implicitly and does not represent conserved/bound water explicitly, which can alter the effective binding-site topology and local hydrogen bond geometry and may contribute to pose or scoring errors. Prior docking benchmarks have shown that incorporating carefully selected key water molecules may improve pose predictions, whereas including all the binding-site water molecules indiscriminately can reduce performance. Therefore, incorporating explicit “bridging” water molecules is a promising direction for future extensions of UniKineG, for example, by leveraging hydrated docking protocols available in the AutoDock suite Vina and further representing retained water molecules as additional nodes/edges in the heterogeneous interaction graph.

Although the AlphaFold structures used herein are generally high confidence at the dataset level (as reflected by Avg. pLDDT statistics), we do not yet incorporate the residue-level pLDDT or PAE into the docking and graph construction steps, nor do we explicitly propagate structural uncertainty into the downstream predictor. Future work could integrate confidence-weighted node/edge features (e.g., down-weighting low-confidence regions), PAE-informed uncertainty in inter-residue geometries, and uncertainty-aware message passing to improve robustness when structural priors are less reliable.

Furthermore, we also use this architecture, which relies heavily on static docked conformations and does not explicitly account for “induced-fit” effects or conformational ensembles [33]. More broadly, dynamic effects relevant to enzyme catalysis, such as conformational flexibility, induced-fit rearrangements, and transition-state stabilization, are not explicitly modeled in the current pipeline, which is particularly relevant for kcat prediction. Since catalysis is inherently dynamic, it is therefore promising to model these transient catalytic states through incorporating MD-derived ensembles (or multiple alternative docked poses as a lightweight ensemble) or expanding SE(3)-equivariant architectures [34] to better capture the variability of conformations. Additionally, because explicit geometric modeling is more computationally expensive, the next work will try to use model distillation to find a balance between being precise and the throughput that is required to screen a library scale [35].

Another limitation is that experimental assay conditions (e.g., the pH, temperature, buffer composition, and cofactors) are not incorporated, primarily because such metadata are inconsistently reported across sources. As a result, we treat kinetic labels as condition agnostic, which may introduce heterogeneous measurement noise and contribute to dataset shifts when evaluating across studies from different laboratories.

This point may partially explain why performance can attenuate on external benchmarks and motivates future work to curate condition metadata when available, include assay covariates as model inputs, or adopt uncertainty-aware objectives that account for label heterogeneity.

Finally, while UniKineG improves predictions using explicit geometry, we did not include a dedicated interpretability and attribution analysis to connect learned geometric features to specific catalytic residues or mechanistic interactions. This is mainly due to the lack of a consistent residue-level mechanistic ground truth at our dataset scale and the effects of the high computational cost and potential instability of perturbation-based explanations (e.g., SHAP-style methods) [36] on residue-level geometric graphs. Therefore, we position the current work as a predictive framework rather than a mechanistic inference tool, and we avoid making residue-level mechanistic claims. In future work, we will explore attribution methods tailored to geometric GNNs (e.g., saliency/IG and attention/edge attribution) on smaller curated benchmarks, where catalytic residues or key interactions are experimentally characterized.

Looking forward, UniKineG opens some promising research directions. We want to try combining QM-derived descriptors with geometric deep learning to be able to obtain reaction energetics beyond purely geometric cues [37]. Second, with the expansion of the graph definition, it can also be applied to multisubstrate reactions, allosteric regulation, and inhibitor design [38]. In the end, we hope for a long-term view of developing a generative paradigm that can reduce our reliance on experimentally derived complex structures and allow for more direct links from sequences to predicted functions [39]. To summarize, with UniKineG, by leveraging structural and geometric priors with geometric deep learning, a robust kinetic predictor is given, as well as the practical scalability of structure–kinetic relationship exploration.

4. Methods

4.1. Dataset Curation and Structural Annotation

Data Source and Initial Filtering. In order to create a high-quality benchmark for the structure-aware kinetic predictor, our data were sourced from the publicly available CataPro repository [14], which contains enzymes’ amino acid sequences, substrates’ SMILES strings, and corresponding kinetic parameters ($k_{\mathit{cat}} \mathrm{and} K_m$). We implemented a multistage curation pipeline to remove incomplete records and standardize inputs. At first, we filtered the entries to keep only the ones that had complete multimodal information: full-length amino acid sequences, validatable SMILES strings, and experimentally determined kinetic values. We do not have a model for the assay conditions (e.g., the pH and temperature) because they are not uniformly reported in different sources, so we treated the reported kinetics as condition-agnostic labels.

Three-Dimensional Structural Generation and Pocket Profiling. Since experimental structures for enzyme–substrate complexes are sparse, we generated reliable 3D structural priors via computational docking. For each enzyme–substrate pair, the substrate’s SMILES was converted to a 3D conformer. For each enzyme, we retrieved the predicted 3D structure from the AlphaFold Protein Structure Database [40,41], using its UniProt [42] accession.

To assess the reliability of AlphaFold-derived structural inputs, we extracted per-residue pLDDT scores from the AlphaFold models (stored in the PDB/mmCIF temperature factor (B-factor) field provided by AlphaFold) and computed a protein-level average pLDDT (Avg. pLDDT) for each unique enzyme structure (N = 6003). The Avg. pLDDT distribution suggests that the AlphaFold-derived enzyme backbones are predominantly high confidence at the dataset level (mean = 93.52, median = 94.91, P5/P95 = 84.08/97.94, and min/max = 37.22/98.72; 84.61% of the enzymes have an Avg. pLDDT of ≥90, and 99.45% have and Avg. pLDDT of ≥70).

We identified candidate binding pockets using FPocket [41] and defined the docking search box (center coordinates and box dimensions) based on the top-ranked pocket. Docking was performed using AutoDock Vina (v1.2.6) [25,43], a rigid receptor, and a flexible ligand within this FPocket-derived search space, and the top-scoring pose was selected to obtain the enzyme–substrate complex geometry (atomic coordinates) for downstream featurization. At present, these confidence metrics (including the PAE) are not used as model features, and structural uncertainty is not explicitly propagated through docking or complex graph construction.

Wild-type Verification and Noise Elimination. A crucial quality-control step attended to implicit vagueness in the initial repository: Wild-type enzymes and their point mutants frequently possessed the same UniProt IDs, thus generating “label noise” sequence variations, which became decoupled from kinetic changes. Given that an individual point mutant was capable of seriously skewing its catalytic efficiency, we conducted a rigorous reannotation process. We used sequence alignment against the UniProt reference database [42] to make it explicit which were wild-type sequences and which were variants. To guarantee that structure–function relationships learned by the model were clean from any contamination from the mutant structures, only verified wild-type enzyme samples were retained for the final training set.

Final Dataset Statistics. We ended up with a dataset of 15,591 high-confidence enzyme–substrate pairs with an abundant tensor of multimodal features, such as 1D amino acid sequences, 2D molecular graphs (from SMILES), 3D pocket coordinates, and the experimental kinetic labels. This curated dataset served as the ground truth for training and evaluating the UniKineG framework.

4.2. Dataset-Splitting Strategies

Standard random splitting. For the baseline performance assessment, we adopted a random split, partitioning the dataset into training (80%), validation (10%), and held-out testing (10%) sets. This split evaluates the model’s ability to interpolate within the known distribution of enzyme–substrate interactions, serving as a reference point for the idealized performance.

Enzyme-unseen OOD evaluation. To assess generalization to novel enzymes, we constructed OOD splits by clustering enzyme sequences with CD-HIT at sequence identity thresholds of 99%, 80%, 60%, and 40%. For each threshold, we performed cluster-level splitting, such that sequences from the same CD-HIT cluster were assigned to only one split, ensuring that every test sequence had the same or a smaller specified identity compared to those of all the training sequences. The 40% cutoff threshold probes the low-homology regime, where sequence similarity provides limited guidance.

Substrate-unseen OOD evaluation. To evaluate the model’s generalization to novel chemical structures, we constructed OOD splits based on ECFP4 fingerprint similarity and Tanimoto coefficients. Specifically, we required each test substrate to have a maximum Tanimoto similarity to any training substrate of τ ≤ 0.4, 0.3, or 0.2. These splits emulate scenarios where predictions are required for compounds substantially dissimilar to those seen during training.

4.3. Representation Learning of Enzymes and Substrates

Enzyme and substrate feature encoding. We encoded enzymes and substrates using pretrained sequence models together with physicochemical descriptors. For enzyme representation, amino acid sequences were processed with ESM-2 (checkpoint: esm2_t33_650M_UR50D) to obtain 1280-dimensional per-residue embeddings, which were extracted from the final transformer layer [44]. We concatenated each residue embedding with a 30-dimensional vector of residue-level physicochemical features (e.g., charge, hydrophobicity, side chain volume) computed from a fixed feature table provided with our code. For substrate representation, we encoded SMILES strings into 768-dimensional embeddings using the pretrained NovoMolGen model [45]. In addition, we computed 45 global molecular descriptors (e.g., logP [46] and the topological polar surface area) from a fixed descriptor table provided with our code and concatenated them with the NovoMolGen embedding.

4.4. Graph Structure Construction

To comprehensively characterize the complex spatial and chemical dependencies within the enzyme–substrate complex, we constructed three interconnected graph structures:

Protein residue graph construction. To balance the computational cost and structural context between computational efficiency and structural information retention, we constructed a residue-level graph for the enzyme. Nodes represent amino acid residues, initialized with the concatenated features of ESM-2 embeddings [44] and 30-dimensional physicochemical vectors. Edges were established between residues, based on spatial proximity: An edge exists if the Euclidean distance between their $C_{\alpha }$ atoms in 3D space is <$10 \AA$. This topology captures the enzyme’s tertiary structure and local pocket geometry. This cutoff threshold is used during graph preconstruction; distance and direction features are computed from node coordinates during message passing.

Substrate molecular graph construction. The substrate was represented as a 2D molecular graph encoding its chemical topology. Nodes correspond to atoms, each featurized by a 45-dimensional vector capturing atomic chemical properties (e.g., atom type, degree, and hybridization state). Edges are defined based on covalent bonds parsed from SMILES strings using RDKit, representing the intrinsic connectivity of the small molecule.

Enzyme–substrate heterogeneous interaction graph. Serving as the core component for explicit intermolecular modeling, we constructed a heterogeneous graph that unifies the enzyme and substrate. The node set comprises the union of enzyme residues and substrate atoms. Intermolecular edges were constructed based on the 3D conformation generated using molecular docking: A connection is established if the spatial distance between any heavy atom of an enzyme residue and a substrate atom is <$5 \AA$. Each intermolecular edge is annotated with geometric features computed from 3D coordinates, including the Euclidean distance and the unit direction vector, which are used as scalar and vector-edge features for geometric message passing.

4.5. UniKineG Network Architecture and Implementation Details

The UniKineG framework was implemented using Python (3.9.19) and PyTorch Geometric (2.6.1) [47]. To initialize the graph with rich semantic priors, we employed a dual-encoder strategy, where enzyme sequences were encoded using the pretrained ESM-2 model (specifically, ESM-2-650M, generating 1280-dimensional embeddings), and substrates were encoded using NovoMolGen (768 dimensions) fused with discrete physicochemical attributes. The core of UniKineG lies in its explicit handling of 3D geometry within a unified coordinate system. We constructed a heterogeneous graph where intraprotein edges represent the geometric/backbone proximity, intraligand edges represent covalent bonds, and bidirectional intermolecular edges are established based on the docking geometry. To explicitly preserve rotational and translational equivariances, node features were split into scalar and vector channels. Vector features were initialized as displacement vectors relative to the sub-graph’s centroid (pos-centroid), replicated across vector channels, while edge features incorporated Euclidean distances (utilized directly as scalars without radial basis function expansion) and unit direction vectors.

The network architecture stacks multiple layers of GVPConv (geometric vector perceptron convolution) to extract intragraph structural features, followed by GVPCrossConv layers that execute bidirectional message passing (protein-to-ligand and ligand-to-protein) to model the interface. The readout phase applies weighted mean/max/add pooling operations to both scalar channels and vector norms, followed by a fusion multilayer perceptron (MLP) to output the target kinetic parameter. We trained independent regression models for $k_{\mathit{cat}}$, $K_m$, and $k_{\mathit{cat}}/K_m$ using the AdamW optimizer [48] with a batch size of 32. The optimization hyperparameters were strictly configured with an initial learning rate of $3 \times 10^{-4}$, a weight decay of $2 \times 10^{-4}$, and coefficients ${\beta }_1 = 0.9$, ${\beta }_2 = 0.999$, and $ϵ = 10^{-8}$. The learning rate followed a warmup cosine annealing schedule, comprising a linear warmup for the first five epochs, followed by cosine decay to near zero over one hundred fifteen epochs. The objective function was a weighted combination of the MSE and Huber loss ($\delta = 0.5$) in a ratio of 0.7:0.3. To mitigate overfitting and ensure robust generalization, we implemented a suite of regularization techniques: feature-level noise augmentation (with a probability of 0.2, generating a perturbed copy of each graph by adding Gaussian noise with σ = 0.005 to randomly selected node feature elements), gradient clipping (with a maximum norm of 0.8), and an early stopping mechanism (with a patience of 25 epochs). Computational cost and scalability. All the experiments were conducted on a single NVIDIA GeForce RTX 4090 GPU (24 GB). With early stopping, a typical training run per task takes approximately 6 h. For scalability, once complex geometries are prepared, the predictor supports batched inference and can be applied to large enzyme–substrate libraries for high-throughput candidate ranking.

4.6. Deep Learning Pipeline for Turnover Number Prediction in UniKineG

To initialize the heterogeneous graph ($G = (V,\mathrm{E})$), we extract raw features from pretrained models. For protein nodes, sequence embeddings (${\mathrm{x}}^{\left(p\right)}$) are derived from ESM-2 (model esm2_t33_650M_UR50D); for substrate nodes, molecular embeddings (${\mathrm{x}}^{\left(l\right)}$) are obtained from NovoMolGen. These features are projected into a unified latent dimension ($d_{\mathrm{model}}$) via linear transformation and layer normalization (LN). To incorporate 3D geometry, let ${\mathrm{r}}_k$ denote the coordinate of node k. We compute the centroid ($c$) for each graph and construct translation-invariant vector features (${\mathrm{V}}_{\mathrm{k}}^{\left(0\right)}$) as follows:

$${\mathrm{s}}_i^{\left(p\right)}=\mathrm{L}\mathrm{N}\left({\mathrm{W}}_p{\mathrm{x}}_i^{\left(p\right)}\right),\hspace{1em}{\mathrm{s}}_j^{\left(l\right)}=\mathrm{L}\mathrm{N}\left({\mathrm{W}}_l{\mathrm{x}}_j^{\left(l\right)}\right)$$ (1)

$${\mathrm{V}}_k^{\left(0\right)}={\mathrm{r}}_k-\mathrm{c}$$ (2)

For any edge connecting node $u$ to $v$ (intramolecular or intermolecular), we compute the relative coordinate vector ($\Delta {\mathrm{r}}_{\mathit{uv}}$) and the Euclidean distance ($d_{\mathit{uv}}$) on the fly. To ensure numerical stability, the normalized unit direction vector (${\widehat{\mathrm{u}}}_{\mathit{uv}}$) is derived by adding a small constant ($\mathsf{ϵ}$) to the denominator. These geometric attributes are fed into the model as scalar edge features (${\mathrm{e}}_{\mathit{uv}}^s$) and vector edge features (${\mathrm{e}}_{\mathit{uv}}^v$), explicitly driving the geometric information flow while preserving $\mathrm{SE}\left(3\right)$ equivariance as follows:

$$\Delta {\mathrm{r}}_{uv}={\mathrm{r}}_v-{\mathrm{r}}_u,\hspace{1em}{d}_{uv}=\Vert \Delta {\mathrm{r}}_{uv}{\Vert }_2,\hspace{1em}{\widehat{\mathrm{u}}}_{uv}={\displaystyle \frac{\Delta {\mathrm{r}}_{uv}}{\Vert \Delta {\mathrm{r}}_{uv}{\Vert }_2+\mathsf{ϵ}}}$$ (3)

The GVP module processes scalar and vector features to update node representations. To preserve 3D structural information, the vector channel undergoes a linear combination, followed by L2 norm extraction. Let $\mathsf{\sigma }$ and $\mathsf{\varphi }$ denote the sigmoid and ReLU activation functions, respectively. The vector-gating mechanism is formulated as follows:

$${\mathrm{V}}^{\prime }={\mathrm{W}}_v\mathrm{V},\hspace{1em}{\mathrm{s}}^{\prime }={\mathrm{W}}_s(\mathrm{s}\parallel \Vert {\mathrm{V}}^{\prime }{\Vert }_2)$$ (4)

$${\mathrm{V}}_{\mathrm{o}\mathrm{u}\mathrm{t}}=\mathsf{\varphi }\left({\mathrm{V}}^{\prime }\right)\odot \mathsf{\sigma }\left({\mathrm{W}}_g{\mathrm{s}}^{\prime }\right)$$ (5)

We stack three layers of GVPConv independently for the protein and substrate graphs. At layer $t$, the update rule for node $v$ aggregates geometric messages from its neighbors ($N\left(v\right)$). The message aggregation step sums the scalar messages (${\mathrm{m}}_s$) and vector messages (${\mathrm{m}}_v$) derived from incident edges as follows:

$$({\widehat{\mathrm{s}}}_{uv},{\widehat{\mathrm{V}}}_{uv})={\mathrm{G}\mathrm{V}\mathrm{P}}_{\mathrm{m}\mathrm{s}\mathrm{g}}\left(\right[{\mathrm{s}}_u^{(t-1)}\parallel {\mathrm{e}}_{uv}^s],[{\mathrm{V}}_u^{(t-1)}\parallel {\mathrm{e}}_{uv}^v\left]\right)$$ (6)

$${\mathrm{m}}_s={\sum _{u\in \mathcal{N}\left(v\right)}\widehat{\mathrm{s}}}_{uv},\hspace{1em}{\mathrm{m}}_v={\sum _{u\in \mathcal{N}\left(v\right)}\widehat{\mathrm{V}}}_{uv}$$ (7)

$$({\mathrm{s}}_v^{\left(t\right)},{\mathrm{V}}_v^{\left(t\right)})=({\mathrm{s}}_v^{(t-1)},{\mathrm{V}}_v^{(t-1)})+{\mathrm{G}\mathrm{V}\mathrm{P}}_{\mathrm{u}\mathrm{p}\mathrm{d}}\left(\right[{\mathrm{s}}_v^{(t-1)}\parallel {\mathrm{m}}_s],[{\mathrm{V}}_v^{(t-1)}\parallel {\mathrm{m}}_v\left]\right)$$ (8)

To model the enzyme–substrate interface, we perform bidirectional cross-graph convolutions. This process allows information to flow across bipartite interface edges ($E_{\mathrm{cross}}$), updating substrate features based on the enzyme context and vice versa, utilizing the same GVP-based message-passing mechanism as follows:

$$({\mathrm{s}}^{\left(l\right)},{\mathrm{V}}^{\left(l\right)})\leftarrow \mathrm{C}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}\mathrm{G}\mathrm{V}\mathrm{P}({\mathrm{s}}^{\left(p\right)},{\mathrm{V}}^{\left(p\right)},{\mathcal{E}}_{p\to l})$$ (9)

$$({\mathrm{s}}^{\left(p\right)},{\mathrm{V}}^{\left(p\right)})\leftarrow \mathrm{C}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}\mathrm{G}\mathrm{V}\mathrm{P}({\mathrm{s}}^{\left(l\right)},{\mathrm{V}}^{\left(l\right)},{\mathcal{E}}_{l\to p})$$ (10)

Global representations for the protein and substrate are obtained using a weighted multiview-pooling strategy. We fuse $\mathrm{mean}$, $\max$, and $\mathrm{sum}$ pooling operations using learnable scalar weights ($w$). The final graph representation ($z_{\mathrm{graph}}$) is constructed by concatenating the pooled scalar features and vector norms. This unified embedding is then passed through an $\mathrm{MLP}$ regression head to predict the target kinetic parameter ($\widehat{y}$) as follows:

$$\mathrm{P}\mathrm{o}\mathrm{o}\mathrm{l}\left(\mathrm{X}\right)=w_1\mathrm{mean}\left(\mathrm{X}\right)+w_2\max (\mathrm{X})+w_3\mathrm{sum}(\mathrm{X})$$ (11)

$$\widehat{y}={\mathrm{M}\mathrm{L}\mathrm{P}}_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}}\left(\right[\mathrm{Pool}\left(s^{\left(p\right)}\right)\parallel \mathrm{Pool}(\Vert {\mathrm{V}}^{\left(p\right)}{\Vert }_2)\parallel \mathrm{Pool}\left({\mathrm{s}}^{\left(l\right)}\right)\parallel \mathrm{Pool}(\Vert {\mathrm{V}}^{\left(l\right)}{\Vert }_2)\left]\right)$$ (12)

4.7. Statistical Evaluation Metrics

We rigorously evaluated the regression performance of UniKineG across distinct testing scenarios (including held-out, enzyme-unseen, and substrate-unseen splits). For each kinetic target ($k_{\mathit{cat}}$, $K_m$, and $k_{\mathit{cat}}/K_m$), we calculated the following metrics independently. The coefficient of determination ($R^2$) measures the proportion of the variance in the dependent variable explained by the model relative to a mean-only baseline as follows:

$$R^2=1-{\displaystyle \frac{\sum _{i=1}^n(y_i-{\widehat{y}}_i{)}^2}{\sum _{i=1}^n(y_i-\overline{y}{)}^2}}$$ (13)

The root-mean-square error ($\mathrm{RMSE}$) quantifies the magnitude of the prediction error, assigning higher penalties to large deviations. The Pearson correlation coefficient ($r$) evaluates the linear correlation between predicted and experimental values, independent of the scale, as follows:

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n(y_i-{\widehat{y}}_i{)}^2}$$ (14)

$$r={\displaystyle \frac{\sum _{i=1}^n(y_i-\overline{y}\left)\right({\widehat{y}}_i-\overline{\widehat{y}})}{\sqrt{\sum _{i=1}^n(y_i-\overline{y}{)}^2}\sqrt{\sum _{i=1}^n({\widehat{y}}_i-\overline{\widehat{y}}{)}^2}}}$$ (15)

where n denotes the total number of samples, $y_i$ represents the log₁₀-transformed experimental value for the $i$th sample, and ${\widehat{y}}_i$ is the corresponding predicted value. Additionally, $\overline{y}$ and $\overline{\widehat{y}}$ denote the means of the experimental and predicted values, respectively.

4.8. Benchmarking Against Representative Deep Learning Models

We benchmarked UniKineG against four representative models (DLKcat, UniKP, CataPro, and CatPred) by retraining their original implementations on identical data splits with fixed random seeds to ensure equitable comparisons. Model generalization was evaluated across three distinct scenarios: a standard held-out test set created by randomly sampling 10% of the dataset; an enzyme-unseen split, where proteins were clustered via CD-HIT at a strict 40% identity threshold (with sensitivity analyses at relaxed thresholds of 60%, 80%, and 99%) to prevent homologous leakage; and a substrate-unseen split based on Bemis–Murcko scaffolds, where we enforced rigorous structural separation by constraining the maximum Tanimoto similarity (using ECFP4 fingerprints) between training and testing molecules to $\tau \le 0.2$, alongside robustness checks at looser thresholds of 0.3 and 0.4.

5. Conclusions

In this study, we developed UniKineG, a structure-guided deep learning framework for predicting enzyme kinetic parameters by integrating enzyme structures and substrate molecules into a shared 3D coordinate system through molecular docking. By representing the docking-aligned enzyme–substrate spatial context as a heterogeneous graph and performing rotation-aware geometric message passing with GVPs, UniKineG explicitly leverages intermolecular geometry to learn interaction patterns relevant to $k_{\mathit{cat}},K_m, \mathrm{and} k_{\mathit{cat}}/K_m$.

Using a curated benchmark of 15,591 wild-type enzyme–substrate pairs, UniKineG achieved strong accuracy in held-out evaluations and remained robust in stringent OOD settings that excluded close enzyme homologs (CD-HIT) and chemically similar substrates (ECFP4, Tanimoto). Ablation analyses indicate that docking-derived geometry, explicit cross-molecular message passing, and directional (vector) geometric features each contribute substantially beyond distance-only proximity, supporting the importance of orientation-sensitive representations for structure-grounded kinetic prediction in diverse biochemical spaces.

The framework depends on the fidelity of docking poses and currently uses static conformations; moreover, assay conditions, such as pH and temperature, were not modeled due to inconsistent reporting across data sources. Future work may incorporate improved complex geometry estimation, conformational ensembles, and complementary energetic descriptors to better capture catalysis-relevant effects. Overall, UniKineG provides a practical computational route for structure-aware kinetic annotation and offers a scalable foundation for exploring structure–kinetic relationships in enzyme discovery, pathway design, and enzyme engineering.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/ijms27041731/s1.

Author Contributions

Conceptualization, X.W. and P.S.; methodology, X.W.; data curation, X.W.; validation, P.S., K.L. and S.L.; writing—original draft preparation, X.W.; writing—review and editing, P.S. and S.L.; funding acquisition, S.L. and J.M. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data supporting the results of this study can be found in the article and Supplementary Materials. The raw data of the enzyme kinetic parameters used for curating UniKineG are available at BRENDA (https://www.brenda-enzymes.org/ (accessed on 11 September 2025)) and SABIO-RK (http://sabio.h-its.org/ (accessed on 11 September 2025)). The enzyme sequence data and AlphaFold-predicted enzyme structures are available at UniProt (https://www.uniprot.org/ (accessed on 11 September 2025)). The processed UniKineG datasets are available at Zenodo (https://doi.org/10.5281/zenodo.18125285 (accessed on 2 January 2026)).

Conflicts of Interest

The authors declare no conflicts of interest.

Funding Statement

This work was financially supported by the National Natural Science Foundation of China (22138004), Zhejiang Province Local Collaborative Innovation Project (2024SDXT001-3), and National Engineering Research Center of Solid-State Brewing.