Multimodal Protein Language Models for Enzyme Kinetic Parameters: From Substrate Recognition to Conformational Adaptation

Fei Wang; Xinye Zheng; Kun Li; Yanyan Wei; Yuxin Liu; Ganpeng Hu; Tong Bao; Jingwen Yang

cs.CVMar 13, 2026

Multimodal Protein Language Models for Enzyme Kinetic Parameters: From Substrate Recognition to Conformational Adaptation

Authors: Fei Wang, Xinye Zheng, Kun Li, Yanyan Wei, Yuxin Liu, Ganpeng Hu, Tong Bao, Jingwen Yang

Organizations: School of Computer Science and Information Engineering, Hefei University of Technology · Institute of Artificial Intelligence, Hefei Comprehensive National Science Center · CVLab, College of Information Technology, United Arab Emirates University · Intelligent Interconnected Systems Laboratory of Anhui Province ·

Abstract

Predicting enzyme kinetic parameters quantifies how efficiently an enzyme catalyzes a specific substrate under defined biochemical conditions. Canonical parameters such as the turnover number ( $k_\text{cat}$ ), Michaelis constant ( $K_\text{m}$ ), and inhibition constant ( $K_\text{i}$ ) depend jointly on the enzyme sequence, the substrate chemistry, and the conformational adaptation of the active site during binding. Many learning pipelines simplify this process to a static compatibility problem between the enzyme and substrate, fusing their representations through shallow operations and regressing a single value. Such formulations overlook the staged nature of catalysis, which involves both substrate recognition and conformational adaptation. In this regard, we reformulate kinetic prediction as a staged multimodal conditional modeling problem and introduce the Enzyme-Reaction Bridging Adapter (ERBA), which injects cross-modal information via fine-tuning into Protein Language Models (PLMs) while preserving their biochemical priors. ERBA performs conditioning in two stages: Molecular Recognition Cross-Attention (MRCA) first injects substrate information into the enzyme representation to capture specificity; Geometry-aware Mixture-of-Experts (G-MoE) then integrates active-site structure and routes samples to pocket-specialized experts to reflect induced fit. To maintain semantic fidelity, Enzyme-Substrate Distribution Alignment (ESDA) enforces distributional consistency within the PLM manifold in a reproducing kernel Hilbert space. Experiments across three kinetic endpoints and multiple PLM backbones, ERBA delivers consistent gains and stronger out-of-distribution performance compared with sequence-only and shallow-fusion baselines, offering a biologically grounded route to scalable kinetic prediction and a foundation for adding cofactors, mutations, and time-resolved structural cues.

Figures & tables

Figure 2: Architecture of the proposed ERBA. It augments a sequence-only PLM with multimodal conditioning on substrate chemistry and pocket geometry. MRCA injects substrate fingerprints into enzyme embeddings to capture recognition specificity, and G-MoE integrates local 3D pocket structure to model conformational adaptation. Update and query paths couple both modules to the backbone, while ESDA aligns representations with the prior PLM, enabling accurate prediction of enzyme kinetic parameters.

Figure 3: G-Gating & Router pools sequence-substrate and structural cues to produce gating logits, activate the top- k geometry-relevant experts, and suppress others. Selected experts transform structure-conditioned features, and an MLP fuses them into a geometry-adaptive representation for kinetic regression.

Method	Venue	Modality			Kinetic Endpoint: $k_{\text{cat}}$				Kinetic Endpoint: $K_{\text{m}}$				Kinetic Endpoint: $K_{\text{i}}$
Method	Venue	$\mathbf{S}_{e}$	$\mathbf{S}_{m}$	$\mathbf{S}_{g}$	R 2 ↑	PCC↑	RMSE↓	MAE↓	R 2 ↑	PCC↑	RMSE↓	MAE↓	R 2 ↑	PCC↑	RMSE↓	MAE↓
Exp I: Existing SOTA Models
DLKcat [ 78 ]	Nat.Catal 2022	✓	✓	-	0.01	0.37	1.78	1.30	-	-	-	-	-	-	-	-
TurNup [ 76 ]	Nat.C 2023	✓	✓	-	0.39	0.65	1.60	1.19	-	-	-	-	-	-	-	-
UniKP [ 61 ]	Nat.C 2023	✓	✓	-	0.13	0.42	1.56	1.14	0.36	0.63	1.02	0.78	-	-	-	-
MPEK [ 48 ]	Brief.Bio 2024	✓	✓	-	0.33	0.59	1.34	1.05	0.30	0.56	1.40	1.09	-	-	-	-

Table 1: Performance comparison of existing SOTA methods and fine-tuned PLM backbones on enzyme kinetic prediction tasks. Results are presented for three kinetic parameters: turnover number (

k_{\text{cat}}

), Michaelis constant (

K_{\text{m}}

), and inhibition constant (

K_{\text{i}}

). The performance metrics include R 2 ↑, PCC↑, RMSE↓, and MAE↓. ERBA consistently outperforms the baselines across all metrics. Notably, the best value in each column is highlighted in red , and the second best in blue . ‡ indicates that the backbone of the PLMs is fine-tuned.

Index	Class Name	Kinetic Endpoint: $k_{\text{cat}}$					Kinetic Endpoint: $K_{\text{m}}$					Kinetic Endpoint: $K_{\text{i}}$
Index	Class Name	Count	R 2 $\uparrow$	PCC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	Count	R 2 $\uparrow$	PCC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	Count	R 2 $\uparrow$	PCC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$
EC-1	Oxidoreductases	679	0.37	0.62	1.32	0.95	1,382	0.55	0.74	0.90	0.69	282	0.58	0.77	1.19	0.92
EC-2	Transferases	334	0.46	0.69	1.22	0.87	1,000	0.53	0.73	0.81	0.61	270	0.38	0.65	1.37	0.99
EC-3	Hydrolases	682	0.43	0.68	1.18	0.88	1,145	0.51	0.72	0.90	0.65	408	0.48	0.71	1.50	1.10
EC-4	Lyases	131	0.50	0.71	1.27	0.92	293	0.56	0.75	0.81	0.61	157	0.65	0.81	1.19	0.84
EC-5	Isomerases	72	0.46	0.73	1.39	0.94	123	0.61	0.78	0.84	0.64	42	0.67	0.83	1.20	0.95

Table 2: Enzyme category analysis across kinetic prediction tasks. The table provides a breakdown of enzyme categories in the datasets for

k_{\text{cat}}

K_{\text{m}}

, and

K_{\text{i}}

prediction tasks. It includes the distribution of each enzyme class, the number of samples per category, and performance metrics for each class. Notably, the best value in each column is highlighted in red , and the second best in blue .

Method	OOD Test @EITLEM- $k_{\text{cat}}$				OOD Test @EITLEM- $K_{\text{m}}$
Method	R 2 ↑	PCC↑	RMSE↓	MAE↓	R 2 ↑	PCC↑	RMSE↓	MAE↓
DLKcat [ 78 ]	0.01	0.15	3.87	3.05	-	-	-	-
TurNup [ 76 ]	0.21	0.38	2.46	2.11	-	-	-	-
UniKP [ 61 ]	0.08	0.20	1.76	1.24	0.14	0.32	1.54	1.08
MPEK [ 48 ]	0.17	0.41	1.65	1.18	0.12	0.35	1.71	1.32
EITLEM [ 82 ]	0.27	0.50	1.43	0.95	0.23	0.43	1.31	1.03

Table 3: Comparison with existing SOTA models on OOD tests.

k_{\text{cat}}

and

K_{\text{m}}

using the EITLEM [ 82 ] test sets.

Figure 4: Log-scaled experimental versus predicted values for the kinetic parameters $k_{\text{cat}}$ , $K_{\text{m}}$ , and $K_{\text{i}}$ . Each plot shows the absolute error less than or equal to 1 as a percentage, denoted as 1- $\text{Radio}_{\text{AE}}$ . The dashed red line represents perfect predictions.

Figure 5: Ablation studies on fusion order and manner. Comparison of different fusion strategies: $\mathbf{S}_{e}$ → $\mathbf{S}_{g}$ → $\mathbf{S}_{m}$ , Concat & MLP, and the proposed $\mathbf{S}_{e}$ → $\mathbf{S}_{m}$ → $\mathbf{S}_{g}$ /ERBA. Percentage improvements across metrics are highlighted in red .

Method	Modality			Kinetic Endpoint: $K_{\text{i}}$
Method	$\mathbf{S}_{e}$	$\mathbf{S}_{m}$	$\mathbf{S}_{g}$	R 2 ↑	PCC↑	RMSE↓	MAE↓
PLM Baseline	✓	-	-	0.49	0.71	1.38	1.05
w / MRCA	✓	✓	-	0.51	0.73	1.32	0.98
w / G-MoE	✓	✓	✓	0.54	0.74	1.27	0.94
w / ESDA (Ours)	✓	✓	✓	0.61	0.78	1.26	0.91

Table 4: Ablation study on the effect of different modules. Performance comparison for

K_{i}

prediction with various configurations: PLM baseline, MRCA, G-MoE, and our ESDA framework.

Class	Kinetic Dataset			Total	Details
Class	$\mathit{k}_{\text{cat}}$	$K_{\text{m}}$	$K_{\text{i}}$	Total
Dataset I (Main Test): $k_{\text{cat}},K_{\text{m}}$ and $K_{\text{i}}$ from [ 71 ]
Entries	23,151	41,174	11,929	76,254
EC 1 Oxidoreductases	7,756	13,931	2,744	24,431	Oxidoreductases catalyze diverse redox reactions by transferring electrons between molecules and substrates, and represent the largest EC class with broad kinetic and functional diversity.
EC 2 Transferases	4,155	10,182	2,706	17,043	Transferases catalyze the transfer of functional groups between diverse substrates, enabling the formation of new chemical bonds and the rapid and efficient interconversion of molecules.
EC 3 Hydrolases	8,065	11,025	4,083	23,173	Hydrolases catalyze the hydrolysis of diverse chemical bonds in biological molecules. They efficiently cleave covalent linkages in various substrates with variable enzyme kinetic parameters.

Table 5: Detailed breakdown of the enzyme kinetic datasets from [ 71 , 82 ] used for training and out-of-distribution (OOD) testing. We provide the number of entries, unique sequences, EC classes, organisms, and additional information for each enzyme class in the main and OOD test datasets.

Index	Class Name	Kinetic Endpoint: $k_{\text{cat}}$				Kinetic Endpoint: $K_{\text{m}}$				Kinetic Endpoint: $K_{\text{i}}$
Index	Class Name	R 2 $\uparrow$	PCC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	R 2 $\uparrow$	PCC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	R 2 $\uparrow$	PCC $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$
(a) Ankh3-5.7B [ 70 ] w/ ERBA
EC-1	Oxidoreductases	0.39	0.68	1.25	0.89	0.51	0.78	0.83	0.61	0.53	0.73	1.29	0.96
EC-2	Transferases	0.44	0.65	1.23	0.87	0.55	0.74	0.78	0.58	0.39	0.65	1.27	0.97
EC-3	Hydrolases	0.45	0.70	1.13	0.85	0.53	0.73	0.85	0.60	0.29	0.60	1.72	1.27
EC-4	Lyases	0.52	0.73	1.20	0.91	0.60	0.79	0.73	0.55	0.54	0.74	1.36	0.99

Table 6: Performance Comparison Across Enzyme Commission Classes. The table compares the performance of different backbone models and the impact of ERBA on kinetic parameter prediction for six EC classes: EC 1 (Oxidoreductases), EC 2 (Transferases), EC 3 (Hydrolases), EC 4 (Lyases), EC 5 (Isomerases), and EC 6 (Ligases). Metrics include R 2 , PCC, RMSE, and MAE for

k_{\text{cat}}

K_{\text{m}}

, and

K_{\text{i}}

, showcasing the effect of model size and architecture on the predictive accuracy across enzyme classes.

Figure 6: Error Distribution Comparison Across Different Backbone Models and ESM Sizes. It shows the error distribution of predicted versus experimental values for three kinetic parameters ( $k_{\text{cat}}$ , $K_{\text{m}}$ , and $K_{\text{i}}$ ) across four backbone models: (a) Ankh3-5.7B [ 70 ] , (b) ProtT5-3B [ 72 ] , (c) ESM2-650M [ 79 ] , and (d) ESM2-3B [ 79 ] , each augmented with ERBA. The plots show the proportion of predictions with absolute error less than or equal to 1, denoted as 1- $\text{Radio}_{\text{AE}}$ .

	Method	Kinetic Endpoint: $K_{\text{i}}$
	Method	R 2 ↑	PCC↑	RMSE↓	MAE↓
Stage 1	w / Concat & Self-Atention [ 83 ]	0.47	0.69	1.44	1.10
Stage 1	w / MRCA (Ours)	0.61	0.78	1.26	0.91

Table 7: Stage 1 (Recognition) ablation on

K_{\text{i}}

: Replacing Concat & Self-Attention with our MRCA markedly improves

R^{2}

and PCC while reducing RMSE/MAE under identical settings.

	Method	Kinetic Endpoint: $K_{\text{i}}$
	Method	R 2 ↑	PCC↑	RMSE↓	MAE↓
Stage 2	w / MoE [ 81 ]	0.50	0.71	1.39	1.05
Stage 2	w / G-MoE (Ours)	0.61	0.78	1.26	0.91

Table 8: Stage 2 (Adaptation) ablation on

K_{\text{i}}

: standard MoE vs. our G-MoE that routes by pocket geometry; geometry-aware experts yield consistent gains across all metrics.

	Method	Kinetic Endpoint: $K_{\text{i}}$
	Method	R 2 ↑	PCC↑	RMSE↓	MAE↓
Optimization	w / $\mathcal{L}_{2}$ Loss [ 85 ]	0.48	0.69	1.42	1.08
Optimization	w / ESDA (Ours)	0.61	0.78	1.26	0.91

Table 9: Objective ablation on

K_{\text{i}}

: plain

\mathcal{L}_{2}

vs. ESDA -regularized objective. Distribution alignment in RKHS stabilizes fine-tuning and improves R 2 /PCC while lowering RMSE/MAE.

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