GAPEK: A General Framework for Multiparameter Enzyme Kinetic Prediction with Adaptive Learning

The enzyme kinetic parameters, including the turnover number, Michaelis constant, and inhibition constant, are key metrics for assessing catalytic performance. Although deep learning models have recently incorporated multimodal information from enzymes and substrates to predict these parameters, several obstacles still persist. First, current data sets suffer from limited size, inconsistency, and a lack of unified standards. Second, most existing approaches prioritize cross-modal consistency but fail to sufficiently exploit the unique information residing in each individual modality. Meanwhile, although a limited number of studies have recognized that collaborative exploration of shared and specific information can enhance model performance, these methods remain difficult to directly apply to enzyme-substrate pairs, as enzyme-substrate relationships are inherently interactive rather than semantically equivalent counterparts. Third, the measured kinetic parameters are often unevenly distributed, which severely undermines the predictive accuracy of existing models when dealing with extreme value ranges. To resolve the above challenges, we first compile Kinetic-DB, a large-scale and consistently formatted data set from public resources. Building upon this data set, we develop GAPEK, a new framework for estimating enzyme kinetic parameters. In particular, an adaptive data augmentation module is devised to enrich the diversity of both enzyme and substrate sequences, thereby alleviating the adverse effects of data imbalance. Subsequently, we perform feature extraction using two pretrained models, ESM-2 for enzymes and Mole-BERT for substrates, to obtain multimodal embeddings. To decouple these complex interacting features, we introduce a tailored dual information exploration module to capture both modality-specific and cross-modal information, further refined by domain classification and distribution alignment loss functions. To explicitly handle the imbalanced data distribution, our base model, GAPEK, incorporates an adaptive density-weighted loss function. Building on this, we propose GAPEK+, which integrates the Squared Error Relevance Area (SERA) function to reconfigure the learning objective. By prioritizing high-relevance regions, GAPEK+ effectively calibrates the model's sensitivity to rare but critical extreme values, substantially mitigating the prediction bias inherent in heavy-tailed regression tasks. Experimental results demonstrate that both GAPEK and GAPEK+ achieve superior performance over existing state-of-the-art approaches, particularly across extreme parameter ranges, highlighting their potential as valuable tools applicable to enzyme engineering, synthetic biology, and drug discovery.