# A Deep Learning-Based Approach for Predicting Michaelis Constants from Enzymatic Reactions
## 1 Introduction  
The enzyme-catalyzed system serves as an essential tool in green chemistry due to its high conversion efficiency, substrate specificity, and mild reaction conditions [1, 2, 3]. For instance, in the field of carbon neutrality technologies, enzymatic catalysis significantly reduces energy consumption compared to traditional thermocatalytic pathways [4]. In synthetic biology, studies indicate that constructing heterologous biosynthetic pathways essentially involves rationally redesigning enzymatic reaction networks [5, 6]. In this process, the Michaelis constant (Km) is defined as the substrate concentration at which an enzymatic reaction reaches half of its maximum reaction velocity [7, 8]. The variation in Km provides fundamental information for understanding cellular metabolic regulation, bioinformatics, and microbial resource allocation optimization. For example, decreasingthe Michaelis constant (Km) of a key enzyme by an order of magnitude can significantly enhance the efficiency of target product biosynthesis [9; 10; 11]. Moreover, the Km parameter can be regarded as a performance metric of the \"bioengineering chip\" and systematically optimizes enzyme-substrate bioinformatics through directed evolution [12; 13] and computational modeling [14; 15]. As a key constant in enzymatic reaction systems, Km plays a crucial role in the quantitative analysis of bioengineering and biosciences processes. In conventional enzyme kinetics studies, experimental determinations of Km involve steady-state kinetic analysis [16], nonlinear fitting using the Michaelis-Menten equation [17], and cross-validation with the Lineweaver-Burk double-reciprocal plot method [18]. However, these approaches are typically time-consuming, which significantly increases experimental complexity [19], and impose strict requirements on substrate solubility and enzyme stability [20]. In recent years, the successful applications of deep learning to various fields of bioinformatics have provided new directions for predicting enzyme kinetic parameters [21]. [PERSON] et al. [22] constructed a dataset containing 16,838 enzyme-substrate pairs and developed DLKcat employing convolutional neural networks (CNNs), graph neural networks (GNNs), and attention mechanisms to predict turnover number (Kcat) values. Furthermore, [PERSON] et al. [23] provided a dataset containing 4281 samples of substrate, enzyme sequence, product, and Kcat values and designed a Kcat prediction model named TurNuP. By incorporating ESM-1b [24] and numerical reaction fingerprints to represent enzymatic reactions, TurNuP enhances the generalization ability of enzyme kinetic parameter predictions. Moreover, [PERSON] et al. [25] proposed a Km prediction model by using molecular fingerprints and graph representations as input features. In this study, we propose a novel deep learning approach called DLERKm for predicting Km values, which incorporates substrates, products, and enzyme sequences as inputs. The model aims to extract features using deep learning methods from enzymatic reactions to predict Km values (DLERKm). By collecting samples from Sabio-RK [26] and UniProt [27] databases and proper data processing, we constructed a new enzymatic reaction dataset including the information of substrates, products, and enzyme sequences. DLERKm uses a reaction pre-trained language model called RXNFP [28] to extract the features of enzymatic reactions described by SMILES strings, and uses a protein pre-trained language model called ESM-2 [29] to extract the features of enzymes described by amino acid sequences. To capture the molecular chemical property changes in the enzymatic reactions, DLERKm represents the molecular sets of substrates and products in the dataset with 1024-dimensional molecular fingerprints. Furthermore, the extracted features are refined by using channel attention mechanisms [30], which are then fed into fully connected layers to output Km prediction values.