# A Deep Learning-Based Approach for Predicting Michaelis Constants from Enzymatic Reactions
## 4 Results
### Comparison with Other Models  
To evaluate the prediction performances of DLERKm, we trained and tested DLERKm and UniKP [39] on the same dataset and compared their prediction results by using four evaluation metrics: RMSE, MAE, R\({}^{2}\), and PCC. As stated above, UniKP utilizes the pre-trained models ProtT5-XL-U50 and Smiles Transformer to extract enzyme sequence and substrate features, which are then combined with the extra tree algorithm to predict enzymatic kinetic parameters. Compared with other similar models, UniKP has been validated in terms of its reliability in real-world bioengineering tasks [42; 43; 44]. Therefore, it is meaningful to use UniKP as a benchmark model for comparison. Figure 4: Prediction results and performances of DLERKm and two variants. (**A**) Scatter plots of prediction results for DLERKm-v1. (**B**) Scatter plots of prediction results for DLERKm-v1. (**C**) Scatter plots of prediction results for DLERKm-v2. (**D**) Violin plot of prediction results for DLERKm and two variants. Figure 5: (**A**) Visualization of channel attention scores for input features for all the test samples. (**B**) Visualization of mean channel attention scores of various types of input features. Figure 6 presents all evaluation metric values of both DLERKm and UniKP. As shown in Table 4, compared with UniKP, DLERKm achieves the improvements of approximately 16.3% and 16.5% in RMSE and MAE on the same test samples. Additionally, the relative improvements of DLERKm over UniKP in terms of R\({}^{2}\) and PCC are 27.7% and 14.9%, respectively. Moreover, as illustrated in Figure 6A,B, the correlation between the predicted Km values of DLERKm and the true values is more significant. Furthermore, we randomly split the test set into ten subsets and recorded the prediction metric values for both models on these ten subsets. As shown in Figure 6C-F, the predictions of DLERKm exhibit better data stability and superior evaluation performance compared with UniKP. Additionally, we also analyzed the distribution of true values in the test set and divided them into four intervals to compare the prediction performances of DLERKm and UniKP at different value scales. As shown in Figure 6G-J, the results  
Figure 6: Km value prediction results of DLERKm and UniKP. (**A**,**B**) Scatter plots and prediction value distributions of DLERKm and UniKP. (**C–F**) Distributions of performance metric values for DLERKm and UniKP on different test subsets. (**G–J**) Comparison of DLERKm and UniKP prediction metric values across different ranges of actual values. show that the evaluation metric values of DLERKm outperform UniKP across all intervals. Specifically, in the four intervals, as shown in Tables S2-S4 of the Supplementary Materials, RMSE, MAE, R2, and PCC achieve improvements of at least approximately 9.32%, 10.55%, 37.58%, and 17.29%, respectively. Moreover, to compare the prediction performances of DLERKm and UniKP across different types of enzymatic reaction, we divided the test samples into two subsets based on wild-type (1550 samples) and mutant enzymatic reactions (475 samples), respectively. As shown in Figure 7, UniKP performs worse than DLERKm in both wild-type and mutant enzymatic reaction test sets. As shown in Table 5, the relative improvements of DLERKm are 16% and 17% for wild-type and mutant enzymatic reactions in terms of RMSE, respectively. Compared with UniKP, DLERKm shows improvements of 16.3%, 37.7%, and 41.2% across the three metrics (MAE, R2, PCC) for wild-type enzymatic reactions. Moreover, the values of above three metrics increase by approximately 16.8%, 41.2%, and 18.8% for mutant enzymatic reactions, respectively. In summary, we demonstrated that DLERKm has exhibited better goodness of fit and shown improvements in all four evaluation metrics (RMSE, MAE, PCC, R2) when trained and tested on the same dataset as UniKP. The results demonstrate that DLERKm is a more reliable method for high-throughput enzyme screening.