NNKcat: deep neural network to predict catalytic constants (Kcat) by integrating protein sequence and substrate structure with enhanced data imbalance handling

Abstract

Catalytic constant (Kcat) is to describe the efficiency of catalyzing reactions. The Kcat value of an enzyme-substrate pair indicates the rate an enzyme converts saturated substrates into product during the catalytic process. However, it is challenging to construct robust prediction models for this important property. Most of the existing models, including the one recently published by Nature Catalysis (Li et al.), are suffering from the overfitting issue. In this study, we proposed a novel protocol to construct Kcat prediction models, introducing an intermedia step to separately develop substrate and protein processors. The substrate processor leverages analyzing Simplified Molecular Input Line Entry System (SMILES) strings using a graph neural network model, attentive FP, while the protein processor abstracts protein sequence information utilizing long short-term memory architecture. This protocol not only mitigates the impact of data imbalance in the original dataset but also provides greater flexibility in customizing the general-purpose Kcat prediction model to enhance the prediction accuracy for specific enzyme classes. Our general-purpose Kcat prediction model demonstrates significantly enhanced stability and slightly better accuracy (R2 value of 0.54 versus 0.50) in comparison with Li et al.'s model using the same dataset. Additionally, our modeling protocol enables personalization of fine-tuning the general-purpose Kcat model for specific enzyme categories through focused learning. Using Cytochrome P450 (CYP450) enzymes as a case study, we achieved the best R2 value of 0.64 for the focused model. The high-quality performance and expandability of the model guarantee its broad applications in enzyme engineering and drug research & development.

Keywords: Kcat; data imbalance; deep neural network; enzyme turnover number; focused learning; machine learning.

Figure 1

A flowchart highlights the key components of Kcat model development in this work. We first constructed the substrate processor and protein processor separately utilizing Dataset #1 and then conducted feature augmentation with both processors. Next, all the generated feature embeddings are combined to train the general-purpose Kcat prediction models. Three parallel experiments are conducted during the training and testing the general-purpose Kcat models. Last, Dataset #2A was further applied to objectively evaluate the general-purpose Kcat models.

Figure 2

The distributions of Dataset #1 and Dataset #2A. Left: Distributions of substrate molecular weights in two datasets. Right: Distributions of amino acid sequence lengths of the proteins. The scatter and half-violin plots display the frequency distribution for each data group. Black dots in the halfviolin plots represent the mean values for these groups. The box plots illustrate the central tendency of the data, highlighting the medians and quartiles for both groups.

Figure 3

The performance of the substrate processor model. (A) The changing RMSE for the training and test sets during the model training process. The marked numbers are RMSE values for the best model (epoch 10). (B) The performance on the training set of the best model (epoch 10). (C) The model performance on the test set of the best model (epoch 10).

Figure 4

The performance of the protein processor. (A) The RMSE changing for the training and test sets during the model training process. The marked numbers are RMSE values for the best model (epoch 27). (B) The performance on the training set of the best model (epoch 27). (C) The performance on the test set of the best model (epoch 27).

Figure 5

The model performance, measured by correlation coefficient square – R2 (left panel) and rootmean-square errors-RMSE (right panel) of top machine learning models. Different random numbers were applied to divide dataset #1 into training and test sets. Higher R2 indicates better correlation between predicted log_2 K_cat values and the experimental ones in dataset #1. Lower RMSE value indicates lower prediction error of log_2 K_cat. GPR: Gaussian process regression; NN: Neural network; SVM: Support vector machine; tree: Decision tree.

Figure 6

The test set performance of the models generated under three random splits on the dataset #1. For a comparison purpose, the performance of the Li et al.’s model constructed using the same dataset is listed as follows: Random number 1357: R²= 0.203; random number 1234: R² = 0.516; random number 0103: R² = 0.543. Note that we reproduced Li et al.’s model using the code they provided in GitHub.

Figure 7

Similarity between substrates and protein sequences from dataset #2A and dataset #1. The sequence similarity is calculated by MUSCLE software.

Figure 8

Illustration of sequence difference between Dataset #1 and Dataset #2A in three different scenarios. Top: Scenario 1; bottom left: Scenario 2; bottom right: Scenario 3.

Figure 9

The performance of the three models on Dataset #2A for external validation. Sequences length ranging from 174 to 1074 amino acids are represented in different colors according to figure legend. The dash line represents the Y = X trendline. A total of 122 records from groups a and B, which include new sequence inputs, are represented by circles (●). Records from group C, where all sequences have exact matches in dataset #1, are depicted as triangles (▲).

Figure 10

Application of three general-purpose models on Dataset #2A for records in group A and B. The sequence identity of a sequence in Dataset #2A and it most similar sequence in Dataset #1 was colored according to the figure legend. The sequence identity is from 34.6% to 100%.

Figure 11

The performance of focused learning models from three parallel experiments. Each column represents an individual experiment. Panels A, B, and C display the distributions of K_cat values for the sublibrary which was randomly split into eight groups. Panels D, E, and F show the model performance under different data splitting conditions, with the axis label on the left for RMSE and the axis label on the right for R². Each individual RMSE and R² value reflects the model performance when a specific group is used as the validation set in the leave-one-group-out approach. The average RMSE and R² values represent the summary statistics when each group is sequentially used as the validation set.