Method for predicting multiple lysine modification sites based on cluster centroids undersampling technique

Abstract

The present application belongs to the field of artificial intelligence algorithm application-biological sequence recognition, and relates to a method for predicting multiple lysine modification sites based on ClusterCentroids undersampling technology. First, through data collection, integration and redundancy removal, the feature space is optimized, the redundant information is reduced, and a batch of protein sequences with significant class imbalance problems are obtained as input data. Then, a multi-label specific position triple amino acid tendency feature extraction algorithm is used to encode the protein sequence to obtain an input feature matrix. Then, the ClusterCentroids framework is used to calculate the cluster center of the majority class to process the unbalanced data set, and ensure that the model has good prediction effect on various modification site prediction. The present application can predict multiple lysine post-translational modification sites through the description and open source code.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence algorithm application - biological sequence recognition, and relates to a method for predicting multiple lysine post-translational modification sites. Background Technology

[0002] Post-translational modifications (PTMs) of proteins are crucial for regulating protein function and have a vital impact on cellular activity. PTMs encompass various modification types, including phosphorylation, methylation, and acetylation, which work together to affect protein structure and function. Abnormal PTMs are closely associated with the occurrence and development of many diseases; therefore, accurate identification of PTM sites is essential for elucidating the molecular mechanisms of biological processes and disease formation.

[0003] In recent years, with the development of artificial intelligence technology, machine learning technology has made significant progress in detecting post-translational modification sites, offering advantages such as lower cost and simpler operation compared to traditional techniques. However, despite these achievements, existing machine learning techniques still face some challenges in accurately predicting various lysine post-translational modification sites:

[0004] 1. Crosstalk problem: Many current inventions predicting multiple lysine post-translational modification sites tend to predict single types of PTMs in isolation, failing to adequately account for the interactions and synergistic effects of different PTMs within a single protein or across proteins. This neglect may underestimate the complexity of protein function regulation, thus affecting the comprehensiveness and accuracy of the predictions.

[0005] 2. Imbalanced Data: In the invention of prediction methods for multiple lysine modification sites, the distribution of sample data among different categories is extremely uneven. This imbalance may cause bias during model training, leading to distortion of evaluation metrics, shift in decision boundaries, and ultimately reducing the stability of the model and the accuracy of predictions.

[0006] 3. Sequence Dependency: The interdependencies among components within a biological sequence are crucial for protein function. However, traditional machine learning models often struggle to accurately capture these complex sequence dependencies, limiting their ability to deeply analyze and effectively apply sequence information.

[0007] 4. Model Interpretability: In the field of biological function prediction, while model accuracy is crucial, model interpretability is equally important. An easily interpretable model can clearly demonstrate its predictive logic, which not only improves the model's transparency but also enhances its credibility.

[0008] Therefore, there is an urgent need to develop a tool that can comprehensively consider the interactions of PTMs (post-translational modifications) on multiple amino acid residues, effectively handle sample imbalance, fully account for sequence dependencies, and possess high robustness and good interpretability. Such a tool can not only accurately predict multiple lysine modification sites but also ensure the interpretability of the results. Summary of the Invention

[0009] To address the aforementioned problems, this invention provides a method for predicting multiple lysine modification sites based on ClusterCentroids undersampling technology.

[0010] The technical solution of the present invention is as follows:

[0011] The data used in this invention are all sourced from CPLM4.0, a database that focuses on recording various position-specific post-translational modifications (PTMs) of lysine residue side chain amino groups in proteins. This database provides a total of 18,978 human protein sequences for this invention. A meticulous and rigorous data processing strategy was employed to construct a suitable dataset for training and testing. However, it was found that this dataset suffers from an extreme imbalance exceeding 100:1, increasing the difficulty of model generalization. Therefore, to address this issue, this invention proposes a ClusterCentroids undersampling technique based on Minibatch Kmeans for predicting various lysine modification sites. Furthermore, this invention employs a multi-label position-specific triplet amino acid tendency feature extraction algorithm, combined with a CNN-based multi-label classifier for classification, ultimately developing a user-friendly predictor. The model was then subjected to SHAP interpretability analysis.

[0012] The method for predicting multiple lysine modification sites based on ClusterCentroids undersampling technology comprises the following steps:

[0013] Step 1: Dataset Construction

[0014] To develop statistical prediction models, constructing reliable training and testing datasets is crucial; therefore, a meticulous and rigorous strategy was adopted. The specific steps are as follows:

[0015] 1.1 Sequence Extraction and Validation: For the 18,978 collected human protein sequences, extraction experiments were conducted to verify peptide fragments modified with lysine (K) as “acetyllysine”, “crotonyllysine”, “methyllysine”, or “succinyllysine” (with K as the center, the sliding window size was 24, i.e., the peptide fragment length was 49). Each peptide fragment can be represented in the form of Equation (1):

[0016] P = R-24 R -23 …R -2 R -1 R1R2…R 23 R 24 (1)

[0017] 1.2 Data Classification and Optimization: For the preprocessed data on the four lysine modifications (acetyllysine, crotonyllysine, methyllysine, and succinyllysine), a total of fifteen categories were obtained. After removing categories with fewer than 60 sequences, the final dataset was divided into eleven categories:

[0018]

[0019] Data category description: This refers to a protein sequence where the lysine residue at the center position contains only acetylated modifications. This refers to protein sequences that contain both acetylation and crotonylation modifications. The ∩ symbol indicates that the sample in this category exhibits multiple post-translational modifications. After removing duplicate peptide fragments from the data, 11 categories were obtained, with the following sample numbers for each category:

[0020] As mentioned above, the number of samples in the first class is 39,938, the number of samples in the second class is 2,463, and so on. To ensure that the performance evaluation of the multi-label prediction model is not overestimated due to sequence redundancy and homology, this invention uses the CD-HIT procedure and sets the threshold to 0.4 to eliminate these potentially homologous sequences and redundant samples. For the obtained 11 classes of data, 70% of each class is randomly selected as training data, and the remaining 30% is used as test data, resulting in the following deredundant segmented dataset: Training set:

[0021]

[0022]

[0023] Test set:

[0024]

[0025]

[0026] Step 2: Feature Extraction

[0027] To enable the computer to recognize the data cleaned in the first stage, feature extraction is performed in this stage. Experimental results show that the multi-tag specific position triple amino acid tendency algorithm performs excellently in the feature representation of lysine sequences for the problem of predicting multiple lysine modification sites. The algorithm consists of three steps, as follows:

[0028] 2.1 Calculate the frequency of each triplet amino acid at each position in each type of lysine sequence to obtain matrix F. t Its mathematical expression is as follows:

[0029]

[0030] in F t (TAA i / j) represents the TAA in the t-th type of lysine sequence. i The frequency of the triamino acid at the j-th position. Therefore, there are a total of 20. 3 A triple amino acid (TAA) s ), TAA i ∈{AAA,AAC,AAD,…YYY}, that is, TAA1=AAA, TAA2=AAC,…,TAA 20 3 =YYY, where i = 1, 2, 3, ..., 20 3 , j = 1, 2, 3, ..., 46.

[0031] 2.2 Calculate the frequency of each diamino acid at each position in the lysine sequences of the ten classes other than class t, and obtain the matrix FF corresponding to class t. t Its mathematical expression is as follows:

[0032]

[0033] in F t (TAA i / j) represents the ten lysine sequences other than class t. i The frequency of the triamino acid at the j-th position.

[0034] 2.3 Constructing the feature matrix F MLPSTAAP

[0035]

[0036] Where f i,j =F t (TAA i / j)-FF t (TAA i / j), F=(F1+F2+…+F 11 ) / 11,FF=(FF1+FF2+…+FF11 / 11.

[0037] Step 3: Handling Data Imbalance

[0038] After feature extraction, data with dimension 46 is obtained. To ensure overall data balance, this invention uses a ClusterCentroids undersampling algorithm based on MinibatchKmeans to process the first type of data. The specifics are as follows:

[0039] 3.1 Data Imbalance Problem:

[0040] Class imbalance in data refers to a situation where there is a significant difference in the number of samples from different classes within a dataset, with the majority class having far more samples than the minority class. This imbalance affects machine learning models primarily in the following ways:

[0041] 1. Model bias: The model may tend to overfit the majority class, resulting in a decrease in the ability to identify the minority class and affecting the overall classification performance.

[0042] 2. Misleading evaluation metrics: In cases of imbalanced data, using accuracy alone as an evaluation criterion may be misleading, because even if the model always predicts the majority class and achieves high accuracy, this does not mean that the model has actual classification ability.

[0043] 3. Decision boundary shift: In pursuit of high accuracy, the model may adjust the decision boundary to favor the majority class, thereby increasing the classification error rate of the minority class and reducing the model's generalization ability.

[0044] 4. Training process issues: Imbalanced data may cause the model to converge to a local optimum during training, making it difficult to cover all categories and sometimes requiring a longer time to converge.

[0045] Therefore, addressing data imbalance is crucial before constructing a classification model. This invention employs ClusterCentroids downsampling technology, which determines representative centers of the majority class through clustering and replaces the original samples with new samples generated from these centers. This effectively alleviates overfitting, enhances the identification of the minority class, and promotes the fairness and predictive performance of the model.

[0046] 3.2 ClusterCentroids Algorithm:

[0047] The ClusterCentroids algorithm is primarily used to adjust the number of samples in a majority of classes to combat imbalance. It performs clustering operations so that samples in these classes can be summarized by a smaller number of representative centroids, replacing the original large number of samples with these centroids. This reduces the number of samples in a particular class, helping to achieve sample equalization. In this way, ClusterCentroids not only reduces the number of samples in the majority class of the dataset but also maintains data diversity, which is beneficial for solving the imbalance problem. The core step of the algorithm involves grouping the classes with larger sample sizes to form multiple representative centroids.

[0048] The ClusterCentroids algorithm framework is as follows:

[0049] 1. Majority Class Clustering: ClusterCentroids uses clustering methods, such as K-means, to reduce the majority class samples to a specified number of "centroids", thereby simplifying the majority class samples.

[0050] 2. Centroids as new samples: These centroids are treated as new minority class samples. The feature values ​​of these centroid samples are usually the average of the cluster centers calculated by a clustering algorithm.

[0051] 3. Sample replacement: The original samples of most categories will be replaced by these centroid samples.

[0052] 4. Data balancing: By adjusting the number of majority class samples and replacing the original samples with centroids that have majority class characteristics, the ClusterCentroids algorithm promotes the balance of the dataset.

[0053] However, because K-means requires multiple iterations to update cluster centers, the computational complexity increases significantly for large datasets, leading to long execution times and high memory consumption. Therefore, the traditional K-means algorithm is inefficient when handling large datasets. Furthermore, in each iteration, the K-means algorithm calculates the distance between all data points and cluster centers, assigns data points to the nearest cluster center, and updates the cluster center positions based on this new distribution. However, this iterative operation can affect the algorithm's convergence efficiency. Especially when dealing with large datasets, the K-means algorithm requires multiple iterations until convergence is reached, and each iteration requires calculating the distance between all data points and all cluster centers, which leads to inefficiency when handling large datasets. This study adopts Minibatch K-means as a clustering algorithm in the undersampling process. In clustering techniques, the Minibatch K-means algorithm, as an improved version of the traditional K-means, improves the efficiency of the clustering process by using small subsets of the data to calculate cluster centers. Minibatch Kmeans effectively shortens the time required for solving the Kmeans algorithm and reduces memory usage, while achieving only a slight difference in clustering results compared to the traditional Kmeans algorithm. The ClusterCentroids algorithm based on Minibatch Kmeans is as follows:

[0054] Algorithm flow:

[0055] Input: Dataset D, number of clusters k, mini-batch size b, maximum number of iterations T

[0056] Output: Cluster centers: {c1, c1, ..., c1} k}

[0057] Cluster label for each sample

[0058] I. Initialize cluster centers:

[0059] Randomly select k data points from the dataset as initial cluster centers. Assume the initial cluster centers are...

[0060] {c1,c1,…,c k}

[0061] II. Initialize the counter:

[0062] Initialize the iteration counter t = 0 to record the number of iterations.

[0063] III. Iterative process:

[0064] During the iteration process, the cluster centers are continuously adjusted so that each cluster center represents the data points within its cluster as much as possible.

[0065] a. Randomly select small batches of data

[0066] We randomly select b samples from dataset D to form a mini-batch dataset M. This reduces computational complexity and improves algorithm efficiency.

[0067] b. Assign samples to the nearest cluster center

[0068] For each sample x in a mini-batch dataset M i :

[0069] Calculate x i To each cluster center c j The distance. Let x i Assign it to the nearest cluster center.

[0070] c. Update cluster centers

[0071] For cluster samples, calculate the mean of all samples.

[0072] Update the cluster centers to the mean value mentioned above to ensure that the cluster centers continuously move closer to the cluster center.

[0073] d. Update the counter

[0074] Increment the counter t by 1 and proceed to the next iteration.

[0075] IV. Termination Conditions:

[0076] When the number of iterations t reaches the maximum number of iterations T, the iteration stops, and the final cluster centers and cluster labels of each sample are output.

[0077] 3.3 Confirm the sampling ratio of the first type of data.

[0078] Since the proportion of the 11 training data categories in the training set of this study is 9279:710:600:454:561:252:360:88:153:454:73, it is clear that the number of the first category is much greater than that of the other ten categories, accounting for more than 71% of the total sample. The difference in the number of samples of the other ten categories is not so significant. Therefore, undersampling was only performed on the first category of data.

[0079] When a low undersampling ratio is used, too many original samples are lost, and the range of the dataset generated after cluster undersampling is significantly reduced. This makes the sampled dataset no longer fully representative of the distribution of the original data. When a high undersampling ratio is used, the sampled dataset can better retain the information of the majority class samples and still has strong performance. However, due to the extremely imbalanced class distribution in the original dataset, a low undersampling ratio may still not be able to eliminate the class imbalance problem in the dataset. To maintain a moderate sampling ratio, an undersampling ratio of 0.1 was chosen as the final undersampling ratio through experiments. After successful sampling, the sample distribution ratio of the 11 classes in the training set is: 928:710:600:454:561:252:360:88:153:454:73.

[0080] 3.3.1 Initialization: Divide the first class of data obtained after feature extraction in the second step into a subset, denoted as D. Set the number of clusters to be performed: k, the number of mini-batch data: b, the maximum number of iterations: T, and the undersampling ratio: 0.1.

[0081] 3.3.2 Randomly select k data points from D as initial cluster centers, denoted as {c1, c2, ..., c3}. k}

[0082] 3.3.3 Randomly select b data points from D, denoted as M.

[0083] 3.3.4 Calculate the relationship between all data in M ​​and {c1, c1, ..., c1}. k The distance of}.

[0084] 3.3.5 Assign each data point in M ​​to the cluster center that is closest to it.

[0085] 3.3.6 Update {c1,c1,…,c k}

[0086] 3.3.7 Repeat the operation between 3.3.2 and 3.3.6 T times.

[0087] 3.3.8 Data is selected based on the minimum distance between points within each cluster center and the centroid, and is used as the undersampled data. The amount of data selected is approximately 9279 * 0.1 ≈ 928.

[0088] 3.4 Combine the data from classes 2-11 with the sampled data from class 1 to form the final training data.

[0089] Step 4: Classification Model Construction

[0090] In this phase, this research aims to construct a powerful, robust, and effective multi-label classification model that captures sequence dependency structures using CNN methods. This phase mainly includes key steps such as loss function definition, activation function selection, convolutional neural network architecture design, and model training and validation. The specific steps are as follows:

[0091] 4.1 Definition of Loss Function

[0092] Loss functions play a crucial role in machine learning and deep learning. In this study, the loss function quantifies the error between the model's predicted sample labels and the actual labels. Considering that each sample's label is a four-dimensional one-hot encoded form, this invention employs a binary cross-entropy loss function suitable for multi-label classification to calculate the model's loss for each sample's predicted label. The specific calculation formula is as follows:

[0093]

[0094] Where N represents the number of samples, y i This represents the true label of the i-th sample. This represents the model's predicted probability for the i-th sample, i.e., the value output by the model. Compared to loss functions such as mean squared error, binary cross-entropy loss penalizes misclassification more severely and can better guide the model to learn the correct classification decision.

[0095] 4.2 Activation Function Selection

[0096] Activation functions in neural networks endow them with the ability to perform nonlinear mappings, enhancing their expressive and approximation capabilities. In this invention, considering the simplicity and efficiency of the ReLU function and its ability to effectively mitigate the vanishing gradient problem, the ReLU function is chosen as the activation function between convolutional and pooling layers, as well as the activation function for the hidden layers in the fully connected portion. In the fully connected output layer, the Sigmoid activation function is used, ensuring that the output four-dimensional vector lies between 0 and 1, representing the model's predicted probabilities for each of the four labels.

[0097] 4.3 Convolutional Neural Network Architecture Design

[0098] To ensure the model fully considers the dependency structure of sequences, this invention employs a feature extraction module constructed with four one-dimensional convolutional layers and pooling layers. Its architecture is designed as follows:

[0099] Convolutional layers:

[0100] 1. Function: The convolutional layer is a core component in CNNs used to extract local features from the input data. By using convolutional kernels, this layer is able to capture local dependencies and patterns in the data.

[0101] 2. Design: The convolution kernel shape used in this study is (3,1), which means that each convolution kernel covers 3 time steps and is used to extract dependency features in sequence data.

[0102] 3. Parameters: The parameter settings for the four convolutional layers are as follows:

[0103] First layer: Conv1d(in_channels=1, out_channels=64, kernel_size=3)

[0104] Second layer: Conv1d(in_channels=64, out_channels=128, kernel_size=3)

[0105] Third layer: Conv1d(in_channels=128, out_channels=256, kernel_size=3)

[0106] Fourth layer: Conv1d(in_channels=256, out_channels=128, kernel_size=3)

[0107] Pooling layer:

[0108] 1. Function: Pooling layers are used to reduce the spatial dimension of features, thereby reducing computation and making feature detection more robust.

[0109] 2. Design: This invention employs max pooling operation, using a pooling filter of size (2,1) with a step size of 2 to achieve downsampling while retaining the most important feature information.

[0110] 3. Effects: Pooling helps reduce the risk of overfitting and makes the model more robust to small changes in the input data.

[0111] Fully connected layer:

[0112] 1. Function: The fully connected layer is located at the end of the model and is responsible for integrating the features extracted by the previous layers and making the final classification decision.

[0113] 2. Design: After convolutional and pooling layers, fully connected layers flatten the features and apply linear transformations, then introduce non-linearity through activation functions to perform complex classification tasks.

[0114] 3. Parameters:

[0115]

[0116] 4. Output: The final fully connected layer outputs a four-dimensional vector, with each dimension corresponding to the probability prediction of a label. The Sigmoid activation function is used to ensure that the output value is between 0 and 1.

[0117] 4.4 Model Training and Validation Testing

[0118] A sample outputs a matrix of (1, 4) from the model, where each of the four positions corresponds to a label with a value between 0 and 1, representing the probability that the sample contains the corresponding label. For example, (0.9, 0.2, 0.3, 0.4) represents the predicted probability of the labels (acetyllysine, crotonyllysine, methyllysine, succinyllysine). The loss function used to train the classifier is set to cross-entropy loss, suitable for classification problems, to measure the difference between the target and the predicted output. This model can fully consider the dependency structure of sequences. In the model training experiments of this invention, the Adam optimizer is sampled with a learning rate lr of 0.001. The optimal model is selected based on five-fold cross-validation and five evaluation metrics (Aiming, Coverage, Accuracy, Absolute_True, Absolute_False). The model performance is tested on an independent test set to obtain the evaluation metrics of the independent test results.

[0119] Step 5: Interpretable Analysis

[0120] To gain a deeper understanding of how the model works during the prediction process and how predicted values ​​are generated, the SHAP method was used to explain the model's prediction process. The following is an introduction to this method:

[0121] SHAP is a game theory-based model interpretation technique. Its core objective is to evaluate the influence of each feature on the prediction result and assign a corresponding interpretability score to each feature. The calculation of SHAP values ​​is based on Shapley value theory, a fair allocation scheme that reasonably attributes the model's final output (e.g., predicted value) to the contribution of each feature. By considering all possible feature combinations, Shapley values ​​can accurately assess the specific impact of each individual feature on the model's prediction. In interpreting deep learning models, Shapley values ​​quantify the contribution of each input feature to the model's prediction performance. A higher absolute value of the Shapley value indicates that the corresponding feature has a greater impact on the prediction result. By applying SHAP analysis, we can gain insights into the underlying causes of the prediction results. In this invention, an in-depth interpretive analysis was performed on the extracted 46-dimensional features, providing a clear explanation of the model's prediction results.

[0122] The beneficial effects of this invention are:

[0123] 1. Most existing inventions are limited to single-type modifications, ignoring the interactions between different PTMs. This invention establishes a multi-tag prediction tool that can be directly used to predict multiple lysine modification sites. It solves the crosstalk problem that previous inventions did not consider.

[0124] 2. The ClusterCentroids undersampling algorithm based on MiniBatchKmeans can effectively solve the sample imbalance problem and improve the model's generalization ability for classes with fewer samples. Furthermore, it achieves similar results to traditional algorithms while reducing memory usage.

[0125] 3. The constructed convolutional neural network architecture can consider the dependencies between sequence elements, fully capture the information in the sequence, and enhance the model's in-depth understanding and effective utilization of sequence information.

[0126] 4. The interpretability analysis of the model based on SHAP values ​​shows that the prediction model constructed in this invention is effective, enhancing the transparency and credibility of the model. Attached Figure Description

[0127] Figure 1 This is a flowchart illustrating the overall technical structure of the present invention.

[0128] Figure 2 This is a diagram of the convolutional neural network architecture constructed in this invention.

[0129] Figure 3 This is the SHAP feature interpretation diagram of the present invention, which is a feature importance ranking diagram for the prediction result of a certain sample.

[0130] Figure 4 This is a comparison of the metrics of the model proposed in this invention with previous models on an independent test set.

[0131] Figure 5 The purpose of this invention is to conduct ablation experiments to verify the effectiveness of the proposed ClusterCentroids undersampling technique. Detailed Implementation

[0132] The specific implementation of the present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0133] This invention proposes an undersampling technique based on centroid clustering for a multi-label classification model to predict eleven types of lysine modification sites in protein sequences. Its architecture is as follows: Figure 1As shown, the model first employs a multi-label, position-specific, three-amino acid bias algorithm to encode protein sequence features. Next, the ClusterCentroids undersampling algorithm is used to undersample the majority class samples to alleviate class imbalance and improve the model's generalization ability to classes with fewer samples. Furthermore, this invention designs a convolutional neural network (CNN)-based architecture, extracting features from feature vectors through multiple convolutional and pooling layers, and converting the extracted features into the final classification result through fully connected layers. During model training, a multi-label binary cross-entropy loss function is used, and the network parameters are optimized through backpropagation to improve the model's prediction accuracy for various lysine modification sites. This invention also comprehensively evaluates the model's performance using five evaluation metrics—Aiming, Coverage, Accuracy, Absolute-True, and Absolute-False—through five-fold cross-validation and independent testing experiments. Experimental results show that the proposed model significantly outperforms existing iMul-kSite and predML-Site models on various lysine modification site prediction tasks. Furthermore, to improve the model's interpretability, the SHAP method was used to analyze the prediction process, revealing the contribution of different features to the prediction results. Finally, to facilitate user adoption of the multi-label prediction model constructed in this invention, a publicly available prediction tool was developed.

[0134] In summary, the multi-lysine modification site prediction and classification model of this invention, through a series of innovative techniques such as ClusterCentroids undersampling, forms a powerful lysine modification site prediction classifier. This classifier can effectively identify and predict multiple lysine modification types in protein sequences, providing scientific and accurate decision support for biological research and drug development.

[0135] Example 1: Data Preprocessing and Feature Extraction

[0136] In this embodiment, a dataset for predicting various lysine modification sites was constructed. Through precise truncation, classification, and optimization of 18,978 sequences, datasets in 11 categories were selected, and redundant samples were removed using the CD-HIT program. Subsequently, features were extracted using the Multi-Label Positional Triple Amino Acid Propensity Algorithm (MLPSTAAP), ensuring the diversity and reliability of the datasets and laying the foundation for model training and evaluation.

[0137] Example 2: Sample Balancing Technique

[0138] In bioinformatics and protein sequence analysis, a centroid-based undersampling technique (ClusterCentroids) is employed to address the imbalance problem in datasets. This method uses MiniBatch K-means clustering to identify and retain representative samples from the majority class, thereby alleviating the imbalance problem while maintaining data diversity and representativeness. Specifically, the process involves using the MLPSTAAP algorithm to feature-encode protein sequences and then employing the ClusterCentroids algorithm to undersample the majority class samples.

[0139] To further verify the effectiveness of the undersampling method, ablation experiments were conducted as shown in Table 1. Figure 5 The performance of the model on a multi-label prediction task was compared between no undersampling, random undersampling, and undersampling using ClusterCentroids. Experimental results show that training on the dataset undersampled using ClusterCentroids significantly improves the model's prediction ability on the minority class, while effectively controlling overfitting on the majority class.

[0140] A key trade-off exists when determining the undersampling ratio: a low undersampling ratio may lead to a significant loss of majority class samples, thus weakening the model's learning ability; while a high undersampling ratio may fail to effectively alleviate class imbalance, causing the model to overfit on the majority class. To find a suitable balance, a series of experimental results were evaluated, as shown in Table 1, to assess the impact of different undersampling ratios on model performance. Table 2 clearly shows that as the undersampling ratio decreases, i.e., the number of samples containing only acetyllysine modification decreases after undersampling, the model's absolute prediction accuracy significantly improves on samples containing only label C (crotonyllysine) and samples containing both C and M ("crotonyllysine", "methyllysine"). The absolute accuracy on samples containing only acetyllysine modification shows a slow decreasing trend, while no significant differences are observed in other classes. Since training neural networks requires a certain amount of sample data, an undersampling ratio that is too low will result in too little data. In order to ensure that the undersampled samples can improve the model's generalization ability for the minority class and also ensure the prediction ability for the majority class, 0.1 is chosen as the final undersampling ratio.

[0141] Table 1. Results of five-fold cross-validation under different sampling methods

[0142]

[0143] Table 2. Absolute accuracy (%) of eleven samples under 5x cross-validation at different undersampling rates

[0144]

[0145] Example 3: Model Performance Evaluation and Comparison

[0146] To enhance the professionalism of this invention, standardized and professional evaluation metrics were used to assess the model's performance. These metrics included: Aiming, Coverage, Accuracy, Absolute-True, and Absolute-False. The proposed model, CNN+ClusterCentrois, was compared with three other existing prediction models: iMul-kSite, mLysPTMpred, and iPTM-mLys, using a five-fold cross-validation experiment. The results are shown in Table 3. The proposed model achieved 86.31%, 80.18%, 78.51%, 73.54%, and 10.94% on the five evaluation metrics, ranking third among the four models.

[0147] Table 3. Results of five-fold cross-validation under different sampling methods

[0148]

[0149] Although the model did not perform exceptionally well in the five-fold cross-validation experiments, comparative experiments on the independent test dataset revealed that the model also demonstrated a certain level of generalization ability on the independent test dataset, significantly outperforming iMul-kSite. Therefore, it can be concluded that while iMul-kSite has good prediction performance on the training set, its performance on the test set indicates a tendency towards overfitting and weak generalization ability; while the CNN+ClusterCentroids model achieves a better balance between fitting ability and generalization ability. Figure 4 As shown, the model constructed in this invention was compared with the accessible web servers iMul-kSite and predML-Site on the independent test dataset constructed in this invention. When observing specific predicted labels, it was found that iMul-kSite and predML-Site had particularly low prediction accuracy on samples containing multiple lysine modification sites. That is, for the vast majority of samples containing multiple labels, the above two prediction models often could only predict one of the multiple labels they contained. However, the data shows that the constructed prediction model has a higher absolute accuracy, and observation of specific prediction metrics reveals that the model can effectively predict samples containing multiple labels. Therefore, the multi-label prediction model constructed in this invention can significantly improve the performance of predicting multiple lysine modification sites, outperforming ensemble binary classification models.

[0150] Example 4: Model Explanation

[0151] Figure 3 The results of SHAP analysis for a specific sample are shown, with the predicted label being (0, 1, 0, 0). These four values ​​correspond to the likelihood that the sample has undergone one of four different types of lysine post-translational modifications (acetyllysine, crotonyllysine, methyllysine, succinyllysine).

[0152] In this analysis, the Shapley value predicted for each label by each feature in the sample was calculated. The explanation is as follows: Figure 3 The vertical axis represents the feature number, while the horizontal axis shows the Shapley value for each feature. In the graph predicting label A, E[f(x)] = 0.52 represents the average probability of being predicted as label A across the entire dataset. Bars pointing to the right represent the positive contribution of a feature to the prediction result, while bars pointing to the left represent the negative contribution. For example, in... Figure 5 In the graph, feature 34 has a positive contribution of 0.01 to the prediction result, while feature 29 has a negative contribution of 0.04. Furthermore, the bars in the graph are arranged in descending order of the absolute influence of each feature on the prediction result. It is clear that when predicting label A, features 29, 18, 11, 10, 15, 9, 24, 34, and 16 have a significant impact on the prediction result; they are key factors in the prediction process. This intuitive demonstration allows us to understand which features play a dominant role in predicting different labels, and the differences in the influence of different features when predicting the same label. This provides an important perspective for a deeper understanding of the model's prediction mechanism.

Claims

1. A method for predicting multiple lysine modification sites based on ClusterCentroids undersampling technology, characterized by the following steps: Step 1: Dataset Construction 1.1 Sequence Extraction and Verification: For human protein sequences, extraction experiments were conducted to verify that the lysine (K) was modified by "acetyllysine", "crotonyllysine", "methyllysine", or "succinyllysine"; each peptide fragment was represented in the form of formula (1): (1) 1.2 Data Classification and Optimization: For the preprocessed data on the four lysine modifications, a total of fifteen categories can be obtained. After removing categories with fewer than 60 sequences, the final dataset is divided into eleven categories: (2) Data category description: This refers to a protein sequence where the lysine residue at the center position contains only acetylated modifications. This refers to protein sequences that contain both acetylation and crotonylation modifications; where ∩ indicates that the sample in this category has multiple post-translational modifications. Step 2: Feature Extraction Feature extraction was performed on the data; a multi-label, positional, triple amino acid propensity algorithm was used. Step 3: Handling Data Imbalance The first type of data is processed using the ClusterCentroids undersampling algorithm based on MinibatchKmeans; the details are as follows: 3.1 Initialization: Divide the first class of data obtained after feature extraction in the second step into a subset, denoted as D; set the number of clusters to be performed: k, the number of mini-batch data: b, the maximum number of iterations: T, and the undersampling ratio: 0.1; 3.2 Randomly select k data points from D as initial cluster centers, denoted as k_k_cluster centers. 3.3 Randomly select b data points from D, denoted as M; 3.4 Calculate the relationship between all data in M ​​and... The distance; 3.5 Assign each data point in M ​​to the cluster center that is closest to it; 3.6 Update 3.7 Repeat the operation between 3.2 and 3.6 T times; 3.8 Data is selected based on the minimum distance between points within each cluster center and the centroid, and is used as the undersampled data; 3.9 Combine the data from classes 2 to 11 with the sampled data from class 1 to form the final training data; Step 4: Classification Model Construction A multi-label classification model is adopted, including a loss function, activation function, and convolutional neural network architecture; the specific steps are as follows: 4.1 Constructing the loss function A binary cross-entropy loss function suitable for multi-label classification was adopted, and the specific calculation formula is as follows: (6) in Indicates the number of samples. Indicates the first The true label of each sample The model represents the first The predicted probability of each sample, i.e., the value output by the model; 4.2 Constructing the activation function The ReLU function is chosen as the activation function between the convolutional and pooling layers, as well as the activation function of the hidden layers in the fully connected part. In the output layer of the fully connected part, the Sigmoid activation function is used so that the output four-dimensional vector is between 0 and 1, which represents the model's prediction probability for each of the four labels. 4.3 Constructing a convolutional neural network architecture; The second step is as follows: 2.1 Calculate the frequency of each triplet amino acid at each position in each type of lysine sequence to obtain a matrix. Its mathematical expression is as follows: (3) in , This indicates the lysine sequence of type t. The frequency of the three amino acids at the j-th position; from this, we can know the total number of amino acids. Three amino acids ( ), ,Right now ,in , ; 2.2 Calculate the frequency of each diamino acid at each position in the lysine sequences of the ten classes other than class t, and obtain the matrix corresponding to class t. Its mathematical expression is as follows: (4) in This represents the lysine sequences of the ten classes other than class t. The frequency of the triamino acid at the j-th position; 2.3 Constructing the Feature Matrix (5) in , , .

2. The method for predicting multiple lysine modification sites based on ClusterCentroids undersampling technology as described in claim 1, characterized in that, In the first step, the number of samples in the first class is 39938, the number of samples in the second class is 2463, and so on. Using the CD-HIT program and setting the threshold to 0.4, for the obtained 11 classes of data, 70% of each class is randomly selected as training data, and the remaining 30% is used as test data, resulting in the following deredundant segmented dataset: Training set: , , , ； Test set: , 3. The method for predicting multiple lysine modification sites based on ClusterCentroids undersampling technology as described in claim 1, characterized in that, In the fourth step, a feature extraction module is constructed using four one-dimensional convolutional layers and pooling layers, with the following architecture: Convolutional layers: The convolutional kernel used has a shape of (3,1), which means that each convolutional kernel covers 3 time steps and is used to extract dependency features in sequence data; The parameter settings for the four convolutional layers are as follows: First layer: Conv1d(in_channels=1,out_channels=64,kernel_size=3) Second layer: Conv1d(in_channels=64,out_channels=128,kernel_size=3) Third layer: Conv1d(in_channels=128,out_channels=256,kernel_size=3) Fourth layer: Conv1d(in_channels=256,out_channels=128,kernel_size=3) Pooling layer: Max pooling is employed, using a pooling filter of size (2,1) with a step size of 2 to achieve downsampling while preserving the most important feature information; Fully connected layer: After convolutional and pooling layers, fully connected layers flatten the features and apply linear transformations, then introduce non-linearity through activation functions for complex classification tasks. The final fully connected layer outputs a four-dimensional vector, with each dimension corresponding to the probability prediction of a label. The Sigmoid activation function is used to ensure that the output value is between 0 and 1.

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