A method for predicting the optimum ph of an enzyme based on the active site and secondary loss

Abstract

The application belongs to the field of protein engineering, and particularly relates to an enzyme optimum pH prediction method based on enzyme active sites and secondary loss; the method comprises the following steps: processing protein sequences of enzymes in a training set by using a GraphEC model to obtain activity values of each amino acid; extracting protein physicochemical characteristics of the protein sequences of the enzymes and processing the same, performing average pooling on the processed characteristics to obtain EMS2 representation and ESMC representation; performing weighted pooling processing on the EMS2 representation by using the activity values of the amino acids to obtain weighted EMS2 representation; fusing the protein physicochemical characteristics, the EMS2 representation, the ESMC representation and the weighted EMS2 representation to obtain joint features; inputting the joint features into a prediction network for processing to obtain enzyme optimum pH prediction results; calculating model total loss and adjusting model parameters according to the model total loss to complete training of the model; and the application greatly improves the prediction accuracy of enzyme optimum pH and has good application prospect.

Description

Technical Field

[0001] This invention belongs to the field of protein engineering, specifically relating to a method for predicting the optimal pH of an enzyme based on its active site and minor losses. Background Technology

[0002] Enzymes, due to their high selectivity and catalytic efficiency, have found wide applications in industry, medicine, and environmental remediation. Improving enzyme catalytic efficiency has become a primary task in enzyme engineering research. Enzymes are highly sensitive to the hydrogen ion concentration (pH) in their environment; pH affects the conformation of the enzyme's active site and its ability to bind substrates. Beyond a specific pH range, enzyme activity typically decreases significantly. Therefore, determining and maintaining the optimal pH of an enzyme ensures that the active site is in the appropriate conformation for catalysis, thereby maximizing enzyme activity. Accurately predicting the optimal pH of an enzyme can also advance developments in multiple fields, including enzyme discovery and engineering, understanding enzyme evolution and function, optimizing industrial biocatalysts, and designing enzyme-based drugs.

[0003] Traditional experimental methods for predicting the pH of enzymes often involve time-consuming and expensive high-throughput analyses. Recent advances in artificial intelligence (AI) have improved the ability to predict protein properties directly from amino acid sequences. Several machine learning or deep learning models have been developed to predict the optimal pH of enzymes. For example, the existing EpHod model introduces effective solutions to two major challenges in pH prediction: data imbalance and the scarcity of experimental pH data. To mitigate the impact of data imbalance, they applied a loss reweighting strategy to guide the model to focus more attention on enzymes active in strongly acidic or alkaline environments. Furthermore, they pre-trained their model on a large dataset of 1.9 million bacterial proteins (pHenv) to address the data scarcity problem. However, pre-training on such a large dataset is computationally expensive, and the inherent imbalance in the pHenv dataset can introduce bias into the model. Another noteworthy approach is OphPred, which utilizes ESM-2 sequence embeddings combined with machine learning algorithms (XGBoost and KNN) to predict optimal pH values. However, these models often rely solely on a single ESM characterization, neglecting domain knowledge related to enzyme pH. Consequently, these general characterizations struggle to achieve satisfactory predictive accuracy. Furthermore, similar enzymes share similar properties, and the accuracy of existing computational tools remains insufficient to guide wet laboratory experiments. The R² coefficient of determination for these models consistently fails to reach 50%, highlighting the need for further improvements in predicting optimal enzyme pH.

[0004] In conclusion, there is an urgent need for a new method to predict the optimal pH of enzymes in order to improve the accuracy of the prediction. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method for predicting the optimal pH of an enzyme based on its active site and minor losses. This method includes:

[0006] Obtain the protein sequence of the enzyme to be predicted and input it into the trained enzyme optimal pH prediction model to obtain the enzyme optimal pH prediction result.

[0007] The training process for the enzyme optimal pH prediction model includes:

[0008] S1: Obtain the protein sequence dataset of the enzyme and divide it into training and test sets. Use the GraphEC model to process the protein sequences of the enzyme in the training set to obtain the activity value of each amino acid.

[0009] S2: Physicochemical characteristics of the protein sequence of the extracted enzyme;

[0010] S3: The protein sequence of the enzyme was processed using the ESM-2 650M model and the ESMC-600M model, respectively, and the processed features were averaged and pooled to obtain EMS2 characterization and ESMC characterization.

[0011] S4: Use the activity value of the amino acid as the weight value corresponding to the amino acid to perform weighted pooling on the EMS2 characterization to obtain the weighted EMS2 characterization.

[0012] S5: Combined protein physicochemical characteristics, EMS2 characterization, ESMC characterization, and weighted EMS2 characterization are used to obtain joint characteristics;

[0013] S6: Input the joint features into the prediction network for processing to obtain the optimal pH prediction results for the enzyme.

[0014] S7: Calculate the total model loss and adjust the model parameters based on the total model loss to obtain the optimal enzyme pH prediction model. Predict the protein sequences in the test set based on the optimal enzyme pH prediction model to complete the model training. The total model loss is the weighted sum of the primary loss and the secondary loss.

[0015] Preferably, the physicochemical characteristics of the enzyme's protein sequence include the number of acidic amino acids, the number of basic amino acids, sequence length, molecular weight, isoelectric point, instability index, hydrophobicity, aromatic ratio, aliphatic amino acid index, and protein type.

[0016] Preferably, the process of obtaining the joint features includes: inputting the protein physicochemical features into a fully connected layer for processing, and performing dimensionality reduction on the EMS2 representation, ESMC representation, and weighted EMS2 representation through two layers of MLP network to obtain four features of a unified dimension; and concatenating the four features of the unified dimension along the channel dimension to obtain the joint features.

[0017] Preferably, the process of inputting the joint features into the prediction network for processing includes: the joint features are processed sequentially through a Dense layer, a BatchNorm layer, an ELU activation layer, and a Dropout layer, and then residually connected with the joint features to obtain residual enhanced features; the residual enhanced features are input into a fully connected layer for processing to obtain the enzyme's optimal pH prediction result.

[0018] Preferably, the process of calculating the total loss of the model includes:

[0019] Calculate the cosine similarity between the current enzyme's EMS2 characterization and the EMS2 characterizations of other enzymes in the training set; use the label corresponding to the enzyme with the highest cosine similarity as the pseudo-label of the current enzyme.

[0020] The primary loss is calculated based on the actual label and the enzyme's optimal pH prediction results, and the secondary loss is calculated based on the pseudo-label and the pseudo-label prediction values.

[0021] The total loss of the model is obtained by weighted summation of the primary and secondary losses.

[0022] Preferably, the main loss is expressed as:

[0023]

[0024] Among them, L pr The main loss is represented by N, and the sample size is represented by w. i y represents the smoothing weights of the label distribution for the i-th sample. i This represents the true label of the i-th sample. This represents the optimal pH prediction result for the i-th sample, and ε represents the stability coefficient.

[0025] Furthermore, the formula for calculating the label distribution smoothing weight is as follows:

[0026]

[0027] Among them, w i P(y) represents the smoothing weights of the label distribution for the i-th sample. i The true label y of the i-th sample i The probability density is given by ε, where ε represents the stability coefficient and α represents the label distribution smoothness coefficient.

[0028] The preferred secondary loss is expressed as:

[0029]

[0030] Among them, L se Represents the secondary loss, N represents the sample size, and r i This represents the pseudo-label of the i-th sample. This represents the pseudo-label prediction value for the i-th sample.

[0031] The beneficial effects of this invention are as follows: This invention associates enzymes with their active sites and captures the rule that similar proteins have similar optimal pH values. Therefore, it combines this relevant knowledge with traditional protein characterization methods and incorporates an optimized loss function calculation method to achieve the best model performance. This invention develops a multimodal prediction model based on enzyme active sites and secondary losses for predicting enzyme optimal pH, which significantly improves the prediction accuracy of enzyme optimal pH and has good application prospects. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the enzyme optimal pH prediction model structure in this invention;

[0033] Figure 2 This figure shows the comparison results between the present invention and the comparative model on the same dataset. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] This invention proposes a method for predicting the optimal pH of an enzyme based on its active site and minor losses, such as... Figure 1 As shown, the method includes the following:

[0036] Obtain the protein sequence of the enzyme to be predicted and input it into the trained enzyme optimal pH prediction model to obtain the enzyme optimal pH prediction result.

[0037] The training process for the enzyme optimal pH prediction model includes:

[0038] S1: Obtain the protein sequence dataset of the enzyme and divide it into training and test sets. Use the GraphEC model to process the protein sequences of the enzyme in the training set to obtain the activity value of each amino acid.

[0039] Obtain the protein sequence dataset of the enzyme. Preferably, the EpHod dataset can be used, retaining its original data partitioning method (randomly selecting 20% ​​of the sequences as the test set for final model performance evaluation; the remaining 80% of the sequences are clustered using MMseqs2 based on the 20% sequence identity to avoid data leakage due to high similarity sequences between the training and test sets). The original dataset contains 9855 sequences. After removing sequences with non-standard amino acids, a total of 9728 tagged protein sequences are obtained, including 7033 in the training set, 1944 in the test set, and 751 in the validation set.

[0040] GraphEC is an EC numbering predictor based on graph geometry learning. Given a protein sequence, it uses a pre-trained protein language model, ProtTrans, to extract evolutionary information while simultaneously using ESMFold to predict protein structure. Next, it constructs a protein graph based on the structural information and extracts geometric information through a geometric feature extraction module. These features are then fed into a graph geometry learning network to learn geometric embeddings, which can be used to predict active sites.

[0041] For obtaining enzyme active sites, this invention uses the GraphEC model to predict active sites in protein sequences. GraphEC calculates a Score value, or activity value, for each amino acid of the protein; the larger the value, the more likely it is to be an active site. Since different proteins have different sequence lengths, to standardize the active site data, all data are uniformly filled to the maximum sequence length in the dataset (1021 amino acids), and the corresponding Score value is assigned to 0.

[0042] S2: Physicochemical characteristics of the protein sequence of the extracted enzyme.

[0043] The physicochemical characteristics of an enzyme's protein sequence include the number of acidic amino acids, the number of basic amino acids, sequence length, molecular weight, isoelectric point, instability index, hydrophobicity, aromatic ratio, aliphatic amino acid index, and protein type.

[0044] The ProteinAnalysis module in the BioPython library was used to calculate the relevant properties of the enzyme, including the number of acidic amino acids, the number of basic amino acids, sequence length, molecular weight, isoelectric point, instability index, hydrophobicity, aromatic ratio, and aliphatic amino acid index; the EC value was directly taken from the sequence information in the EpHod database.

[0045] S3: The protein sequence of the enzyme was processed using the ESM-2 650M model and the ESMC-600M model, respectively, and the processed features were averaged and pooled to obtain EMS2 characterization and ESMC characterization.

[0046] The ESM-2 650M model is one of the models in the ESM-2 series. Based on the Transformer architecture, it captures the structural, functional, and evolutionary characteristics of amino acid sequences through deep learning. The ESMC-600M model is a parallel model series of ESM3 generative models. Based on the Transformer architecture, it uses a self-attention mechanism to identify complex relationships in protein sequences, focusing on creating representations of the underlying biology of proteins.

[0047] This invention uses the ESM-2 650M and ESMC-600M models to process the protein sequences of the enzyme, respectively, and uses average pooling to process each protein, obtaining 1280-dimensional and 1152-dimensional vectors, i.e., EMS2 representation and ESMC representation, respectively. For example, a protein sequence (e.g., length L) is input into the ESM model, and the model generates a D-dimensional vector for each amino acid (ESM-2: D = 1280; ESMC: D = 1152). The output shape is L×D (e.g., 300 amino acids → 300×1280 matrix). Average pooling is the averaging of the vectors of L amino acids by dimension, compressing the L×D matrix into a 1×D global vector (e.g., 1×1280).

[0048] S4: Use the activity value of the amino acid as the weight value corresponding to the amino acid to perform weighted pooling on the EMS2 characterization to obtain the weighted EMS2 characterization.

[0049] To incorporate enzyme active site information into the model, the obtained active site data, i.e., amino acid activity values, were used to weight the ESM2 representation. Both the active site data and the ESM2 representation data were already filled to the maximum number of amino acids in 1021 dimensions. Therefore, the score value of each amino acid was directly used as the weight value for that amino acid, and weighted pooling was applied to the ESM2 representation. The final result was a 1280-dimensional vector after weighted pooling, i.e., the weighted ESM2 representation.

[0050] S5: Combined characteristics are obtained by fusing protein physicochemical features, EMS2 characterization, ESMC characterization, and weighted EMS2 characterization.

[0051] This invention employs a multi-feature fusion deep neural network architecture. By integrating the physicochemical properties of proteins with the sequence representations of pre-trained language models (ESM-2 and ESMC), it ultimately outputs the optimal pH prediction value for the protein. First, it fuses the protein's physicochemical features, EMS2 representation, ESMC representation, and weighted EMS2 representation to obtain joint features, specifically:

[0052] The protein physicochemical features are input into a fully connected layer and linearly transformed to 512 dimensions. The EMS2, ESMC, and weighted EMS2 representations are then dimensionality-reduced using a two-layer MLP network (Linear(input dimension → 1024) → ReLU → Dropout → Linear(1024 → 512) → ReLU) to obtain four features of a unified dimension. This design enhances feature representation through nonlinear transformation, while the Dropout layer (dropout rate = 0.5) alleviates overfitting. The four features of the unified dimension are then concatenated along the channel dimension to form a 2048-dimensional joint feature. This concatenation method preserves the independence of the original features, providing a rich information foundation for subsequent residual blocks.

[0053] S6: Input the joint features into the prediction network for processing to obtain the optimal pH prediction results for the enzyme.

[0054] To address the gradient vanishing problem in deep networks, the prediction network employs four residual blocks to further extract higher-order features. The structure of each block is as follows:

[0055] Dense layer: A fully connected layer (Linear) that maintains 2048-dimensional input and output;

[0056] BatchNorm layer: A normalization layer that accelerates convergence and improves stability;

[0057] ELU activation layer (Exponential Linear Unit): provides nonlinearity and alleviates gradient sparsity;

[0058] Dropout(rate=0.5): Randomly deactivates the virus to improve generalization.

[0059] After being processed by four residual blocks, the joint features are residually connected to the joint features to obtain residual enhanced features. The residual connection ensures lossless information transmission. Through iterative optimization of residual blocks, the model can gradually integrate physicochemical properties and sequence semantic features, and capture the complex patterns of pH regulation.

[0060] Finally, the 2048-dimensional residual enhancement features are mapped to a 1-dimensional output through a fully connected layer (Linear) to obtain the optimal pH prediction result for the enzyme.

[0061] S7: Calculate the total model loss and adjust the model parameters based on the total model loss to obtain the optimal enzyme pH prediction model. Based on the optimal enzyme pH prediction model, predict the protein sequences in the test set to complete the model training.

[0062] The process of calculating the total loss of the model includes:

[0063] Calculate the cosine similarity between the current enzyme's EMS2 characterization and the EMS2 characterizations of other enzymes in the training set; the cosine similarity is expressed as:

[0064]

[0065] Where S represents cosine similarity, A represents the EMS2 representation of the current enzyme, B represents the EMS2 representation of other enzymes, D represents the vector dimension, and A i B represents the i-th dimension vector in the current EMS2 characterization of the enzyme. i The i-th dimension vector represents the EMS2 characterization of other enzymes.

[0066] The label corresponding to the enzyme with the highest cosine similarity is used as the pseudo-label for the current enzyme. To avoid data leakage, for each sequence in the training set, similar proteins are searched within the training set; for the test set and validation set, similar proteins are searched within the training set.

[0067] The primary loss is calculated based on the true label and the enzyme's optimal pH prediction results, while the secondary loss is calculated based on the pseudo-label and its predicted values. The secondary loss is mainly used to correct and optimize the primary loss, and the hyperparameter w... i In other words, label distribution smoothing weights are used to enhance sparse data prediction and balance uneven label distribution. i The numerical value is determined by the sparsity of the data interval.

[0068] The main losses are expressed as follows:

[0069]

[0070] For the optimal pH of proteins, most data is concentrated in the neutral range, with fewer data points for acidic and basic proteins. This imbalanced distribution leads to lower prediction accuracy for acidic and basic regions compared to the neutral range. To address this issue, this invention introduces an LDS reweighting strategy. This method divides the training data into 100 sub-regions based on the pH distribution range. Each region is reweighted according to data density when calculating the loss, ultimately decreasing the loss weight of high-density regions and increasing the loss weight of low-density regions. This method can optimize the low prediction accuracy in acidic and basic regions. The relevant calculation formulas are shown below:

[0071]

[0072] The Gaussian kernel function is used here. In the formula, the kernel function is adjusted as follows: Where σ is the bandwidth, controlling the width and smoothness of the kernel, and y i y represents the true label of sample i. j P(y) represents the true label of sample j, and n represents the total amount of data used to calculate the label density;i ) represents the label value y i The probability density, P(y) i The value of ) reflects y i The density of nearby data points, ε represents the stability coefficient, used to ensure numerical stability, and takes a value of 1e. -8 α represents the label distribution smoothing coefficient. The hyperparameter α is used to control the adjustment intensity of the label distribution smoothing weights (controlling the fineness of the interval density; this parameter will be used as a hyperparameter, and the optimal value will be automatically found in the hyperparameter grid search, with a range of 0 to 1); when calculating the interval density, when α = 0, all weights are 1 (equivalent to disabling LDS); when 0 < α < 1, the weight distribution will be smoothed, reducing the influence of extreme weights (preventing a few samples from having excessive weights); when α > 1, the weight differences will be amplified (more aggressively emphasizing low-frequency samples); in the preferred embodiment of the present invention, α is 0.3.

[0073] The essence of this formula is to use each data point y j Place a Gaussian "bell curve" at the center, then superimpose and normalize all the curves to obtain an overall probability density estimate.

[0074] Secondary losses are represented as follows:

[0075]

[0076] The total model loss is obtained by weighted summation of the primary and secondary losses. The total model loss is expressed as:

[0077]

[0078] Among them, L total w represents the total loss of the model, N represents the number of samples, and w i y represents the smoothing weights of the label distribution for the i-th sample. i This represents the true label of the i-th sample. λ represents the optimal pH prediction result for the i-th sample; aux This represents the balance coefficient, used to control the impact of minor losses on the total loss; r i This represents the pseudo-label of the i-th sample. This represents the pseudo-label prediction value for the i-th sample.

[0079] To balance the secondary and primary losses, a hyperparameter λ is introduced. aux To balance the two losses and find the optimal parameters. λ aux The larger the value of λ, the greater the secondary loss; a value of 0 means no secondary loss is introduced. After adjustment, the optimal λ is... aux It is 0.3.

[0080] The model parameters are adjusted based on the total model loss, and iterative training is continuously performed. Training stops when the total model loss converges or reaches the maximum preset number of iterations. The current model parameters are saved to obtain the optimal enzyme pH prediction model. The optimal enzyme pH prediction model is then used to predict protein sequences in the test set to complete the model training.

[0081] The enzyme protein sequence to be predicted is obtained and input into a trained enzyme optimal pH prediction model to obtain the enzyme optimal pH prediction result.

[0082] Using the same dataset and data partitioning method, this invention was retrained with other comparative models (EpHod, CatOpt, Seq2pHopt, OphPred, and Venus-DREAM) and evaluated using a test set. The metrics used were MAE, RMSE, R2, Pearson, and Spearman; where MAE is the mean absolute error, used to measure the prediction accuracy of the predictive model on continuous data. It measures the average absolute difference between predicted and true values, indicating the average deviation between the predicted and true values; the smaller the MAE, the more accurate the model's prediction; RMSE, the root mean square error, is sensitive to outliers (squaring amplifies the impact of large errors) and focuses more on samples with large prediction bias; the smaller the RMSE, the more accurate the model's prediction; R² is used to evaluate the explanatory power of a regression model on the data, that is, the proportion of the dependent variable variation that the model can explain to the total variation; the larger the R², the more accurate the model's prediction; Pearson correlation coefficient measures the linear correlation between two continuous variables; the larger the Pearson coefficient, the more accurate the model's prediction; Spearman correlation coefficient measures the monotonic relationship between two variables (continuous or ordinal categorical); the larger the Spearman coefficient, the more accurate the model's prediction.

[0083] like Figure 2 As shown, in comparison with other models, the model proposed in this invention achieves the best results on all evaluation metrics, with MAE significantly outperforming other works. Compared to other single models that only use ESM for characterization, the multimodal composite model of this invention utilizes enzyme-based domain knowledge and advanced loss calculation methods, achieving optimal performance.

[0084] In summary, this invention associates enzymes with their active sites and captures the rule that similar proteins have similar optimal pH values. Therefore, by combining this relevant knowledge with traditional protein characterization methods and incorporating optimized loss function calculation methods, the best model performance is achieved, significantly improving the prediction accuracy of enzyme optimal pH and demonstrating promising application prospects.

[0085] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the optimal pH of an enzyme based on its active site and minor losses, characterized in that, include: Obtain the protein sequence of the enzyme to be predicted and input it into the trained enzyme optimal pH prediction model to obtain the enzyme optimal pH prediction result. The training process for the enzyme optimal pH prediction model includes: S1: Obtain the protein sequence dataset of the enzyme and divide it into training and test sets. Use the GraphEC model to process the protein sequences of the enzyme in the training set to obtain the activity value of each amino acid. S2: Physicochemical characteristics of the protein sequence of the extracted enzyme; S3: The protein sequence of the enzyme was processed using the ESM-2 650M model and the ESMC-600M model, respectively, and the processed features were averaged and pooled to obtain the EMS2 characterization and ESMC characterization. S4: Use the activity value of the amino acid as the weight value corresponding to the amino acid to perform weighted pooling on the EMS2 characterization to obtain the weighted EMS2 characterization. S5: Integrate protein physicochemical features, EMS2 characterization, ESMC characterization, and weighted EMS2 characterization to obtain joint features; the process of obtaining joint features includes: inputting protein physicochemical features into a fully connected layer for processing, and performing dimensionality reduction on EMS2 characterization, ESMC characterization, and weighted EMS2 characterization through two layers of MLP network to obtain four features of a unified dimension; concatenating the four features of the unified dimension along the channel dimension to obtain joint features; S6: Input the joint features into the prediction network for processing to obtain the optimal pH prediction results for the enzyme. S7: Calculate the total model loss and adjust the model parameters based on the total model loss to obtain the optimal enzyme pH prediction model. Predict the protein sequences in the test set based on the optimal enzyme pH prediction model to complete the model training. The total model loss is the weighted sum of the primary loss and the secondary loss.

2. The method for predicting the optimal pH of an enzyme based on its active site and minor losses according to claim 1, characterized in that, The physicochemical characteristics of the protein sequence of the enzyme include the number of acidic amino acids, the number of basic amino acids, sequence length, molecular weight, isoelectric point, instability index, hydrophobicity, aromatic ratio, aliphatic amino acid index, and protein type.

3. The method for predicting the optimal pH of an enzyme based on its active site and minor losses according to claim 1, characterized in that, The process of inputting the joint features into the prediction network includes: the joint features are processed sequentially through the Dense layer, BatchNorm layer, ELU activation layer and Dropout layer, and then residually connected with the joint features to obtain residual enhanced features; the residual enhanced features are then input into the fully connected layer for processing to obtain the enzyme's optimal pH prediction result.

4. The method for predicting the optimal pH of an enzyme based on its active site and minor losses according to claim 1, characterized in that, The process of calculating the total loss of the model includes: Calculate the cosine similarity between the current enzyme's EMS2 characterization and the EMS2 characterizations of other enzymes in the training set; use the label corresponding to the enzyme with the highest cosine similarity as the pseudo-label of the current enzyme. The primary loss is calculated based on the actual label and the enzyme's optimal pH prediction results, and the secondary loss is calculated based on the pseudo-label and the pseudo-label prediction values. The total loss of the model is obtained by weighted summation of the primary and secondary losses.

5. The method for predicting the optimal pH of an enzyme based on its active site and minor losses according to claim 1, characterized in that, The main losses are expressed as follows: ； in, Indicates the main losses, Indicates the number of samples. This represents the smoothing weights of the label distribution for the i-th sample. This represents the true label of the i-th sample. This represents the optimal pH prediction result for the i-th sample. This represents the stability coefficient.

6. The method for predicting the optimal pH of an enzyme based on its active site and minor losses according to claim 5, characterized in that, The formula for calculating the label distribution smoothing weights is: ； in, This represents the smoothing weights of the label distribution for the i-th sample. The true label of the i-th sample The probability density, Represents the stability coefficient. This represents the label distribution smoothing coefficient.

7. The method for predicting the optimal pH of an enzyme based on its active site and minor losses according to claim 1, characterized in that, Secondary losses are represented as follows: ； in, Indicates secondary losses. Indicates the number of samples. This represents the pseudo-label of the i-th sample. This represents the pseudo-label prediction value for the i-th sample.

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