A protein sequence design method and device based on a Graphormer algorithm and a storage medium

Abstract

This invention relates to a protein sequence design method, apparatus, and storage medium based on the Graphormer algorithm. The method includes: representing the protein structure as a graph, using individual amino acids as nodes and the connections between amino acids as edges; extracting initial edge features and initial node features of the protein; concatenating the initial node features of the protein with a random matrix, adjusting the dimensions through a linear layer, and adding positional encoding information to obtain node features, which are used as input to the GPD model; concatenating the initial edge features of the protein with a matrix and then passing them through two linear layers to obtain edge features, which are embedded into the attention matrix of the GPD model; constructing and training a GPD model for designing protein sequences with a fixed backbone; and designing protein sequences based on the GPD model, node features, and edge features. Compared with existing technologies, this invention has a higher sequence recovery rate and higher design sequence diversity.

Description

Technical Field

[0001] This invention relates to the field of protein sequence design model construction technology, and in particular to a protein sequence design method, apparatus and storage medium based on the Graphormer algorithm. Background Technology

[0002] De novo protein design aims to design proteins with specific structures or functions. Protein design is a core problem in protein engineering, used for example to improve enzyme catalytic efficiency and antibody affinity. Protein design involves two key tasks: protein backbone design and fixed-backbone protein sequence design. Fixed-backbone protein sequence design aims to design amino acid sequences that fold into a specific protein backbone structure. Specifically, the designed sequence not only needs to fold into the desired structure but also needs to possess a specific function. This task is also known as the inverse protein folding problem.

[0003] Methods for designing protein sequences with fixed backbones can be divided into two categories: protein sequence design based on classical energy functions and protein sequence design based on deep learning. Protein sequence design based on classical energy functions, such as the widely used Rosetta series methods, minimizes the energy function of the target structure by searching for combinations of sequences and conformations. These methods rely not only on the precise definition of the protein energy function but also on the efficiency of the sampling algorithm. Their accuracy and computational speed need further improvement. With the rapid development of deep learning technology, protein sequence design based on deep learning has achieved good results in recent years. Deep learning-based protein sequence design can provide fast and accurate protein design, sparking a revolution in the field.

[0004] The Po-Ssu Huang lab built a 3D CNN model to predict residue types and rotamer dihedrals in an autoregressive manner. ProteinSolver encodes nodes as amino acid types and edges as distances between amino acids, treating sequence design as a constraint satisfaction problem. Structure Transformer extends the Transformer to graph-based protein 3D structure encoding. The ESM-IF1 model was trained using 12 million structures predicted by AlphaFold2. ProteinMPNN extends the Structure Transformer by adding a dummy Cb atom and random decoding instead of forward decoding. These methods focus on improving sequence recovery, but neglect the diversity between designed sequences, resulting in insufficient spatial coverage of the designed sequences. This often leads to designed sequences being very similar to natural sequences, especially core protein sequences.

[0005] Ideally, the designed sequence should cover a broad protein sequence space and exhibit high sequence diversity. Current methods also employ hyperparameters to enhance the diversity and variability of the designed sequence. For example, StructureTransformer and ABACUS-R construct skewed distributions using hyperparameters (temperature T in StructureTransformer and α in ABACUS-R) to improve the diversity and variability of the designed sequence. However, the values ​​of hyperparameters differ across methods, exhibiting a high degree of subjectivity. Summary of the Invention

[0006] The purpose of this invention is to provide a protein sequence design method, device, and storage medium based on the Graphormer algorithm, which improves the diversity between sequences while maintaining a high sequence recovery rate.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A protein sequence design method based on the Graphormer algorithm includes the following steps:

[0009] S1. Represent the protein structure as a graph: with individual amino acids as nodes and the connections between amino acids as edges;

[0010] S2, Extract the initial edge features of the protein;

[0011] S3. Extract the initial node features of the protein;

[0012] S4. The initial node features of the protein are concatenated with a random matrix, and the dimensions are adjusted through a linear layer. Position encoding information is added to obtain the node features, which are then used as the input to the GPD model.

[0013] S5. The initial edge features of the protein are concatenated into a matrix and then passed through two linear layers to obtain the edge features, which are then embedded into the attention matrix of the GPD model.

[0014] S6. Construct and train a GPD model for designing fixed backbone protein sequences. The GPD model includes six identical Graphormer modules connected in sequence, a linear layer processing, and a softmax. The Graphormer modules are built based on Graphormer blocks, and each Graphormer block includes an attention matrix.

[0015] S7. Design protein sequences based on GPD model, node features and edge features.

[0016] Both the initial node features and the initial edge features are translation- and rotation-invariant.

[0017] The initial edge features include a distance matrix, a displacement vector, a rotation quaternion, and the shortest path to the residues.

[0018] The initial node features include dihedral angles, predicted secondary structure, amino acid centrality, and initial protein sequence encoding.

[0019] The specific steps of concatenating the initial node features of the protein with a random matrix are as follows:

[0020] Calculate the sine and cosine values ​​of the dihedral angle to obtain the dihedral angle sine matrix and cosine matrix respectively;

[0021] The predicted secondary structure and the initial protein sequence encoding are respectively input into the embedding layer to obtain the secondary structure embedding matrix and the initial protein sequence encoding embedding matrix;

[0022] Generate normally distributed random matrices based on random number seeds;

[0023] The dihedral sine and cosine matrices, the secondary structure embedding matrix and the initial protein sequence encoding embedding matrix, the amino acid centrality matrix, and the random matrix are spliced ​​together.

[0024] The Graphormer module includes a Graphormer block, a first regularization module, a feedforward module, and a second regularization module connected in sequence. The input of the first regularization module includes the output of the Graphormer block and the initial node features, and the input of the second regularization module includes the output of the feedforward module and the output of the first regularization module.

[0025] The specific processing procedure of the Graphormer block is as follows: the input node features are processed through three linear layers to obtain Q, K, and V matrices. The Q and K matrices are multiplied to obtain the result matrix. The result matrix and the edge features are processed through softmax and then input into the attention matrix. The output of the attention matrix is ​​multiplied with the V matrix and then processed through a linear layer to obtain the output of the Graphormer block.

[0026] The GPD model is trained using the Adam optimizer to minimize the loss function, which is the classification cross-entropy.

[0027] A protein sequence design device based on the Graphormer algorithm includes a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement the method described above.

[0028] A storage medium having a program stored thereon, which, when executed, implements the method described above.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] (1) The GPD model of the present invention directly applies Graphormer to the representation of protein three-dimensional structure based on graph. Compared with the traditional Transformer architecture, the GPD model embeds edge features in the attention matrix, which enables the network to integrate node features and edge features at the same time.

[0031] (2) The present invention adds a normally distributed random matrix generated by random number seed to the node features, which makes the generated sequence more diverse and broadens the potential design space of the sequence. Attached Figure Description

[0032] Figure 1 This is a flowchart of the method of the present invention;

[0033] Figure 2 The diagram illustrates the node and edge features of a protein graph. A represents the dihedral angle of the protein backbone; B represents two design strategies for GFP proteins: one is to pre-specify specific amino acids, and the other is to design proteins from scratch; C represents an undirected graph; D represents the edge features using two residues in ubiquitin as an example; and E represents the distance matrix, basic matrix, and shortest path matrix between amino acids.

[0034] Figure 3 Here is the architecture diagram of the GPD model, where A is the overall architecture diagram of the GPD model; B is the detailed diagram of the Graphormer block; C is the edge feature processing diagram; and D is the node feature processing diagram.

[0035] Figure 4 The following is a comparison chart of the recovery rate, consistency, and diversity of different models in the examples. In the chart, A represents the performance of different models on 103 single-chain proteins; B represents the performance of different models on 14 de novo proteins.

[0036] Figure 5 The values ​​represent the frequencies of different amino acid classes in the examples, where A is the Pearson correlation coefficient between the designed and original sequences; B is the frequency of different amino acid classes on single-chain proteins; and C is the frequency of different amino acid classes on de novo proteins.

[0037] Figure 6 The following are density maps of RMSD and pLDDT: A shows the density map of RMSD calculated by comparing the predicted structures of 10,300 sequences designed for 103 single-chain proteins with the corresponding original structures, using AlphaFold2 to predict their structures; B shows the density map of RMSD calculated for 1,400 sequences designed for 14 de novo proteins; C shows the density map of pLDDT scores for the predicted structures of single-chain proteins; and D shows the density map of pLDDT scores for the predicted structures of de novo proteins.

[0038] Figure 7 This is a schematic diagram of the results of using AlphaFold2 to predict the structure of the design sequence. The design sequence of the GPD model is a superposition of the structure predicted by AlphaFold2 and the original structure. Detailed Implementation

[0039] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0040] This embodiment uses the CATH single-stranded non-redundant protein database and employs a dataset with sequence homology below 40%. After data cleaning, a total of 30,966 records were obtained. The ratio of the training set, validation set, and test set is 29,868:1,000:98.

[0041] Based on the above dataset, this embodiment provides a protein sequence design method based on the Graphormer algorithm, such as... Figure 1 As shown, it includes the following steps:

[0042] S1. Represent the protein structure as a graph: use individual amino acids as nodes and the relationships between amino acids (such as distance, interaction, etc.) as edges.

[0043] Therefore, two types of graph features can be extracted from the main chain structure of proteins: node features and edge features. Both the node and edge features introduced in this embodiment possess translation and rotation invariance.

[0044] S2. Extract the initial edge features of the protein. In this embodiment, the initial edge features include the distance matrix, the movement vector, the rotation quaternion, and the shortest pathway.

[0045] 21) Distance matrix

[0046] The distance matrix refers to the pairwise distances between all main chain atoms, in order to... Units, such as Figure 2 As shown in D, the value is two Cs. α The modulus of the atom forming vector This distance matrix is ​​characterized by translation and rotation invariance.

[0047] 22) Displacement vector

[0048] First, consider the C-chain structure of amino acids. α The amino acid-specific coordinate system O is constructed from the atoms, the main chain N atoms, and the main chain C atoms, as shown below:

[0049]

[0050] Then calculate C for all main chains. α The representation of the displacement vectors between any two atoms in the amino acid-specific coordinate system O, such as... Figure 2 As shown in D.

[0051]

[0052] Since an amino acid-specific coordinate system O is defined, this displacement vector feature is transformed into a feature with translation and rotation invariance.

[0053] 23) Rotation Quaternions

[0054] Given a specific coordinate system O for amino acids, calculate the rotation quaternion corresponding to the coordinate system rotation matrix between each pair of residues. Because this quaternion represents the relative rotation between each pair of residues, it also has translation and rotation invariance.

[0055] 24) Shortest path of residues

[0056] Based on the calculated distance matrix, To determine whether there is contact between two amino acids, a contact matrix is ​​constructed. Using this contact matrix as the Laplacian matrix of the graph, the shortest path between any two amino acids is calculated, as follows: Figure 2 As shown in E.

[0057] S3. Extract the initial node features of the protein. In this embodiment, the initial node features include dihedral angles ( The main chain secondary structure, amino acid centrality, and initial protein sequence encoding were predicted using the DSSP (Define Secondary Structure of Proteins) algorithm, along with φ.

[0058] 31) Dihedral angle

[0059] Extracting the dihedral angles of the main chain from the main chain structure. And φ, such as Figure 2 As shown in Figure A.

[0060] 32) Main chain two-dimensional structure

[0061] Based on the obtained dihedral angles of the main chain, the DSSP algorithm is used to perform an eight-category calculation on the secondary structure of the main chain, which are: 3 10 -helix, α-helix, π-helix, hydrogen bonded turn, β-harpin, β-bridge, bend, loop.

[0062] 33) Amino acid centrality

[0063] The centrality of each node is calculated using the Laplacian matrix obtained by calculating the shortest path to the residues, and this centrality is used as the centrality of the residues.

[0064] 34) Initial protein sequence encoding

[0065] The initial protein sequence encodes 22 categories (20 common amino acids, 1 labeled as other amino acids, and 1 labeled as not designed). For complete de novo sequence design, all sites are labeled as not designed. If key sites (such as catalytic sites or certain electrochemical environments) need to be preserved, they can be specified in advance, such as... Figure 2 As shown in B.

[0066] S4. Concatenate the initial protein node features with a random matrix, adjust the dimensions through a linear layer, and add positional encoding information to obtain the node features, which are then used as input to the GPD model. Figure 3 As shown in D.

[0067] S41. Calculate the sine and cosine values ​​of the dihedral angle to obtain the dihedral angle sine matrix and cosine matrix respectively;

[0068] S42. Input the predicted secondary structure and the initial protein sequence encoding into the embedding layer to obtain the secondary structure embedding matrix and the initial protein sequence encoding embedding matrix, respectively.

[0069] S43. Generate a normally distributed random matrix based on a random number seed;

[0070] S44. Concatenate the dihedral sine and cosine matrices, the secondary structure embedding matrix and the initial protein sequence encoding embedding matrix, the amino acid centrality matrix and the random matrix.

[0071] S45. Adjust the dimensions of the concatenated features through a linear layer and add positional encoding information to obtain node features.

[0072] S5. The initial edge features of the protein are concatenated into a matrix and then passed through two linear layers to obtain the edge features, which are then embedded into the attention matrix of the GPD model, such as... Figure 3 As shown in C.

[0073] S6. Construct and train a GPD model for designing fixed backbone protein sequences. The GPD model consists of six identical Graphormer modules connected in sequence (e.g., ...). Figure 3 (as shown in the dashed box of A), linear layer processing, and softmax.

[0074] The GPD model directly applies the Graphormer algorithm to the graph features of proteins, enabling the network to integrate both node and edge features simultaneously.

[0075] The Graphormer module includes a Graphormer block, a first regularization module, a feedforward module, and a second regularization module connected in sequence. The input to the first regularization module includes the output of the Graphormer block and initial node features. The input to the second regularization module includes the output of the feedforward module and the output of the first regularization module. Figure 3 As shown in Figure A.

[0076] The specific processing procedure of the Graphormer block is as follows: the input node features are processed through three linear layers to obtain Q, K, and V matrices. Matrix multiplication is performed on the Q and K matrices to obtain the result matrix. The result matrix and edge features are then processed through softmax and input into the attention matrix. The output of the attention matrix is ​​then multiplied with the V matrix and passed through a linear layer to obtain the output of the Graphormer block. Figure 3 As shown in B.

[0077] The GPD model is trained using the Adam optimizer to minimize the loss function, which is the classification cross entropy. The initial learning rate is 0.001. The mini-batch size during model training is 64, and the training epochs are 500.

[0078] This embodiment uses the PyTorch framework for training on the Pi 2.0 high-performance supercomputer at Shanghai Jiao Tong University, using NVIDIA Tesla V100 GPUs with 32GB of memory per GPU.

[0079] S7. Design protein sequences based on GPD model, node features and edge features.

[0080] This embodiment uses the Wilcoxon signed-rank test to compare the performance differences between different models. All statistical analyses were performed in R version 3.6.1.

[0081] The experimental verification content of this embodiment is as follows:

[0082] p1) Evaluate the performance of different models

[0083] Based on the above method, this embodiment evaluates the performance of the GPD model on two independent test sets: single-chain proteins (containing 103 proteins) and de novo proteins (containing 14 proteins). Three metrics are used to evaluate the performance: sequence recovery, identity between designed sequences, and diversity between designed sequences. Sequence recovery is the proportion of identical amino acids at corresponding positions in the designed and reference sequences relative to the total length. Sequence identity is the proportion of identical amino acids at corresponding positions between any two designed sequences relative to the total length. Sequence diversity is 1 minus the proportion of similar amino acids at corresponding positions between any two designed sequences relative to the total length. Sequence recovery and sequence diversity are two important metrics in fixed-backbone protein sequence design; they influence and counterbalance each other. A higher sequence recovery rate comes at the cost of lower sequence diversity, and vice versa. Both sequence recovery and sequence diversity should be considered simultaneously in fixed-backbone protein sequence design.

[0084] like Figure 4As shown, the sequence recovery rates of the GPD model on single-chain proteins and de novo proteins were 27.9% ± 5.3% and 46.2% ± 4.7%, respectively, with sequence consistency among designed sequences at 60.8% ± 4.9% and 65.8% ± 3.4%, respectively. Sequence diversity among designed sequences was 28.0% ± 4.9% and 21.9% ± 2.5%, respectively. The GPD model showed significantly higher sequence recovery rates than the ProteinSolver and Structure Transformer models on both single-chain and de novo proteins, but lower rates only on single-chain proteins compared to the ESM-IF1 model. The ESM-IF1 model training set included 12 million structures predicted by AlphaFold2 in addition to the CATH dataset, while other models were trained only on the CATH dataset. More datasets would help improve model performance. The sequence diversity of the GPD model on de novo proteins was slightly higher than that of the ESM-IF1 model (P = 0.058). There was no significant difference in sequence diversity between the GPD and ESM-IF1 models on single-chain proteins (P = 0.625). Higher sequence diversity means that the designed sequences cover a wider sequence space. Considering these metrics, the GPD model outperforms the ProteinSolver and Structure Transformer models, and achieves similar performance to the ESM-IF1 model with less training data. Furthermore, compared to other models, the GPD model's designed sequences show a more concentrated distribution of recovery rate, consistency, and diversity scores, indicating that the GPD model has higher robustness.

[0085] During the model comparison process, 100 sequences were designed for each single-chain protein and de novo protein, resulting in a total of 11,700 sequences. It was found that the sequence lengths designed based on the ProteinSolver, Structure Transformer, and ESM-IF1 models differed from the reference sequence lengths, with the proportions of sequences with different lengths being 1.71%, 24.78%, and 1.20%, respectively. However, the sequence lengths designed using the GPD model were exactly the same as the corresponding reference sequence lengths.

[0086] p2) Frequency of different amino acid classifications

[0087] like Figure 5As shown in Figure A, among the four models—ProteinSolver, Structure Transformer, ESM-IF1, and GPD—the Pearson correlation coefficients for the frequency of each amino acid between the designed and reference sequences were 0.851, 0.882, 0.919, and 0.778 for single-chain proteins, respectively; and 0.925, 0.910, 0.874, and 0.807 for de novo proteins, respectively. The GPD model showed lower Pearson correlation coefficients for both single-chain and de novo proteins compared to other methods, indicating that the sequences designed using the GPD model exhibit higher sequence diversity.

[0088] Figure 5 BC shows the frequency of different amino acid categories. Based on folding ability, amino acids can be divided into two categories: random-biased amino acids (alanine, glycine, proline, arginine, glutamine, serine, glutamic acid, and lysine) and structure-biased amino acids (the other 12 amino acids). Compared with other methods, the sequences designed by the GPD model have a higher frequency of structure-biased amino acids and a correspondingly lower frequency of random-biased amino acids. More structure-biased amino acids can better promote protein folding.

[0089] p3) AlphaFold2 Predicted Sequence Structure

[0090] For each model, AlphaFold2 was used to predict the structures of 10,300 sequences generated from 103 single-chain proteins and 1,400 sequences generated from 14 de novo proteins. The predicted structures were then compared to corresponding reference structures to calculate the RMSD. Figure 6 AB is the density plot of RMSD. Figure 6 CD is the density map of pLDDT scores (predicted local distance difference test scores, pLDDT) for AlphaFold2 predicted structures. Based on RMSD and pLDDT, ProteinSolver performs poorly on both single-chain and de novo proteins. For the StructureTransformer, ESM-IF1, and GPD models, the top 5 sequences with the highest RMSD ranking (sorted from smallest to largest) were selected. For single-chain proteins, the average RMSD values ​​of the top 5 sequences were as follows: and For the de novo protein, the average RMSD values ​​of the top 5 sequences were as follows: and Their RMSD is all less than This indicates that the predicted sequences can fold well. For single-chain proteins, the average pLDDT value of the predicted structures from the top 5 sequences is greater than 70, and for de novo proteins, the average pLDDT value of the predicted structures from the top 5 sequences is greater than 88. In summary, the sequences designed by the Structure Transformer model, the ESM-IF1 model, and the GPD model have stable folding capabilities and outperform ProteinSolver.

[0091] For 14 de novo proteins, the sequence with the smallest RMSD predicted by the GPD model is as follows: Figure 7 As shown. The GPD model design sequence was superimposed using the predicted and reference structures from AlphaFold2. The figure shows the name of each de novo protein and its corresponding RMSD. The average RMSD of the 14 de novo proteins is... (from arrive ).

[0092] p4) Online Server

[0093] This embodiment develops an online analysis tool called GPDGenerator. This server, based on a pre-trained GPD model, takes a PDB file as input and outputs the designed sequence. The analysis interface requires the user to input a PDB file, and the user can also pre-specify amino acids at specific positions. The results interface outputs the designed sequence in Fasta format and shows the sequence recovery rate. The input protein length should be less than 400 residues, and to conserve computational resources, the number of designed sequences should be less than 100.

[0094] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0095] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A protein sequence design method based on the Graphormer algorithm, characterized in that, Includes the following steps: S1. Represent the protein structure as a graph: with individual amino acids as nodes and the connections between amino acids as edges; S2, Extract the initial edge features of the protein; The initial edge features include a distance matrix, a displacement vector, a rotation quaternion, and the shortest path to the residues; S3. Extract the initial node features of the protein; the initial node features include dihedral angles, predicted secondary structure, amino acid centrality, and initial protein sequence encoding; both the initial node features and the initial edge features are translation- and rotation-invariant. S4. The initial node features of the protein are concatenated with a random matrix, and the dimensions are adjusted through a linear layer. Position encoding information is added to obtain the node features, which are then used as the input to the GPD model. The specific steps of concatenating the initial node features of the protein with a random matrix are as follows: Calculate the sine and cosine values ​​of the dihedral angle to obtain the dihedral angle sine matrix and cosine matrix respectively; The predicted secondary structure and the initial protein sequence encoding are respectively input into the embedding layer to obtain the secondary structure embedding matrix and the initial protein sequence encoding embedding matrix; Generate normally distributed random matrices based on random number seeds; The dihedral sine and cosine matrices, the secondary structure embedding matrix and the initial protein sequence encoding embedding matrix, the amino acid centrality matrix, and the random matrix are spliced ​​together. S5. The initial edge features of the protein are concatenated into a matrix and then passed through two linear layers to obtain the edge features, which are then embedded into the attention matrix of the GPD model. S6. Construct and train a GPD model for designing fixed backbone protein sequences. The GPD model includes six identical Graphormer modules connected in sequence, a linear layer processing, and a softmax. The Graphormer modules are built based on Graphormer blocks, and each Graphormer block includes an attention matrix. The Graphormer module comprises a Graphormer block, a first regularization module, a feedforward module, and a second regularization module connected in sequence. The input to the first regularization module includes the output of the Graphormer block and initial node features. The input to the second regularization module includes the output of the feedforward module and the output of the first regularization module. The specific processing procedure of the Graphormer block is as follows: the input node features are passed through three linear layers to obtain Q, K, and V matrices. Matrix multiplication is performed on the Q and K matrices to obtain the result matrix. The result matrix and edge features are processed by softmax and then input into the attention matrix. The output of the attention matrix is ​​multiplied by the V matrix and then passed through a linear layer to obtain the output of the Graphormer block. S7. Design protein sequences based on GPD model, node features and edge features.

2. The protein sequence design method based on the Graphormer algorithm according to claim 1, characterized in that, The GPD model is trained using the Adam optimizer to minimize the loss function, which is the classification cross-entropy.

3. A protein sequence design device based on the Graphormer algorithm, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-2.

4. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the method as described in any one of claims 1-2.

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