Methods and systems for end-to-end protein design and analysis verification

Abstract

The application provides a method and system capable of end-to-end protein design and analysis verification, and can generate protein or protein complex structure and sequence according to specific requirements, and the method comprises the following steps: performing loss calculation on the three-dimensional structure of the initialized protein sequence obtained through the structure prediction algorithm independently developed by the company based on confidence, stability, target correlation; continuously improving the designed protein sequence and structure based on the Markov chain Monte Carlo algorithm or gradient regression according to the obtained loss; and putting the designed protein structure into a sequence design model to optimize the side chain, and obtaining the optimal candidate protein through screening. The method can train the model to be specific and automatic for protein design, and can generate a new artificial protein which is completely different from natural protein in structure and sequence.

Description

Technical Field

[0001] This invention belongs to the fields of bioinformatics and deep learning, and specifically relates to a method and system that can complete protein design and analysis testing end-to-end. Background Technology

[0002] Proteins are essential carriers and components of life functions. The three-dimensional spatial structure of proteins, formed during evolution, has laid the foundation for their functions such as catalysis, binding, and signal transduction within cells. However, natural proteins are limited by the evolutionary cycle and the probability of discovery through biological experiments. Many functional needs remain unmet in human production and daily life, such as in biomedical and synthetic biology applications. Artificial protein design can fill this gap. Traditional directed evolution methods use wet experiments to continuously mutate and modify peptide chains close to the target protein to generate proteins with new or enhanced functions. However, this method is not only time-consuming and costly but also has a low success rate. Therefore, there is an urgent need for effective computational methods to empower protein design, achieving automated and rational design of artificial proteins.

[0003] Computational protein design primarily falls into two categories: one combines virtual directed evolution (point mutation) with molecular docking or molecular dynamics models, optimizing the target protein sequence through random mutation and simulated screening; the other uses deep learning computational models to predict the function of the designed protein sequence and then optimizes it to generate the target protein sequence that best matches the prediction. The first type of method has not been widely adopted in practical applications due to the difficulty in accurately calculating binding energies with molecular docking models (such as Rosetta, Schrodinger, and Yasara) and the excessively long simulation times and parameter dependence of molecular dynamics models (such as GROMACS and CADEE). These methods often require a combination of luck, computational power, and experience in protein design. Therefore, deep learning-based protein sequence design has become a fiercely contested area in biological science discovery in recent years. Most mature models use the target protein sequence as input and optimize the sequence using predictive models to generate the final designed sequence.

[0004] Patent document 202211084612.4 discloses a method, apparatus, electronic device, and storage medium for protein generation. It continuously optimizes candidate protein sequences by predicting their structures and comparing them with the structures of target proteins. The process mainly consists of four steps:

[0005] 1. Generate candidate proteins by sampling based on the target protein;

[0006] 2. Input the sequence of the candidate protein into the single-sequence protein secondary / tertiary structure prediction model to obtain the structural information of the candidate protein;

[0007] 3. Based on the structural information of the candidate protein and the target protein, perform relevant quality assessments on the candidate protein and obtain the quality assessment results of the candidate protein;

[0008] 4. The candidate protein sequences are continuously optimized based on the quality assessment results, and finally, if the assessment meets the standards, the candidate protein is determined as the final designed protein;

[0009] This process is a standard computational process in the field of protein design, but it does not provide a specific implementation plan. For example, the loss function and protein sequence update method described in detail in this invention have a relatively broad scope, which is not conducive to practical application compared with the model of this invention.

[0010] The main difference between this process and the model of this invention in step 1 is the initialization method for designing proteins based on the target protein. The process of this invention can adopt either random sampling initialization or specified sequence initialization. Although sampling by fitting the target protein can more closely approximate the function of the target protein during the optimization process and avoid the difficulty of optimization, it lacks design diversity, and therefore it is difficult to make the protein exhibit characteristics that surpass those of the natural target protein during the design process.

[0011] In step 2 of this process, only the three-dimensional structure of a single-sequence protein can be predicted. However, the process of this invention can predict the structure of multi-chain protein complexes, thus enabling the design of more complex protein-binding ligands and protein complexes.

[0012] The evaluation criteria adopted in step 3 of this process include the evaluation of primary and secondary structures, such as the similarity between the primary / secondary structure and the original target structure. However, the model of this invention only evaluates the tertiary structure of the protein, thereby avoiding the problem that the primary / secondary structure fails to fit and predict the protein function well (i.e., as is well known, protein function depends on the tertiary structure. Some proteins with very different sequences have similar functions because they have similar tertiary structures. If the primary / secondary structure is used for prediction, it will add unnecessary noise to the evaluation effect of the designed protein).

[0013] The current process in step 3 only covers losses in similarity and confidence such as torsion angle loss and LpTM, without assessing protein stability and consistency as in the process of this invention. Therefore, the generated protein may lack syntheticity and thermal stability. Furthermore, relying solely on losses such as similarity and confidence can only assess the fit to the target protein, and cannot enable the more flexible designs achievable by the method of this invention, such as generating proteins based on motifs, generating binding ligands for specified target proteins in the absence of known motifs, or designing complexes with fixed lengths and chain numbers.

[0014] The process does not provide specific protein sequence optimization methods and strategies (such as MCMC, gradient regression) in step 4, and therefore only shows the industry-standard computational process, which is not unique.

[0015] Patent document CN112289372B discloses a protein structure design method and device based on deep learning. It uses a graph generation model to generate amino acid sequences based on the sequence and structure of a target protein, and then performs structure prediction and molecular dynamics optimization on the sequences. The process mainly consists of four steps:

[0016] 1. Determine or generate the sequence and three-dimensional structure information of target proteins based on biomarkers;

[0017] 2. Input the sequence and three-dimensional structure information of the target protein into a graph neural network model to train and generate an amino acid sequence;

[0018] 3. Perform homologous protein matching and backbone prediction on the generated amino acid sequences;

[0019] 4. Optimize the design of protein backbones based on molecular dynamics simulations;

[0020] This model also designs proteins through the prediction and optimization of three-dimensional structures, but the main difference between it and the process of this invention is:

[0021] This model employs a complex graph neural network based on targeted structures to design protein sequences, while the model of this invention can directly design protein sequences through gradient backpropagation based on a structure prediction model. Not only are the design philosophies completely different, but the method of this invention also boasts superior computational efficiency and is more conducive to global optimization. Furthermore, starting from the targeted protein structure limits the protein design target to only a small portion of the achievable goals covered by the protein design method described in this invention, and cannot complete the design and optimization work for motif proteins, proteins with specified symmetries, etc., covered by this method.

[0022] This model optimizes designed proteins based on molecular dynamics simulations, which limits its speed and places excessive demands on computing power; a single molecular dynamics simulation often takes several minutes to several hours. In contrast, the method of this invention employs a completely different artificial intelligence generation algorithm, where the AI ​​model can rapidly optimize thousands to tens of thousands of design sequences. Summary of the Invention

[0023] The purpose of this invention is to overcome the shortcomings and deficiencies of existing technologies and provide a method and system for end-to-end protein design and analysis. This system can generate protein or protein complex structures and sequences according to specific needs, such as designing proteins with a certain motif, designing target ligand-binding proteins of a specified length, or designing complexes of a specified length and chain number. All of these can follow the unified design approach proposed in this invention. The method includes: calculating the loss based on confidence, stability, and target relevance using the three-dimensional structure obtained from the initialized protein sequence through the company's independently developed structure prediction algorithm; continuously improving the designed protein sequence and structure based on the obtained loss using Markov chain Monte Carlo algorithm or gradient regression; optimizing the side chains of the designed protein structure by placing it into a sequence design model, and then selecting the optimal candidate protein. This method uses a trainable model to concretize and automate protein design, and can generate novel artificial proteins with structures and sequences completely different from natural proteins.

[0024] The objective of this invention can be achieved through the following methods:

[0025] In a first aspect, the present invention provides a method for end-to-end protein design and analysis, comprising the following steps:

[0026] A1. Initialize the protein sequence or sequence code required according to the specified length, compile it with one-hot encoding, and input it into the protein folding algorithm TRFold2 for prediction of the three-dimensional structure.

[0027] A2. Based on the predicted three-dimensional structure, give the confidence score and the loss representing stability, and calculate the corresponding loss according to the specific design purpose. Integrate all the required losses into a learnable loss function.

[0028] A3. Update the original sequence using gradient descent or Markov chain Monte Carlo algorithm based on the loss function, then repeat step A2 to calculate the new loss and update the protein sequence again; perform iterative optimization to obtain the optimal candidate protein structure and sequence, i.e. the design result with the lowest loss.

[0029] A4. Input the obtained optimal candidate protein structure into the sequence design model for side chain reconstruction optimization to better fit the design structure and increase stability; perform analysis and verification of the reconstructed sequence based on the open-source algorithm AlphaFold2, and obtain the optimal design protein after screening.

[0030] Preferably, in step A1, the protein folding algorithm TRFold2 is independently developed by our company, with application number 2023104312745, and its application in this invention includes the following steps:

[0031] Step S1: Obtain residue pairs encoded by the input sequence and update them using a triangular update mechanism;

[0032] Step S2: The current residue pair encoding and the target sequence encoding are updated using an invariant point attention neural network to update the current target sequence encoding;

[0033] Step S3: Update the main chain framework based on the interaction information between residue pairs encoded by the current target sequence, and calculate the torsion angles between residues and atoms to predict the protein structure.

[0034] Preferably, in step S1, the residue pair encoding includes one-hot encoding of the distance between β carbon atoms of the residue, the location of α carbon atoms around each residue, and residue site mask information.

[0035] Preferably, in step S1, the triangular update mechanism updates the encoding of residue pairs by using the edges of adjacent residue pairs to ensure that the encoding satisfies the triangular inequality property in 3D space.

[0036] The triangular update mechanism includes a triangular product update mechanism and a triangular self-attention update mechanism; wherein, the triangular product update mechanism updates the residue edges by using the neighboring edge information that forms a triangle with the opposite edge of the residue, and includes a product layer based on outward bordering edges and a product layer based on inward bordering edges.

[0037] The product layer based on the outward border and the product layer based on the inward border are respectively adopted as follows:

[0038] E ij =g(E ij )⊙f(∑ k g(E ik )⊙g(E jk ));

[0039] E ij =g(E ij )⊙f(∑ k g(E ki )⊙g(E kj ));

[0040] Among them, E ij denoted by , g represents the superposition function of the linear layer and the activation function, and f represents the superposition function of the layer normalization and the linear layer.

[0041] The triangular self-attention update mechanism updates the residue edges by using the information of the neighboring edges that are adjacent to the start / end points of the residue's opposite edge. It includes a triangular attention layer based on the start point and a triangular attention layer based on the end point.

[0042] The triangular attention layer based on the start point and the triangular attention layer based on the end point respectively adopt:

[0043] E ij =trans(att(Q) ij K ik V ik ));

[0044] E ij =trans(att(Q) ij K kj V kj ))

[0045] Among them, Q ij K ij V ij E respectively ij The derived query, key, and value vectors used for self-attention computation, att represents the self-attention update model, and trans represents the transition layer containing regularization and activation functions.

[0046] Preferably, in step S2, the invariant point attention neural network employs the following: the sequence encoding calculates the query, key, and value vectors for each amino acid in the coding space and 3D space respectively through a linear layer; then, the attention matrix of the coding space and the attention matrix of the 3D space based on the global invariance of the initial main chain framework are calculated according to the attention mechanism; and the current residue pair encoding is introduced as the deviation value of the attention matrix to obtain the final attention matrix. The target sequence encoding is then updated iteratively through the attention matrix.

[0047] Preferably, the step of iteratively updating the target sequence encoding through the attention matrix employs:

[0048]

[0049]

[0050]

[0051]

[0052] Where, m i A represents the encoding of the i-th residue in the target sequence. ij E represents the attention between residues i and j in the attention matrix. ij V represents the encoding of residue pair edge (i, j). j m i The self-attention value corresponding to the encoding space. mj The corresponding self-attention value in 3D space. This indicates that residue pairs encode a weighted output through self-attention, o i This represents the weighted output of the value in the encoding space. This represents the weighted output in 3D space, where Ti represents the main chain framework of residue i, and Linear represents the linear layer.

[0053] Preferably, the initial main chain framework T i use:

[0054] The main chain framework is initialized with an identity transformation:

[0055]

[0056] All amino acids are placed at the origin of the global coordinate system.

[0057] Preferably, in step S3, the main chain framework update based on the current target sequence encoding adopts:

[0058]

[0059]

[0060]

[0061] Where, m i a represents the encoding of the i-th residue in the updated target sequence. i b i c i d i Main chain framework T i Calculate the rotation matrix R i An important component Main chain framework T i The deviation coordinates in the diagram.

[0062] Preferably, in step A1, the initialization is performed using the following method:

[0063] Randomly generate initial logits of X to N N×L×A (0, 0.01);

[0064] Where N is the number of initial sequences, usually 1, L is the sequence length, and A represents the number of amino acid types, which is 21 (20 natural amino acids and 1 gap); when the design target is a protein of a specified length, L is initialized to the specified length; when the design target is a complex with a specified number of chains, L is initialized to the total length of the complex.

[0065] The protein sequence, obtained by passing through the softmax and argmax layers, is compiled using one-hot encoding and used as input to the structure prediction model.

[0066] In the subsequent gradient descent derivative calculation, the reparameter method is used for gradient backpropagation. If the amino acids in the target motif region need to remain unchanged during the design process, the amino acid type of the motif region will be set to the known motif sequence during initialization, and the region will be coded during gradient descent and Markov chain Monte Carlo update to keep its sequence unchanged. If the design purpose is to optimize and modify natural proteins, the initial sequence also includes the corresponding protein sequence.

[0067] Preferably, in step A1, the input to the protein three-dimensional structure prediction method TRFold2 is a sequence randomly initialized by the initialization method or a known protein sequence to be optimized;

[0068] If the design target is a complex, the initial sequences of each protein chain in the complex are spliced ​​together as input to the three-dimensional structure prediction method TRFold2.

[0069] If the design target is a protein that binds to a specified ligand, such as a polypeptide that binds to a specified protein, the input is a sequence assembled from the initial design protein sequence and the sequence of the specified ligand protein, and the three-dimensional structure of the specified ligand is used as the template input for TRFold2.

[0070] Preferably, in step A2, the confidence score loss is the overall score of the designed protein, including the entropy loss function of the TRFold2 structure prediction, L H and the TRFold2 scoring loss function, representing the design stability and reliability, L TR ;

[0071] Wherein, let the entropy loss function for predicting the structure of protein TRFold2 be L. H The calculation method is as follows:

[0072]

[0073] in d describes the distance between each pair of amino acid residues i and j in the protein, ω, θ, θ T , Describes the torsion angle between pairs i and j of each amino acid residue in the protein; m ij =1 If a specified motif exists, and amino acid residues i and j are both in the motif and the distance between them is less than 20 Å, then m = 1. ij =0;

[0074]

[0075] Let k be the cross-entropy for classification, where k is the number of classes based on the distance and torsion angle between amino acid residues i and j predicted by TRFold2.

[0076]

[0077] Where β = 1 is used if the amino acid residue pairs ij are included in the cross-entropy calculation, otherwise β = 0; p(y ij ) represents the probability value of the corresponding distance or torsion angle predicted by TRFold2;

[0078] Among them, the TRFold2 scoring loss function, L TR The calculation method is as follows:

[0079] L TR =f(0.9-pLDDT)

[0080] Where pLDDT is the score for the predicted protein structure output by TRFold2, and f is the ReLU function.

[0081] Preferably, in step A2, the corresponding loss is calculated including at least one of phantom fit, phantom structural similarity, and structural symmetry.

[0082] Prior to step A2, the calculation of the corresponding loss according to the specific design purpose includes the fitting loss of the phantom, L. M Similarity loss of phantom structure, L RMSD Structural symmetry loss, L S Among them, the phantom fit loss, L M To describe the fit between the designed protein and the target motif, and for use when designing a specific motif, its specific form is as follows:

[0083]

[0084] in d describes the distance between each pair of amino acid residues i and j in the protein, ω, θ, θ T , This describes the torsion angle between amino acid residue pairs i and j in the protein; mij = 1 if amino acid residues i and j are both in the specified motif and the distance between them is less than 20 Å, otherwise m ij =0; p(y ij ) represents the probability value of the corresponding distance or torsion angle predicted by TRFold2;

[0085] Among them, the phantom structure similarity loss, LRMSD To describe the structural similarity between the designed protein and the target motif, and for use when designing a specific motif, its specific form is as follows:

[0086]

[0087] Where min is the minimization function, T is the three-dimensional transformation from the designed structure to the specified phantom structure, l is the number of amino acids contained in the phantom, and q i p represents the main chain atomic coordinates of residue i contained in the motif. i To design the main chain atom coordinates of residue i in the TRFold2 predicted structure of the protein;

[0088] Among them, structural symmetry loss, L s To describe the consistency of the designed protein with a specified symmetry, and is applicable when designing for a specified structural symmetry, its specific form is:

[0089]

[0090] Where n is the specified symmetry order, such as 3 for C3 symmetry, and c i Let be the coordinates of the centroid of the i-th part in the symmetrical structure, and let be the coordinates of the parts in clockwise order.

[0091] Prioritize that, in step A2, the integration of the various loss functions involves a weighted sum of the aforementioned losses according to the design objective, specifically in the following form:

[0092] L total =w H L H +w TR L TR +w M L M +w RMSD L RMSD +w S L S +w E L E

[0093] Among them, w H For the loss function L H The corresponding weights, w TR For the loss function L TR The corresponding weights, w M For the loss function L M The corresponding weights, w RMSD For the loss function L RMSD The corresponding weights, w S For the loss function L S The corresponding weights, wE For the loss function L E The corresponding weights, the specific values ​​of which are determined based on design requirements; L H and L TR This is the loss function term that is used consistently in the design; other loss function terms are enabled or disabled based on design requirements. E For loss functions not described in the above description, including the phantom display loss function, the design confidence prediction pTM loss function, and the radius of gyration loss function, developers can add them according to design requirements.

[0094] Preferably, in step A3, the loss function is a weighted summation loss;

[0095] In each round of updates, the gradient descent method uses the reparameter method to backpropagate gradients through the argmax function to update the designed protein sequence; the Markov chain Monte Carlo method calculates the above loss by analyzing the amino acid sequence of the randomly mutated protein and determines whether the mutation update is accepted according to the conventional Markov chain Monte Carlo acceptance criteria.

[0096] The probability of random mutation updates includes 70% substitution, 15% deletion and 15% addition. When substitution and addition are performed, any one of 20 natural amino acids is randomly selected in a uniform distribution. In addition, random mutations are selected at a single residue site in the designed protein or at multiple residue sites in the designed protein.

[0097] Among them, the update acceptance probability of the Markov chain Monte Carlo method, A i for:

[0098]

[0099] Where min is the minimum value function, L i Let T be the loss value updated in step i. i This is the temperature value at the time of the i-th update.

[0100] The design can adopt a combination of gradient descent and Markov chain Monte Carlo methods. Generally, gradient descent is used for initial optimization first, followed by MCMC for further optimization. The number of iterations is determined according to the design target requirements, and usually ranges from hundreds to thousands.

[0101] Prior to step A4, the TRFold2 predicted structure of the designed protein corresponding to the minimum loss function is used as the input of the sequence design model. Based on the distance and torsion angle information between the atoms of the protein main chain, the model uses a neural network to predict the most suitable protein sequence and achieve side chain filling. It is worth noting that sequence reconstruction optimization can avoid sequence overfitting that occurs in steps 2 and 3, and significantly improve the design success rate of the method.

[0102] Prioritize that, in step A4, the screening method involves using the obtained reconstructed and optimized sequence as the MSA input to the open-source method AlphaFold2. If the design target is a protein binding to a specified ligand, then the structure of this ligand protein is used as additional AlphaFold2 template information input. The pLDDT score and predicted structure of AlphaFold2 are compared with the RMSD score of the structure designed by the method, and sorted according to the specified design target to select the optimal design result. Here, pLDDT ∈ [0, 1] represents the output of AlphaFold2; a larger value indicates a better design result. RMSD score is also considered. RMSD for:

[0103]

[0104] Where min is the minimization function, T is the three-dimensional transformation from the AlphaFold2 predicted structure to the designed structure, L is the designed protein length, and p i Here are the main chain atom coordinates of residue i in the AlphaFold2 predicted structure, and d i To design the main chain atomic coordinates of residue i in the structure, Score RMSD A lower score indicates a better design result. pLDDT greater than 70 and a higher score... RMSD A value less than 1.5 is a commonly used screening criterion.

[0105] Secondly, the present invention provides a system capable of end-to-end protein design and analysis, the system comprising:

[0106] Module A1 initializes the protein sequence or sequence code to be designed according to the specified length, performs one-hot compilation, and inputs it into the protein folding algorithm TRFold2 for prediction of the three-dimensional structure.

[0107] Module A2: Based on the predicted 3D structure, it provides a confidence score and a loss representing stability, and calculates the corresponding loss according to the specific design purpose, integrating all the required losses into a learnable loss function.

[0108] Module A3 updates the original sequence using gradient descent or Markov chain Monte Carlo algorithm based on the loss function, then repeatedly triggers Module A2 to calculate the new loss and update the protein sequence again; iterative loop optimization is performed to obtain the optimal candidate protein structure and sequence, i.e., the design result with the lowest loss.

[0109] Module A4 inputs the obtained optimal candidate protein structure into the sequence design model for side chain reconstruction optimization to fit the design structure and increase stability; the reconstructed sequence is analyzed and tested based on the open-source algorithm AlphaFold2, and the optimal design protein is obtained after screening.

[0110] Compared with the prior art, the present invention has the following beneficial effects:

[0111] (1) This invention provides a solution for protein design based on artificial intelligence technology, TRDesign, by organically combining our self-developed protein three-dimensional structure prediction model TRFold2 with the generation method. It solves the problems of low efficiency and low success rate of traditional protein computational design models based on coarse energy function calculation. It can set loss functions according to various specified targets to quickly design and optimize proteins.

[0112] (2) The method of the present invention is based on a deep learning model for predicting the three-dimensional structure of proteins, which can learn the relationship between protein sequence and structure and function more comprehensively. This avoids the loopholes and deviations that occur in traditional fragment splicing design methods based on experience and limited physicochemical understanding, and can better optimize the sequence / structure while achieving the specified target characteristics.

[0113] (3) By combining the protein design model with a multivariate loss function, the present invention can switch different loss functions for different targets, thereby enabling the design of a wide range of proteins, such as proteases, specified ligand-binding peptides, symmetric complexes, etc., and can specify the corresponding loss function according to the design requirements, which efficiently solves the problem that traditional protein design is limited to specific protein types or design targets.

[0114] (4) This invention provides specific three-dimensional design structures that can be organically combined with various confidence / physicochemical indicators. Furthermore, it utilizes sequence design models to reconstruct and optimize side chains, thereby solving secondary problems associated with traditional design methods, such as difficulty in protein synthesis, high aggregation, and structural instability. This results in the generation of novel proteins that truly conform to the folding principle. In summary, this protein design method achieves precise and automated design for various proteins, and the resulting artificial protein synthesis rate and stability exceed those of various traditional methods. Attached Figure Description

[0115] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0116] Figure 1 Design flowcharts for proteins;

[0117] Figure 2 The test results for the protein with specified 7th order symmetry designed for Example 1;

[0118] Figure 3 Protein test results for the specified RSV F motif designed for Example 2. Detailed Implementation

[0119] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The following examples are implemented under the premise of the technical solution of the present invention, providing detailed implementation methods and specific operating procedures, which will help those skilled in the art to further understand the present invention. It should be noted that the scope of protection of the present invention is not limited to the following embodiments; any adjustments and improvements made under the concept of the present invention are all within the scope of protection of the present invention.

[0120] refer to Figure 1 This invention provides a method for end-to-end protein design and analysis, comprising the following steps:

[0121] A1. Initialize the protein sequence or sequence code required according to the specified length, compile it with one-hot encoding, and input it into the protein folding algorithm TRFold2 for prediction of the three-dimensional structure.

[0122] A2. Based on the predicted three-dimensional structure, give the confidence score and the loss representing stability, and calculate the corresponding loss according to the specific design purpose. Integrate all the required losses into a learnable loss function.

[0123] A3. Update the original sequence using gradient descent or Markov chain Monte Carlo algorithm based on the loss function, then repeat step A2 to calculate the new loss and update the protein sequence again; perform iterative optimization to obtain the optimal candidate protein structure and sequence, i.e. the design result with the lowest loss.

[0124] A4. Input the obtained optimal candidate protein structure into the sequence design model for side chain reconstruction optimization to better fit the design structure and increase stability; perform analysis and verification of the reconstructed sequence based on the open-source algorithm AlphaFold2, and obtain the optimal design protein after screening.

[0125] Example 1

[0126] This embodiment provides a method for end-to-end design and analysis of 7th-order symmetric proteins, including the following steps:

[0127] A1. Initialize the protein sequence or sequence code required according to the specified length, compile it with one-hot encoding, and input it into the protein folding algorithm TRFold2 for prediction of the three-dimensional structure.

[0128] A2. Based on the predicted 3D structure, give the confidence score and the loss representing stability, and calculate the structural symmetry loss. Integrate all the required losses into a learnable loss function.

[0129] A3. Update the original sequence using gradient descent or Markov chain Monte Carlo algorithm based on the loss function, then repeat step A2 to calculate the new loss and update the protein sequence again; perform iterative optimization to obtain the optimal candidate protein structure and sequence, i.e. the design result with the lowest loss.

[0130] A4. Input the obtained optimal candidate protein structure into the sequence design model for side chain reconstruction optimization to better fit the design structure and increase stability; perform analysis and verification of the reconstructed sequence based on the open-source algorithm AlphaFold2, and obtain the optimal design protein after screening.

[0131] Preferably, in step A1, the initialization is performed using the following method:

[0132] Randomly generate initial logits of X to N N×L×A (0, 0.01);

[0133] Where N is the number of initial sequences, usually 1, L is the sequence length, and A represents the number of amino acid types, which is 21 (20 natural amino acids and 1 gap); since the design target is a 7-mer complex, L is initialized to the total length of the complex.

[0134] The protein sequence, obtained by passing through the softmax and argmax layers, is compiled using one-hot encoding and used as input to the structure prediction model.

[0135] In the subsequent gradient descent differentiation, the reparameterization method is used for gradient backpropagation;

[0136] Preferably, in step A1, the input to the protein three-dimensional structure prediction method TRFold2 is a sequence randomly initialized by the initialization method or a known protein sequence to be optimized;

[0137] Since the target is a complex, the initial sequences of each protein chain in the complex are spliced ​​together and used as input for the three-dimensional structure prediction method TRFold2.

[0138] Preferably, in step A2, the confidence score loss is the overall score of the designed protein, including the entropy loss function of the TRFold2 structure prediction, L H and the TRFold2 scoring loss function, representing the design stability and reliability, L TR ;

[0139] Wherein, let the entropy loss function for predicting the structure of protein TRFold2 be L. H The calculation method is as follows:

[0140]

[0141] in d describes the distance between each pair of amino acid residues i and j in the protein, ω, θ, θ T , Describes the torsion angle between pairs i and j of each amino acid residue in the protein; m ij =1 If a specified motif exists, and amino acid residues i and j are both in the motif and the distance between them is less than 20 Å, then m = 1. ij =0;

[0142]

[0143] Let k be the cross-entropy for classification, where k is the number of classes based on the distance and torsion angle between amino acid residues i and j predicted by TRFold2.

[0144]

[0145] Where β = 1 is used if the amino acid residue pairs ij are included in the cross-entropy calculation, otherwise β = 0; p(y ij ) represents the probability value of the corresponding distance or torsion angle predicted by TRFold2;

[0146] Among them, the TRFold2 scoring loss function, L TR The calculation method is as follows:

[0147] L TR =f(0.9-pLDDT)

[0148] Where pLDDT is the score for the predicted protein structure output by TRFold2, and f is the ReLU function.

[0149] Preferably, in step A2, the corresponding loss is calculated including at least one of phantom fit, phantom structural similarity, and structural symmetry.

[0150] Prioritize step A2, calculating the corresponding loss based on the design objective of a 7th-order symmetry protein, including structural symmetry loss, L. S ;

[0151] Among them, structural symmetry loss, L S To describe the consistency of the designed protein with a specified symmetry, and is applicable when designing for a specified structural symmetry, its specific form is:

[0152]

[0153] Where n is the specified symmetry order, which is 7 in this embodiment, and c i Let be the coordinates of the centroid of the i-th part in the symmetrical structure, and let be the coordinates of the parts in clockwise order.

[0154] Prioritize that, in step A2, the integration of the various loss functions involves a weighted sum of the aforementioned losses according to the design objective, specifically in the following form:

[0155] When designing proteins with specified symmetry structures, the loss can be set to:

[0156] L total =w H L H +w TR L TR +w s L s +w E L E

[0157] Among them, w H For the loss function L H The corresponding weights, w TR For the loss function L TR The corresponding weights, w S For the loss function L S The corresponding weights, w E For the loss function L E The corresponding weights, the specific values ​​of which are determined based on design requirements; L H and L TR This is the loss function term that is used consistently in the design; other loss function terms are enabled or disabled based on design requirements. E For loss functions not described in the above description, including the phantom display loss function, the design confidence prediction pTM loss function, and the radius of gyration loss function, developers can add them according to design requirements.

[0158] Preferably, in step A3, the loss function is a weighted summation loss;

[0159] In each round of updates, the gradient descent method uses the reparameter method to backpropagate gradients through the argmax function to update the designed protein sequence; the Markov chain Monte Carlo method calculates the above loss by analyzing the amino acid sequence of the randomly mutated protein and determines whether the mutation update is accepted according to the conventional Markov chain Monte Carlo acceptance criteria.

[0160] The probability of random mutation updates includes 70% substitution, 15% deletion and 15% addition. When substitution and addition are performed, any one of 20 natural amino acids is randomly selected in a uniform distribution. In addition, random mutation can be performed on a single residue site or multiple residue sites in the protein.

[0161] Among them, the update acceptance probability of the Markov chain Monte Carlo method, A i for:

[0162]

[0163] Where min is the minimum value function, L i Let T be the loss value updated in step i. i This is the temperature value at the time of the i-th update.

[0164] The design can adopt a combination of gradient descent and Markov chain Monte Carlo methods. Generally, gradient descent is used for initial optimization first, followed by MCMC for further optimization. The number of iterations is determined according to the design target requirements. In this embodiment, 500 steps of gradient descent are used for initial optimization of the sequence, and 1000 steps of MCMC are used for subsequent optimization.

[0165] Prior to step A4, the TRFold2 predicted structure of the designed protein corresponding to the minimum loss function is used as the input of the sequence design model. Based on the distance and torsion angle information between the atoms of the protein main chain, the model uses a neural network to predict the most suitable protein sequence and achieve side chain filling. It is worth noting that sequence reconstruction optimization can avoid sequence overfitting that occurs in steps 2 and 3, and significantly improve the design success rate of the method.

[0166] Prioritize that, in step A4, the screening method involves using the obtained reconstructed and optimized sequence as the MSA input to the open-source method AlphaFold2. If the design target is a protein binding to a specified ligand, then the structure of this ligand protein is used as additional AlphaFold2 template information input. The pLDDT score and predicted structure of AlphaFold2 are compared with the RMSD score of the structure designed by the method, and sorted according to the specified design target to select the optimal design result. Here, pLDDT ∈ [0, 1] represents the output of AlphaFold2; a larger value indicates a better design result. RMSD score is also considered. RMSD for:

[0167]

[0168] Where min is the minimization function, T is the three-dimensional transformation from the AlphaFold2 predicted structure to the designed structure, L is the designed protein length, and p i Here are the main chain atom coordinates of residue i in the AlphaFold2 predicted structure, and d i To design the main chain atomic coordinates of residue i in the structure, Score RMSD A lower score indicates a better design result. pLDDT greater than 70 and a higher score... RMSD A value less than 1.5 is a commonly used screening criterion. The results of the 7th-order symmetric protein design test are as follows: Figure 2 As shown.

[0169] Example 2

[0170] This embodiment provides a method for end-to-end protein design and analysis using a specified RSV F motif, including the following steps:

[0171] A1. Initialize the protein sequence or sequence code required according to the specified length, compile it with one-hot encoding, and input it into the protein folding algorithm TRFold2 for prediction of the three-dimensional structure.

[0172] A2. Based on the predicted 3D structure, give the confidence score and the loss representing stability, and calculate the fit of the phantom and the phantom structure similarity loss. Integrate all the required losses into a learnable loss function.

[0173] A3. Update the original sequence using gradient descent or Markov chain Monte Carlo algorithm based on the loss function, then repeat step A2 to calculate the new loss and update the protein sequence again; perform iterative optimization to obtain the optimal candidate protein structure and sequence, i.e. the design result with the lowest loss.

[0174] A4. Input the obtained optimal candidate protein structure into the sequence design model for side chain reconstruction optimization to better fit the design structure and increase stability; perform analysis and verification of the reconstructed sequence based on the open-source algorithm AlphaFold2, and obtain the optimal design protein after screening.

[0175] Preferably, in step A1, the initialization is performed using the following method:

[0176] Randomly generate initial logits of X to N N×L×A (0, 0.01);

[0177] Where N is the number of initial sequences, usually 1, L is the sequence length, and A represents the number of amino acid types, which is 21 (20 natural amino acids and 1 gap). When the design target is a protein of a specified length, L is initialized to the specified length. When the design target is a complex with a specified number of chains, L is initialized to the total length of the complex.

[0178] The protein sequence, obtained by passing through the softmax and argmax layers, is compiled using one-hot encoding and used as input to the structure prediction model.

[0179] In the subsequent gradient descent derivative calculation, the reparameter method is used for gradient backpropagation. The amino acids in the target motif region remain unchanged during the design process. During initialization, the amino acid type of the motif region is set to the known RSV F motif sequence, and the region is coded during gradient descent and Markov chain Monte Carlo update to keep its sequence unchanged.

[0180] Preferably, in step A1, the input to the protein three-dimensional structure prediction method TRFold2 is a sequence randomly initialized by the initialization method or a known protein sequence to be optimized;

[0181] If the design target is a protein binding to a specified ligand, such as a polypeptide binding to a specific protein, the input is a sequence assembled from the initial design protein sequence and the sequence of the specified ligand protein. The three-dimensional structure of the specified ligand is used as the template input for TRFold2. In this embodiment, the design of a protein with an RSV F motif involves directly inputting the known motif region sequence and adding random sequences to both ends to generate the initial protein sequence.

[0182] Preferably, in step A2, the confidence score loss is the overall score of the designed protein, including the entropy loss function of the TRFold2 structure prediction, L H and the TRFold2 scoring loss function, representing the design stability and reliability, L TR ;

[0183] Wherein, let the entropy loss function for predicting the structure of protein TRFold2 be L. H The calculation method is as follows:

[0184]

[0185] in d describes the distance between each pair of amino acid residues i and j in the protein, ω, θ, θ T , Describes the torsion angle between pairs i and j of each amino acid residue in the protein; m ij =1 If a specified motif exists, and amino acid residues i and j are both in the motif and the distance between them is less than 20 Å, then m = 1. ij =0;

[0186]

[0187] Let k be the cross-entropy for classification, where k is the number of classes based on the distance and torsion angle between amino acid residues i and j predicted by TRFold2.

[0188]

[0189] Where β = 1 is used if the amino acid residue pairs ij are included in the cross-entropy calculation, otherwise β = 0; p(y ij ) represents the probability value of the corresponding distance or torsion angle predicted by TRFold2;

[0190] Among them, the TRFold2 scoring loss function, L TR The calculation method is as follows:

[0191] L TR =f(0.9-pLDDT)

[0192] Where pLDDT is the score for the predicted protein structure output by TRFold2, and f is the ReLU function.

[0193] Preferably, in step A2, the corresponding loss is calculated including at least one of phantom fit, phantom structural similarity, and structural symmetry.

[0194] Prior to step A2, the calculation of the corresponding loss according to the specific design purpose includes the fitting loss of the phantom, L. M Similarity loss of phantom structure, L RMSD Structural symmetry loss, L S Among them, the phantom fit loss, L MTo describe the fit between the designed protein and the target motif, and for use when designing a specific motif, its specific form is as follows:

[0195]

[0196] in d describes the distance between each pair of amino acid residues i and j in the protein, ω, θ, θ T , Describes the torsion angle between pairs i and j of each amino acid residue in the protein; m ij =1 If amino acid residues i and j are both in the specified motif and the distance between them is less than 20 Å, otherwise m ij =0; p(y ij ) represents the probability value of the corresponding distance or torsion angle predicted by TRFold2;

[0197] Among them, the phantom structure similarity loss, L RMSD To describe the structural similarity between the designed protein and the target motif, and for use when designing a specific motif, its specific form is as follows:

[0198]

[0199] Where min is the minimization function, T is the three-dimensional transformation from the designed structure to the specified phantom structure, l is the number of amino acids contained in the phantom, and q i p represents the main chain atomic coordinates of residue i contained in the motif. i To design the main chain atom coordinates of residue i in the TRFold2 predicted structure of the protein;

[0200] This embodiment specifies the RSV F phantom.

[0201] Prioritize that, in step A2, the integration of the various loss functions involves a weighted sum of the aforementioned losses according to the design objective, specifically in the following form:

[0202] When designing proteins with a certain motif structure, the loss can be set to:

[0203] L total =w H L H +w TR L TR +w M L M +w RMSD L RMSD +w E L E

[0204] Among them, wH For the loss function L H The corresponding weights, w TR For the loss function L TR The corresponding weights, w M For the loss function L M The corresponding weights, w RMSD For the loss function L RMSD The corresponding weights, w E For the loss function L E The corresponding weights, the specific values ​​of which are determined based on design requirements; L H and L TR This is the loss function term that is used consistently in the design; other loss function terms are enabled or disabled based on design requirements. E For loss functions not described in the above description, including the phantom display loss function, the design confidence prediction pTM loss function, and the radius of gyration loss function, developers can add them according to design requirements.

[0205] Preferably, in step A3, the loss function is a weighted summation loss;

[0206] In each round of updates, the gradient descent method uses the reparameter method to backpropagate gradients through the argmax function to update the designed protein sequence; the Markov chain Monte Carlo method calculates the above loss by analyzing the amino acid sequence of the randomly mutated protein and determines whether the mutation update is accepted according to the conventional Markov chain Monte Carlo acceptance criteria.

[0207] The probability of random mutation updates includes 70% substitution, 15% deletion and 15% addition. When substitution and addition are performed, any one of 20 natural amino acids is randomly selected in a uniform distribution. In addition, random mutation can be performed on a single residue site or multiple residue sites in the protein.

[0208] Among them, the update acceptance probability of the Markov chain Monte Carlo method, A i for:

[0209]

[0210] Where min is the minimum value function, L i Let be the loss value after the i-th step update, and Ti be the temperature value at the time of the i-th step update.

[0211] The design can adopt a combination of gradient descent and Markov chain Monte Carlo methods. Generally, gradient descent is used for initial optimization first, followed by MCMC for further optimization. The number of iterations is determined according to the design target requirements. In this embodiment, 500 steps of gradient descent are used for initial optimization of the sequence, and 1000 steps of MCMC are used for subsequent optimization.

[0212] Prior to step A4, the TRFold2 predicted structure of the designed protein corresponding to the minimum loss function is used as the input of the sequence design model. Based on the distance and torsion angle information between the atoms of the protein main chain, the model uses a neural network to predict the most suitable protein sequence and achieve side chain filling. It is worth noting that sequence reconstruction optimization can avoid sequence overfitting that occurs in steps 2 and 3, and significantly improve the design success rate of the method.

[0213] Prioritize that, in step A4, the screening method involves using the obtained reconstructed and optimized sequence as the MSA input to the open-source method AlphaFold2. If the design target is a protein binding to a specified ligand, then the structure of this ligand protein is used as additional AlphaFold2 template information input. The pLDDT score and predicted structure of AlphaFold2 are compared with the RMSD score of the structure designed by the method, and sorted according to the specified design target to select the optimal design result. Here, pLDDT ∈ [0, 1] represents the output of AlphaFold2; a larger value indicates a better design result. RMSD score is also considered. RMSD for:

[0214]

[0215] Where min is the minimization function, T is the three-dimensional transformation from the AlphaFold2 predicted structure to the designed structure, L is the designed protein length, and p i Here are the main chain atom coordinates of residue i in the AlphaFold2 predicted structure, and d i To design the main chain atomic coordinates of residue i in the structure, Score RMSD A lower score indicates a better design result. pLDDT greater than 70 and a higher score... RMSD A value less than 1.5 is a commonly used screening criterion.

[0216] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0217] In the description of this application, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0218] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for end-to-end protein design and analysis, characterized in that, The method includes the following steps: A1. Initialize the protein sequence or sequence code required according to the specified length, compile it with one-hot encoding, and input it into the protein folding algorithm TRFold2 for prediction of the three-dimensional structure. A2. Based on the predicted three-dimensional structure, give the confidence score and the loss representing stability, and calculate the corresponding loss according to the specific design purpose. Integrate all the required losses into a learnable loss function. The confidence score loss is the overall score of the designed protein, including the entropy loss function for TRFold2 structure prediction. and the TRFold2 scoring loss function, which represents the design's stability and reliability. ; Wherein, let the entropy loss function for predicting the structure of protein TRFold2 be... The calculation method is as follows: in , This describes the distance between each pair of amino acid residues i and j in the protein. This describes the torsion angle between amino acid residue pairs i and j in the protein; if a specified motif exists, and both amino acid residues i and j are within the motif and the distance between them is less than 20 Å, then... In other cases ; Let k be the classification cross-entropy, where k is the number of classifications based on the distance and torsion angle between amino acid residues i and j predicted by TRFold2. If amino acid residue pairs ij are included in the cross-entropy calculation, then 1; In other cases ; The probability value for the corresponding distance or torsion angle predicted by TRFold2; Among them, the TRFold2 scoring loss function, The calculation method is as follows: Where pLDDT is the score of the predicted protein structure output by TRFold2, and f is the ReLU function; The calculation of the corresponding loss based on the specific design purpose includes the fit loss of the phantom. Similarity loss of phantom structure Structural symmetry loss Among them, the motif fit loss, To describe the fit between the designed protein and the target motif, and for use when designing a specific motif, its specific form is as follows: in , This describes the distance between each pair of amino acid residues i and j in the protein. This describes the torsion angle between amino acid residue pairs i and j in the protein; if both amino acid residues i and j are in the specified motif and the distance between them is less than 20 angstroms, then... In other cases ; The probability value for the corresponding distance or torsion angle predicted by TRFold2; Among them, the phantom structure similarity loss To describe the structural similarity between the designed protein and the target motif, and for use when designing a specific motif, its specific form is as follows: Where min is the minimization function, and T is the three-dimensional transformation from the designed structure to the specified phantom structure. This refers to the number of amino acids contained in the motif. Let i be the main chain atomic coordinates of residue i contained in the motif. To design the main chain atom coordinates of residue i in the TRFold2 predicted structure of the protein; Among them, structural symmetry loss, To describe the consistency of the designed protein with a specified symmetry, and is applicable when designing for a specified structural symmetry, its specific form is: Where n is the specified symmetry order. Let be the coordinates of the centroid of the i-th part in the symmetrical structure, and let the parts be arranged in clockwise order. The integration of the various loss functions involves a weighted sum of the losses mentioned above, based on the design objectives. The specific form of this sum is as follows: in, loss function Corresponding weights loss function Corresponding weights loss function Corresponding weights loss function Corresponding weights loss function Corresponding weights loss function The corresponding weights, the specific values ​​of which are determined according to design requirements; and The loss function term is the one that is always used in the design; other loss function terms are enabled or not depending on the design requirements. Loss functions other than those described in the above description include the phantom presentation loss function, the design confidence prediction pTM loss function, and the radius of gyration loss function; A3. Update the original sequence using gradient descent or Markov chain Monte Carlo algorithm based on the loss function, then repeat step A2 to calculate the new loss and update the protein sequence again; perform iterative optimization to obtain the optimal candidate protein structure and sequence, i.e. the design result with the lowest loss. A4. Input the obtained optimal candidate protein structure into the sequence design model for side chain reconstruction optimization to fit the design structure and increase stability; perform analysis and verification of the reconstructed sequence based on the open source algorithm AlphaFold2, and obtain the optimal design protein after screening.

2. The method for end-to-end protein design and analysis according to claim 1, characterized in that, In step A1, the initialization is performed using the following method: Randomly generate initial logits as ; Where N is the number of initial sequences, usually 1, L is the sequence length, and A represents the number of amino acid types, which is 21; when the design target is a protein of a specified length, L is initialized to the specified length; when the design target is a complex with a specified number of chains, L is initialized to the total length of the complex. The protein sequence, obtained by passing through the softmax and argmax layers, is compiled using one-hot encoding and used as input to the structure prediction model. In the subsequent gradient descent derivative calculation, the reparameter method is used for gradient backpropagation. If the amino acids in the target motif region need to remain unchanged during the design process, the amino acid type of the motif region will be set to the known motif sequence during initialization, and the region will be coded during gradient descent and Markov chain Monte Carlo update to keep its sequence unchanged. If the design purpose is to optimize and modify natural proteins, the initial sequence also includes the corresponding protein sequence.

3. The method for end-to-end protein design and analysis according to claim 1, characterized in that, In step A1, the input to the protein three-dimensional structure prediction method TRFold2 is either a sequence randomly initialized by the initialization process or a known protein sequence to be optimized. If the design target is a complex, the initial sequences of each protein chain in the complex are spliced ​​together as input to the three-dimensional structure prediction method TRFold2. If the design target is a protein that binds to a specified ligand, the input is a sequence assembled from the initial design protein sequence and the sequence of the specified ligand protein, and the three-dimensional structure of the specified ligand is used as the template input for TRFold2.

4. The method for end-to-end protein design and analysis according to claim 1, characterized in that, In step A3, the loss function is a weighted summation loss; In each round of updates, the gradient descent method performs backpropagation of gradients through the argmax function using the reparameter method to update the designed protein sequence. The Markov chain Monte Carlo method calculates the above loss by analyzing the amino acid sequence of the protein after random mutation and determines whether the mutation update is accepted according to the conventional Markov chain Monte Carlo acceptance criteria. The probability of random mutation updates includes 70% replacement, 15% deletion and 15% addition. When replacing or adding, any one of 20 natural amino acids is randomly selected in a uniform distribution. In addition, random mutations are selected at a single residue site in the designed protein or multiple residue sites in the designed protein. Among them, the Markov chain Monte Carlo method updates the acceptance probability. for: Where min is the minimum value function. This represents the loss value updated in step i. This is the temperature value at the time of the i-th update. The design can adopt a combination of gradient descent and Markov chain Monte Carlo methods. Gradient descent is used for initial optimization first, and then MCMC is used for further optimization. The number of iterations is determined according to the design objectives.

5. The method for end-to-end protein design and analysis according to claim 1, characterized in that, In step A4, the TRFold2 predicted structure of the designed protein corresponding to the minimum loss function is used as the input of the sequence design model. Based on the distance and twist angle information between the atoms of the protein main chain, the model uses a neural network to predict the most suitable protein sequence and achieve side chain filling.

6. The method for end-to-end protein design and analysis according to claim 1, characterized in that, In step A4, the screening process involves using the obtained reconstructed and optimized sequence as MSA input to the open-source method AlphaFold2. If the design target is a protein binding to a specified ligand, the structure of this ligand protein is used as additional AlphaFold2 template information input. The pLDDT score and predicted structure of AlphaFold2 are compared with the RMSD score of the structure designed by the above method, and the results are sorted according to the specified design target to select the optimal design result. For the output of AlphaFold2, score the RMSD. for: Where min is the minimization function, T is the three-dimensional transformation from the AlphaFold2 predicted structure to the designed structure, and L is the length of the designed protein. Here are the main chain atom coordinates of residue i in the AlphaFold2 predicted structure. The coordinates of the main chain atoms of residue i in the design structure.

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