Gene design and evolutionary path inference method based on adaptive band-constrained depth model

Abstract

The application relates to a gene design and evolutionary path inference method based on an adaptive band constraint deep model. First, a random gene sequence set is generated and converted into an evolvability vector containing evolutionary information, and the mutation robustness thereof is calculated. A deep auto-encoding network is constructed, model parameters are optimized through prototype clustering and small batch training, the evolvability vector is encoded into a low-dimensional representation, and an evolvability space is obtained. Then, a deep regression model is established to predict the protein expression level corresponding to the gene sequence. The low-dimensional vector and the expression value are combined into a low-dimensional tensor, the expression value is mapped into fitness through Monte Carlo sampling, and then an adaptive fitness topographic map showing the evolutionary track is generated. Finally, the tensor is stained according to the mutation robustness, and the gene sequence with the target property is screened. The scheme improves the gene design efficiency, and solves the problem that the fitness topography is difficult to represent the genotype evolutionary information.

Description

Technical Field

[0001] This invention relates to the fields of computer science, big data genomics, and gene sequence design, and specifically to a gene design and evolutionary path inference method based on an adaptive constrained deep model. Background Technology

[0002] In the evolution of gene expression, the evolution of cis-regulatory elements (CREs) plays a dominant role. Mutations in these regulatory sequences interfere with their binding to transcription factors, thereby altering the temporal patterns, spatial distribution, and expression levels of gene expression, ultimately affecting the phenotypic traits and adaptive capacity of organisms. Notably, transcription factors evolve more slowly due to the need to coordinate the regulation of multiple target genes, while CREs exhibit faster evolutionary dynamics. This difference leads to cis-regulatory elements being considered a crucial molecular basis for driving the evolution of phenotypic diversity.

[0003] Currently, the regulatory sequence space increases exponentially with the number of base pairs; for example, an 80-base-pair sequence has 4... 80 One possibility is that traditional studies, often based on local neighborhood sampling of natural sequences, only cover a very small portion of the sequence space and cannot globally characterize the sequence-expression-fitness relationship. Traditional adaptive landscapes are typically grouped by genotype based on sequence similarity, but genotypes with similar sequences may have vastly different functions. The high dimensionality of the genotype space makes it difficult for traditional methods to effectively visualize and analyze global evolutionary paths, and the rational design of regulatory sequences in synthetic biology relies on inefficient trial-and-error experiments. Deep learning technology, with its powerful nonlinear fitting capabilities and feature abstraction potential, offers new ideas for constructing global sequence-expression mappings and designing sequences. However, in the field of regulatory sequence evolution modeling, existing models ignore evolutionary constraints, leading to unstable performance of synthetically designed sequences in real biological environments. Therefore, there is an urgent need to develop a novel technical solution to comprehensively address the problems existing in current technologies. Summary of the Invention

[0004] The purpose of this invention is to provide a gene design and evolutionary path inference method based on an adaptive constrained deep model, which can globally characterize the relationship between sequence-expression-fitness and design gene sequences through an evolutionary space.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for gene design and evolutionary path inference based on an adaptive constrained deep model includes the following steps:

[0007] R1: With fixed base pairs as constraints, insert a random sequence of L base pairs into the middle region, i.e. a sequence that may not exist in nature, and transform it into an evolutionary vector E containing evolutionary information, and calculate the corresponding mutation robustness.

[0008] R2: Construct AANet, an autoencoder model with prototype regularization;

[0009] R3: Perform mini-batch iterative training on AANet based on the partial evolvable vector E output by R1 to dynamically determine the number of prototype parameters of AANet; complete the full training of AANet using all evolvable vectors E, and input the evolvable vectors E into the encoder of AANet to output the projection of the evolvable vectors in the low-dimensional space, that is, construct the evolvable space.

[0010] R4: Construct a Transformer deep prediction model, and generate gene sequences separately according to the method of R1 to train the Transformer model. Input the gene sequences obtained in R1 into the trained deep prediction model to obtain the expression level corresponding to each vector.

[0011] R5: The low-dimensional spatial projection of the evolutionary vector obtained in R3 and the protein expression level obtained in R4 are fused into a low-dimensional tensor; Monte Carlo sampling is performed on the low-dimensional tensor, and the fitness value of the sampling point is calculated through a preset protein expression level-fitness mapping function. Based on the spatial distribution of the fitness value, a contour map of the fitness landscape is generated.

[0012] R6: Based on mutation robustness, extract evolutionary sequences that meet the conditions from the low-dimensional fitness landscape tensor.

[0013] Specifically, step R1 is as follows:

[0014] R1-1: Gene sequence is generated by fixing the base pairs at the beginning and end and using L random base pairs in the middle;

[0015] R1-2: For each base sequence s0 of length L, considering only single-base mutations, there are 3 possible mutation sequences for each base, for a total of 3L mutation possibilities. Each mutation sequence s0 within its 3L mutation neighborhood... i Calculate the difference d in predicted expression values i =f(s) i )-f(s0), where f(s) represents the expression value predicted by the deep model;

[0016] R1-3: Put all d i Sort the values ​​so that they satisfy d i ≤d i+1This yields a monotonically increasing 240-dimensional evolutionary vector E = [d1, d2, ..., d...]. 3L ].

[0017] R1-4: Calculate mutation robustness: for any given base sequence s i First, a 3L mutation neighborhood was constructed. Then, the number of variants in this neighborhood whose expression changes were less than a threshold ε was counted. This threshold was set to twice the standard deviation of whole-genome protein expression (ε = 2σ). The mutation robustness calculation formula is as follows:

[0018]

[0019] In the formula Indicates the difference in expression d ij The number of variants below a threshold. Evolutionary analysis shows that gene regulatory elements subject to stable selection typically exhibit significantly enhanced mutational robustness, a property that effectively buffers the impact of random mutations on key phenotypic traits.

[0020] Specifically, step R2 is as follows:

[0021] R2-1: Construct a network model with an encoder EN and a decoder DN. The encoder EN consists of multiple fully connected layers, taking a sequence s as input to L network nodes. These L nodes are connected to k-1 network nodes (the outputs of the encoder EN) through multiple fully connected layers. Here, L is the input sequence s. i The length of the sequence is given by , and k is the number of prototypes. The network accepts a sequence s. i A prototype space of a specific dimension k is generated through the encoder EN.

[0022] The decoder DN is a mirror image of the encoder EN. The input of DN is the output of EN, and the output of DN is L network nodes. DN reconstructs the points in the prototype space as much as possible.

[0023] R2-2: Prototype analysis is a high-dimensional data dimensionality reduction method based on the principle of extreme values. Its mathematical model represents the observed dataset E as a convex combination of a finite set of prototypes. These prototypes are essentially homotypes in the feature space that represent extreme trade-offs. For example, in evolutionary biology, different prototypes may correspond to the optimal phenotypic configuration for a specific ecological niche. The formula for prototype analysis is as follows:

[0024]

[0025] This includes prototype regularization constraints:

[0026]

[0027] α ij ≥0, i=1,…,n,j=1,…,k

[0028] c1,…,c k It is a prototype, the dimensions of the prototype and s i The same dimension, α ij It is a constraint of convex combination, and F is the encoder EN in R2-1. Based on the idea of ​​prototype analysis, any sequence E... i It can be linearly represented by a convex combination of prototypes:

[0029] Because there are constraints Therefore, the number of prototypes set in the network can be reduced to k-1, and the remaining one can be reproduced through this constraint.

[0030] R2-3: The network reconstruction loss is as follows:

[0031]

[0032] Specifically, step R3 is as follows:

[0033] R3-1: Train AANet with mini-batch using the partial evolvability vector E obtained in step R1: Train the same batch of data with different numbers of prototypes k, calculate the reconstruction loss of the network corresponding to different numbers of prototypes using the MSE formula in R2-2, and select the points with smaller reconstruction loss and fewer prototypes.

[0034] R3-2: Input all the evolvable vectors E obtained in step R1 into the autoencoder network constructed in R2. The specific steps are as follows:

[0035] The number of prototypes is determined in step R3-1, the network parameters are set, and the autoencoder network is trained with all evolutionary vectors as input.

[0036] Extract all low-dimensional output vectors of encoder EN, and all vectors form an evolutionary space.

[0037] Specifically, step R4 is as follows:

[0038] R4-1: The Transformer-based DNA-protein expression prediction model adjusts the structure by converting the DNA sequence into a high-dimensional vector through an embedding layer and superimposing positional encodings to preserve sequence order. A pure encoder architecture with N stacked layers is employed, each containing a multi-head self-attention module and a feedforward network. The multi-head attention module computes multi-level global dependencies between bases in parallel, the feedforward network enhances local feature representation, and residual connections and layer normalization ensure training stability. Finally, the global features output by the encoder are pooled and mapped to continuous protein expression prediction values ​​through a fully connected layer.

[0039] R4-2: Regenerate a random dataset. In the training dataset, the ATCG equivalents of sequences are converted to one-hot encodings, and each gene sequence has its corresponding gene expression level, which is used as the output. Train the Transformer model using this dataset.

[0040] R4-3: Convert the ATCG equivalents of all sequences generated in R1 into one-hot encodings, and feed them into the deep prediction model trained in R4-2. Let the deep prediction model network be a function f, and obtain the expression of all evolutionary vectors as f(E).

[0041] Specifically, step R5 is as follows:

[0042] R5-1: Generate low-dimensional tensors using the evolvability vectors obtained from R3.

[0043] R5-2: Perform Monte Carlo simulation on the low-dimensional tensor obtained in R5-1, randomly sample 1000 points, use a curve from protein expression value to fitness, perform cubic spline interpolation on the fitness axis, and map the corresponding protein expression value obtained in R4 to fitness, scaling the fitness to between 0 and 1.

[0044] R5-3: At this point, the fitness value of each point in the low-dimensional tensor is between 0 and 1. A contour plot can then be drawn using these points to obtain a low-dimensional fitness landscape map. This map can be used to study evolutionary paths, quantify gene epistasis, and perform a range of other research.

[0045] Specifically, step R6 is as follows:

[0046] R6-1: The mutation robustness MR obtained in R1-4 is used to stain the low-dimensional tensor obtained in R5-1.

[0047] R6-2: Since the regulatory sequences of genes whose expression levels are subject to stable selection are often more robust to mutation effects, this graph is analyzed to examine the tensor distribution and extract the evolutionary sequence E that meets the criteria. For example, if genes whose expression levels are subject to stable selection are needed, then sequence E, which has better mutation robustness, is selected. i .

[0048] R6-3: Due to the evolvability vector E i and gene sequence s i One-to-one correspondence, therefore through E i The gene sequence s can be deduced. i The gene design and evolutionary path inference method based on an adaptive constrained deep model provided in the above technical solution has the following advantages compared with existing technologies:

[0049] 1. This invention utilizes evolvability vectors to collect evolutionary information for each gene sequence. By traversing the predictive impact of all single-base mutations in the sequence on the phenotype—that is, traversing the evolutionary possibilities of the gene—an evolvability vector is constructed for each genotype, comprehensively characterizing its potential to generate phenotypic variations. Compared to traditional methods that group based on gene sequence similarity, the constructed fitness landscape directly links genotype mutations with phenotypic changes, avoiding reliance on sequence similarity.

[0050] 2. The high dimensionality of the genotype space makes it difficult for traditional methods to effectively visualize and analyze global evolutionary paths. This invention achieves low-dimensional and effective visualization of the fitness landscape through a prototype-regularized autoencoder network. Synthetic biology suffers from inefficient trial-and-error experiments that rely on designing regulatory sequences. This invention utilizes deep learning techniques to construct sequence-expression level models and autoencoder models. Through the evolutionary space, target sequences can be quickly found, improving the efficiency of trial-and-error experiments for designing regulatory sequences. Attached Figure Description

[0051] Figure 1 This is the autoencoder model in the embodiments of the present invention;

[0052] Figure 2 This is the method for constructing the evolvability vector of the present invention;

[0053] Figure 3 This refers to the Transformer model in this embodiment of the invention;

[0054] Figure 4 This refers to the evolvability space in the embodiments of the present invention;

[0055] Figure 5 This is a flowchart illustrating the specific implementation of the gene design and evolutionary path inference method based on an adaptive constrained deep model in this invention. Detailed Implementation

[0056] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0057] This embodiment uses the generated regulatory sequences and the protein expression levels of the genes they control as an example, and combines them with the appendix. Figures 1-4 The present invention will be further analyzed and explained.

[0058] The gene design and evolutionary path inference method based on adaptive constrained deep models includes the following steps:

[0059] Step 1: Generate a random gene sequence with the first 13 and last 17 base pairs fixed and the middle 80 base pairs random. Then, convert the middle 80 base pairs into an evolutionary vector E containing evolutionary information (see reference). Figure 1 ):

[0060] 1.1 100,000 gene sequences were generated by fixing the first 13 and last 17 bases and randomly selecting the middle 80 bases;

[0061] 1.2 For each base sequence s0 of length L, considering only single-base mutations, there are 3 possible mutation sequences for each base, resulting in a total of 3L mutation possibilities. Each mutation sequence s0 within its 3L mutation neighborhood... i Calculate the difference d in predicted expression values i =f(s) i )-f(s0), where f(s) represents the expression value predicted by the deep model;

[0062] 1.3 All d i Sort the values ​​so that they satisfy d i ≤d i+1 This yields a monotonically increasing 240-dimensional evolutionary vector D = [d1, d2, ..., d...]. 3L ].

[0063] 1.4 Using formulas To calculate mutation robustness, the threshold ε was set to twice the standard deviation of genome-wide protein expression levels (ε = 2σ). This represents the number of variants whose expression differences are less than a threshold (reference). Figure 1 ).

[0064] Step 2: Construct the AANet model with prototype regularized autoencoder and construct the Transformer deep prediction model, specifically as follows:

[0065] 2.1 Construct a network model with encoder EN and decoder DN. Encoder EN consists of multiple fully connected layers, with input being a sequence of L network nodes; it is connected to k-1 network nodes through multiple fully connected layers, which are the outputs of encoder EN; where L is the input sequence s. i The length of the sequence is given by , and k is the number of prototypes. The network accepts a sequence s. i A prototype space of a specific dimension k is generated through the encoder EN.

[0066] The decoder DN is a mirror image of the encoder EN. The input of DN is the output of EN, and the output of DN is L network nodes. DN reconstructs the points in the prototype space as much as possible.

[0067] 2.2 The formula for prototype analysis is as follows:

[0068]

[0069] This includes prototype regularization constraints:

[0070]

[0071] α ij ≥0, i=1,…,n,j=1,…,k

[0072] c1,…,c k It is a prototype, the dimensions of the prototype and s i The same dimension, α ij It is a constraint of convex combination, and F is the encoder EN in R2-1. Based on the idea of ​​prototype analysis, any sequence E... i It can be linearly represented by a convex combination of prototypes:

[0073] Because there are constraints Therefore, the number of prototypes set in the network can be reduced to k-1, and the remaining one can be reproduced through this constraint.

[0074] 2.3 The network reconstruction loss is as follows:

[0075]

[0076] Step 3: Train AANet with a mini-batch of the partially evolvable vectors E obtained in Step 1 to determine the number of prototypes required for AANet obtained in Step 2; Train AANet with all the evolvable vectors E and feed them into the encoder part of the autoencoder to obtain a two-dimensional representation of the evolvable vectors, i.e., the evolvability space.

[0077] 3.1 Using different numbers of prototypes, train the same batch of data, and use the MSE formula in step 2.2 to calculate the reconstruction loss of the network corresponding to different numbers of prototypes.

[0078] 3.2 Plot the elbow diagram with the number of prototypes on the horizontal axis and the reconstruction loss on the vertical axis. The number of prototypes corresponding to the elbow inflection point is 3. According to the constraints, the number of nodes in the middle layer of the network is 2.

[0079] 3.3 Following step 3.1, the prototype quantity is determined to be 3. The network parameters are set, and the number of nodes in the middle layer is set to 2 (refer to...). Figure 2 The autoencoder network is trained by inputting all the evolvable vectors.

[0080] 3.4 Since the number of prototypes is determined to be 3, all 2D output vectors of encoder EN are extracted. All vectors form an evolutionary space, and all vectors are wrapped in the prototype vectors.

[0081] Step 4: Input all the evolvable vectors obtained in Step 1 into the trained deep prediction model to obtain the expression level corresponding to each vector.

[0082] 4.1 The Transformer-based DNA-protein expression prediction model transforms the DNA sequence into a high-dimensional vector through an embedding layer by adjusting the structure, and then superimposes positional encodings to preserve sequence order (see reference). Figure 3 A pure encoder architecture with three stacked layers is employed, each containing a multi-head self-attention module and a feedforward network. The multi-head attention module computes multi-level global dependencies between bases in parallel, while the feedforward network enhances local feature representation. Residual connections and layer normalization ensure training stability. Finally, the global features output by the encoder are pooled and mapped to continuous protein expression predictions through fully connected layers. The attention weights simultaneously provide interpretable evidence for key regulatory base regions.

[0083] 4.2 Regenerate 100,000 random datasets using the method in step 1. In the training dataset, the ATCG values ​​of the sequences are converted into one-hot encodings, and each gene sequence has its corresponding gene expression level, which is used as the output. Train the Transformer model using this dataset.

[0084] 4.3 Convert the ATCG equivalents of all sequences generated in step 1 into one-hot encodings and feed them into the deep prediction model trained in step 4.1. Let the deep prediction model network be a function f, and obtain the expression of all evolutionary vectors as f(E).

[0085] Step 5, following Step 3, determines the optimal number of prototypes to be 3, which yields a 2D representation of the evolvability vector. A 2D scatter plot is then generated. Sampling is performed on the scatter plot, and the protein expression value is mapped to fitness using a curve. Finally, a contour plot is drawn to obtain a low-dimensional fitness landscape.

[0086] R5-1: Generate a low-dimensional tensor using the evolvability vector obtained in step 3.

[0087] R5-2: Perform Monte Carlo simulation on the low-dimensional tensor obtained in step 5.1, randomly sample 1000 points, use a curve from protein expression value to fitness, perform cubic spline interpolation on the fitness axis, and map the corresponding protein expression value obtained in step 4 to fitness, scaling the fitness to between 0 and 1.

[0088] R5-3: At this point, the fitness value of each point in the low-dimensional tensor is between 0 and 1. A contour plot can then be drawn using these points to obtain a low-dimensional fitness landscape map. This map can be used to study evolutionary paths, quantify gene epistasis, and perform a range of other research.

[0089] Step 6: Based on mutation robustness, extract the evolutionary sequence that meets the conditions from the low-dimensional fitness landscape tensor.

[0090] 6.1 The low-dimensional tensor obtained in step 5.1 is stained with the mutation robustness MR obtained in step 1.4.

[0091] 6.2 Since gene regulatory elements that play a role in stable selection usually exhibit significantly enhanced mutation robustness, analysis of low-dimensional tensors reveals that sequences that are subject to strong stable selection in gene expression are often far from the prototype 1.

[0092] 6.3 Depending on the desired properties, such as finding a sequence that has undergone strong stable selection, look as far away from prototype 1 as possible.

[0093] The gene sequence exploration and design method provided in this embodiment uses an evolutionary vector to represent the evolutionary potential of a gene, comprehensively characterizing its potential to generate phenotypic variations and avoiding reliance on sequence similarity; at the same time, a Transformer deep model is used to predict gene expression levels from gene sequences, achieving an accurate sequence-expression level correspondence.

[0094] Meanwhile, this invention utilizes a prototype regularized autoencoder network to achieve low-dimensional and efficient visualization of the fitness landscape. Target sequences can be quickly identified through the fitness landscape, improving the efficiency of trial-and-error experiments for designing regulatory sequences. In summary, the method of this invention effectively solves the problem of large variations in the fitness landscape caused by grouping based on gene sequence similarity in existing methods; it improves the efficiency of trial-and-error experiments for designing regulatory sequences and also possesses high computational speed, thus making it suitable for real-world applications.

[0095] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. For those skilled in the art, after learning the contents described in the present invention, several equivalent changes and substitutions can be made without departing from the principle of the present invention. These equivalent changes and substitutions should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for gene design and evolutionary path inference based on an adaptive constrained deep model, characterized in that, Includes the following steps: R1: With fixed base pairs as constraints, insert a random sequence of L base pairs into the middle region, i.e. a sequence that may not exist in nature, and transform it into an evolutionary vector E containing evolutionary information, and calculate the corresponding mutation robustness. R2: Construct AANet, an autoencoder model with prototype regularization; R3: Perform mini-batch iterative training on AANet based on the partially evolvable vector E output by R1 to dynamically determine the number of prototype parameters of AANet; The entire training of AANet is completed using all the evolvable vectors E, and the evolvable vectors E are input into the encoder of AANet to output the projection of the evolvable vectors in the low-dimensional space, that is, to construct the evolvable space. R4: Construct a Transformer deep prediction model, and generate gene sequences separately according to the method of R1 to train the Transformer model. Input the gene sequences obtained in R1 into the trained deep prediction model to obtain the expression level corresponding to each vector. R5: The low-dimensional spatial projection of the evolutionary vector obtained in R3 and the protein expression level obtained in R4 are fused into a low-dimensional tensor; Monte Carlo sampling is performed on the low-dimensional tensor, and the fitness value of the sampling point is calculated through a preset protein expression level-fitness mapping function. Based on the spatial distribution of the fitness value, a contour map of the fitness landscape is generated. R6: Based on mutation robustness, extract evolutionary sequences that meet the conditions from the low-dimensional fitness landscape tensor.

2. The gene design and evolutionary path inference method based on an adaptive constrained deep model according to claim 1, characterized in that, Step R1 is as follows: R1-1: Gene sequence is generated by fixing the base pairs at the beginning and end and using L random base pairs in the middle; R1-2: For each base sequence of length L Considering only single-base mutations, each base corresponds to 3 possible mutation sequences, for a total of 3L possible mutations; each mutation sequence in its 3L mutation neighborhood... Calculate the difference in predicted expression values ,in, Represents the expression value predicted by the deep model; R1-3: The base sequence All of them Sort the values ​​so that they satisfy This yields a monotonically increasing 3L-dimensional evolutionary vector. ; R1-4: Calculate mutation robustness: for any given base sequence First, its 3L mutation neighborhood was constructed, and then the expression level changes in this neighborhood that were less than a threshold were statistically analyzed. The number of variants; this threshold is set at twice the standard deviation of genome-wide protein expression levels. The formula for calculating mutation robustness is: In the formula Indicates differences in expression The number of variants below the threshold; evolutionary analysis shows that gene regulatory elements subject to stable selection typically exhibit significantly enhanced mutational robustness, a property that effectively buffers the impact of random mutations on key phenotypic traits.

3. The gene design and evolutionary path inference method based on an adaptive constrained deep model according to claim 1, characterized in that, Step R2 is as follows: R2-1: Construct a network model with encoder EN and decoder DN; where encoder EN consists of multiple fully connected layers, and the input is a sequence of 3L network nodes; it is connected to k-1 network nodes, i.e., the output of encoder EN, through multiple fully connected layers; where 3L is the input sequence. The length of the sequence is given by k, which is the number of prototypes; the network accepts a sequence. The prototype space of dimension k is generated by encoder EN; The decoder DN is a mirror image of the encoder EN. The input of DN is the output of EN, and the output of DN is 3L network nodes. The DN reconstructs the points in the prototype space as much as possible. R2-2: Prototype analysis is a high-dimensional data dimensionality reduction method based on the principle of extreme values. Its mathematical model will analyze the observed dataset. It is expressed as a convex combination of a finite set of prototypes; these prototypes are essentially pure forms in the feature space representing extreme trade-offs; the formula for prototype analysis is as follows: This includes prototype regularization constraints: It is a prototype, the dimensions of the prototype and The same dimensions It is a constraint of convex combination. It is the encoder EN in R2-1; based on the idea of ​​prototype analysis, any sequence It can be linearly represented by a convex combination of prototypes: ; Because there are constraints Therefore, the number of prototypes set in the network is reduced to k-1, and the remaining one can be reproduced through this constraint; R2-3: Network reconstruction loss: .

4. The gene design and evolutionary path inference method based on an adaptive constrained deep model according to claim 1, characterized in that, Step R3 is as follows: R3-1: Train AANet with mini-batches of the partially evolvable vectors E obtained in step R1. The specific steps are as follows: Using different numbers of prototypes k, the same batch of data was trained. The reconstruction loss of the network corresponding to different numbers of prototypes was calculated using the MSE formula of R2-2. Points with smaller reconstruction loss and fewer prototypes were selected. R3-2: Input all the evolvable vectors E obtained in step R1 into the autoencoder network constructed in R2. The specific steps are as follows: The number of prototypes is determined in step R3-1, the parameters of the network are set, and the autoencoder network is trained with all the inputs of the evolvable vectors. Extract all low-dimensional output vectors of encoder EN, and all vectors form an evolutionary space.

5. The gene design and evolutionary path inference method based on an adaptive constrained deep model according to claim 1, characterized in that, The entire gene sequence obtained in R1 is fed into the trained deep prediction model. Step R4 is as follows: R4-1: The Transformer model, after adjustment, can be used for the task of predicting protein expression levels from DNA sequences; its input is a DNA sequence of length L, which needs to be converted into a high-dimensional vector for each base through an embedding layer, and position encoding is superimposed to preserve sequence order features; Since the task is regression prediction rather than sequence generation, the model retains only the encoder part and stacks N layers. It combines a multi-layer self-attention mechanism to capture long-range dependencies in the DNA sequence. Finally, the global features output by the encoder are mapped to continuous values ​​through a fully connected layer. The output is the predicted protein expression level of a single sample. R4-2: The Transformer encoder consists of a multi-layered stacked structure, with each layer containing two core modules: a self-attention mechanism and a feedforward neural network. First, the self-attention mechanism calculates the correlation weights between all bases in the sequence, using multi-head attention to capture different levels of regulatory patterns in parallel. Then, the feedforward network performs non-linear transformations on the vector at each position to enhance the ability to express local features. Each layer alleviates the gradient vanishing problem through residual connections and normalization. Finally, the encoder outputs a global feature vector of the same length as the input sequence, which integrates the global dependencies and local structural information of the DNA sequence and is directly mapped to the predicted value of protein expression through a fully connected layer. R4-3: Regenerate a random dataset using the method in R1. In the training dataset, the ATCG equivalents of the sequences are converted into one-hot encodings. Each gene sequence has its corresponding gene expression level, which is used as the output. Train the Transformer model using this dataset. R4-4: Convert the ATCG equivalents of all sequences generated in R1 into one-hot encodings, and feed them into the deep prediction model trained in R4-3, allowing the deep prediction model network to act as a function. The representation of all evolutionary vectors is obtained as follows: .

6. The gene design and evolutionary path inference method based on an adaptive constrained deep model according to claim 1, characterized in that, Step R5 is as follows: R5-1: Generate low-dimensional tensors using the evolvability vectors obtained from R3; R5-2: Perform Monte Carlo simulation on the low-dimensional tensor obtained in R5-1, randomly sample 1000 points, use a curve from protein expression value to fitness, perform cubic spline interpolation on the fitness axis, and use the corresponding protein expression value obtained in R4 to map it to fitness, scaling the fitness to between 0 and 1. R5-3: At this point, the fitness value of each point in the low-dimensional tensor is between 0 and 1. Then, a contour map is drawn through these points to obtain a low-dimensional fitness landscape map. On this map, we can study evolutionary paths or conduct a series of studies on the quantification of gene epistasis.

7. The gene design and evolutionary path inference method based on an adaptive constrained deep model according to claim 1, characterized in that, Step R6 is as follows: R6-1: Stain the low-dimensional tensor obtained in R5-1 with the mutation robustness MR obtained in R1-4; R6-2: Since the regulatory sequences of genes whose expression levels are subject to stable selection are often more robust to mutation effects, this graph is analyzed to determine the tensor distribution and extract the evolutionary sequence E that meets the criteria. For genes whose expression levels are subject to stable selection, sequences with better mutation robustness are selected. ; R6-3: Due to the evolutionary vector and gene sequence One-to-one correspondence, therefore through Reverse the gene sequence .

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