Multi-target Pareto leading edge-based mRNA (messenger ribonucleic acid) coding region optimization method

Abstract

The invention discloses an mRNA coding region optimization method based on a multi-target Pareto leading edge. The mRNA coding region optimization method comprises the following steps: determining a CDS region in a target mRNA sequence as an optimization variable; generating an initial population based on the optimization variable; calculating a plurality of fitness evaluation indexes for each individual in the initial population; judging a dominating relationship among individuals based on fitness indexes, and screening non-dominated individuals to form a Pareto hierarchical relationship of the population; screening a next generation of population based on a Pareto hierarchical relationship; generating a new generation of population based on the screened next generation of population; and repeatedly executing until the index inter-generation difference value is continuously lower than a preset threshold value for multiple generations. According to the mRNA coding region optimization method based on the multi-target Pareto leading edge, the problem that in the prior art, mRNA coding region optimization is difficult to consider multi-target collaboration and exploration depth is solved.

Description

A multi-objective Pareto frontier-based method for optimizing mRNA coding regions Technical Field

[0001] This invention belongs to the field of bioinformatics technology, specifically relating to a method for optimizing mRNA coding regions based on multi-objective Pareto frontiers. Background Technology

[0002] Messenger RNA (mRNA), as the information carrier between DNA and protein, has wide applications in vaccine development and protein replacement therapy. In recent years, with the successful application of mRNA vaccines in epidemic prevention and control, their stability and translation efficiency have become key factors determining drug efficacy. Existing technologies have proposed various mRNA sequence optimization strategies, such as enhancing stability through nucleotide modification or introducing regulatory elements like the α / β-globin UTR and Kozak sequences to improve expression levels. Furthermore, several quantitative optimization tools have been developed at the algorithmic level, such as the CAI optimization algorithm targeting the codon fitness index (CAI), the CDSfold algorithm based on minimum free energy (MFE), the dual-objective LinearDesign algorithm combining CAI and MFE (Baidu), and the segmented optimization mRNAid algorithm (Merck). These methods have achieved effective optimization on single or limited metrics.

[0003] However, the above methods have significant limitations: dynamic programming algorithms are difficult to extend to multi-objective scenarios; traditional genetic algorithms, while capable of generating Pareto solutions, suffer from insufficient search depth in complex sequence spaces and are prone to local convergence; furthermore, most methods rely on weighted scoring mechanisms, resulting in limited solution set diversity and an inability to fully approximate the theoretical Pareto front. Particularly in coding sequence (CDS) optimization, the lack of efficient algorithms that balance multi-objective collaboration and global exploration capabilities limits further improvements in mRNA drug performance. Summary of the Invention

[0004] The purpose of this invention is to provide a method for optimizing mRNA coding regions based on multi-target Pareto frontiers, which solves the problem in existing technologies that it is difficult to balance multi-target synergy and exploration depth in mRNA coding region optimization.

[0005] The technical solution adopted in this invention is an mRNA coding region optimization method based on multi-target Pareto fronts, comprising:

[0006] Step 1: Determine the optimization variable: Obtain the target mRNA sequence and determine the CDS region in the target mRNA sequence as the optimization variable; Step 2: Generate the initial population: Generate an initial population based on the optimization variable; Step 3: Multi-index fitness evaluation: Calculate multiple fitness evaluation indices for each individual in the initial population; Step 4: Population screening: Based on the fitness evaluation indices, determine the dominance relationship between individuals and screen non-dominant individuals to form the Pareto hierarchy of the population; screen the next generation population based on the Pareto hierarchy; Step 5: Population iteration: Generate a new generation population based on the screened next generation population; Step 6: Repeat steps 3 to 5 until the intergenerational difference of the indices is lower than the preset threshold for multiple consecutive generations.

[0007] The invention is further characterized by generating an initial population based on optimization variables, including: converting the target mRNA sequence into a protein sequence; and generating an initial population based on the protein sequence using a hierarchical random sampling method based on the uniform probability of synonymous codons.

[0008] A hierarchical random sampling method based on uniform probability of synonymous codons is used to generate the initial population. Specifically, the global sequence space corresponding to the target protein sequence is used as the sampling object, and the set of synonymous codons corresponding to each amino acid position in the protein is used as a separate sampling dimension. For each independent sampling dimension, an equal selection probability is assigned to all synonymous codons in the set. For each initial individual to be generated, each amino acid position is processed one by one: in the set of codons corresponding to each amino acid position, a codon is randomly selected as the codon for that position according to the set uniform probability. The codon selection for all amino acid positions is completed in sequence to form a complete initial individual. This process is repeated until a preset number of initial individuals are generated to form the initial population.

[0009] Multiple fitness evaluation metrics include any 2 to 4 of the following: codon fitness index (CAI), minimum free energy (MFE), transcription initiation efficiency (TIE), and maximum step distance (MLD).

[0010] The Codon Fit Index (CAI) is defined as the set average of codon usage preferences and is calculated based on the following formula:

[0011] In the formula, Represents each individual in the population; represents the preference for using the j-th codon; L represents the total length of the sequence encoding; the minimum free energy MFE, estimated using ViennaRNA software, uses the minimum free energy algorithm to generate the lowest free energy value under a single optimal structure, as shown below:

[0012] Transcription initiation efficiency (TIE) is defined as the pairwise probability of the first N amino acids in the CDS region, and is expressed as follows:

[0013] In the formula, is the pairing probability of the j-th codon; the maximum ladder distance (MLD) is defined as the longest pairing strand in the mRNA secondary structure. Iteration of the possible starting sites of each pairing strand was performed using a double-ended queue, and its corresponding maximum length was calculated, as shown below:

[0014] In the formula, It is the pairing chain distance calculated from the starting point of the pairing length using the j-th codon.

[0015] Based on the fitness evaluation indicators that have been unified in direction, a fitness evaluation indicator set F is selected; based on the fitness evaluation indicator set F, the individual dominance conditions are set, as follows:

[0016]

[0017] Based on the above conditions, all non-dominant individuals in the population are grouped into a Pareto front. The Pareto front is calculated multiple times without replay to form the Pareto hierarchy of the population.

[0018] Based on the Pareto hierarchy, a diversity selection algorithm is used to select the next generation population. Specifically, starting from the highest Pareto level, complete levels are retained sequentially. When the total number of retained individuals reaches 1.5 times the size of the population in each generation, level retention is stopped. A uniform quota for each intermediate level to be retained until the next generation is preset, and the quota is allocated using a recursive algorithm. After determining the available quota for each level, multiple fitness evaluation indicators are normalized, and the KNN algorithm is used to cluster the individuals in each level. Individuals that meet the quota are selected from the clustering results. The selected individuals from each level are combined layer by layer to form the next generation population.

[0019] Based on the Pareto hierarchy, a frontier optimal selection algorithm is used to select the next generation of the population. Specifically, starting from the highest Pareto level, individuals from the lower levels are removed sequentially until the total number of remaining individuals reaches the population size. When the total number of individuals in the last level exceeds the population size, the KNN algorithm is used to cluster the individuals in the last level, and individuals that meet the population size are selected from the clustering results. The selected individuals from each level are then combined layer by layer to form the next generation of the population.

[0020] Based on the selected next-generation population, a random generation algorithm is used to generate a new generation population. Specifically, several codons are randomly selected uniformly from the sequence codons of the parent individual and mutated to generate offspring individuals.

[0021] Based on the selected next-generation population, a directional generation algorithm is used to generate a new generation population. The generation of the new generation population using the directional generation algorithm includes two processes: gradient optimization and active exploration. Gradient optimization generates new offspring individuals through the conjugate gradient method composed of differential gradient and temporal gradient. Active exploration is responsible for sampling the codon positions with insufficient exploration rate and converting them into probability density before generating new offspring individuals.

[0022] New offspring individuals are generated through gradient optimization, specifically including: First, for the parent individual... Calculate the difference gradient in its neighboring set of individuals. , means as follows:

[0023] In the formula, k represents an algebra; Indicates the distance decay weight. Represents the weight normalization coefficient. Represents the parent individual With neighboring paternal individuals Codon differences; , Let represent the individual weights of individual i and its neighboring individual j, respectively. Indicates the gradient direction. Dominate hour If positive, then negative; secondly, a temporal mechanism is introduced to preserve recent evolutionary trends, with the temporal gradient between each generation being passed in an exponentially decaying manner, as shown below:

[0024] In the formula, , Let represent the temporal gradients of the k-th generation and the (k+1)-th generation, respectively; This represents the weighting coefficients; finally, the differential gradients from all historical generations are weighted and fused to obtain the parent individual. conjugate gradient at ... , means as follows:

[0025] Based on the predefined mutation number m and conjugate gradient The converted probability density is based on the parent individual. Select a predetermined number of m codon subsequences from the encoded sequence and perform probability density mutation to generate new offspring individuals. .

[0026] New offspring individuals are generated through active exploration, specifically including: individual derivation based on differential gradients. Synonymous codon sampling weights , means as follows:

[0027] Then, the position of each amino acid was calculated. Position weight Position weight The average absolute contribution of the usage of all synonymous codons at this position is calculated according to the following formula:

[0028] In the formula, Indicates the first The frequency of use of a synonymous codon at this position; Indicates amino acids A subset of synonymous cryptography Indicates the extraction of amino acids The length of the synonymous cipher subset; subsequently, by adjusting the positional weights of each generation. By performing time aggregation, the overall sampling coverage of an individual's history is obtained, as shown below:

[0029] In the formula, This represents the weight of position j in generation t; based on the predefined number of mutations m and ... The converted probability density, choose Low-value, underexplored codon sites undergo mutation to generate new offspring individuals.

[0030] The beneficial effects of this invention are as follows: Based on a multi-objective Pareto front-based mRNA coding region optimization method, this invention can perform a thorough search for each optimization objective in a real, feasible sequence space at once, ultimately obtaining multiple different high-quality solutions simultaneously. In addition to the traditional optimization metrics CAI and MFE, this invention introduces two new metrics: Translation Initiation Efficiency (TIE) and Maximum Gradient Distance (MLD), thereby improving the accuracy of predicting mRNA translation efficiency and stability. To address the problem of high search difficulty in existing mRNA sequences, this invention combines differential evolution and intergenerational memory to design a novel progeny generation and selection algorithm, making the optimization results closer to the theoretical Pareto front and ensuring the diversity of results. Attached Figure Description

[0031] Figure 1 is a flowchart of the mRNA coding region optimization method based on multi-objective Pareto front of the present invention; Figure 2 is a solution set diagram of the optimal Pareto front obtained by the method of the present invention in a single solution process. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0033] Example 1: This invention utilizes a multi-objective Pareto front-based mRNA coding region optimization method, as shown in Figure 1. This method achieves efficient, multi-dimensional, collaborative optimization of the mRNA CDS region by constructing a complete genetic evolutionary framework.

[0034] Step 1: Determine the optimization variable: Obtain the target mRNA sequence and determine the CDS region in the target mRNA sequence as the optimization variable.

[0035] In this context, the optimization variable is the coding sequence (CDS) in the messenger RNA responsible for encoding a specific protein. Its nucleotide arrangement directly determines the amino acid sequence of the translation product. The CDS region is a major component of mRNA and a key region affecting translation efficiency, structural stability, and other parameters. Setting the CDS as the optimization variable means that the entire optimization process searches only within its allowed range of synonymous codon substitutions, ensuring that the final generated sequence still encodes the same protein, thereby maintaining the consistency of biological function.

[0036] Step 2: Generate Initial Population: An initial population is generated based on the optimization variables to initiate the optimization iteration process. The diversity and coverage of the initial population directly affect the algorithm's global search capability. To avoid bias towards specific host-preferred codons that could lead to search space shifts, this embodiment employs a hierarchical random sampling method based on the uniform probability of synonymous codons to generate the initial individuals.

[0037] Step 3: Multi-metric fitness evaluation: Multiple fitness evaluation metrics are calculated for each individual in the initial population. These metrics quantify the performance of the mRNA sequence across different functional dimensions, covering aspects such as translation efficiency and structural stability. Each individual corresponds to a set of metric values, forming its coordinates in a multi-dimensional target space. Fitness evaluation is the basis for distinguishing the quality of individuals and directly affects subsequent selection and evolutionary direction. The metrics used in this invention include, but are not limited to: Codon Adaptation Index (CAI), Minimum Free Energy (MFE), Translation Initiation Efficiency (TIE), and Maximum Length of Paired Domain (MLD). These metrics together constitute a multi-dimensional evaluation system, enabling optimization to move beyond a single dimension and pursue a balanced improvement in overall performance.

[0038] Step 4: Population selection: Based on fitness evaluation indicators, determine the dominance relationship between individuals and select non-dominant individuals to form the Pareto hierarchy of the population; select the next generation population based on the Pareto hierarchy; Step 5: Population iteration: Generate a new generation population based on the selected next generation population; Step 6: Repeat steps 3 to 5 until the intergenerational difference of the indicator is lower than the preset threshold for multiple consecutive generations.

[0039] Through the steps described above, this application achieves simultaneous optimization of multiple key performance indicators within a real and feasible mRNA sequence space. By employing a CDS-based optimization variable definition, it ensures that all candidate sequences correctly encode the target protein. The introduction of a multi-indicator synergistic evaluation system avoids functional imbalances caused by single-indicator optimization. The construction of a Pareto-dominated hierarchical screening mechanism effectively preserves diverse advantageous solutions and overcomes the subjective bias of traditional weighted methods. The design of a dynamically adjustable iterative strategy balances search breadth and depth, significantly improving the ability to approximate the theoretical optimum. In summary, this method solves the technical challenge of simultaneously considering multi-target synergy and in-depth exploration in existing mRNA coding region optimization techniques, providing a reliable and efficient computational tool for designing high-performance mRNA sequences.

[0040] Example 2, based on the above examples, further provides: generating an initial population based on optimization variables, including: converting the target mRNA sequence into a protein sequence; and generating an initial population based on the protein sequence using a hierarchical random sampling method based on the uniform probability of synonymous codons.

[0041] In this process, the target mRNA sequence is converted into a protein sequence to eliminate the influence of the input sequence on the population, thereby ensuring that the subsequent optimization process is not affected by the input sequence.

[0042] Furthermore, based on the obtained protein sequence, a hierarchical random sampling method based on the uniform probability of synonymous codons is used to generate an initial population. Specifically: this method uses the global sequence space corresponding to the target protein sequence as the sampling object, and takes the set of synonymous codons corresponding to each amino acid position in the protein as a separate sampling dimension; the space composed of all possible mRNA sequences encoding the same protein is regarded as the basic space for optimization search. This space is composed of the selection and combination of uniform codons at each codon position, and its mathematical form can be expressed as a Cartesian product, as follows:

[0043] in, This represents the encoding of the j-th amino acid. The set of all synonymous codons.

[0044] For each independent sampling dimension, all synonymous codons within the set are assigned an equal probability of selection, without favoring any particular codon. This design ensures that, while maintaining the amino acid sequence, each codon variant has an equal chance of occurrence in the initial stage. For each initial individual to be generated, each amino acid position is processed sequentially: from the codon set corresponding to each amino acid position, a codon is randomly selected as the codon for that position according to a set uniform probability. This process is repeated for all amino acid positions to form a complete initial individual. This process is repeated until a preset number of initial individuals are generated, forming the initial population. The size of the initial population can be set according to actual computing resources and the length of the target sequence. Compared with traditional random mutation methods, the initial population generated by this method exhibits higher diversity, better coverage, and unbiasedness, laying a broad and balanced search foundation for the entire optimization process.

[0045] Example 3, based on the above examples, further provides: multiple fitness valence indicators including any 2 to 4 indicators from codon fitness index (CAI), minimum free energy (MFE), transcription initiation efficiency (TIE), and maximum step distance (MLD).

[0046] The Codon Adaptation Index (CAI) is used to assess mRNA expression efficiency. It quantifies the codon usage preference of mRNA, indicating its compatibility with the target species' translation system. Furthermore, the CAI index is positively correlated with the number of suitable tRNAs in the cell, thus affecting the efficiency and accuracy of protein translation. CAI is defined as the ensemble mean of codon usage preferences, expressed as follows:

[0047] In the formula, Represents each individual in the population; The j-th codon usage preference is represented by a predefined human codon usage preference table; L represents the total length of the sequence encoding.

[0048] Minimum Free Energy (MFE) is a traditional indicator of mRNA stability, representing the energy score of the most stable conformation among all potential secondary structures of the mRNA sequence. Among indicators assessing in vitro hydrolytic stability, MFE shows the strongest correlation. Using ViennaRNA software, the minimum free energy algorithm proposed by Zuker & Stiegler (1981) was employed to generate the lowest free energy value for a single optimal structure. Considering the indicator design, a lower MFE (i.e., a more negative value) represents stronger structural stability in the calculation... To control the direction of the dominant solution calculation, negative values ​​are used, as shown below:

[0049] Transcription initiation efficiency (TIE), as a supplementary indicator to translation efficiency, is defined as the average pairing probability of the first few codons (e.g., the first 30) in the secondary structure of the CDS region. This indicator can be calculated by using a dynamic programming-based partition function algorithm (such as the McCaskill algorithm) to calculate the base pairing probability in the mRNA thermodynamic ensemble; alternatively, it can be calculated by considering whether the secondary structure of the optimal structure is consistent. A higher pairing probability indicates lower translation initiation efficiency; therefore, to maintain a consistent optimization direction, TIE is calculated using negative values. This invention calculates TIE based on secondary structure rather than a partition function. , means as follows:

[0050] In the formula, It is the pairing probability of the j-th codon.

[0051] Maximum Ladder Distance (MLD) is defined as the longest pairing strand in the mRNA secondary structure and is used to assess the probability of immune-mediated degradation. Longer double-stranded structures are more easily recognized by in vivo degradation systems, leading to rapid mRNA clearance. Since MLD examines the widest distance of the secondary structure, rather than the distance of the starting position, this invention iterates over each possible starting site of the pairing strand using a double-ended queue approach and calculates its corresponding maximum length. Similarly, to meet the requirement of maximizing the objective function, MLD is used in the fitness evaluation with a negative value, as shown below:

[0052] In the formula, It is the pairing chain distance calculated from the starting point of the pairing length using the j-th codon.

[0053] The four indicators mentioned above analyze the overall performance of the mRNA coding region from three dimensions: translation efficiency, structural stability, and in vivo immunogenicity. These four indicators are interdependent. Therefore, allowing for flexible selection of any combination of two to four indicators in practical applications allows for customized optimization strategies for specific application scenarios (e.g., using all four indicators in vaccine long-length sequence design, while therapeutic short peptide production focuses on using only CAI and MFE), while avoiding the search space expansion problem caused by multi-objective conflicts.

[0054] Through the above-described steps, this application achieves synergistic modeling and trade-off optimization of the multidimensional performance of mRNA coding regions. By introducing two new evaluation metrics, TIE and MLD, the accuracy of predicting translation initiation efficiency and in vivo stability is significantly improved, resolving the problem that traditional methods relying solely on CAI and MFE lead to optimization results deviating from actual biological effects.

[0055] Example 4, based on the above examples, further provides: selecting a fitness evaluation index set F based on the unified fitness evaluation index; and setting individual dominance conditions based on the fitness evaluation index set F, as follows:

[0056]

[0057] Based on the above conditions, all non-dominant individuals in the population are grouped into a Pareto front. The Pareto front is calculated multiple times without replay to form the Pareto hierarchy of the population.

[0058] First, the fitness evaluation metric set F is selected. This refers to choosing a combination of metrics from multiple candidate metrics to evaluate individual performance. This set must contain at least two metrics, which can be CAI and MFE, CAI and TIE, MFE and MLD, or any combination of four metrics. The specific composition of set F can be flexibly configured according to actual optimization needs. For example, in applications that emphasize expression efficiency, CAI and TIE are prioritized; while in applications that emphasize stability, MFE and MLD are given more attention. This design allows the algorithm to adapt to different user preferences and experimental goals, enhancing the method's versatility and scalability.

[0059] Secondly, regarding the aforementioned individual dominance conditions: for two individuals in the population... and If an individual In all metrics Their performance was no worse than And is strictly superior to at least one metric. Then it is called Dominate This condition does not rely on any manually set weighting coefficients, avoiding the bias caused by subjective weighting in the traditional weighted summation method, and can objectively identify a better solution.

[0060] Finally, all non-dominated individuals in the population are grouped into a Pareto front. The current population is then traversed, and all individuals not dominated by any other individual are selected, forming the first Pareto front. Subsequently, the individuals in the first layer are removed from the population, and the same process is repeated to obtain the second layer of non-dominated individuals, forming the second Pareto front. This operation is repeated until the population is empty, thus forming the Pareto hierarchy of the population. In this Pareto hierarchy, each level represents a set of individuals with similar levels of superiority or inferiority. The first level is the currently optimal set of non-dominated solutions, and subsequent levels are successively the sets of second-best solutions dominated by the previous level. The Pareto hierarchy is the fundamental basis for guiding population evolution.

[0061] This scheme, by introducing strict dominance rules based on a unified directional index and constructing a multi-level Pareto hierarchy, enables the algorithm to effectively identify and retain multiple high-quality solutions that excel in different objectives without the need for preset weights. This solves the problem of traditional single-objective weighted methods easily overlooking key non-dominated solutions, avoids the one-sided optimization results caused by conflicts between indices, and ultimately outputs a set of candidate sequence schemes that combine high performance and diversity, significantly improving the scientific rigor and practicality of mRNA coding region optimization.

[0062] Example 5, based on the above examples, further provides: using a diversity selection algorithm to screen the next generation population based on Pareto hierarchy.

[0063] Specifically, the algorithm starts from the highest Pareto level and retains complete levels sequentially. Level retention stops when the total number of retained individuals reaches 1.5 times the population size of each generation. This setting ensures that not only the current optimal solution set is retained, but also a certain proportion of intermediate level individuals are included, thereby expanding the candidate solution pool and preventing high-quality but not yet fully mature solutions from being prematurely eliminated. This retention threshold, higher than the conventional population size, provides ample selection space for subsequent refined screening.

[0064] The system pre-determines the uniform quota to be retained by each intermediate layer to the next generation, and uses a recursive algorithm to allocate the quota. The system also pre-determines the uniform quota to be retained by each layer, and dynamically adjusts the final number of individuals that can be retained in each layer by combining the actual number of individuals in that layer with the overall distribution, so as to ensure that the quota allocation meets the overall control requirements and takes into account the reasonable coverage within each layer.

[0065] After determining the available quotas for each layer, multiple fitness evaluation metrics are normalized to eliminate the influence of differences in dimensions. Subsequently, the KNN (K-Nearest Neighbors) algorithm is used to cluster individuals at each layer, selecting individuals that meet the quota requirements from the clustering results. KNN clustering effectively identifies the density distribution characteristics of individuals in the target space, thereby selecting relatively dispersed and representative individuals from each layer as components of the next generation population, thus enhancing the coverage breadth of the population in the solution space.

[0066] Finally, the selected individuals from each level are combined layer by layer to form the next generation population. This population includes both high-fitness frontier solutions and diverse potential solutions from the middle levels, achieving a synergistic unity between optimization directionality and search breadth.

[0067] This method addresses population selection mechanisms in multi-objective genetic evolution processes, aiming to balance optimization advancement with the maintenance of solution set diversity. By selectively preserving individuals at different Pareto levels in stages, the algorithm is particularly suitable for the early stages of optimization. When high-quality non-dominated solutions are still relatively sparse, it helps to more comprehensively approximate the theoretical Pareto front, improving the overall quality and robustness of the final optimization results.

[0068] Example 6, based on the above examples, further provides: using the frontier optimal selection algorithm to screen the next generation population based on Pareto hierarchy.

[0069] The algorithm's implementation consists of two stages: Stage 1: Starting from the highest Pareto level (Level 1), individuals from the worst levels are sequentially removed until the total number of remaining individuals reaches the population size. If the total number of individuals exceeds the population size after retaining the last level, the algorithm proceeds to Stage 2.

[0070] The second stage involves using the KNN algorithm to perform cluster analysis on the individuals in the last layer within a multidimensional fitness index space, selecting individuals that fit the population size from the clustering results. KNN clustering, as a last-layer pruning tool, compensates for the distribution bias that might result from simply truncating by level.

[0071] This algorithm employs a fast convergence-oriented selection strategy. Its core idea is to prioritize retaining individuals at the optimal level within the current population, driving the population closer to the theoretical Pareto front through intense selection pressure. This algorithm is particularly suitable for the mid-to-late stages of the optimization process, and is especially effective when the population has initially approached a high-quality solution region, the need for diversity exploration decreases, and the need for accuracy improvement increases.

[0072] Example 7, building upon the above examples, further provides the following: A new generation population is generated using a random generation algorithm based on the selected next-generation population. Specifically, several codons are randomly selected uniformly from the sequence codons of the parent individual for mutation, generating offspring individuals. Furthermore, to avoid population degradation due to duplicate individuals, uniqueness verification is performed during the generation process: after each new individual is generated, its sequence is compared with already generated individuals and the existing population. If identical sequences exist, mutation is repeated until a unique solution is obtained globally.

[0073] This method introduces non-directional mutation operations to perform synonymous substitutions of codons in coding regions while maintaining the amino acid sequence, thereby exploring a wider range of feasible solutions. Due to its simplicity and low computational cost, it is particularly suitable for the initial stage of optimization where the solution space needs to be rapidly covered. Therefore, it achieves the technical effects of increasing population diversity, enhancing global search capabilities, and supporting the continuous expansion of multi-objective Pareto fronts.

[0074] Example 8, building upon the above examples, further provides the following: A directional generation algorithm is used to generate a new generation population, comprising two processes: gradient optimization and active exploration. Gradient optimization generates new offspring individuals using a conjugate gradient method composed of differential gradients and temporal gradients. Active exploration samples codon positions with insufficient exploration rates and converts them into probability densities before generating new offspring individuals. During genetic evolution, an offspring generation mechanism with a clear search direction is constructed based on existing optimization information in the current population. By introducing two synergistic mechanisms—gradient optimization and active exploration—this algorithm significantly improves search efficiency and optimization depth while maintaining population diversity, and is particularly suitable for the complex search space of mRNA coding sequences (CDS).

[0075] Specifically, the directional generation algorithm includes two core processes: (i) the gradient optimization process, which generates new offspring individuals through gradient optimization.

[0076] First, regarding the father individual Calculate the difference gradient in its neighboring set of individuals. , means as follows:

[0077] In the formula, k represents an algebra; Indicates the distance decay weight. Represents the weight normalization coefficient. Represents the parent individual With neighboring paternal individuals Codon differences; , Let represent the individual weights of individual i and its neighboring individual j, respectively. These weights are represented by a One-Hot encoded weight vector, indicating the synonymous codons selected at each amino acid site. Indicates the gradient direction. Dominate hour If positive, then negative.

[0078] This step is based on the paternal individuals in the current population. A directional search vector is calculated based on the sequence differences and Pareto dominance relationships between the two individuals and their neighboring individuals. Specifically, a directional search vector is calculated only when the codon differences between the two individuals are... Only when the cutoff radius is smaller than the preset cutoff radius is it included in the differential calculation range, thereby ensuring that the individuals being compared have sufficiently similar secondary structure configurations, making the local optimization information comparable and instructive.

[0079] Secondly, a temporal mechanism is introduced to preserve recent evolutionary trends. The temporal gradient between each generation is transmitted in an exponentially decaying manner, as shown below:

[0080] In the formula, , Let represent the temporal gradients of the k-th generation and the (k+1)-th generation, respectively; This represents the weighting coefficient.

[0081] This mechanism gives more influence to recent evolutionary paths, enabling the algorithm to have short-term memory capabilities, which helps maintain an effective search direction in high-dimensional undiscontinuous discrete spaces.

[0082] Finally, the differential gradients of all historical generations are weighted and fused to obtain the parent individual. conjugate gradient at ... , means as follows:

[0083] This conjugate gradient integrates spatial neighborhood relationships and temporal evolution trends, effectively guiding the direction of mutation. Based on the probability density distribution transformed from this conjugate gradient, a larger absolute value of the gradient indicates that the position has been frequently adjusted and effectively in historical optimization, corresponding to a higher mutation probability. From the parent individual... Select a preset number of characters in the encoded sequence. Targeted mutations are performed at each codon site to generate new offspring individuals. This process prioritizes sites that have the potential to improve fitness along the gradient direction, thereby achieving efficient local search.

[0084] (ii) Active exploration process, that is, generating new offspring individuals through active exploration.

[0085] To prevent the algorithm from being overly focused on the current advantageous region and thus failing to explore the global region, an active exploration mechanism was designed to discover potential but not yet fully sampled sequence regions.

[0086] First, the individual values ​​are derived based on the differential gradient. Synonymous codon sampling weights This is used to evaluate the relative activity of different codons in the current optimized environment, and is represented as follows:

[0087] Then, the position of each amino acid was calculated. Position weight , defined as the average absolute contribution of the usage of all synonymous codons at that position:

[0088] in, Indicates the first The frequency of use of synonymous codons at this position. Low The position of the value indicates that the corresponding codon combination has not been fully sampled for a long time, and there is a blind spot in the exploration.

[0089] Furthermore, by assigning positional weights to each generation... By performing time aggregation, the overall sampling coverage of an individual's history is obtained, as shown below:

[0090] In the formula, This represents the weight of position j in generation t; the resulting weight is... The vector reflects the historical exploration intensity of each codon site. When generating new individuals, based on... The probability density of the transition should be selected preferentially. Mutations at lower sites actively fill sparse regions, thereby generating new offspring individuals.

[0091] The two processes described above complement each other: gradient optimization focuses on efficient improvement within the neighborhood of known high-quality solutions, ensuring the algorithm can deeply explore local optima; while active exploration guarantees broad coverage of the entire sequence space, preventing the algorithm from falling into local optima traps. Through their combined effect, the directional generation algorithm not only improves search efficiency but also enhances the quality and breadth of the Pareto solution set.

[0092] Through the above-described steps, this application achieves efficient construction of a new generation population based on a directional generation algorithm. Due to the adoption of a gradient optimization mechanism, the algorithm can advance along the gradient optimization path in the real feasible mRNA sequence space, significantly improving search efficiency and the ability to approximate the theoretical Pareto front. Simultaneously, the active exploration mechanism ensures continuous coverage of insufficiently sampled regions, effectively maintaining the diversity of the solution set. Therefore, this method is particularly suitable for multi-objective, high-dimensional, discontinuous, and discrete mRNA CDS sequence optimization scenarios.

[0093] To verify the effectiveness and accuracy of the method of this invention, it was applied to the mRNA optimization of Fireflyluciferase (Fluc) protein, with CAI and MFE selected as the fitness evaluation metrics. The method of this invention obtained a solution set with CAI ranging from 0.65 to 0.98 in a single solution run, as shown in Figure 2. This single-run solution set size and target coverage are not achieved by Baidu's LinearDesign algorithm or Merck's segmented optimization mRNAid algorithm.

Claims

1. A method for optimizing mRNA coding regions based on multi-objective Pareto fronts, characterized in that, Includes: Step 1: Determine the optimization variable: Obtain the target mRNA sequence and determine the CDS region in the target mRNA sequence as the optimization variable; Step 2: Generate initial population: Generate an initial population based on the optimization variables; Step 3: Multi-index fitness evaluation: Calculate multiple fitness evaluation indices for each individual in the initial population; Step 4: Population selection: Based on the fitness evaluation indices, determine the dominance relationship between individuals, and select non-dominant individuals to form the Pareto hierarchy of the population; select the next generation population based on the Pareto hierarchy; Step 5: Population iteration: Generate a new generation population based on the selected next generation population; Step 6: Repeat steps 3 to 5 until the intergenerational difference of the indices is lower than the preset threshold for multiple consecutive generations.

2. The mRNA coding region optimization method based on multi-objective Pareto front according to claim 1, characterized in that, The process of generating an initial population based on the optimization variables includes: converting the target mRNA sequence into a protein sequence; and generating an initial population based on the protein sequence using a hierarchical random sampling method based on the uniform probability of synonymous codons.

3. The mRNA coding region optimization method based on multi-objective Pareto front according to claim 2, characterized in that, The method of generating the initial population using a hierarchical random sampling method based on the uniform probability of synonymous codons is as follows: The global sequence space corresponding to the target protein sequence is used as the sampling object; the set of synonymous codons corresponding to each amino acid position in the protein is taken as a separate sampling dimension; for each independent sampling dimension, an equal selection probability is assigned to all synonymous codons within the set; for each initial individual to be generated, each amino acid position is processed sequentially: in the codon set corresponding to each amino acid position, a codon is randomly selected as the codon for that position according to a set uniform probability, and the codon selection for all amino acid positions is completed in sequence to form a complete initial individual; this process is repeated until a preset number of initial individuals are generated, forming the initial population.

4. The mRNA coding region optimization method based on multi-objective Pareto front according to claim 1, characterized in that, The fitness evaluation metrics include any 2 to 4 of the following: codon fitness index (CAI), minimum free energy (MFE), transcription initiation efficiency (TIE), and maximum step distance (MLD).

5. The mRNA coding region optimization method based on multi-objective Pareto front according to claim 4, characterized in that, The codon fitness index (CAI) is defined as the set average of codon usage preferences and is calculated based on the following formula: In the formula, Represents each individual in the population; represents the preference for using the j-th codon; L represents the total length of the sequence encoding; the minimum free energy MFE, estimated using ViennaRNA software, uses the minimum free energy algorithm to generate the lowest free energy value under a single optimal structure, as shown below: The transcription initiation efficiency (TIE) is defined as the pairwise probability of the first N amino acids in the CDS region, expressed as follows: In the formula, is the pairing probability of the j-th codon; the maximum ladder distance (MLD) is defined as the longest pairing strand in the mRNA secondary structure. Iteration of the possible starting sites of each pairing strand was performed using a double-ended queue, and its corresponding maximum length was calculated, as shown below: In the formula, It is the pairing chain distance calculated from the starting point of the pairing length using the j-th codon.

6. The mRNA coding region optimization method based on multi-objective Pareto front according to claim 5, characterized in that, Based on the fitness evaluation indicators that have been unified in direction, a fitness evaluation indicator set F is selected; based on the fitness evaluation indicator set F, the individual dominance conditions are set, as follows: Based on the above conditions, all non-dominant individuals in the population are grouped into a Pareto front. The Pareto front is calculated multiple times without replay to form the Pareto hierarchy of the population.

7. The mRNA coding region optimization method based on multi-objective Pareto front according to claim 6, characterized in that, Based on the Pareto hierarchy, a diversity selection algorithm is used to screen the next generation of the population. Specifically, starting from the highest Pareto level, complete levels are retained sequentially. When the total number of retained individuals reaches 1.5 times the size of the population in each generation, the level retention is stopped. The intermediate layer retains a uniform quota for each subsequent generation, and a recursive algorithm is used to allocate the quota. After determining the available quota for each layer, multiple fitness evaluation indicators are normalized, and the KNN algorithm is used to cluster individuals in each layer. Individuals that meet the quota requirements are selected from the clustering results. The selected individuals in each layer are then combined layer by layer to form the next generation population.

8. The mRNA coding region optimization method based on multi-objective Pareto front according to claim 6, characterized in that, Based on the Pareto hierarchy, a frontier optimal selection algorithm is used to select the next generation of the population. Specifically, starting from the highest Pareto level, individuals from the lower levels are removed sequentially until the total number of remaining individuals reaches the population size. When the total number of individuals in the last level exceeds the population size, the KNN algorithm is used to cluster the individuals in the last level, and individuals that meet the population size are selected from the clustering results. The selected individuals from each level are then combined layer by layer to form the next generation of the population.

9. The method for mRNA coding region optimization based on multi-objective Pareto front according to any one of claims 7-8, characterized in that, Based on the selected next-generation population, a random generation algorithm is used to generate a new generation population. Specifically, several codons are randomly selected uniformly from the sequence codons of the parent individual and mutated to generate offspring individuals.

10. The method for mRNA coding region optimization based on multi-objective Pareto front according to any one of claims 7-8, characterized in that, Based on the selected next-generation population, a directional generation algorithm is used to generate a new generation population. The generation of the new generation population using the directional generation algorithm includes two processes: gradient optimization and active exploration. The gradient optimization generates new offspring individuals through the conjugate gradient method composed of differential gradient and temporal gradient. The active exploration is responsible for sampling the codon positions with insufficient exploration rate and converting them into probability density before generating new offspring individuals.

11. The method for optimizing mRNA coding regions based on multi-objective Pareto fronts according to claim 10, characterized in that, New offspring individuals are generated through gradient optimization, specifically including: First, for the parent individual... Calculate the difference gradient in its neighboring set of individuals. , means as follows: In the formula, k represents an algebra; Indicates the distance decay weight. Represents the weight normalization coefficient. Represents the parent individual With neighboring paternal individuals Codon differences; 、 Let represent the individual weights of individual i and its neighboring individual j, respectively. Indicates the gradient direction. Domination hour If positive, then negative; secondly, a temporal mechanism is introduced to preserve recent evolutionary trends, with the temporal gradient between each generation being passed in an exponentially decaying manner, as shown below: In the formula, 、 Let represent the temporal gradients of the k-th generation and the (k+1)-th generation, respectively; This represents the weighting coefficients; finally, the differential gradients from all historical generations are weighted and fused to obtain the parent individual. conjugate gradient at ... , means as follows: Based on the predefined mutation number m and conjugate gradient The converted probability density is based on the parent individual. Select a predetermined number of m codon subsequences from the encoded sequence and perform probability density mutation to generate new offspring individuals. 。 12. The mRNA coding region optimization method based on multi-objective Pareto front according to claim 11, characterized in that, New offspring individuals are generated through active exploration, specifically including: individual derivation based on differential gradients. Synonymous codon sampling weights , means as follows: Then, the position of each amino acid was calculated. Position weight The position weight The average absolute contribution of the usage of all synonymous codons at this position is calculated according to the following formula: In the formula, Indicates the first The frequency of use of a synonymous codon at this position; Indicates amino acids A subset of synonymous cryptography Indicates the extraction of amino acids The length of the synonymous cipher subset; subsequently, by assigning positional weights to each generation. By performing time aggregation, the overall sampling coverage of an individual's history can be obtained, as shown below: In the formula, This represents the weight of position j in generation t; based on the predefined number of mutations m and ... The converted probability density, choose Low-value, underexplored codon sites undergo mutation to generate new offspring individuals.

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