A method for predicting protein secondary structure combining q-hmm and rules

Abstract

The application discloses a protein secondary structure prediction method combining q-HMM and rules, and comprises the following steps: firstly, establishing q-HMM and optimizing the model by using association rules; secondly, training q-HMM parameters; thirdly, using the model parameters to perform prediction; and finally, obtaining the predicted protein secondary structure chain. The classical HMM is improved to q-HMM, a bidirectional q-HMM suitable for protein secondary structure prediction is established, the influence of the adjacent amino acid primary structure and secondary structure is considered, and the defects of the inherent time sequence characteristics of the classical HMM are made up; meanwhile, the rules are integrated to improve the prediction accuracy of the model, the bidirectional prediction improves the calculation speed, and the defects of the rule prediction are made up.

Description

Technical Field

[0001] This invention belongs to the field of protein secondary structure prediction, and in particular, it is a protein secondary structure prediction method that combines q-HMM and rules. Background Technology

[0002] Since the Human Genome Project was officially launched at the end of the last century, scientists have worked tirelessly to overcome numerous challenges, finally completing the mapping of the human genome at the beginning of this century. Humanity has since entered the post-genomic era, and proteomics research is one of the most important research topics in life sciences during this era. The primary task in studying the proteome is to investigate its function and structure. It is generally accepted in the scientific community that protein secondary structure prediction is a precursor to overall protein structure prediction. Protein secondary structure refers to the specific conformation formed by the spindle or folding of the polypeptide backbone atoms along a certain axis; that is, the spatial arrangement of the polypeptide backbone atoms, excluding amino acid side chains.

[0003] The main forms of protein secondary structure include α-helices, β-sheets, β-turns, and random coils. Due to the large molecular weight of proteins, different peptide segments within a single protein molecule may contain different forms of secondary structure. The secondary structure of a protein is not simply an α-helix or β-sheet, but rather a combination of these different conformations, and the proportions of different peptide segments usually vary. Therefore, finding a highly accurate method for predicting protein secondary structure would play a crucial role in subsequent research on protein function and structure.

[0004] Existing methods for predicting protein secondary structure mainly include: hidden Markov models, stereochemistry methods, neural network methods, hydrogen bond number methods, etc., which can be roughly divided into two generations.

[0005] First-generation prediction methods assumed that amino acids in a polypeptide sequence fold independently when forming secondary structures, unaffected by interactions between amino acids. Therefore, prediction methods at this stage were primarily statistical. These methods mainly relied on the properties of individual residues, classifying amino acids into helical, folded, and turn-forming groups or cleavage groups, and then using this information to identify fragments in the amino acid sequence that might form various secondary structures. However, this assumption is incorrect; increasing research and experiments have demonstrated the existence of localized influences within the sequence. The Chou-Fasman method is a prime example of this first-generation prediction approach, with an accuracy rate of approximately 50%-60%.

[0006] Second-generation prediction methods: Numerous studies and experiments have demonstrated that local interactions also influence secondary structure formation. Prediction methods of this era generally utilize sliding window techniques to account for these local effects. The general approach is as follows: the known amino acid sequence of a protein is divided into several fragments using a fixed-size window, and then useful information is extracted from these fragments. While this type of prediction method considers local effects, it does not account for the influence between different window fragments or the interactions between long-range amino acids. Therefore, its prediction accuracy remains only around 60%-65%. Methods in this generation include GOR3 and Levin. Summary of the Invention

[0007] The purpose of this invention is to provide a protein secondary structure prediction method that combines q-HMM and rules to improve the accuracy of protein secondary structure prediction.

[0008] The technical solution to achieve the purpose of this invention is as follows:

[0009] A method for predicting protein secondary structure combining q-HMM and rules, comprising the following steps:

[0010] Step 1: Establish q-HMM (Quantum Hidden Markov Model): Define the set of protein secondary structure state sequences S, the set of protein primary structure observation sequences V, the state transition tensor A in q-HMM, the emission tensor B in q-HMM, and the initial tensor π in q-HMM;

[0011] Step 2: Extract association rules: Define association rule parameters, calculate the confidence and support of the extracted protein secondary structure rules, compare the confidence and support thresholds to generate frequent itemsets, and finally obtain strong association rules;

[0012] Step 3: Solve for q-HMM parameters using statistical methods: Train q-HMM model parameters: Use the Baum-Welch algorithm to iteratively calculate the q-HMM model parameters, and use the reestimation formula to obtain the state transition tensor A, the emission tensor B, and the initial tensor π in the q-HMM.

[0013] Step 4: Use model parameters to perform bidirectional prediction based on association rules: Determine the starting position for protein secondary structure prediction based on the strong association rules obtained in Step 2; Use the protein sequence fragment and the state transition tensor A, emission tensor B, and initial tensor π in the q-HMM obtained in Step 3, and combine the Viterbi algorithm to perform bidirectional iteration to predict the entire protein secondary structure chain.

[0014] The significant advantages of this invention compared to existing technologies are:

[0015] (1) This invention establishes a bidirectional q-HMM suitable for protein secondary structure prediction, which improves the classic HMM into a q-HMM. It takes into account the influence of the primary and secondary structures of neighboring amino acids, and can make full use of the local action information of the residues on both sides, thus making up for the defects caused by the inherent temporal characteristics of the classic HMM.

[0016] (2) This invention provides an algorithm for predicting the secondary structure of proteins by combining q-HMM with rule prediction. It combines the advantages of the two prediction methods. While using q-HMM, it incorporates rules to improve the accuracy of model prediction, and at the same time makes up for the shortcomings of rule prediction. Attached Figure Description

[0017] Figure 1 This is a flowchart of the protein secondary structure prediction method combining q-HMM and rules according to the present invention.

[0018] Figure 2 This diagram illustrates the positional correspondence between the primary and secondary structures of a protein sequence. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0020] The present invention provides a protein secondary structure prediction method combining q-HMM and rules, comprising the following steps:

[0021] Step 1: Establishing a q-HMM (Quantum-Hidden Markov Model): This invention establishes a q-HMM based on an improved high-order HMM to solve the problem of protein secondary structure prediction in the life sciences. Inspired by the phenomenon of quantum entanglement, a mechanism for the influence of observations on state values ​​is introduced into the high-order HMM, hence the name q-HMM, where q stands for quantum.

[0022] 1.1 Define model state and observations

[0023] 1) N represents the number of states considered in the model, i.e., the types of secondary structures, namely α-helix, β-sheet and β-turn, and random coil. This invention represents the set of protein secondary structure states as S = {s1, s2, ..., s...} i , …s N}, where s i This represents a state of the secondary structure of a protein. Let there be a sequence of states Q = Q1, Q2, ..., Q... s Q T Q s This represents the state of the protein binary structure at the s-th position.

[0024] 2) M represents the number of observations considered in the model, i.e., the number of protein primary structure types predicted (20 amino acids). This invention represents the set of protein primary structure observations as V = {v1, v2, ..., v...} j , ..., v M}, where v j This represents an amino acid. Let there be an observation sequence O = O1, O2, ..., O s , ..., O T O s This represents the observed value of the protein's primary structure at the s-th position.

[0025] 1.2 Constructing Model Parameters

[0026] 1) State transition tensor in q-HMM in Let each component of tensor A represent the first n state values ​​from position t. and the first m observations The state Q transitions to position t t =s i The probability P, i.e.

[0027]

[0028] Where 1 ≤ i1, ..., i n , i≤N, 1≤j1,…,j m ≤M.

[0029] 2) Emission tensor in q-HMM in For each component of the emission tensor B, let represent the first n state values ​​from a position t. and the first m observations Observation O transferred to position t t =v k The probability P, i.e.

[0030]

[0031] Where 1 ≤ i1, ..., i n ≤N, 1≤k, j1,…,j m ≤M.

[0032] 3) Initial tensors in q-HMM in Let each component of the emission tensor π represent all n state values ​​that satisfy the initial position. Given m observation values The probability P of a given protein sequence, where n≥m+1, i.e.

[0033]

[0034] Where 1 ≤ i1, ..., i n ≤N, 1≤j1,…,j m ≤M.

[0035] Using the parameters S, V, A, B, π and the known initial m observations O n-m , ..., O n-1 For any protein primary structure chain, a corresponding protein secondary structure chain can be predicted.

[0036] Step 2: Extract association rules

[0037] 2.1 Define association rule parameters

[0038] Define itemsets That is, the total set of each position of the primary and secondary structure of the protein sequence extracted each time after data screening, where h i h' represents the observation at the i-th position among the m1+n+m2 positions of the protein primary structure observation in the protein sequence fragment, and h′ represents the overall state of the protein secondary structure at the m positions of the protein sequence fragment.

[0039] Define the preceding term This refers to the set of locations in each extracted protein fragment that, according to the present invention, are hypothesized to have an impact on the protein's secondary structure. There are a total of 1 influential locations and 2... l There are several cases, each of which It is one of 20 possible values ​​among the observed primary structure values ​​of a protein.

[0040] Define the term Y = {h′ = S′}, where S′ is the protein secondary structure state sequence, and each position in the state sequence is one of three possible states. Figure 2 This diagram illustrates the positional correspondence between the primary and secondary structures of a protein sequence.

[0041] Define X∪Y as the event that the protein's primary structure fragment X and the protein's secondary structure fragment Y occur simultaneously.

[0042] Traverse all protein sequences, define the total number of extracted fragments |K|, define the number of all preceding terms as σ(X), and define the number of fragments in which the primary structure fragment X and the secondary structure fragment Y of all proteins appear simultaneously as σ(X∪Y).

[0043] 2.2 Calculate the confidence and support of the extracted protein secondary structure rules.

[0044] Association rules are the rules governing the correspondence between the primary structure of a protein and its secondary structure within a transaction set. This refers to the rules extracted by this invention.

[0045] Support With confidence level They are defined as follows:

[0046]

[0047]

[0048] Where X∪Y represents the event that the protein's primary structure fragment X and the protein's secondary structure fragment Y occur simultaneously.

[0049] 2.3. Identify rules by comparing thresholds.

[0050] Association rule discovery refers to finding all rules whose support is greater than or equal to the lower bound of support (minsup) and whose confidence is greater than or equal to the lower bound of confidence (minconf). In other words, a rule set R is defined as follows:

[0051]

[0052]

[0053] Among them, satisfying The preceding terms are the set of frequent preceding terms. The set of rules R that satisfy the above conditions is the protein secondary structure rule found in this invention, which is used to complete the optimization of q-HMM.

[0054] The method described above is used to traverse all proteins to find frequent itemsets and generate strong association rules. In the q-HMM, a confidence level of 0.9 is selected.

[0055] Step 3: Solve for q-HMM parameters using statistical methods.

[0056] For supervised learning, we directly use counting to solve for the model parameters. Assume we have the observed sequences of the protein's primary structure and the corresponding sequences of its secondary structure states from the training data. Then, we can use maximum likelihood estimation to estimate the model parameters.

[0057] Suppose that the number of samples in all our protein file samples that satisfy a certain initial hidden state is C(h). Then the probability estimate of the initial state is:

[0058]

[0059] Assuming that the first n state values ​​and the first m observations at a certain position t are already determined, the frequency of transitioning to state i at position t is: The estimated value of the state transition tensor is:

[0060]

[0061] Assuming that the first n state values ​​and the first m observations at position t are already determined, the frequency of the observation value k transitioning to position t is: The emission tensor estimate is then:

[0062]

[0063] With proper calculation, we can transform the entire problem into an optimization problem, namely, finding the parameters that maximize the probability.

[0064] Step 4: Combine association rules with model parameters for bidirectional prediction.

[0065] This invention uses model parameters and a given observation sequence to find the optimal state sequence. The Viterbi algorithm is employed. The Viterbi algorithm essentially uses dynamic programming to solve the prediction problem in a Hidden Markov Model (HMM), specifically to find the path with the highest probability. In this case, each path corresponds to a state sequence. According to the principles of dynamic programming, the optimal path has the following property: if the optimal path passes through node t... So this path starts from node To the finish line Part of the path, for the node To the finish line Of all possible partial paths, the one in question must be optimal. Based on this principle, we only need to start from position t = n and recursively calculate the maximum probability of each partial path with state i at position t = n, until we obtain the maximum probability of each path with state i at position t = T. The maximum probability at position t = T is the probability P of the optimal path. * The endpoint of the optimal path This is also obtained simultaneously. Then, in order to find the nodes of the optimal path, starting from the endpoint, the nodes are obtained step by step from the end to the beginning. Obtain the optimal path

[0066] 3.1 Label the iteration variable δ t (i1, ..., i) n ) and ψ t (i1, ..., i) n ) is used as an iteration parameter.

[0067] This invention provides a given observation sequence O = O1O2…O T To a single optimal probability maximum state sequence Q = Q1Q2…Q TThe n secondary structure states at position t of the path refer to {Q} t-n Q t-n+1 Q t}

[0068] This invention records the n secondary structure states at position t as follows: The maximum probability among all paths is δ t (i1, ..., i) n ),Right now

[0069]

[0070] Where n+1<t≤T, and δ t (i1, ..., i) n ) represents the most likely state of the first n protein secondary structures at position t-1, and calculates the most likely state of the first n protein secondary structures at position t.

[0071] In this invention, the n states before position t are defined as follows: All individual paths i1, i2, ..., i T The nth node of the path with the highest probability is ψ t (i1, ..., i) n ),Right now

[0072]

[0073] Where n+1≤t≤T, and ψ t (i1, ..., i) n Let t be the most likely state of the first n protein secondary structures at position t-1. Calculate the most likely state of the first n protein secondary structures at position t.

[0074] 3.2 Predicting protein secondary structure using Viterbi iteration

[0075] 3.2.1 Initialize the iteration parameter δ:

[0076]

[0077] Among them, the observed value O n This represents the observation at the nth position (i.e., the terminal position) of the protein's secondary structure, where the initial tensor components of the model parameters are... With the emission tensor components These are the model parameters obtained in step two.

[0078] 3.2.2 Recursively update the iterative parameter δ backwards. t (i1, ..., i) n ):

[0079] Based on the most probable states of the secondary structures of the first n proteins at position t-1, calculate the most probable states of the first n proteins at position t.

[0080]

[0081] Let the final iteration result be ψ. t (i1, ..., i) n ):

[0082]

[0083] 3.2.3 Termination of Iteration: The probability value of finding the optimal state sequence

[0084]

[0085] Where P * This represents the probability of the optimal state sequence occurring.

[0086]

[0087] in The last n values ​​of the optimal state sequence.

[0088] 3.2.4 Backtracking Path:

[0089] Where n represents the n states considered in the model, ψ t+n This refers to the final node of the iteration. Secondary structure of protein at position t

[0090]

[0091] By tracing back sequentially, the complete protein secondary structure predicted by this invention can be obtained.

[0092] 3.2.5. Application of protein rules for bidirectional prediction

[0093] This invention ultimately yields protein secondary structure rules. Based on q-HMM, protein rules are incorporated to optimize prediction results. Unlike directly using q-HMM to predict from the beginning of each protein chain, this method first traverses the protein sequence to be predicted, determines the location of the protein rules, and uses this as the starting point for protein secondary structure prediction. Here, q-HMM is combined to simultaneously predict both ends of the protein (amino and carboxyl terms).

[0094] Example Solution:

[0095] In this invention, based on q-HMM, we selected different values ​​of m and n (m = 0, 2, 3, 4; n = 1, 2, 3). The results obtained after the above three steps are shown below. The case where m = 0 corresponds to the accuracy of predicting protein secondary structure using a standard high-order HMM model. The case where m > 0 corresponds to the accuracy of predicting protein secondary structure using the optimized q-HMM. As can be seen from the table below, the accuracy of this invention can reach 70%-80%. After considering the influence of observed values ​​on state values, the overall prediction accuracy is significantly improved, consistent with expectations. Furthermore, this invention shows that in this study, the larger the values ​​of m and n, the higher the accuracy. The following are the overall prediction accuracy of protein secondary structure under different values ​​of m and n:

[0096] Table 1: Prediction Accuracy

[0097] m＝0 m＝2 m＝3 m＝4 n＝1 0.43254060 0.49395046 0.59887369 0.70407926 n＝2 0.43103408 0.52999804 0.62069746 0.72288769 n＝3 0.43084891 0.63347759 0.73115717

[0098] The association rules identified in step 2 have a confidence level greater than 3 × 10⁻⁶. -5 (sup>3×10 -5 The rules governing the secondary structure of proteins are as follows:

[0099] Table 2: Correspondence Rules Between Primary and Secondary Structures of Some Proteins

[0100]

[0101]

[0102] Considering the gradual optimization based on q-HMM, after multiple experiments, it was found that adding protein rules has a very positive impact on prediction accuracy. A single protein strand was randomly selected by computer, and two methods were used to predict its secondary structure. The comparison results showed that the prediction accuracy of the secondary structure of the single protein strand without rules was 0.590323, while the prediction accuracy of the two-way secondary structure of the single protein strand with rules was 0.769355. The results indicate that the method of adding rules to q-HMM for prediction is effective, and this method can greatly improve the prediction accuracy.

Claims

1. A method for predicting protein secondary structure combining q-HMM and rules, characterized in that, Includes the following steps: Step 1: Establish q-HMM (Quantum Hidden Markov Model): Define the set of protein secondary structure state sequences. A collection of observed sequences of protein primary structure State transition tensor in q-HMM Emission tensor in q-HMM Initial tensors in q-HMM ; protein secondary structure state sequence set ,in A state representing the secondary structure of a protein; Protein primary structure observation sequences are represented as sets. ,in It represents an amino acid; State transition tensor in q-HMM ,in For state transition tensor Each component of a dimension represents the condition that satisfies a certain condition. position before Each state value and the previous Given that the first observation has been determined, the process shifts to the second observation. The position's state value is The probability of; Emission tensor in q-HMM ,in For the emission tensor Each component of a dimension represents the condition that satisfies the condition in the first dimension. position before Each state value and the previous Given that the first observation has been determined, the process shifts to the second observation. The observed value of the location The probability of; Initial tensor in q-HMM ,in For the initial tensor Each component of a dimension represents all elements that satisfy the initial position. The state values ​​are known The probability of a protein sequence given a given observation condition; Step 2: Extract association rules: Define association rule parameters, calculate the confidence and support of the extracted protein secondary structure rules, compare the confidence and support thresholds to generate frequent itemsets, and finally obtain strong association rules; The association rule parameters include: a set of all protein sequence fragments extracted from the protein sequence file that could potentially become rules. Define the total number of extracted segments. Define the quantity of all preceding terms as Define all protein primary structure fragments and protein secondary structure fragments The number of simultaneous occurrences of fragments is ; The preceding terms for defining protein fragments With the following item and define the quantity of all preceding terms. and all protein primary structure fragments and protein secondary structure fragments The number of simultaneous occurrences of fragments is Calculate the confidence level of extracted protein secondary structure With support ; The final strong association rule is one that satisfies the condition that the support is greater than or equal to the lower bound of the support. The confidence level is greater than or equal to the lower bound of the confidence level. All rules constitute the rule set. Support Confidence in As the lower bound of support, This is the lower bound of the confidence level; For all protein primary structure fragments and protein secondary structure fragments The number of fragments appearing simultaneously; This represents the total number of extracted segments; For the quantity of all preceding terms; Step 3: Solve for q-HMM parameters using statistical methods: Use the Baum-Welch algorithm to iteratively calculate the q-HMM model parameters, and use the reestimation formula to obtain the state transition tensor in the q-HMM. Emission tensor in q-HMM Initial tensor in q-HMM ; State transition tensor in q-HMM Emission tensor in q-HMM Initial tensor in q-HMM They are respectively: in For state transition tensor The components of each dimension, For all protein file samples, satisfying a certain condition. position before Each state value and the previous Given that the first observation has been determined, the process shifts to the second observation. The position's state value is The probability of; where For state transition tensor The components of each dimension, For all protein files in the sample, the one that satisfies the condition in the first... position before Each state value and the previous Given that the first observation has been determined, the process shifts to the second observation. The observed value of the location The probability of; where For the initial tensor The components of each dimension, Of all protein files in the sample, all satisfy the initial position. The state values ​​are known The probability of a protein sequence under a given observation condition; N, M, and P represent the total number of occurrences. The number of protein file samples that satisfy a specific initial hidden state; Step 4: Perform bidirectional prediction using model parameters in conjunction with association rules: Based on the strong association rules obtained in Step 2, determine the starting position for protein secondary structure prediction; utilize the protein sequence fragment and the state transition tensor in the q-HMM obtained in Step 3. Emission tensor in q-HMM Initial tensors in q-HMM The entire protein secondary structure chain was predicted by combining the Viterbi algorithm with bidirectional iteration. The predicted protein structure is as follows: in For consideration in the model A state, This refers to the final node of the final iteration; The Protein secondary structure at each location ; among which position The state is The maximum probability of each path is defined at position. Status is All individual paths The path with the highest probability in the middle is the first Each node is , To find the optimal sequence of states.

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