CN108804870A - Key protein matter recognition methods based on Markov random walks - Google Patents
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Abstract
The key protein matter recognition methods based on Markov random walks that the object of the present invention is to provide a kind of, belongs to technical field of biological information.Key protein matter recognition methods based on Markov random walks：Use the thought of Markov random walks, the score for indicating its significance level is assigned to each vertex, the score on all vertex constitutes the vector of n row, provides the initial value of score, random walk and is modified in transmission in a network by score according to certain probability；The descending arrangement of score value is finally pressed, output score value is correspondingkA protein is final result.The present invention merges biological attribute and topological property improves the accuracy of identification key protein matter, while keeping prediction result more accurate, improves the efficiency of prediction.
Description
Technical field
The invention belongs to technical field of biological information, random by Markov mainly in protein-protein interaction network
The technology of the algorithm identification key protein matter of migration, more particularly to network topological information and protein bio attribute in PPI networks
The method for identifying key protein matter.
Background technology
Protein is the indispensable substance of institute in vital movement, almost takes part in all periods of vital movement, and is closed
Key protein is even more to have played the effect that do not replace in this course, the missing of key protein matter may cause life entity without
Method is survived.Therefore, identify that the key protein matter in PPI networks not only facilitates the adjusting and controlling growth process for understanding cell, and
Help can be provided to the research of biological evolution mechanism.In addition, in biomedical sector, the identification of key protein matter is controlled in disease
It treats and the design etc. of drug target cell has great importance.
Before the present invention proposes, the identification field of key protein matter most begins by the topological characteristic of network to know
Not, for example, degree centrality (DC), betweenness center (BC), local average degree of communication (LAC), Li et al. people fusion PPI and gene table
Centrality Measurement Method PeC, Zhang et al. fusion PPI network topology characteristics are proposed up to data and gene co-expressing information carries
CoEWC methods are gone out, but the shortcomings that these methods identification key protein matter is：(1) it only considered possessed by network itself
Topological characteristic, and have ignored the intrinsic biological characteristic of protein.(2) the PPI networks obtained by Bioexperiment, which exist, makes an uproar
Sound so that there are false positives for protein interaction data.
Invention content
The purpose of the present invention, which is that, overcomes drawbacks described above, develops the key protein matter identification based on Markov random walks
Method.Key protein matter recognition methods based on Markov random walks uses the thought of Markov random walks, to each
Vertex assigns the score for indicating its significance level, and the score on all vertex constitutes the vector of n row, provides the initial of score
Value random walk and is modified according to certain probability by score in transmission in a network.It is finally descending by score value
Arrangement, the corresponding k protein of output score value is final result.
Key protein matter recognition methods based on Markov random walks, is mainly characterized by following steps：
(1) PPI networks and biological information are inputted；
(2) according to the attribute value on protein vertex and side right value, the weight q between protein vertex is calculated, builds weight
Matrix；
(3) all attribute values are normalized, build attribute matrix；
(4) according to the interaction relationship between protein vertex, transfer matrix is built；
(5) according to PageRank algorithms, iteration obtains score vector r, determines to return to probability P by the attribute on vertex；
(6) it obtains object function and object function is optimized, to initial value r, q declines formula using gradient and changes
Generation update；
(7) r after acquisition iteration(t)=(r1,r2,…,rn) the descending sequence of value, after sequence it is maximum k value for close
Key protein.
The step (2) calculates the weight q between protein vertex according to the attribute value and side right value on protein vertex,
Build weight matrix：By step (1) according to PPI networks, the weight between protein passes through common neighbours' phase between them
It is acquired like degree, based on expression similarity, GO semantic similarities.
All attribute values are normalized the step (3), build attribute matrix:Pass through Z-Score or normalization
Method makes attribute value all be included in (0,1) range, and all vertex attribute vectors constitute an attribute matrix.
Advantages of the present invention and effect are that this method not only considers the topological characteristic of protein-protein interaction network, together
When have also contemplated the biological attribute of protein, and then overcome data noise it is high caused by negative effect.Merge biological attribute and
Topological property improves the accuracy of identification key protein matter, while keeping prediction result more accurate, improves the efficiency of prediction.
Extend the technology biological information field application range and practicability.
Description of the drawings
Fig. 1 --- the present invention is based on the flow diagrams of the key protein matter recognition methods of Markov random walks.
Fig. 2 --- present invention figure compared with the quantity for the key protein matter that other methods identify.
Fig. 2 a be the present invention preceding 100 protein in key protein matter number comparison figure；
Fig. 2 b be the present invention preceding 200 protein in key protein matter number comparison figure；
Fig. 2 c be the present invention preceding 300 protein in key protein matter number comparison figure；
Fig. 2 d be the present invention preceding 400 protein in key protein matter number comparison figure；
Fig. 2 e be the present invention preceding 500 protein in key protein matter number comparison figure；
Fig. 2 f be the present invention preceding 600 protein in key protein matter number comparison figure；
The statistical indicator results contrast figure of Fig. 3 --- the present invention and other methods.
Specific implementation mode
The present invention technical thought be：Biological attribute and topological property are combined, the think of of Markov random walks is used
Think, the score for indicating its significance level is assigned to each vertex, and the score on all vertex constitutes the vector of n row, provides
The initial value of score random walk and is modified according to certain probability by score in transmission in a network.That is root first
The weight between protein is obtained according to common neighbours' similarity, based on expression similarity, GO semantic similarities, weight square can be obtained
Battle array constitutes an attribute matrix according to all vertex attribute vectors.Secondly, vertex is obtained by protein interaction relationship
Transition probability between, thus to obtain transfer matrix.It is final to obtain object function, and object function is optimized, finally
Identify key protein matter.Fusion biological attribute and topological property help to understand the function of agnoprotein matter, special for explaining
Determine the molecular mechanism important in inhibiting of function, while important theoretical foundation can be provided medicine target cell design etc..Institute
Naturally enough it is suitable for the detection of key protein matter with the key protein matter recognition methods based on Markov random walks.
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
As shown in Figure 1, the key protein matter recognition methods based on Markov random walks, includes the following steps：
Step 1:Input PPI networks and biological information
Step 2：According to the attribute value on protein vertex and side right value, the weight q between protein vertex, structure power are calculated
Weight matrix
Common neighbours' similarity (NTE)：The topological characteristic of protein-protein interaction network is in the identification of key protein matter
There is irreplaceable status, according to " center-lethal " rule, key protein matter is more likely that cluster exists in a network
, therefore, we use common neighbours' similarity (NTE) as one of index to weigh the key of protein.In non-directed graph G
In (V, E), common neighbours' similarity between protein u and v is expressed as：
NTE (u, v)=| Cu∩Cv|+1 formula (1)
Wherein, Cu(or Cv) indicate PPI nodes u (or v) neighbours set；|Cu∩Cv| indicate node u and
The number of the common neighbours of v, the i.e. number of triangle belonging to side.By adding " 1 " come so that result is all higher than behind result
0, to avoid going wrong in standardising process.
Gene expression similarity (GES)：Since gene expression data acquisition is easier and in the identification of key protein matter
There is extensive use in field, while the gene co-expressed more likely becomes key protein matter, so we use gene table
Up to similarity (GES) as an index for weighing key protein matter.The gene calculated between protein u and v that we use
The formula for expressing similarity is as follows：
Wherein, s is the quantity of sample in gene expression data, and U and V are the gene code of corresponding protein u, v, UiWith
ViExpressions of the gene U and V in corresponding sample i is indicated respectively,WithIt is being averaged for the expression of gene U and V
Value, then o (U) and o (v) indicates the standard deviation of the expression of gene U, V respectively.
GO semantic similarities (GOS)：Gene ontology (gene ontology, GO) is the molecule work(of gene (gene outcome)
The relevant information of energy, biological process and cell components provides a specification, accurate terminology.To the semanteme of GO terms
Similitude carries out the importance that measurement is GO applications, and GO semantic similarities are the biological properties based on gene to disclose
The functional similarity of gene, and two connected key protein matter more likely participate in the same bioprocess.Permitted in recent years
More scholars are proposed the measure of GO Semantic Similarities, we calculate GO semantic similarities, the party using the method for Lin
The characteristics of method, is：First, two standardization that compare the sum of information content of concept；Secondly, it is assumed that be compared two are general
Thought is independent.GO semantic similarities between protein u, v are defined using following formula：
Wherein, the protein u and v, c of gene U, V codings interaction1、c2The respectively GO terms of gene U, V, S (c1,
c2) it is node c1、c2Nearest public ancestor node set, the example probabilistic of variable c is P (c), PmsBe they it is public most
The probability that nearly ancestors occur.
In PPI networks, the weight (w between proteinij) can be acquired by the similarity between them, it is specific to calculate
Formula is as follows：
wij=a1NTE(i,j)+a2GES(i,j)+a3GOS (i, j) formula (5)
Wherein, parameter a1、a2、a3In (0,1) range, and and it is 1.
Matrix W=[wij] be PPI networks weight matrix, wijFor side (vi, vj) on weight：
Step 3：All attribute values are normalized, attribute matrix is built
All properties value is standardized (can be such that attribute value is all included in (0,1) with Z-Score or method for normalizing
In range), all vertex attribute vectors constitute an attribute matrix B=[bij]nxm。
Step 4：According to the interaction relationship between protein vertex, transfer matrix is built；
Provide constant k<N finds out the maximum k protein of importance, i.e. Top-k, referred to as key protein matter in G.I
Using Markov random walks thought, to each vertex viAssign a score r for indicating its significance leveli (0), own
The score value on vertex constitutes a score vectorFor the column vector of n × 1, the initial value of r is provided, according to
Certain probability migration and is modified in transmission in a network by score.From viIt is transmitted to vjDefinition of probability be：
In this way, the transition probability between all-pair constitutes the transfer matrix P=[p of n × nij]。
Step 5：According to PageRank algorithms, iteration obtains score vector r, determines to return to probability P by the attribute on vertex
In traditional PageRank algorithms based on random walk, score vector r is updated with following iteration：
r(k+1)=α PΤr(k)+(1-α)P0Formula (8)
Wherein α is constant, α ∈ (0,1), P0∈ (0,1) is constant, is that the particle of migration returns to the probability of Original Departure Point.
In the algorithm that this chapter is proposed, we use the attribute b on vertexiTo determine to return to probability P0If
HereFor the column vectors of m × 1, qjFor the weight of j-th of attribute, such formula is：
r(k+1)=α PΤr(k)+(1-α)P0=α PΤr(k)+(1-α)B·q(k)Formula (10)
If function is (10) formula and r(k+1)Square error：
We will find out r, q so that J (r, q) is minimum, that is, solves following optimization problem：
Constraints r>0, q>0 refers to r, and all score values in q are all positive number.
Step 6：Obtain object function and object function optimized, to initial value r, q using gradient decline formula into
Row iteration updates
After obtaining object function, we start to optimize object function.Ask J for r, the local derviation of q first：From formula (11)：
J (r, q)=(α PΤ·r+(1-α)B·q-r)Τ·(αPΤR+ (1- α) Bq-r) formula (13)
=α2rΤPPΤr+2α(1-α)rΤP·B·q-2αrΤP·r+(1-α)2qΤBΤB·q-2(1-α)rΤB·q+rΤr
It can be obtained by formula (13)：
According to above-mentioned gradient, for initial value r(0), q(0), we decline formula using gradient and are updated with regard to row iteration：
Wherein, ρ is iteration sum.
Step 7：R after acquisition iteration(t)=(r1,r2,…,rn) the descending sequence of value, maximum k value is after sequence
Key protein matter.
Embodiment：
In order to verify the performance for the algorithm EPM that this chapter is proposed, we are by the quantity of the key protein matter of identification and other
Five kinds of methods (DC, BC, LAC, PeC and CoEWC) are compared.To each method we select top100, top200,
The protein identification result of top300, top400, top500 and top600 are as Candidate Set, to the protein in each Candidate Set
It seeks common ground again with the key protein matter set of standard, to obtain the quantity of true key protein matter in Candidate Set, experiment knot
Fruit is as shown in Figure 2.
It can be seen that from Fig. 2 a, 2b, 2c, 2d, 2e, 2f, in yeast PPI networks, the algorithm EPM that we are proposed is knowing
Effect that will be good than other methods can be obtained in other key protein matter, take top100, top200, top300, top400,
When the key protein matter of top500 and top600 is as Candidate Set, the protein amounts that algorithm that this chapter is proposed identifies are apparent
Higher than other methods.Wherein, compared with PeC methods, before taking top100, top200, top300, top400, top500 and
When top600 protein, 16.4%, 18.8%, 19.5%, 19.4%, 20.5% and has been respectively increased in the accuracy rate of EPM
22.6%.
In order to further show advantages of the EPM in prediction key protein matter, we attempt in a smaller data set
The difference of upper (taking 200 protein of top) analysis EPM and other methods.We find out Chong Die with EPM in this 200 protein
Protein, and key analysis is carried out to remaining protein, as shown in table 1.
1 key protein matter volume comparison analysis of table
Table 1 analyzes the key protein matter identified in the data set of top200 by EPM and other 5 kinds of methods and non-pass
The quantity of key protein compares.Wherein MiIndicate other 5 kinds of centrality methods for comparison, | EPM ∩ Mi| it is EPM and other
The quantity of the key protein matter overlapping of method identification, | Mi- EPM | expression passes through MiIdentify and pass that EPM could not be identified
The quantity of key protein, it is similar, | EPM-Mi| indicate that EPM is identified and MiFail the number of key protein matter identified
Amount.It should be clear that coming from table, by EPM rather than the number of key protein matter that identifies of other methods
Amount is significantly more than the quantity for the key protein matter that other methods rather than EPM are identified, and the key identified by EPM methods
The quantity of non-key protein is also significantly less than other methods in protein.These results show EPM algorithms consider topology and
More biological informations can effectively improve the prediction result of key protein matter.
In order to further evaluate performance of the EPM methods in terms of key protein matter prediction, we by its in other five kinds
Disposition method is compared, we introduce statistics performance estimating method, including 6 evaluation indexes, sensibility sensitivity
(SN), specific specificity (SP), positive ident value positive predictive value (PPV), feminine gender mark
Value negative predictive value (NPV), F- assess F-measure (F) and precision accuracy (ACC), these
The definition difference of statistical indicator is as follows：
SN indicates the ratio that key protein matter is predicted correctly.
SP indicates the ratio that non-key protein is correctly excluded.
PPV indicates the ratio correctly identified in the key protein matter identified.
NPV indicates to be predicted correctly as the ratio of non-key protein in the protein excluded.
F indicates the harmonic-mean of susceptibility and positive predictive value.
ACC indicates the ratio of correct result in all recognition results.
Wherein, it refers to that key protein matter is correctly identified as key protein that TP (True Positives), which represents true positives,
The quantity of matter；It refers to that the non-key egg of key protein matter is mistakenly identified as by algorithm that FP (False positives), which represents false positive,
The quantity of white matter；It refers to that non-key protein is identified as non-key protein that TN (True Negatives), which represents true negative,
Quantity；It refers to that key protein matter is mistakenly identified as non-key protein that FN (False Negatives), which represents false negative,
Quantity.Above six kinds of fingers target value is bigger, illustrates that the recognition performance of algorithm is better, the result of calculation of the statistical indicator of each method is such as
Shown in Fig. 2.
From figure 3, it can be seen that 6 indexs of EPM estimate obviously higher than other five kinds of centrality in either method,
Compared with DC, BC and LAC method based on network topology, the accuracy rate of EPM is significantly higher, and with incorporated gene expression number
According to PeC methods compare, the algorithm of this chapter can still obtain higher accuracy rate.
Claims (6)
1. the key protein matter recognition methods based on Markov random walks, which is characterized in that the recognition methods includes as follows
Step：
(1) PPI networks and biological information are inputted；
(2) according to the attribute value on protein vertex and side right value, the weight q between protein vertex is calculated, builds weight matrix；
(3) all attribute values are normalized, build attribute matrix；
(4) according to the interaction relationship between protein vertex, transfer matrix is built；
(5) according to PageRank algorithms, iteration obtains score vector r, determines to return to probability P by the attribute on vertex；
(6) it obtains object function and object function is optimized, to initial value r, q declines formula using gradient and is iterated more
Newly；
(7) r after acquisition iteration(t)=(r1,r2,…,rn) the descending sequence of value, maximum k value is crucial egg after sequence
White matter.
2. the key protein matter recognition methods according to claim 1 based on Markov random walks, which is characterized in that institute
Attribute value and side right value of the step (2) according to protein vertex are stated, the weight q between protein vertex is calculated, builds weight square
Battle array：By step (1) according to PPI networks, the weight between protein passes through common neighbours' similarity between them, gene table
It is acquired up to similarity, GO semantic similarities；
Common neighbours' similarity is expressed as：
NTE (u, v)=| Cu∩Cv|+1 formula (1)
Wherein, CuIndicate the set in the neighbours of PPI nodes u, CvIndicate the collection in the neighbours of PPI nodes v
It closes；|Cu∩Cv| indicate the number of the common neighbours of node u and v, the i.e. number of triangle belonging to side；
The formula for calculating the gene expression similarity between protein u and v is as follows：
Wherein, s is the quantity of sample in gene expression data, and U and V are the gene code of corresponding protein u, v, UiAnd ViPoint
Not Biao Shi expressions of the gene U and V in corresponding sample i,WithIt is the average value of the expression of gene U and V, thenWithThe standard deviation of the expression of gene U, V is indicated respectively；
GO semantic similarities are calculated using the method for Lin：
Wherein, the protein u and v, c of gene U, V codings interaction1、c2The respectively GO terms of gene U, V, S (c1,c2) be
Node c1、c2Nearest public ancestor node set, the example probabilistic of variable c is P (c), PmsIt is node c1、c2It is public nearest
The probability that ancestors occur；
In PPI networks, the weight w between proteinijIt is acquired by the similarity between two protein, specific formula for calculation
It is as follows：
wij=a1NTE(i,j)+a2GES(i,j)+a3GOS (i, j) formula (5)
Wherein, parameter a1、a2、a3In (0,1) range, and a1、a2、a3The sum of be 1；
Matrix W=[wij] be PPI networks weight matrix, wijFor side (vi, vj) on weight：
3. the key protein matter recognition methods according to claim 1 based on Markov random walks, which is characterized in that institute
It states step (2) all attribute values are normalized, the method for building attribute matrix is：Pass through Z-Score or normalization side
Method makes attribute value all be included in (0,1) range, and all vertex attribute vectors constitute an attribute matrix.
4. the key protein matter recognition methods according to claim 1 based on Markov random walks, which is characterized in that institute
Step (4) is stated according to the interaction relationship between protein vertex, the method for building transfer matrix is：
Provide constant k<N finds out the maximum k protein of importance, i.e. Top-k, referred to as key protein matter in G；Using
The thought of Markov random walks, to each vertex viAssign a score r for indicating its significance leveli (0), all vertex
Score value constitutes a score vectorFor the column vector of n × 1, the initial value of r is provided, according to certain
Probability migration and is modified in transmission in a network by score；From viIt is transmitted to vjDefinition of probability be：
In this way, the transition probability between all-pair constitutes the transfer matrix P=[p of n × nij]。
5. the key protein matter recognition methods according to claim 1 based on Markov random walks, which is characterized in that institute
Step (5) is stated according to PageRank algorithms, iteration obtains score vector r, and the specific side for returning to probability P is determined by the attribute on vertex
Method is：
In traditional PageRank algorithms based on random walk, score vector r is updated with following iteration：
r(k+1)=α PTr(k)+(1-α)P0Formula (8)
Wherein α is constant, α ∈ (0,1), P0∈ (0,1) is constant, is that the particle of migration returns to the probability of Original Departure Point；Use vertex
Attribute biTo determine to return to probability P0If
HereFor the column vectors of m × 1, qjFor the weight of j-th of attribute, such formula is：
r(k+1)=α PTr(k)+(1-α)P0=α PTr(k)+(1-α)B·q(k)Formula (10)
If function is (10) formula and r(k+1)Square error：
Find out r, q so that J (r, q) is minimum, that is, solves following optimization problem：
Constraints r>0, q>0 refers to r, and all score values in q are all positive number.
6. the key protein matter recognition methods according to claim 1 based on Markov random walks, which is characterized in that institute
It states step (6) to obtain object function and optimize object function, to initial value r, q declines formula using gradient and is iterated
Newer method is：
After obtaining object function, object function is optimized：
Ask J for r, the local derviation of q first：From formula (11)：
J (r, q)=(α PT·r+(1-α)B·q-r)T·(αPTR+ (1- α) Bq-r) formula (13)
=α2rTPPTr+2α(1-α)rTP·B·q-2αrTP·r+(1-α)2qTBTB·q-2(1-α)rTB·q+rTr
It can be obtained by formula (13)：
According to above-mentioned gradient, for initial value r(0), q(0), decline formula using gradient and row iteration updated：
Wherein, ρ is iteration sum.
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| Publication number | Priority date | Publication date | Assignee | Title |
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