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Genomics Inform > Volume 18(4); 2020 > Article
Blokh, Gitarts, and Stambler: An information-theoretical analysis of gene nucleotide sequence structuredness for a selection of aging and cancer-related genes

Abstract

We provide an algorithm for the construction and analysis of autocorrelation (information) functions of gene nucleotide sequences. As a measure of correlation between discrete random variables, we use normalized mutual information. The information functions are indicative of the degree of structuredness of gene sequences. We construct the information functions for selected gene sequences. We find a significant difference between information functions of genes of different types. We hypothesize that the features of information functions of gene nucleotide sequences are related to phenotypes of these genes.

Introduction

The problem of analyzing symbolic sequences appears in many areas of research, such as “big data” [1] and “dynamic systems” [2]. The most significant example of a symbolic sequence is nucleotide sequence. Moreover, a nucleotide sequence is an interesting and important mathematical object. Of special importance is the task of clustering nucleotide sequences [3-6]. A nucleotide sequence is hereby referred to as a sequence whose elements assume the values A, C, G, T. First the mathematical analysis of nucleotide sequences was suggested by the physicist Gamow in 1954 [7]. The problem of symbols relation of nucleotide sequences was first discussed by the physicist Yockey in the 1950s [8]. About 50 years later, in 2003, the mathematician Gelfand noted that “the use of mathematics in studying gene sequences is an adequate language” [9]. This implied the finding of formal (mathematical) properties of gene nucleotide sequences. Yet, insufficient attention has been paid to this subject.
The main method of investigating numeric sequences (or discrete numerical time series) is the construction and analysis of autocorrelation functions. However, the principal difference of numeric sequences from nucleotide sequences is that the nucleotides in the sequence take the symbolic values A, C, G, T. This means that statistical apparatus cannot be used for the analysis of such sequences, insofar as statistics does not have theoretically justified measures of correlation between symbolic (discrete) random variables. The impossibility of utilizing theoretically justified statistical methods in genetics has been noted earlier [10]. Therefore, information theory, having a solid theoretical justification, has been increasingly used in the study of biological data. Earlier we have applied information theory to analyze data on aging-related diseases [11,12], including cancer [13-15]. The approach described in [13] is presented in the monograph [16].
An overview of the use of information theory for the analysis of biological sequences, in particular DNA sequences, has been presented earlier [17-19]. In the work by Li (1990) [20], mutual information was first used as a measure of correlation for autocorrelation symbolic sequence function. However, mutual information is a non-normalized value, and therefore it does not allow the researchers, in the general case, to compare different mutual information functions for different symbolic sequences.
The present work, for the first time, uses normalized mutual information as a measure of correlation to construct an autocorrelation function for the symbolic (nucleotide) sequence. Hence, we will refer to this function as information function. The use of normalized mutual information allows us to compare information functions of any symbolic sequences. The present article presents an algorithm for distributing sets of genes according to their information functions, that is, according to the interconnection between elements in the nucleotide sequences of these genes. Each value of the information function estimates the interconnection between elements of a nucleotide sequence with a corresponding lag. The set of all the values of the information function provides an estimate for the interconnection of the elements in a nucleotide sequence with all the lags, that is to say, it provides an estimate of the degree of structuredness of that sequence.
It may be hypothesized that genes with “close” information functions may produce similar phenotypes, and the proposed approach may help reveal unknown phenotypic properties of genes according to their nucleotide sequences.

Methods

Gene sequences

To illustrate the algorithm of distribution, we consider the nucleotide sequences of 14 genes. Table 1 lists the genes and their sizes as the number of nucleotides. The data on the genes’ sequences were obtained from NCBI Gene database (https://www.ncbi.nlm.nih.gov/gene).
The genes used in this study—BCL2, mTOR, FOXO3, FOXO1, IGF1, BRCA2, BRCA1, Klotho, Sirtuin 1, p16, BECN1, CCND1, Sirtuin 6, APOE—were selected for the most part insofar as these genes are often recognized as being involved in aging processes and often constitute networks in aging-associated pathways [21,22]. Hence both their phenotypic properties and their possible mutual relation could be suggested.

Mathematical analysis

Let X be a symbolic random variable with a distribution function as follows:
X: x1, x2, , xnP:  p1, p2, , pn.
Entropy of random variable X is as follows:
H(X)=-i=1npilog pi.
Let X and Y be symbolic random variables. The mutual information between the variables X and Y is as follows:
I(X;Y) = H(X) + H(Y)  H(XY),  
where H(XY) is the entropy of the product of the random variables X and Y.
Let X and Y be symbolic random variables. The normalized mutual information (also termed “uncertainty coefficient”) is as follows:
C(X,Y)=I(X;Y)H(Y)=H(X)+H(Y)-H(XY)H(Y)
The normalized mutual information has the following properties.
(1) 0 ≤ C(X;Y) ≤ 1.
(2) C(X;Y) = 0 if and only if the random variables X and Y are independent (no correlation between the variables).
(3) C(X;Y) = 1 if and only if there is a functional relation (correlation or influence) between X and Y.
Let x(n) = (x(1), x(2), …, x(n),…) represent discrete time series having symbolic values.
Let x(n+j) = (x(1 + j), x(2 + j),…, x(n + j),…) be a time series x(n) with a lagj.
The auto-mutual information of the time series x(n) with a lagj equals:
I(x(n); x(n + j)) = H(x(n)) + H(x (n + j)) – H(x(n), x(n + j)).
The normalized auto-mutual information of the time series x(n) with a lagj equals:
C(x(n);x(n+j))=I(x(n);x(n+j))H(x(n+j))=H(x(n))+H(x(n+j))-H(x(n), x(n+j))H(x(n+j))
The normalized mutual information C(x(n); x(n+j)) is then calculated as a function of the lagj.
We shall refer to function F(j)=C(x(n); x(n + j)) as the information function of the discrete time series x(n).
Properties of the information function F(j) are as follows.
(1) 0 ≤ F(j) ≤ 1.
(2) F(j) = 0 if and only if x(n) and x(n + j) are mutually independent.
(3) F(j) = 1 if and only if there exists a functional relationship between x(n) and x(n + 1).
Let {x1(n), x2(n), …, xk(n)} be a set of discrete time series, whose elements are symbols, e.g. gene nucleotide sequences, n = 1, 2, 3,…, and the maximum value n for a sequence xi(n) 1 ≤ i ≤ k equals the number of elements in this nucleotide sequence.
The algorithm of distributing a set of time series {x1(n), x2(n), …, xk(n)} consists of three procedures: (1) construction of an information function matrix; (2) ranking of columns of the information function matrix; and (3) application of a multiple comparisons method.

Construction of an information function matrix

For each time series xi (n) 1 ≤ i≤ k, we construct the information function as follows:
Fi(j) 1 ≤ i ≤ k, 1 ≤ j ≤ m,
where m is the number of lags in the information function.
We obtain the k x m [Fi(j)] matrix of values of the information functions, i.e., a matrix where each row is an information function of the corresponding time series.

Ranking of columns of the information function matrix

Each row of [Fi(j)] matrix is an information function of time series, and each column contains the values of information functions corresponding to the same lag.
For each column of [Fi(j)] matrix, we rank its entries and assign the rank 1 to the smallest entry of the column. We obtain k x m matrix of ranks [ri(j)], with each column of the matrix containing ranks from 1 to k.
We estimate the element interconnection of the i-th time series as compared to the element interconnection of other time series by the sum of all the elements of i-th row of the matrix [ri(j)]. Such an estimation allows us to use multiple comparisons of rank statistics for the comparison of time series interconnection.

Application of a multiple comparisons method

We compare rank sums using the Newman-Keuls test [23]. This test provides adequate results in the analysis of biomedical data, including aging-related multimorbidity [11,12], and is appropriate for the present problem.

Results

The values and clustering of gene information functions

Following the above algorithm for distributing a set of time series, we calculate and cluster the values of gene information functions, as follows.
(1) For each gene, out of the 14 genes under consideration, we calculate the information function with 12 lags. We obtain the information functions matrix [Fi(j)] 1 ≤ i ≤ 14, 1 ≤ j ≤ 12 (Table 2).
(2) We rank the entries of each column of the information function matrix, while attributing to the least values the rank 1. We obtain the rank matrix [ri(j)] 1 ≤ i ≤ 14, 1 ≤ j ≤ 12 (Table 3).
Let us consider Table 3 as the Friedman statistical model [24] and examine the row effect of this table.
Hypotheses:
H0: There is no row effect (“null hypothesis”).
H1: The null hypothesis is invalid.
Critical range:
The sample is “large”, therefore, the critical range is the upper 1%-range of χ213 distribution.
Let us calculate the χ2-criterion. This gives us χ2 = 91.65. The critical range is χ213 > 27.69. Since 91.65 > 27.69, the null hypothesis with respect to Table 3 is rejected. Thus, according to the Friedman test, the row effect has been found. Hence, there is a difference between the rows under consideration.
For multiple comparisons, we use the Newman-Keuls test. We obtain /Ri - Ri+1/ > 8.93, where Ri and Ri+1 are elements of the column “Sum of ranks” in the i-th and (i+1)-th rows of Table 3, respectively. By multiple comparisons, we construct the clustering shown in Table 4.
The obtained clustering possesses the following properties: (1) For two neighboring sets of Table 4, the smallest element of one set and the greatest element of another set located nearby are significantly different (αT = 0.01); (2) Elements belonging to the same set do not differ from each other (αT = 0.01).
Note that the differences between cluster 1 (APOE gene) and all the other elements (genes) are statistically significant (αT = 0.01). The same holds true for cluster 3 (BECN1 gene), cluster 4 (mTOR gene), and cluster 7 (IGF1 gene).

The significance of gene information functions

The domain of the information functions under consideration is the set {Lag 1, Lag 2, Lag 3, … , Lag 12}, and the values are the set of real numbers 0 to 1. We perform the comparative analysis of the values of information functions on the domain of those functions.
In Table 2, each row represents the values of the information function of a corresponding gene. We rank the values of each row of Table 2, attributing rank 1 to the least value. We obtain Table 5.
We evaluate the values of the information functions in Lag j as the sum of elements of the column Lag j of Table 5. Let us consider Table 5 as the Friedman statistical model, and examine the column effect of this table.
Hypotheses:
H0: There is no column effect (“null hypothesis”).
H1: The null hypothesis is invalid.
Critical range:
The sample is “large”, therefore, the critical range is the upper 1%‒range of χ211 distribution.
Let us calculate the χ2-criterion. This gives us χ2 = 121.5. The critical range is χ211 > 24.73. Since 121.5 > 24.73, the null hypothesis with respect to Table 4 is rejected. Thus, according to the Friedman test, the column effect has been found. Hence, there is a difference between the columns under consideration.
For multiple comparisons, we use the Newman-Keuls test. We obtain /Ri ‒ Ri+1/ > 9.64, where Ri and Ri+1 are elements of the column “Sum of ranks” in the i-th and (I + 1)-th rows of Table 5, respectively. By multiple comparisons, we construct the clustering shown in Table 6.
The obtained clustering possesses the following properties: (1) For two neighboring sets of Table 5, the smallest element of one set and the greatest element of another set located nearby are significantly different (αT = 0.01); (2) Elements belonging to the same set do not differ from each other (αT = 0.01).
Note that the differences between cluster 1 (Lag 1) and all the elements are statistically significant (αT = 0.01). The same holds true for cluster 2 (Lag 2), cluster 3 (Lag 6), and cluster 4 (Lag 3).
The values of the information functions in Lag 6 are greater than the values of the information functions in Lag 3, Lag 4, and Lag 5. This signifies that, for the group of genes under consideration, the interconnection between elements distanced five elements from each other is greater than the interconnection between elements located closer together, namely distanced 2, 3, and 4 elements from each other.

Discussion

In this work we established a novel information theory based method for the evaluation of the level of structuredness of gene sequences (information function) by the sequences’ normalized mutual information. This new method may serve as an additional structural evaluation tool for genomic analysis, and for omics biomarkers analysis generally. In the future, it may be possible to associate between the gene structuredness as evaluated by the present method and the expression and phenotype of particular genes under consideration. Here we, for the first time, describe the methodology to calculate the gene structuredness, while the association of the gene structuredness with gene expression and phenotypic function will be the task of future work.
Even though the present work only describes the methodology, some hypotheses may be advanced considering the possible association of the value of gene structuredness as shown here by the clustering (Table 4) with some known phenotypic properties of the selected genes considered in this study. Thus the genes APOE, BECN1, mTOR, and IGF1 each form a separate cluster according to their level of structuredness. This may indicate that each of these genes possesses properties not common for the other genes. The genes FOXO1 and FOXO3 are in the same cluster, which may be expected for the genes of the same group. Interestingly, the genes BRCA1 and BRCA2 are found in different clusters. As it has been demonstrated, the BRCA1 and BRCA2 genes are associated with different types of tumors, and this distinction may have been reflected in the information function (structuredness) of these genes [25,26].
Of special interest are clusters 2 and 5. Сluster 2 includes the genes Sirtuin 1 and Sirtuin 6, together with the genes CCND1, p16, and BRCA1. A special characteristic of all these five genes in cluster 2 is that under conditions of overexpression, these genes are associated with oncological diseases, though not necessarily under conditions of normal expression or under-expression [27-32]. On the other hand, a characteristic feature of cluster 5 is that all the three genes in this cluster—Klotho, BRCA2, and BCL2—under conditions of under-expression are associated with oncological diseases [33-35]. Yet, under normal expression or overexpression, such an association is not observed. Thus it may be hypothesized that the level of gene sequence structuredness, at least in the present gene selection, may be somehow associated with effects of extreme gene expression, either overexpression or under-expression. Yet, a clarification of such a hypothesis, as well as positing and testing additional hypotheses for a potential association of gene structure and function, will require further extensive investigation.

Notes

Authors’ Contribution

Conceptualization: DB, IS. Data curation: IS, JG. Formal analysis: DB, JG. Methodology: DB. Writing – original draft: DB, IS. Writing – review & editing: DB, IS.

Conflicts of Interest

No potential conflict of interest relevant to this article was reported.

Table 1.
Genes used for the construction of information functions and their sizes as the number of nucleotides
No. Gene Gene size (No. of nucleotides)
1 BCL2 196,935
2 mTOR 166,967
3 FOXO3 124,947
4 FOXO1 110,934
5 IGF1 85,980
6 BRCA2 84,193
7 BRCA1 81,189
8 Klotho 50,083
9 Sirtuin 1 33,722
10 p16 27,292
11 BECN1 14,185
12 CCND1 13,370
13 Sirtuin 6 8,496
14 APOE 3,647

Note: In the first four genes, the numbers of nucleotides exceed 100,000.

Table 2.
Normalized mutual information
Gene Lag 1 Lag 2 Lag 3 Lag 4 Lag 5 Lag 6 Lag 7 Lag 8 Lag 9 Lag 10 Lag 11 Lag 12
APOE 0.027149 0.002646 0.00367 0.002773 0.003221 0.010847 0.003922 0.00447 0.004731 0.004429 0.004188 0.003196
BRCA1 0.022034 0.004159 0.003791 0.002832 0.002345 0.004025 0.00123 0.00345 0.002544 0.002233 0.002244 0.002206
p16 0.011972 0.007661 0.003112 0.003958 0.001811 0.004812 0.002174 0.003145 0.00315 0.003304 0.001438 0.002992
Sirtuin 6 0.033637 0.00474 0.002757 0.001858 0.002086 0.006216 0.001017 0.003024 0.002727 0.002613 0.000491 0.002431
Sirtuin 1 0.016229 0.004515 0.003718 0.002581 0.002479 0.003866 0.001941 0.002843 0.003234 0.001934 0.002365 0.002714
mTOR 0.025724 0.003696 0.002441 0.001687 0.001643 0.002398 0.001071 0.002092 0.001761 0.001208 0.000958 0.001191
BCL2 0.024063 0.004531 0.001164 0.002247 0.00083 0.002089 0.000997 0.001539 0.000749 0.00125 0.000493 0.001013
BECN1 0.025643 0.003635 0.00203 0.001389 0.001729 0.002412 0.001329 0.001668 0.002501 0.002151 0.001305 0.001334
BRCA2 0.019161 0.003686 0.001769 0.001204 0.001096 0.001903 0.001236 0.001632 0.0019 0.001326 0.00089 0.001334
CCND1 0.021874 0.006757 0.004128 0.003507 0.00188 0.004093 0.002921 0.001539 0.002939 0.002369 0.002 0.003324
FOXO1 0.021496 0.003354 0.001571 0.001381 0.001337 0.001946 0.000961 0.001452 0.001385 0.001303 0.00074 0.001029
FOXO3 0.023727 0.004032 0.00149 0.001242 0.001189 0.001845 0.001215 0.001161 0.00133 0.001025 0.000623 0.00093
IGF1 0.026729 0.003 0.000673 0.001228 0.000587 0.000979 0.000544 0.001135 0.000639 0.00051 0.000284 0.00048
Klotho 0.020122 0.00376 0.001905 0.001739 0.001148 0.001732 0.001059 0.001482 0.001822 0.001409 0.001414 0.001559
Table 3.
Table of ranks: ranking by columns
Gene Lag 1 Lag 2 Lag 3 Lag 4 Lag 5 Lag 6 Lag 7 Lag 8 Lag 9 Lag 10 Lag 11 Lag 12 Sum of ranks
APOE 13 1 11 11 14 14 14 14 14 14 14 13 147
BRCA1 7 9 13 12 12 10 8 13 9 10 12 9 124
p16 1 14 10 14 9 12 12 12 12 13 10 12 131
Sirtuin 6 14 12 9 8 11 13 4 11 10 12 2 10 116
Sirtuin 1 2 10 12 10 13 9 11 10 13 8 13 11 122
mTOR 11 6 8 6 7 7 6 9 5 3 7 5 80
BCL2 9 11 2 9 2 6 3 5.5 2 4 3 3 59.5
BECN1 10 4 7 5 8 8 10 8 8 9 8 6.5 91.5
BRCA2 3 5 5 1 3 4 9 7 7 6 6 6.5 62.5
CCND1 6 13 14 13 10 11 13 5.5 11 11 11 14 132.5
FOXO1 5 3 4 4 6 5 2 3 4 5 5 4 50
FOXO3 8 8 3 3 5 3 7 2 3 2 4 2 50
IGF1 12 2 1 2 1 1 1 1 1 1 1 1 25
Klotho 4 7 6 7 4 2 5 4 6 7 9 8 69
Table 4.
Gene distribution according to sums of ranks
No. Cluster Sub-cluster Gene Sum of ranks
1 Cluster 1 APOE 147
2 Cluster 2 2.1 CCND1 132.5
3 2.2 p16 131
4 2.3 BRCA1 124
5 2.4 Sirtuin 1 122
6 2.5 Sirtuin 6 116
7 Cluster 3 BECN1 91.5
8 Cluster 4 mTOR 80
9 Cluster 5 5.1 Klotho 69
10 5.2 BRCA2 62.5
11 5.3 BCL2 59.5
12 Cluster 6 6.1 FOXO1 50
13 6.2 FOXO3 50
14 Cluster 7 IGF1 25
Table 5.
Table of ranks: ranking by rows
Gene Lag 1 Lag 2 Lag 3 Lag 4 Lag 5 Lag 6 Lag 7 Lag 8 Lag 9 Lag 10 Lag 11 Lag 12
APOE 12 11 9 7 5 10 1 8 6 3 4 2
BRCA1 12 11 5 9 2 10 3 6 7 8 1 4
p16 12 10 8 3 4 11 2 9 7 6 1 5
Sirtuin 6 12 11 9 5 4 10 2 7 8 1 3 6
Sirtuin 1 12 11 10 6 5 9 2 8 7 4 1 3
mTOR 12 11 6 10 3 9 4 8 2 7 1 5
BCL2 12 11 7 4 6 9 2 5 10 8 1 3
BECN1 12 11 8 3 2 10 4 7 9 5 1 6
BRCA2 12 11 10 8 2 9 5 1 6 4 3 7
CCND1 12 11 9 6 5 10 2 8 7 4 1 3
FOXO1 12 11 9 7 5 10 6 4 8 3 1 2
FOXO3 12 11 7 10 5 8 4 9 6 3 1 2
IGF1 12 11 10 8 2 7 1 5 9 3 4 6
Klotho 12 11 10 8 2 7 1 5 9 3 4 6
Sum of ranks 168 153 117 94 52 129 39 90 101 62 27 60
Table 6.
Distribution of lags
No. Cluster Sub-cluster Lag Sum of ranks
1 Cluster 1 Lag 1 168
2 Cluster 2 Lag 2 153
3 Cluster 3 Lag 6 129
4 Cluster 4 Lag 3 117
5 Cluster 5 5.1 Lag 9 101
6 5.2 Lag 4 94
7 5.3 Lag 8 90
8 Cluster 6 6.1 Lag 10 62
9 6.2 Lag 12 60
10 6.3 Lag 5 52
11 Cluster 7 Lag 7 39
12 Cluster 8 Lag 11 27

References

1. Wong KC. Big data challenges in genome informatics. Biophys Rev 2019;11:51–54.
crossref pmid pmc pdf
2. Masoller C, Hong Y, Ayad S, Gustave F, Barland S, Pons AJ, et al. Quantifying sudden changes in dynamical systems using symbolic networks. New J Phys 2015;17:023068.
crossref
3. James BT, Luczak BB, Girgis HZ. MeShClust: an intelligent tool for clustering DNA sequences. Nucleic Acids Res 2018;46:e83.
crossref pmid pmc pdf
4. Priness I, Maimon O, Ben-Gal I. Evaluation of gene-expression clustering via mutual information distance measure. BMC Bioinformatics 2007;8:111.
crossref pmid pmc
5. Song L, Langfelder P, Horvath S. Comparison of co-expression measures: mutual information, correlation, and model based indices. BMC Bioinformatics 2012;13:328.
crossref pmid pmc
6. Androulakis IP, Yang E, Almon RR. Analysis of time-series gene expression data: methods, challenges, and opportunities. Annu Rev Biomed Eng 2007;9:205–228.
crossref pmid pmc
7. Gamow G. Possible mathematical relation between deoxyribonucleic acid and proteins. Biol Meddel Kongel Danske Vidensk Selsk 1954;22:1–13.

8. Yockey HP, Platzman RL, Quastler H. Symposium on Information Theory in Biology, 1956 Oct 29-31, Gatlinburg, Tennessee. New York: Pergamon Press, 1958.

9. Gelfand IM. Speech at the meeting of Royal East Research, September 3, 2003. Matematicheskoe Prosveshenie 2004;3:13–14.

10. Scheffe H. The Analysis of Variance. Hoboken: John Wiley & Sons, 1999.

11. Blokh D, Stambler I. The application of information theory for the research of aging and aging-related diseases. Prog Neurobiol 2017;157:158–173.
crossref pmid
12. Blokh D, Stambler I, Lubart E, Mizrahi EH. An information theory approach for the analysis of individual and combined evaluation parameters of multiple age-related diseases. Entropy 2019;21:572.
crossref pmc
13. Blokh D, Stambler I, Afrimzon E, Shafran Y, Korech E, Sandbank J, et al. The information-theory analysis of Michaelis-Menten constants for detection of breast cancer. Cancer Detect Prev 2007;31:489–498.
crossref pmid
14. Blokh D, Zurgil N, Stambler I, Afrimzon E, Shafran Y, Korech E, et al. An information-theoretical model for breast cancer detection. Methods Inf Med 2008;47:322–327.
crossref pmid pdf
15. Blokh D, Stambler I, Afrimzon E, Platkov M, Shafran Y, Korech E, et al. Comparative analysis of cell parameter groups for breast cancer detection. Comput Methods Programs Biomed 2009;94:239–249.
crossref pmid
16. Gutierrez Diez PJ, Russo IH, Russo J. The Evolution of the Use of Mathematics in Cancer Research. New York: Springer, 2012.

17. Vinga S. Information theory applications for biological sequence analysis. Brief Bioinform 2014;15:376–389.
crossref pmid pdf
18. Roman-Roldan R, Bernaola-Galvan P, Oliver JL. Application of information theory to DNA sequence analysis: a review. Pattern Recognit 1996;29:1187–1194.
crossref
19. Durbin R, Eddy SR, Krogh A, Mitchison G. Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge: Cambridge University Press, 1998.

20. Li W. Mutual information functions versus correlation functions. J Stat Phys 1990;60:823–837.
crossref pdf
21. Atzmon G. Longevity Genes: A Blueprint for Aging. New York: Springer, 2015.

22. Singh PP, Demmitt BA, Nath RD, Brunet A. The genetics of aging: a vertebrate perspective. Cell 2019;177:200–220.
crossref pmid pmc
23. Glantz SA. Primer of Biostatistics. 4th ed. New York: McGraw-Hill, 1994.

24. Conover WJ. Practical Nonparametric Statistics. New York: Wiley-Interscience, 1999.

25. Roy R, Chun J, Powell SN. BRCA1 and BRCA2: different roles in a common pathway of genome protection. Nat Rev Cancer 2011;12:68–78.
crossref pmid pmc pdf
26. Joosse SA. BRCA1 and BRCA2: a common pathway of genome protection but different breast cancer subtypes. Nat Rev Cancer 2012;12:372.
crossref pdf
27. Shan YS, Hsu HP, Lai MD, Hung YH, Wang CY, Yen MC, et al. Cyclin D1 overexpression correlates with poor tumor differentiation and prognosis in gastric cancer. Oncol Lett 2017;14:4517–4526.
crossref pmid pmc
28. Romagosa C, Simonetti S, Lopez-Vicente L, Mazo A, Lleonart ME, Castellvi J, et al. p16(Ink4a) overexpression in cancer: a tumor suppressor gene associated with senescence and high-grade tumors. Oncogene 2011;30:2087–2097.
crossref pdf
29. Shimizu Y, Luk H, Horio D, Miron P, Griswold M, Iglehart D, et al. BRCA1-IRIS overexpression promotes formation of aggressive breast cancers. PLoS One 2012;7:e34102.
crossref pmid pmc
30. Jin X, Wei Y, Xu F, Zhao M, Dai K, Shen R, et al. SIRT1 promotes formation of breast cancer through modulating Akt activity. J Cancer 2018;9:2012–2023.
crossref pmid pmc
31. Ran LK, Chen Y, Zhang ZZ, Tao NN, Ren JH, Zhou L, et al. SIRT6 overexpression potentiates apoptosis evasion in hepatocellular carcinoma via BCL2-associated X protein-dependent apoptotic pathway. Clin Cancer Res 2016;22:3372–3382.
crossref pmid
32. Bosch-Presegue L, Vaquero A. The dual role of sirtuins in cancer. Genes Cancer 2011;2:648–662.
crossref pmid pmc
33. Mencke R, Olauson H, Hillebrands JL. Effects of Klotho on fibrosis and cancer: a renal focus on mechanisms and therapeutic strategies. Adv Drug Deliv Rev 2017;121:85–100.
crossref pmid
34. Saha S, Mandal P, Ganguly S, Jana D, Ayaz A, Banerjee A, et al. Decreased expression of BRCA2 accelerates sporadic breast cancer progression. Indian J Surg Oncol 2015;6:378–383.
crossref pmid pmc pdf
35. Gaudette BT, Dwivedi B, Chitta KS, Poulain S, Powell D, Vertino P, et al. Low expression of pro-apoptotic Bcl-2 family proteins sets the apoptotic threshold in Waldenstrom macroglobulinemia. Oncogene 2016;35:479–490.
crossref pmid pdf
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