新型表示模式下的DNA序列和RNA二级结构分析方法研究
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摘要
随着人类基因组计划的开展,以及对各种序列、结构和功能的研究,产生了庞大的生物数据。对这些生物数据进行科学的分析、处理推动了生物信息学的发展。序列和结构的相似性分析是生物信息学的基础,通过相似性分析获得的大量的序列或结构信息可以用来推断基因的结构、功能和进化关系,因此生物序列或结构分析研究已成为生物信息学领域中一个非常重要的研究课题。序列和结构的分析主要包括相似性分析、突变分析、进化分析和功能分析。而突变分析、进化分析和功能分析都是以序列和结构的相似性分析为基础的,因此本文将基于DNA序列和RNA二级结构的新型表达模式给出DNA序列和RNA二级结构的相似性分析方法,进而给出点突变分析和进化树构建方法。
论文在综述了序列和结构分析方法的研究现状的基础上,对基于双核苷酸和编码序列的图形表示方法,RNA二级结构的编码方式,基于RNA二级结构编码序列的点突变分析和结构比对方法,基于序列图形表示的相似性分析方法和系统进化树构建方法进行了系统的研究,本文取得的研究成果主要有：
1.提出了一种基于核苷酸二联体理化性质的DNA序列的3D图形表示,并给出基于图形表示的序列相似性分析方法。碱基之间的相互作用对序列所决定的结构和功能起着非常重要的作用。为了提供一种简单直接地展示序列信息的方法,本课题在分析了DNA序列的相邻双重核苷的性质的基础上,给出了一种DNA序列的3D曲线族表示方法,并基于几何中心所构建的协方差矩阵,给出了序列间非相似性的一种度量方式。实验结果表明,该方法能准确地度量序列间的相似性。准确的相似距离矩阵的计算将有助于推断物种之间的亲缘关系,有助于找出各种物种之间特别是人类与其他物种之间的联系。并且以某种生物为研究对象来研究人类的各种生理生化机理。
2.提出了一种基于编码方式的序列比较方法和序列相似性分析方法。根据DNA序列的编码规则,本课题给出了解决序列比较中四个基本问题的方法,同时,基于编码序列给出了一种DNA序列的3D表示,并进行序列相似性分析。序列编码方式简单直接地展示了序列信息,有助于更好地实现突变分析可视化,从而推断疾病发生的机理。序列的编码方式也为序列比较提供了一种很好的数学模型,易于发现序列间的相似性和差异性,便于基因的检测和基因功能区的预测。
3.提出了一种RNA二级结构的编码方法,给出了基于编码序列和异或操作的点突变分析和结构比对方法。针对现有的RNA二级结构预测和功能预测算法因多序列比对而具有鲁棒性和结构数不敏感等问题,针对RNA二级结构表示法中主要的高复杂性和退化问题,本文分别给出了RNA二级结构一种简单和扩展的编码方式。该方式能很好地区分自由基和基对,能区分含假结在内的不同结构类。同时,基于简单的三位编码方式,给出了RNA二级结构比较方法和点突变分析方法。基于扩展的编码方式,给出了一种新型的结构比对方法,并通过实验验证了该方法的有效性。
4.分别提出了一种基于模糊聚类的进化树构建算法和基于最小生成树算法的进化树构建算法。本文分别以已获得的相似性和非相似性矩阵为研究基础,给出了基于模糊聚类的进化树构建算法。该方法用相似性矩阵替代了距离矩阵,并在系统进化树的构建过程中相似矩阵不需要重新调整。很好地体现了物种之间的关系,并降低了时间复杂度。同时,给出了一种基于完全图的最小生成树算法并应用于进化树的构建,也取得了较好的效果。
With the rapid development of Human Genome Project (HGP) and advancement of gene sequence, structure and functioning study, more and more bioinformatics data are generated. The enormous data are typically processed efficiently by automated modern analysis approaches. Similarity analysis provides the sequential and structured information to infer or estimate the structure, functioning and evolution relation, hence becomes a fundamental study subject of bioinformatics. The sequence or structure analysis consists of similarity analysis, mutation analysis, phylogenetic analysis and function analysis, which are based on similarity analysis of sequence and structure. Therefore, the dissertation proposed the methods of similarity analysis of DNA sequence and RNA secondary structure based on the new representation models of DNA sequence and RNA secondary structure, it proposed methods of mutation analysis and construction of phylogenetic tree at the same time.
The dissertation reviewed the recent advances of sequential and structure analysis advances first, and then study graphical representation of DNA sequences based on dual nucleotides, numerical coding method of RNA secondary structure, the methods of the analysis of mutation and structure alignment based on the coding sequences of RNA secondary structure, sequence similarity analysis based on graphical representation and construction of phylogenetic tree.
The main contents are listed as follows:
a) The author proposed a 3D graphical representation of DNA sequences based on physical and chemical properties of dual nucleotides, and gave a similarity analysis. It is known that the dependency and interaction between bases are very important for determining the structure and function of the sequences. To give a simple and intrinsic visualization of gene sequences, the dissertation proposed a 3D curve representation of DNA sequences with a dissimilarity measure of sequences based on geometric center covariance matrixes. The experiment showed the proposed approach can measure the similarity of sequences precisely which helps further infer the relation and relationship of species, especially those between human and other species. It may help discover human mechanics based on studies on other species as well.
b) The author proposed a sequence comparison method and similarity analysis method based on coding scheme. According to DNA coding principle, the dissertation proposed a method that solved four basic problems. It could make analysis of similarity between DNA sequences. The coding method of sequence, which demonstrates sequences efficiently and makes the analysis of mutation visible, helps find out mechanism of diseases. Besides, the coding method provides a better mathematical model to figure out the similarity or dissimilarity between DNA sequences, in the sense that it improves genetic test and the prediction of gene functions.
c) The author proposed a coding scheme of RNA secondary structure, and gave mutation analysis and structure comparison based on coding and XOR operator. The representation of RNA secondary structure is very complex and easily degenerated. The proposed coding method and its extension can well separate the free base and base pair, and distinguish the different structures including pseudoknot. Based on three digits coding, the dissertation presented RNA secondary structure comparison method, analysis method of mutation. And the dissertation proposed a novel structure comparison method based on coding rules. The experiment showed the excellence of the method.
d) The author proposed two novel phylogenetic tree construction methods based on fuzzing clustering and minimum spanning tree that essentially make use of the proposed similarity and dissimilarity matrix.
论文在综述了序列和结构分析方法的研究现状的基础上,对基于双核苷酸和编码序列的图形表示方法,RNA二级结构的编码方式,基于RNA二级结构编码序列的点突变分析和结构比对方法,基于序列图形表示的相似性分析方法和系统进化树构建方法进行了系统的研究,本文取得的研究成果主要有：
1.提出了一种基于核苷酸二联体理化性质的DNA序列的3D图形表示,并给出基于图形表示的序列相似性分析方法。碱基之间的相互作用对序列所决定的结构和功能起着非常重要的作用。为了提供一种简单直接地展示序列信息的方法,本课题在分析了DNA序列的相邻双重核苷的性质的基础上,给出了一种DNA序列的3D曲线族表示方法,并基于几何中心所构建的协方差矩阵,给出了序列间非相似性的一种度量方式。实验结果表明,该方法能准确地度量序列间的相似性。准确的相似距离矩阵的计算将有助于推断物种之间的亲缘关系,有助于找出各种物种之间特别是人类与其他物种之间的联系。并且以某种生物为研究对象来研究人类的各种生理生化机理。
2.提出了一种基于编码方式的序列比较方法和序列相似性分析方法。根据DNA序列的编码规则,本课题给出了解决序列比较中四个基本问题的方法,同时,基于编码序列给出了一种DNA序列的3D表示,并进行序列相似性分析。序列编码方式简单直接地展示了序列信息,有助于更好地实现突变分析可视化,从而推断疾病发生的机理。序列的编码方式也为序列比较提供了一种很好的数学模型,易于发现序列间的相似性和差异性,便于基因的检测和基因功能区的预测。
3.提出了一种RNA二级结构的编码方法,给出了基于编码序列和异或操作的点突变分析和结构比对方法。针对现有的RNA二级结构预测和功能预测算法因多序列比对而具有鲁棒性和结构数不敏感等问题,针对RNA二级结构表示法中主要的高复杂性和退化问题,本文分别给出了RNA二级结构一种简单和扩展的编码方式。该方式能很好地区分自由基和基对,能区分含假结在内的不同结构类。同时,基于简单的三位编码方式,给出了RNA二级结构比较方法和点突变分析方法。基于扩展的编码方式,给出了一种新型的结构比对方法,并通过实验验证了该方法的有效性。
4.分别提出了一种基于模糊聚类的进化树构建算法和基于最小生成树算法的进化树构建算法。本文分别以已获得的相似性和非相似性矩阵为研究基础,给出了基于模糊聚类的进化树构建算法。该方法用相似性矩阵替代了距离矩阵,并在系统进化树的构建过程中相似矩阵不需要重新调整。很好地体现了物种之间的关系,并降低了时间复杂度。同时,给出了一种基于完全图的最小生成树算法并应用于进化树的构建,也取得了较好的效果。
With the rapid development of Human Genome Project (HGP) and advancement of gene sequence, structure and functioning study, more and more bioinformatics data are generated. The enormous data are typically processed efficiently by automated modern analysis approaches. Similarity analysis provides the sequential and structured information to infer or estimate the structure, functioning and evolution relation, hence becomes a fundamental study subject of bioinformatics. The sequence or structure analysis consists of similarity analysis, mutation analysis, phylogenetic analysis and function analysis, which are based on similarity analysis of sequence and structure. Therefore, the dissertation proposed the methods of similarity analysis of DNA sequence and RNA secondary structure based on the new representation models of DNA sequence and RNA secondary structure, it proposed methods of mutation analysis and construction of phylogenetic tree at the same time.
The dissertation reviewed the recent advances of sequential and structure analysis advances first, and then study graphical representation of DNA sequences based on dual nucleotides, numerical coding method of RNA secondary structure, the methods of the analysis of mutation and structure alignment based on the coding sequences of RNA secondary structure, sequence similarity analysis based on graphical representation and construction of phylogenetic tree.
The main contents are listed as follows:
a) The author proposed a 3D graphical representation of DNA sequences based on physical and chemical properties of dual nucleotides, and gave a similarity analysis. It is known that the dependency and interaction between bases are very important for determining the structure and function of the sequences. To give a simple and intrinsic visualization of gene sequences, the dissertation proposed a 3D curve representation of DNA sequences with a dissimilarity measure of sequences based on geometric center covariance matrixes. The experiment showed the proposed approach can measure the similarity of sequences precisely which helps further infer the relation and relationship of species, especially those between human and other species. It may help discover human mechanics based on studies on other species as well.
b) The author proposed a sequence comparison method and similarity analysis method based on coding scheme. According to DNA coding principle, the dissertation proposed a method that solved four basic problems. It could make analysis of similarity between DNA sequences. The coding method of sequence, which demonstrates sequences efficiently and makes the analysis of mutation visible, helps find out mechanism of diseases. Besides, the coding method provides a better mathematical model to figure out the similarity or dissimilarity between DNA sequences, in the sense that it improves genetic test and the prediction of gene functions.
c) The author proposed a coding scheme of RNA secondary structure, and gave mutation analysis and structure comparison based on coding and XOR operator. The representation of RNA secondary structure is very complex and easily degenerated. The proposed coding method and its extension can well separate the free base and base pair, and distinguish the different structures including pseudoknot. Based on three digits coding, the dissertation presented RNA secondary structure comparison method, analysis method of mutation. And the dissertation proposed a novel structure comparison method based on coding rules. The experiment showed the excellence of the method.
d) The author proposed two novel phylogenetic tree construction methods based on fuzzing clustering and minimum spanning tree that essentially make use of the proposed similarity and dissimilarity matrix.
引文
[1]Venter J C, Adams M D, Myers E W, et al. The sequence of the human genome. Science,2001,291(5507):1304-1351
[2]骆嘉伟.基因数据相似性分析方法研究：[湖南大学博士学位论文].长沙：湖南大学,2008
[3]Altschul S F, Gish W, Miller W et al. Basic local alignment search tool. Mol Biol, 1990,215(2):403-410
[4]Pearson W R, Lipman D J. Improved tools for biological sequence comparison. Proc Nat Acad Sci,1988,85(8):2444-2448
[5]Aravind L, Koonin E V. Gleaning non-trivial structural functional and evolutionary information about proteins by iterative database searches. Mol Biol,1999,287(2):1023-1040
[6]Muller A, MacCallum R M, Sternberg M J. Benchmarking PSIBLAST in genome annotation. Mol Biol,1999,293(1):1257-1271
[7]Plewniak F, Thompson J D, Poch O. Ballast:blast post-processing based on locally conserved segments. Bioinformatics,2000,16(9):750-759
[8]Tsoka S, Ouzounis CA. Recent developments and future directions in computational genomics. FEBS Lett,2000,480(3):42-48
[9]Nevill-Manning C G, Wu T D, Brutlag D L. Highly specific protein sequence motifs for genome analysis. Proc Natl Acad Sci,1998,95(3):5865-5871
[10]Nevill-Manning C G, Wu T D, Brutlag D L. Highly specific protein sequence motifs for genome analysis. Proc Natl Acad Sci,1998,95(3):5865-5871
[11]Phillips A, Janies D, Wheeler W. Multiple sequence alignment in phylogenetic analysis. Molecular Phylogenetics and Evolution,2000,16(9):317-330
[12]Aravind L, Watanabe H, Lipman D J et al. Lineage-specific loss and divergence of functionally linked genes in eukaryotes. Proc Natl Acad Sci,2000,97(10): 11319-11324
[13]Eisen J A. Assessing evolutionary relationships among microbes from whole-genome analysis. Curr Opin Microbiol,2000,3(5):475-480
[14]Koonin E V, Aravind L, Kondrashov A S. The impact of comparative genomics on our understanding of evolution. Cell,2000,101(6):573-576
[15]Cuff J A, Barton G J. Application of multiple sequence alignment profiles to improve protein secondary structure prediction. Proteins,2000,40(2):502-511
[16]Zimmermann K, Gibrat J F. In unison:regularization of protein secondary structure predictions that makes use of multiple sequence alignments. Protein Eng,1998,11(10):861-865
[17]Alexandrov N N, Luethy R. Alignment algorithm for homology modelling and threading. Protein Sci,1998,7(2):254-258
[18]Holm L, Sander C. Protein folds and families:sequence and structure alignments. Nucleic Acids Res,1999,27(1):244-247
[19]张春霆.用几何学方法分析DNA序列.中国科学基金,1999,13(3)：152-153
[20]Hamori E, Ruskin J. H curves:a novel method of representation of nucleotide series especially suited for long DNA sequences. J Biol Chem,1983,258(1): 1318-1327
[21]Gates M A.A simple way to look at DNA. J Theor Biol,1986,119(9):319-328
[22]Nandy A. Graphical representation of long DNA sequences. Curr Sci,1994, 66(12):821
[23]Leong P M. Random walk and gap plots of DNA sequences. Computer Application Biosciences,1995,11(5):503
[24]Guo X F, Randic M, Basak S C. A novel 2-D graphical representation of DNA sequences of low degeneracy. Chem Phys Lett,2001,350:106-112
[25]Zhang R, Zhang C T. Z Curves:An Intuitive Tool for Visualizing and Analyzing DNA sequences. J Biomol Struc Dynamics,1994,11(4):767-782
[26]Chen LL, Qu HY, Zhang CT, et al. ZCURVE_CoV:a new system to recognize protein coding genes in coronavirus genomes and its applications in analyzing SARS-CoV genomes. Biochemical and Biophysical Research Communications, 2003,307(9):382-388
[27]Zheng WX, Chen LL, Qu HY, et al. Coronavirus phylogeny based on a geometric approach. Molecular Phylogenetics and Evolution,2005,36(7):224-232
[28]Guo FB, Ou HY, Zhang CT. ZCURVE:a new system for recognizing protein coding genes in bacterial and archaeal genomes. Nucleic Acids Res,2003,31(8): 1780-1789
[29]于成龙.DNA序列的图形表示及其相似性分析：[浙江大学硕士学位论文].杭州：浙江大学,2006.
[30]Liao B, Wang TM. New 2D Graphical Representation of DNA Sequences. Journal of Computational Chemistry,2004,25(11):1364-1368
[31]Liao B. A 2D graphical representation of DNA sequence. Chemical Physics Letters,2005,401(12):196-199
[32]Liao B, Wang TM.3-D graphical representation of DNA sequences and their numerical characterization, J Mol Str:THEOCHEM,2004,68(6):209-212
[33]Zhang Y, Liao B, Ding K. On 3DD-curves of DNA sequences. Molecular Simulation,2006,32(1):29-34
[34]Liao B, Zhu W, Liu Y.3D graphical representation of DNA sequence without degeneracy and its application in constructing phylogenetic tree. Match Commun Math Comput Chem,2006,56(8):209-216
[35]Randic M. On characterization of DNA primary sequences a condensed matrix. Chem Phys Lett,2000,317(9):29-34
[36]Randic M. Condensed Representation of DNA Primary Sequences. J Chem Inf Comput Sci,2000,40(5):50-56
[37]Randic M, Basak S C. Characterization of DNA primary sequences based on the average distances between bases. J Chem Inf Comput Sci,2001,41(6):561-568
[38]Liao B, Ding KQ, A Graphical Approach to analyzing DNA sequences, Journal of Computational Chemistry,2005,26:1519-1523
[39]Liao B, Luo JW, Li RF, Zhu W. RNA Secondary structure 2D graphical representation without degeneracy. International Journal of Quantum Chemistry,2006,106(8):1749-1755
[40]Liao B, Liu YS, Li RF, Zhu W. Coronavirus phylogeny based on triplets of nucleic acids bases. Chemical Physic Letters,2006,421:313-318
[41]Liao B, Xiang XY, Zhu W, Coronavirus phylogeny based on 2D graphical representation of DNA sequence, Journal of Computational Chemistry,2006,27(11):1196-1202
[42]Wang WP, Liao B, Wang TM. A grapchical method to construct phylogenetic tree. International Journal of Quantum Chemistry,2006,106(9):1998-2006
[43]Liao B, Shan XZ, Zhu W, Li RF. Phylogenetic tree construction based on 2D graphical representation. Chemical Physic Letters,2006,422(1-3):282-288
[44]Liao B, Zhu W, Luo JW, Li RF. RNA Secondary Structure Mathematical Representation without Degeneracy. MATCH Communication in Mathematical and in Computer Chemistry,2007,57(3),687-695
[45]Cao Z, Liao B, Li RF. A group of 3D graphical representation of DNA sequences based on dual nucleotides. International Journal of Quantum Chemistry,2008,108:1485-1490
[46]Huang GH, Liao B, Li YF, Liu ZB. H-L curve:A novel 2D graphical representation for DNA sequences. Chemical Physics Letters,2008,462(1-3): 129-132
[47]Zheng WX, Zhang CT. Biological Implications of Isochore Boundaries in the Human Genome. Journal of Biomolecular Structure and Dynamics,2008,25, 327-336.
[48]Gao F, Zhang CT. Ori-Finder:a web-based system for finding oriCs in unannotated bacterial genomes. BMC Bioinformatics,2008,9, 79.
[49]Zhang R, Lin Y, Zhang CT.Greglist. a database listing potential G-quadruplex regulated genes. Nucleic Acids Research,2008,36, D372-D376.
[50]Hao BL. Fractals from genomes-exact solutions of a biology-inspired problem. Physica A,2000,282,225-246.
[51]Hao BL, Lee HC, Zhang SY. Fractals related to long DNA sequences and complete genomes. Chaos, Solitons and Fractals,2000,11,825-836.
[52]Qi J, Wang B, Hao BL. Whole genome prokaryote phylogeny without sequence alignment:a k-string composition approach. Journal of Molecular Evolution, 2003,58(1),1-11.
[53]王树林.生物子序列频数分布与肿瘤亚型分类模型研究：[国防科技大学博士学位论文].长沙：国防科技大学,2008
[54]Chen WY, Liao B, Liu YS, Zhu W, Su ZZ. A numerical representation of DNA sequence and its applications, MATCH Communications in Mathematical and in Computer Chemistry,2008,60(2):291-300
[55]Chen WY, Liao B, Xiang XY, Zhu W. An Improved Binary Represntation of DNA Sequences and Its Applications. MATCH Communications in Mathematical and in Computer Chemistry,2009,61(3):767-780
[56]Cao Z, Liao B, Li RF, Zhu W. A three-dimensional cube representation of RNA secondary structure and its application. Journal of Computational and Theoretical Nanoscience,2009,6,1478-1481
[57]Gilbert D G. Dot plot sequence comparisons on Macintosh computers. Comput Appl Biosci,1990,6(2):117-128
[58]Huang Y, Zhang L. Rapid and sensitive dot-matrix methods for genome analysis. Bioinformatics,2004,20(4):460-466
[59]Needleman S, Wunsch C. A general method applicable to the search for similarities in the amino acid sequence of two proteins. J.Mol.Biol.1970,48(3): 443-453
[60]Smith T F, Waterman M S. Identification of common molecular subsequences. J. Mol. Biol.,1981,147(2):195-197.
[61]孙啸,陆祖宏,谢建明.生物信息学基础.北京：清华大学出版社,2006,105-107
[62]Thompson JD, Higgins DG, Gibson TJ. CLUSTALW:improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice. Nucleic Acids Res. 1994,22 (22):4673-4680
[63]Feng D F, Doolittle R F. Progressive sequence alignment as a prerequisite to correct phylogenetic trees. Journal of Molecular Evolution,1987,25(4): 351-360
[64]Feng D F, Doolittle R F. Progressive sequence alignment of amino acid sequences and construction of phylogenetic trees from them. Methods Enzymology,1996,266(1):368-382
[65]Osamu GH. Significant Improvement in Accuracy of Multiple Protein Sequence Alignments by Iterative Refinement as Assessed by Reference to Structural Alignments. Journal of Molecular Biology,1996,264(4):823-838
[66]Anders K, Michael B, et al. Hidden Markov Models in Computational Biology: Applications to Protein Modeling. Journal of Molecular Biology,1994,235(5): 1501-1531
[67]Jin K, Sakti P, Chung MJ. Multiple sequence alignment using simulated annealing. Computer Applications in the Biosciences,1994,10(4):419-426
[68]Alexander VL, Jacob E, Soren B. Multiple alignment using simulated annealing: branch point definition in human mRNA splicing. Nucleic Acids Research, 1992,20(10):2511-2516
[69]Notredame C, Higgins DG, et al. SAGA:sequence alignment by genetic algorithm. Nucleic Acids Research,1996,24(8):1515-1524
[70]Berger MP, Munson PJ. A novel randomized iterative strategy for aligning multiple protein sequence. Computer Applications in the Biosciences,1991,7(4): 479-484
[71]Lawrence CE, Altschul S, et al. Detecting subtle sequence signals:a Gibbs sampling strategy for multiple alignment. Science,1993,262:208-214
[72]Corpet F. Multiple sequence alignment with hierarchical clustering. Nucleic Acids Research,1988,16(22):10881-10890
[73]Robert C. Edgar. MUSCLE:multiple sequence alignment with high accuracy and high throughput. Nucleic Acids Research,2004,32(5):1792-1797
[74]张敏,方伟武,张俊华,等.基于迭代渐进多序列比对算法研究.计算机工程,2005,31(17)：32-33
[75]张敏.生物序列比对算法研究现状与展望.大连大学学报,2004,25(4)：75-79.
[76]Yuan CX, Liao B, Wang TM. New 3D graphical representation of DNA sequences and their numerical characterization, Chemical Physics Letters,2003, 379:412-417
[77]Liao B, Zhu W, Liu Y.3D graphical representation of DNA sequence without degeneracy and its applications in constructing phylogenic tree. MATCH Communications in Mathematical and in Computer Chemistry,2006,56:209-216
[78]Liao B, Tan MS, Ding KQ. A 4D representation of DNA sequences and its application. Chemical Physic Letters,2005,402:380-383
[79]Liao B, Wang TM. Analysis of similarity of DNA sequences based on triplets. J. Chem. Inf. Comput. Sci,2004,44:1666-1670
[80]Randic M, Varacko M, Plavsic D. Novel 2-D graphical representation of DNA sequences and their numerical characterization. Chemical Physics Leter,2003, 368:1-6
[81]Randic M, Varacko M, Nandy A, et al. On 3-D graphical representation of DNA primary sequences and their numerical characterization. J Chem Inf Comput Sci, 2000,40:1235-1244
[82]Li W, Fang WW, Ling L J,et al. Phylogeny based on whole genome as inferred from complete information set analysis. Journal of Biological Physics,2002, 28(3):439-447
[83]Wang J H, Fang W W, Ling L J, et al. Gene's functional arrangement as a measure of the phylogenetic relationships of microorganisms. Journal of Biological Physics,2002,28 (1):55-62
[84]Jin L X, Fang W W, Tang H W. Prediction of protein structural classes by a new measure of information discrepancy. Computational Biology and Chemistry, 2003,27 (3):373-380
[85]张立震,唐焕文.一种基于子序列分布的蛋白质结构类预测方法.计算机与应用化学,2003,23(3)：1-6
[86]沈世镒.生物序列突变与比对的结构分析.北京：科学出版社,2004,1-12
[87]阮庆国,陆春叶.基因突变分析技术综述, 国外医学遗传学分册,21(5),1998,225-231
[88]Huang GH, Liao B, Zhang W, Gong F. A Novel Method for Sequence Alignment and Mutation Analysis. MATCH Communications in Mathematical and in Computer Chemistry,2008,59(3):635-645
[89]Pauplin Y. Direct calculation of a tree length using a distance matrix. J. Mole. Evol.,2004,51(1):41-47
[90]Ranwez V, Gascuel O. Improvement of distance-based phylogenetic methods by a local maximum likelihood approach using triplets, Molecular Biology and Evolution,2002,19 (11):1952-1963
[91]Holder M, Lewis PO. Phylogeny estimation:traditional and Bayesian approaches. Nature Reviews Genetics,2003,4(3):275-284
[92]Hordijk W, Gascuel O. Improving the efficiency of SPR moves in phylogenetic tree search methods based on maximum likelihood. Bioinformatics,2005,21 (24): 4338-4337
[93]Barker D. LVB:Parsimony and simulated annealing in the search for phylogenetic trees. Bioinformatics,2004,20 (2):274-275
[94]Sebastien R. A short proof that phylogenetic tree reconstruction by maximum likelihood is Hard. IEEE/ACM Transactions on Computational Biology and Bioinformatics,2006,3 (1):92-94
[95]Dopazo J., Carazo J.M..Phylogenetic Reconstruction using an unsupervised growing neural network that adopts the topology of a phylogenetic tree. Mol.Biol.Evol.1997,44:226-233.
[96]Feng L, Latifur K, Farokh B, et al. A dynamically growing self-organizing tree(DGSOT) for hierarchical clustering gene expression profiles. Bioinformatics.2004,20:2605-2617.
[97]蒋宗礼,许光俊.基于神经网络的多叉系统进化树构造.哈尔滨工程大学学报.2006,27：27-31
[98]Takezaki N. Tie trees generated by distance methods of phylogenetic reconstruction. Mol.Biol.Evol.1998,15:727-737
[99]Zuker M. On Finding All suboptial Foldings of an RNA Molecule. Science, 1989,244:48-52
[100]Zuker M., Jaeger, Turner D, A comparison of optimal and suboptimal RNA secondary structures predicted by free energy minimization with structures determined by Phylogenetic comparison. NucleicAcidsRes,1991,19(10):2707-2714
[101]Lee SY, Nussinov R, Mazel JV. Tree graphs of RNA secondary structures and their comparison. Computer Biomed. Res,1989,22:461-473
[102]Shapiro B, Zhang K. Comparing multiple RNA secondary structures using tree comparisons. Computer.Appl.Biosci,1990,6(4):309-318
[103]Luo JW, Liao B, Li RF, Zhu W. RNA Secondary Structure 3D Graphical Representation without Degeneracy. Journal of Mathematical Chemistry,2006,39:629-636
[104]邹权,郭茂祖,张涛涛.RNA二级结构预测方法综述.电子学报,2008,36(2)：331-337
[105]Sankoff D. Simultaneous solution of the RNA folding, alignment and protosequence problems. SIAM J ournal on Applied Mathematics,1985,45 (5):810-825
[106]Gorodkin J, Stricklin'SL, Stormo G. Discovering common stemloop motifs in unaligned RNA sequences. Nucleic Acids Research,2001,29 (10):2135 2144
[107]Mathews D, Turner D. An algorithm for finding the secondary structure common to two RNA sequences. Journal of Molecular Biology,2002,317 (2):191-203
[108]Randic M, Varacko M, Plavsic D. Novel 2-D graphical representation of DNA sequences and their numerical characterization. Chemical Physics Leter,2003, 368:1-6
[109]Randic M, Varacko M, Nandy A, et al. On 3-D graphical representation of DNA primary sequences and their numerical characterization. J Chem Inf Comput Sci,2000,40:1235-1244
[110]Qi ZH, Qi XQ. Novel 2D graphical representation of DNA sequence based on dual nucleotides. Chemical Physics Letters,2007,440:139-144
[111]Liu ZB, Liao B, Zhu W, Huang GH. A 2-D graphical representation of DNA sequence based on dual nucleotides and its application. International Journal of Quantum Chemistry,2009,109(5):948-958
[112]Huang GH, Liao B, Li RF. Similarity studies of DNA sequences based on a new 2D graphical representation. Biophysical Chemistry,2009,143:55-59
[113]Cao Z, Liao B, Li RF. A Group of 3D Graphical Representation of DNA Sequences Based on Dual Nucleotides, Internal Journal of Quantum Chemistry, 2008,108:1485-1490
[114]Li C, Yu XQ, Helal N. Similarity analysis of DNA sequences based on codon usage. Chemical Physics Letters,2008,459:172-174
[115]Chen W, Zhang YS. Three distances for rapid similarity analysis of DNA sequences. MATCH Commun. Math.Comput.Chem.,2009,61:781-788
[116]廖波.计算分子生物学中若干问题研究：[大连理工大学博士学位论文].大连： 大连理工大学,2004
[117]Liao B, Wang TM. A 3D graphical representation of RNA secondary structures. J Biomol Struct Dyn,2004,21(6):827-832
[118]Liao B, Ding KQ, Wang TM. On a six-dimensional representation of RNA secondary structures. J Biomol Struct Dyn,2005,22(4):455-63
[119]Liao B, Wang TM. On a seven-dimensional representation of RNA secondary structures. Molecular Simulation,2005,31 (14):1063-1071
[120]Bai FL, Zhu W, Wang TM. Analysis of similarity between RNA secondary structures. Chemical Physics Letters,2005,408(4):258-263
[121]Yao YH, Nan XY, Wang TM. A class of 2D graphical representations of RNA secondary structures and the analysis of similarity based on them. Journal of Computational Chemistry,2005,26(13):1339-1346
[122]Mark D, Stephen LC, Andy DA, et al. Phylogenetic approaches for the analysis of mitochondrial genome sequence data in the Hymenoptera-A lineage with both rapidly and slowly evolving mitochondrial genomes. Molecular Phylogenetics and Evolution,2009,52(2):512-519
[123]Wu ZG, Shen X, Sun MA, et al. Phylogenetic analyses of complete mitochondrial genome of Urechis unicinctus (Echiura) support that echiurans are derived annelids. Molecular Phylogenetics and Evolution,2009, 52(2):558-562
[124]Duarte A, Veiga I, Tavares L. Genetic diversity and phylogenetic analysis of Feline Coronavirus sequences from Portugal. Veterinary Microbiology, 2009,138 (1-2):163-168
[125]谢季坚,刘承平.模糊数学方法及其应用(第三版).武汉：华中科技大学出版社，2007
[2]骆嘉伟.基因数据相似性分析方法研究：[湖南大学博士学位论文].长沙：湖南大学,2008
[3]Altschul S F, Gish W, Miller W et al. Basic local alignment search tool. Mol Biol, 1990,215(2):403-410
[4]Pearson W R, Lipman D J. Improved tools for biological sequence comparison. Proc Nat Acad Sci,1988,85(8):2444-2448
[5]Aravind L, Koonin E V. Gleaning non-trivial structural functional and evolutionary information about proteins by iterative database searches. Mol Biol,1999,287(2):1023-1040
[6]Muller A, MacCallum R M, Sternberg M J. Benchmarking PSIBLAST in genome annotation. Mol Biol,1999,293(1):1257-1271
[7]Plewniak F, Thompson J D, Poch O. Ballast:blast post-processing based on locally conserved segments. Bioinformatics,2000,16(9):750-759
[8]Tsoka S, Ouzounis CA. Recent developments and future directions in computational genomics. FEBS Lett,2000,480(3):42-48
[9]Nevill-Manning C G, Wu T D, Brutlag D L. Highly specific protein sequence motifs for genome analysis. Proc Natl Acad Sci,1998,95(3):5865-5871
[10]Nevill-Manning C G, Wu T D, Brutlag D L. Highly specific protein sequence motifs for genome analysis. Proc Natl Acad Sci,1998,95(3):5865-5871
[11]Phillips A, Janies D, Wheeler W. Multiple sequence alignment in phylogenetic analysis. Molecular Phylogenetics and Evolution,2000,16(9):317-330
[12]Aravind L, Watanabe H, Lipman D J et al. Lineage-specific loss and divergence of functionally linked genes in eukaryotes. Proc Natl Acad Sci,2000,97(10): 11319-11324
[13]Eisen J A. Assessing evolutionary relationships among microbes from whole-genome analysis. Curr Opin Microbiol,2000,3(5):475-480
[14]Koonin E V, Aravind L, Kondrashov A S. The impact of comparative genomics on our understanding of evolution. Cell,2000,101(6):573-576
[15]Cuff J A, Barton G J. Application of multiple sequence alignment profiles to improve protein secondary structure prediction. Proteins,2000,40(2):502-511
[16]Zimmermann K, Gibrat J F. In unison:regularization of protein secondary structure predictions that makes use of multiple sequence alignments. Protein Eng,1998,11(10):861-865
[17]Alexandrov N N, Luethy R. Alignment algorithm for homology modelling and threading. Protein Sci,1998,7(2):254-258
[18]Holm L, Sander C. Protein folds and families:sequence and structure alignments. Nucleic Acids Res,1999,27(1):244-247
[19]张春霆.用几何学方法分析DNA序列.中国科学基金,1999,13(3)：152-153
[20]Hamori E, Ruskin J. H curves:a novel method of representation of nucleotide series especially suited for long DNA sequences. J Biol Chem,1983,258(1): 1318-1327
[21]Gates M A.A simple way to look at DNA. J Theor Biol,1986,119(9):319-328
[22]Nandy A. Graphical representation of long DNA sequences. Curr Sci,1994, 66(12):821
[23]Leong P M. Random walk and gap plots of DNA sequences. Computer Application Biosciences,1995,11(5):503
[24]Guo X F, Randic M, Basak S C. A novel 2-D graphical representation of DNA sequences of low degeneracy. Chem Phys Lett,2001,350:106-112
[25]Zhang R, Zhang C T. Z Curves:An Intuitive Tool for Visualizing and Analyzing DNA sequences. J Biomol Struc Dynamics,1994,11(4):767-782
[26]Chen LL, Qu HY, Zhang CT, et al. ZCURVE_CoV:a new system to recognize protein coding genes in coronavirus genomes and its applications in analyzing SARS-CoV genomes. Biochemical and Biophysical Research Communications, 2003,307(9):382-388
[27]Zheng WX, Chen LL, Qu HY, et al. Coronavirus phylogeny based on a geometric approach. Molecular Phylogenetics and Evolution,2005,36(7):224-232
[28]Guo FB, Ou HY, Zhang CT. ZCURVE:a new system for recognizing protein coding genes in bacterial and archaeal genomes. Nucleic Acids Res,2003,31(8): 1780-1789
[29]于成龙.DNA序列的图形表示及其相似性分析：[浙江大学硕士学位论文].杭州：浙江大学,2006.
[30]Liao B, Wang TM. New 2D Graphical Representation of DNA Sequences. Journal of Computational Chemistry,2004,25(11):1364-1368
[31]Liao B. A 2D graphical representation of DNA sequence. Chemical Physics Letters,2005,401(12):196-199
[32]Liao B, Wang TM.3-D graphical representation of DNA sequences and their numerical characterization, J Mol Str:THEOCHEM,2004,68(6):209-212
[33]Zhang Y, Liao B, Ding K. On 3DD-curves of DNA sequences. Molecular Simulation,2006,32(1):29-34
[34]Liao B, Zhu W, Liu Y.3D graphical representation of DNA sequence without degeneracy and its application in constructing phylogenetic tree. Match Commun Math Comput Chem,2006,56(8):209-216
[35]Randic M. On characterization of DNA primary sequences a condensed matrix. Chem Phys Lett,2000,317(9):29-34
[36]Randic M. Condensed Representation of DNA Primary Sequences. J Chem Inf Comput Sci,2000,40(5):50-56
[37]Randic M, Basak S C. Characterization of DNA primary sequences based on the average distances between bases. J Chem Inf Comput Sci,2001,41(6):561-568
[38]Liao B, Ding KQ, A Graphical Approach to analyzing DNA sequences, Journal of Computational Chemistry,2005,26:1519-1523
[39]Liao B, Luo JW, Li RF, Zhu W. RNA Secondary structure 2D graphical representation without degeneracy. International Journal of Quantum Chemistry,2006,106(8):1749-1755
[40]Liao B, Liu YS, Li RF, Zhu W. Coronavirus phylogeny based on triplets of nucleic acids bases. Chemical Physic Letters,2006,421:313-318
[41]Liao B, Xiang XY, Zhu W, Coronavirus phylogeny based on 2D graphical representation of DNA sequence, Journal of Computational Chemistry,2006,27(11):1196-1202
[42]Wang WP, Liao B, Wang TM. A grapchical method to construct phylogenetic tree. International Journal of Quantum Chemistry,2006,106(9):1998-2006
[43]Liao B, Shan XZ, Zhu W, Li RF. Phylogenetic tree construction based on 2D graphical representation. Chemical Physic Letters,2006,422(1-3):282-288
[44]Liao B, Zhu W, Luo JW, Li RF. RNA Secondary Structure Mathematical Representation without Degeneracy. MATCH Communication in Mathematical and in Computer Chemistry,2007,57(3),687-695
[45]Cao Z, Liao B, Li RF. A group of 3D graphical representation of DNA sequences based on dual nucleotides. International Journal of Quantum Chemistry,2008,108:1485-1490
[46]Huang GH, Liao B, Li YF, Liu ZB. H-L curve:A novel 2D graphical representation for DNA sequences. Chemical Physics Letters,2008,462(1-3): 129-132
[47]Zheng WX, Zhang CT. Biological Implications of Isochore Boundaries in the Human Genome. Journal of Biomolecular Structure and Dynamics,2008,25, 327-336.
[48]Gao F, Zhang CT. Ori-Finder:a web-based system for finding oriCs in unannotated bacterial genomes. BMC Bioinformatics,2008,9, 79.
[49]Zhang R, Lin Y, Zhang CT.Greglist. a database listing potential G-quadruplex regulated genes. Nucleic Acids Research,2008,36, D372-D376.
[50]Hao BL. Fractals from genomes-exact solutions of a biology-inspired problem. Physica A,2000,282,225-246.
[51]Hao BL, Lee HC, Zhang SY. Fractals related to long DNA sequences and complete genomes. Chaos, Solitons and Fractals,2000,11,825-836.
[52]Qi J, Wang B, Hao BL. Whole genome prokaryote phylogeny without sequence alignment:a k-string composition approach. Journal of Molecular Evolution, 2003,58(1),1-11.
[53]王树林.生物子序列频数分布与肿瘤亚型分类模型研究：[国防科技大学博士学位论文].长沙：国防科技大学,2008
[54]Chen WY, Liao B, Liu YS, Zhu W, Su ZZ. A numerical representation of DNA sequence and its applications, MATCH Communications in Mathematical and in Computer Chemistry,2008,60(2):291-300
[55]Chen WY, Liao B, Xiang XY, Zhu W. An Improved Binary Represntation of DNA Sequences and Its Applications. MATCH Communications in Mathematical and in Computer Chemistry,2009,61(3):767-780
[56]Cao Z, Liao B, Li RF, Zhu W. A three-dimensional cube representation of RNA secondary structure and its application. Journal of Computational and Theoretical Nanoscience,2009,6,1478-1481
[57]Gilbert D G. Dot plot sequence comparisons on Macintosh computers. Comput Appl Biosci,1990,6(2):117-128
[58]Huang Y, Zhang L. Rapid and sensitive dot-matrix methods for genome analysis. Bioinformatics,2004,20(4):460-466
[59]Needleman S, Wunsch C. A general method applicable to the search for similarities in the amino acid sequence of two proteins. J.Mol.Biol.1970,48(3): 443-453
[60]Smith T F, Waterman M S. Identification of common molecular subsequences. J. Mol. Biol.,1981,147(2):195-197.
[61]孙啸,陆祖宏,谢建明.生物信息学基础.北京：清华大学出版社,2006,105-107
[62]Thompson JD, Higgins DG, Gibson TJ. CLUSTALW:improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice. Nucleic Acids Res. 1994,22 (22):4673-4680
[63]Feng D F, Doolittle R F. Progressive sequence alignment as a prerequisite to correct phylogenetic trees. Journal of Molecular Evolution,1987,25(4): 351-360
[64]Feng D F, Doolittle R F. Progressive sequence alignment of amino acid sequences and construction of phylogenetic trees from them. Methods Enzymology,1996,266(1):368-382
[65]Osamu GH. Significant Improvement in Accuracy of Multiple Protein Sequence Alignments by Iterative Refinement as Assessed by Reference to Structural Alignments. Journal of Molecular Biology,1996,264(4):823-838
[66]Anders K, Michael B, et al. Hidden Markov Models in Computational Biology: Applications to Protein Modeling. Journal of Molecular Biology,1994,235(5): 1501-1531
[67]Jin K, Sakti P, Chung MJ. Multiple sequence alignment using simulated annealing. Computer Applications in the Biosciences,1994,10(4):419-426
[68]Alexander VL, Jacob E, Soren B. Multiple alignment using simulated annealing: branch point definition in human mRNA splicing. Nucleic Acids Research, 1992,20(10):2511-2516
[69]Notredame C, Higgins DG, et al. SAGA:sequence alignment by genetic algorithm. Nucleic Acids Research,1996,24(8):1515-1524
[70]Berger MP, Munson PJ. A novel randomized iterative strategy for aligning multiple protein sequence. Computer Applications in the Biosciences,1991,7(4): 479-484
[71]Lawrence CE, Altschul S, et al. Detecting subtle sequence signals:a Gibbs sampling strategy for multiple alignment. Science,1993,262:208-214
[72]Corpet F. Multiple sequence alignment with hierarchical clustering. Nucleic Acids Research,1988,16(22):10881-10890
[73]Robert C. Edgar. MUSCLE:multiple sequence alignment with high accuracy and high throughput. Nucleic Acids Research,2004,32(5):1792-1797
[74]张敏,方伟武,张俊华,等.基于迭代渐进多序列比对算法研究.计算机工程,2005,31(17)：32-33
[75]张敏.生物序列比对算法研究现状与展望.大连大学学报,2004,25(4)：75-79.
[76]Yuan CX, Liao B, Wang TM. New 3D graphical representation of DNA sequences and their numerical characterization, Chemical Physics Letters,2003, 379:412-417
[77]Liao B, Zhu W, Liu Y.3D graphical representation of DNA sequence without degeneracy and its applications in constructing phylogenic tree. MATCH Communications in Mathematical and in Computer Chemistry,2006,56:209-216
[78]Liao B, Tan MS, Ding KQ. A 4D representation of DNA sequences and its application. Chemical Physic Letters,2005,402:380-383
[79]Liao B, Wang TM. Analysis of similarity of DNA sequences based on triplets. J. Chem. Inf. Comput. Sci,2004,44:1666-1670
[80]Randic M, Varacko M, Plavsic D. Novel 2-D graphical representation of DNA sequences and their numerical characterization. Chemical Physics Leter,2003, 368:1-6
[81]Randic M, Varacko M, Nandy A, et al. On 3-D graphical representation of DNA primary sequences and their numerical characterization. J Chem Inf Comput Sci, 2000,40:1235-1244
[82]Li W, Fang WW, Ling L J,et al. Phylogeny based on whole genome as inferred from complete information set analysis. Journal of Biological Physics,2002, 28(3):439-447
[83]Wang J H, Fang W W, Ling L J, et al. Gene's functional arrangement as a measure of the phylogenetic relationships of microorganisms. Journal of Biological Physics,2002,28 (1):55-62
[84]Jin L X, Fang W W, Tang H W. Prediction of protein structural classes by a new measure of information discrepancy. Computational Biology and Chemistry, 2003,27 (3):373-380
[85]张立震,唐焕文.一种基于子序列分布的蛋白质结构类预测方法.计算机与应用化学,2003,23(3)：1-6
[86]沈世镒.生物序列突变与比对的结构分析.北京：科学出版社,2004,1-12
[87]阮庆国,陆春叶.基因突变分析技术综述, 国外医学遗传学分册,21(5),1998,225-231
[88]Huang GH, Liao B, Zhang W, Gong F. A Novel Method for Sequence Alignment and Mutation Analysis. MATCH Communications in Mathematical and in Computer Chemistry,2008,59(3):635-645
[89]Pauplin Y. Direct calculation of a tree length using a distance matrix. J. Mole. Evol.,2004,51(1):41-47
[90]Ranwez V, Gascuel O. Improvement of distance-based phylogenetic methods by a local maximum likelihood approach using triplets, Molecular Biology and Evolution,2002,19 (11):1952-1963
[91]Holder M, Lewis PO. Phylogeny estimation:traditional and Bayesian approaches. Nature Reviews Genetics,2003,4(3):275-284
[92]Hordijk W, Gascuel O. Improving the efficiency of SPR moves in phylogenetic tree search methods based on maximum likelihood. Bioinformatics,2005,21 (24): 4338-4337
[93]Barker D. LVB:Parsimony and simulated annealing in the search for phylogenetic trees. Bioinformatics,2004,20 (2):274-275
[94]Sebastien R. A short proof that phylogenetic tree reconstruction by maximum likelihood is Hard. IEEE/ACM Transactions on Computational Biology and Bioinformatics,2006,3 (1):92-94
[95]Dopazo J., Carazo J.M..Phylogenetic Reconstruction using an unsupervised growing neural network that adopts the topology of a phylogenetic tree. Mol.Biol.Evol.1997,44:226-233.
[96]Feng L, Latifur K, Farokh B, et al. A dynamically growing self-organizing tree(DGSOT) for hierarchical clustering gene expression profiles. Bioinformatics.2004,20:2605-2617.
[97]蒋宗礼,许光俊.基于神经网络的多叉系统进化树构造.哈尔滨工程大学学报.2006,27：27-31
[98]Takezaki N. Tie trees generated by distance methods of phylogenetic reconstruction. Mol.Biol.Evol.1998,15:727-737
[99]Zuker M. On Finding All suboptial Foldings of an RNA Molecule. Science, 1989,244:48-52
[100]Zuker M., Jaeger, Turner D, A comparison of optimal and suboptimal RNA secondary structures predicted by free energy minimization with structures determined by Phylogenetic comparison. NucleicAcidsRes,1991,19(10):2707-2714
[101]Lee SY, Nussinov R, Mazel JV. Tree graphs of RNA secondary structures and their comparison. Computer Biomed. Res,1989,22:461-473
[102]Shapiro B, Zhang K. Comparing multiple RNA secondary structures using tree comparisons. Computer.Appl.Biosci,1990,6(4):309-318
[103]Luo JW, Liao B, Li RF, Zhu W. RNA Secondary Structure 3D Graphical Representation without Degeneracy. Journal of Mathematical Chemistry,2006,39:629-636
[104]邹权,郭茂祖,张涛涛.RNA二级结构预测方法综述.电子学报,2008,36(2)：331-337
[105]Sankoff D. Simultaneous solution of the RNA folding, alignment and protosequence problems. SIAM J ournal on Applied Mathematics,1985,45 (5):810-825
[106]Gorodkin J, Stricklin'SL, Stormo G. Discovering common stemloop motifs in unaligned RNA sequences. Nucleic Acids Research,2001,29 (10):2135 2144
[107]Mathews D, Turner D. An algorithm for finding the secondary structure common to two RNA sequences. Journal of Molecular Biology,2002,317 (2):191-203
[108]Randic M, Varacko M, Plavsic D. Novel 2-D graphical representation of DNA sequences and their numerical characterization. Chemical Physics Leter,2003, 368:1-6
[109]Randic M, Varacko M, Nandy A, et al. On 3-D graphical representation of DNA primary sequences and their numerical characterization. J Chem Inf Comput Sci,2000,40:1235-1244
[110]Qi ZH, Qi XQ. Novel 2D graphical representation of DNA sequence based on dual nucleotides. Chemical Physics Letters,2007,440:139-144
[111]Liu ZB, Liao B, Zhu W, Huang GH. A 2-D graphical representation of DNA sequence based on dual nucleotides and its application. International Journal of Quantum Chemistry,2009,109(5):948-958
[112]Huang GH, Liao B, Li RF. Similarity studies of DNA sequences based on a new 2D graphical representation. Biophysical Chemistry,2009,143:55-59
[113]Cao Z, Liao B, Li RF. A Group of 3D Graphical Representation of DNA Sequences Based on Dual Nucleotides, Internal Journal of Quantum Chemistry, 2008,108:1485-1490
[114]Li C, Yu XQ, Helal N. Similarity analysis of DNA sequences based on codon usage. Chemical Physics Letters,2008,459:172-174
[115]Chen W, Zhang YS. Three distances for rapid similarity analysis of DNA sequences. MATCH Commun. Math.Comput.Chem.,2009,61:781-788
[116]廖波.计算分子生物学中若干问题研究：[大连理工大学博士学位论文].大连： 大连理工大学,2004
[117]Liao B, Wang TM. A 3D graphical representation of RNA secondary structures. J Biomol Struct Dyn,2004,21(6):827-832
[118]Liao B, Ding KQ, Wang TM. On a six-dimensional representation of RNA secondary structures. J Biomol Struct Dyn,2005,22(4):455-63
[119]Liao B, Wang TM. On a seven-dimensional representation of RNA secondary structures. Molecular Simulation,2005,31 (14):1063-1071
[120]Bai FL, Zhu W, Wang TM. Analysis of similarity between RNA secondary structures. Chemical Physics Letters,2005,408(4):258-263
[121]Yao YH, Nan XY, Wang TM. A class of 2D graphical representations of RNA secondary structures and the analysis of similarity based on them. Journal of Computational Chemistry,2005,26(13):1339-1346
[122]Mark D, Stephen LC, Andy DA, et al. Phylogenetic approaches for the analysis of mitochondrial genome sequence data in the Hymenoptera-A lineage with both rapidly and slowly evolving mitochondrial genomes. Molecular Phylogenetics and Evolution,2009,52(2):512-519
[123]Wu ZG, Shen X, Sun MA, et al. Phylogenetic analyses of complete mitochondrial genome of Urechis unicinctus (Echiura) support that echiurans are derived annelids. Molecular Phylogenetics and Evolution,2009, 52(2):558-562
[124]Duarte A, Veiga I, Tavares L. Genetic diversity and phylogenetic analysis of Feline Coronavirus sequences from Portugal. Veterinary Microbiology, 2009,138 (1-2):163-168
[125]谢季坚,刘承平.模糊数学方法及其应用(第三版).武汉：华中科技大学出版社，2007