Chaos game representation walk model for the protein sequences

A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CCR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA（p, d, q） model is introduced into the protein sequence analysis. This model is applied to simulating real CCR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA（p, d, q） model.

Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation

Chaos game representation （CGR） is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima （WTMM） method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonueleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.

Chaos game representation of functional protein sequences,and simulation and multifractal analysis of induced measures

Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation （CGR） of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems （RIFS） in fractal theory to simulate the measure based on their chaos game representations. This method helps to extract some features of functional protein sequences, and furthermore the biological functions of these proteins. Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed. We find that the CGRs have clear fractal patterns. The numerical results show that the RIFS can simulate the measure based on the CGR very well. The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences. The estimated probability matrices in the RIFS with different biological functions are evidently different. Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions. From the values of the Dq curves, one sees that these functional protein sequences are not completely random. The Dq of all linked functional proteins studied are multifractal-like and sufficiently smooth for the Cq （analogous to specific heat） curves to be meaningful. Furthermore, the Dq curves of the measure μ based on their CCRs for different orders to link the functional protein sequences are almost identical if q 〉 0. Finally, the Ca curves of all linked functional proteins resemble a classical phase transition at a critical point.

A novel method to reconstruct phylogeny tree based on thechaos game representation

We developed a new approach for the reconstruction of phylogeny trees based on the chaos game representation (CGR) of biological sequences. The chaos game representation (CGR) method generates a picture from a biological sequence, which displays both local and global patterns. The quantitative index of the biological sequence is extracted from the picture. The Kullback-Leibler discrimination information is used as a diversity indicator to measure the dissimilarity of each pair of biological sequences. The new method is inspected by two data sets: the Eutherian orders using concatenated H-stranded amino acid sequences and the genome sequence of the SARS and coronavirus. The phylogeny trees constructed by the new method are consistent with the commonly accepted ones. These results are very promising and suggest more efforts for further developments.

Simulation for chaos game representation of genomes by recurrent iterated function systems

Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.

Similarity Studies of Corona Viruses through Chaos Game Representation

The novel coronavirus (SARS-COV-2) is generally referred to as Covid-19 virus has spread to 213 countries with nearly 7 million confirmed cases and nearly 400,000 deaths. Such major outbreaks demand classification and origin of the virus genomic sequence, for planning, containment, and treatment. Motivated by the above need, we report two alignment-free methods combing with CGR to perform clustering analysis and create a phylogenetic tree based on it. To each DNA sequence we associate a matrix then define distance between two DNA sequences to be the distance between their associated matrix. These methods are being used for phylogenetic analysis of coronavirus sequences. Our approach provides a powerful tool for analyzing and annotating genomes and their phylogenetic relationships. We also compare our tool to ClustalX algorithm which is one of the most popular alignment methods. Our alignment-free methods are shown to be capable of finding closest genetic relatives of coronaviruses.

Evolutionary Relationship of Protein Sequences of SARS-CoV-2 and Other Viruses through Chaos Game Representation

Comparison between different biological sequences is a key step in bioinformatics when analyzing similarities of sequences and phylogenetic relationships. A method of graphically representing biological sequences known as Chaos Game Representation (CGR) has achieved many applications in the studies of bioinformatics. The key issue in the application of CGR is to extract as many useful features as possible from CGR. Initially, CGR was applied to DNA sequences, but in this paper, a CGR-based approach is used to extract suitable features for comparing protein sequences of SARS-CoV-2 and other viruses. For this aim, several viral protein sequences from 12 groups are considered and CGR centroid, amino acid frequency, compounded frequency, Shannon entropy, and Kullback-Lieber Discrimination Information are applied to find the inter-relationship among the sequences. The experimental results demonstrate the potential strengths of CGR-based method for examining the evolutionary relationship of protein sequences. Our method is powerful for extracting effective features from protein sequences, and therefore important in classifying proteins and inferring the phylogeny of viruses.

基于CGR的DNA序列的时间序列模型(英文)

利用DNA序列的混沌游戏表示(chaos game representation,CGR),提出了将2维DNA图谱转化成相应的类谱格式的方法。该方法不仅提供了一个较好的视觉表示,而且可将DNA序列转化成一个时间序列。利用CGR坐标将DNA序列转化成CGR弧度序列,并引入长记忆ARFIMA(p,d,q)模型去拟合此类序列,发现此类序列中有显著的长相关性且拟合度很好。

基于蛋白质CGR的线粒体蛋白质序列比对

利用蛋白质混沌游走表示法(PCGR)提出一种新的蛋白质序列比对方法。通过计算两序列之间的PCGR点距离,就可以找到所有的局部相似片断。根据氨基酸的化学物理性质把氨基酸分成4和7类,针对分类与无分类的各种情况进行蛋白质序列比对。为了更直观地描述比对结果,采用点阵图来表示比对数据,不仅能显示两序列间所有相同片断,还可以体现出序列的相似性。

基于矩阵图谱表达法的蛋白质序列的相似性分析

在DNA序列的混沌游走方法(CGR)及DNA序列的4线图谱表达方法(4-LGR)的基础上,提出了一种新型DNA序列的表达方法—矩阵图谱表达法(MGR),并进一步,在DNA序列的上述三种表达式基础上,分别推广建立了基于经典HP模型的蛋白质序列的图谱表达法,对蛋白质序列的相似性进行了比较验证。研究表明:矩阵图谱表达方法不仅能够说明蛋白质序列间的相似性,而且与传统的方法相比,该方法更具有灵活性和变通性。

真核生物DNA非编码区的组分分析

在全基因组水平上 ,用直方图、混沌表示灰度图、距离差异度和信息熵差异度四种方法 ,研究了拟南芥、线虫、果蝇的DNA内含子、基因间隔区DNA、外显子三种区域的核苷酸短序列组分及组分复杂度 .结果表明 :a 不同基因组之间 ,不管基因数目多少 ,用 4种方法得到的外显子部分其组分复杂度都比较接近 ,而非编码区部分的组分复杂度却很大 .这一点定量地说明了物种之间的复杂程度 ,主要不体现在编码区部分 ,而体现在非编码区部分 .b 同一基因组中 ,内含子的核苷酸短序列组分复杂度都是相似的 ,外显子和intergenicDNA部分的组分复杂度也是相似的 .c 内含子和intergenicDNA在转录、剪切、二级结构等方面有很大的不同 ,但它们在核苷酸短序列组分上的差异却很小 ,说明内含子和intergenicDNA在转录、剪切、二级结构上的不同并不通过核苷酸短序列组分来进行限制 .

基于混沌游走方法的Rh血型系统中RHD基因的分析

利用基于经典HP模型的蛋白质序列混沌游走方法(chaos game representation,CGR),给出了RHD基因的蛋白质序列CGR图,可视作蛋白质序列二级结构的一个特征图谱描述,对临床上的血型鉴别有一定的参考价值.另外,还根据由Jeffrey在1990年提出的描绘DNA序列的CGR方法,给出了RHD基因的DNA序列的CGR图,并且根据RHD基因DNA序列的CGR图算出了RHD基因相应的马尔可夫两步转移概率矩阵,从概率矩阵表可以看出RHD基因对编码氨基酸的三联子的第3个碱基的使用偏好性.

蛋白质序列混沌游戏表示模拟效果的优化

蛋白质序列的可视化表示——混沌游戏表示呈现出明显的分形特征.根据分形的产生机理,可以用递归迭代函数系统很好地模拟蛋白质序列的混沌游戏表示.在实验中发现,其模拟效果可以进一步优化,可能有助于更准确地进行物种亲缘关系的分析.

Early-warning signals for an outbreak of the influenza pandemic

Over the course of human history, influenza pandemics have been seen as major disasters, so studies on the influenza virus have become an important issue for many experts and scholars. Comprehensive research has been performed over the years on the biological properties, chemical characteristics, external environmental factors and other aspects of the virus, and some results have been achieved. Based on the chaos game representation walk model, this paper uses the time series analysis method to study the DNA sequences of the influenza virus from 1913 to 2010, and works out the early-warning signals indicator value for the outbreak of an influenza pandemic. The variances in the CCR wall〈 sequences for the pandemic years （or ＋ -1 to 2 years） are significantly higher than those for the adjacent years, while those in the non-pandemic years are usually smaller. In this way we can provide an influenza early-warning mechanism so that people can take precautions and be well prepared prior to a pandemic.

一种基于混沌游走表示法的种系发生树构建

针对生物信息学领域中种系发生树构建这一重要课题的需要,利用DNA碱基序列的频度混沌游走表示法,提出一种碱基序列自重复性的度量和一种序列间相关性的度量,并由此出发,提出了一种新的以此种相关性为依据的聚类方法。利用这样的方法,通过GenBank中获取的线粒体DNA数据构建了一棵包含20个物种的种系发生树。实验结果验证了新提出的度量方法以及聚类方法在种系发生树构建问题上的有效性。此外,由于这种方法使用碱基序列的图形表示法,而非传统的串形表示法,避免了建树过程中序列间联配的步骤。

基于DNA序列混沌游戏表示的相似性分析

基于DNA序列的混沌游戏表示,利用对应测度矩阵的最大特征值组成的6维向量来刻画DNA序列,并利用向量间的相关距离对11种物种的beta球蛋白基因的第1个外显子编码序列进行相似性分析,所得结果与生物学中的进化关系基本一致.

蛋白质序列的多重分形性质及其Rényi熵率

一系列DNA和蛋白质序列的可视化研究通过几何图像形式展现了序列结构,从CGR到k串理论,只是通过迭代法把相应的碱基或氨基酸转化成数值,进而绘制成图形,没有对应的严格数学理论支持.文中将分形理论与信息论方法相结合,把蛋白质混沌游走表示法的多重分形维数和符号序列的Rényi熵率之间通过概率测度μ建立对应关系,从而使蛋白质序列的研究转为符号序列的可视化分析,在生物信息学上具有一定的应用前景.

递归迭代函数系统对DNA序列可视化表示的模拟

DNA序列的可视化表示——混沌游戏表示(CGR)呈现出了分形特征.根据分形的产生机理,文章用递归迭代函数系统(RIFS)模型模拟了DNA序列的混沌游戏表示,并通过比较递归迭代函数系统的吸引子的不变测度与混沌游戏表示的测度之间的差异,得出该方法对DNA序列的混沌游戏表示的逼近效果良好这一结论.基于该方法,人们可以对DNA序列的混沌游戏表示作进一步的分析.

甲型流感病毒DNA序列的长记忆ARFIMA模型

流感病毒分为三类:甲型(A型),乙型(B型),丙型(C型).在这三种类型中甲型(A型)流感病毒是最致命的流感病毒,对人类引起了严重疾病.本文对甲型流感病毒DNA序列建立了一种新的时间序列模型,即CGR(Chaos Game Representation)弧度序列.利用CGR坐标将甲流病毒DNA序列转换成CGR弧度序列,且引入长记忆ARFIMA模型去拟合此类序列,发现随机找来的10条H1N1序列,10条H3N2序列都具有长相关性且拟合很好,并且还发现这两种序列可以尝试用不同的ARFIMA模型去识别,其中H1N1可用ARFIMA(0,d,5)模型去识别,H3N2可用ARFIMA(1,d,1)模型去识别.

流感大爆发的多重早期预警信号

基于CGR-混沌游走模型,本文对选取自1913-2012年的流感病毒HA蛋白质序列用时间序列方法来研究,从而得出流感大爆发的早期预警信号的多重指标值.基于详细HP模型先对蛋白质序列建立CGR-混沌游走模型,再求方差、延迟2自相关系数,发现大流行年(-+1至2年)的混沌游走序列的方差和自相关系数都明显高于相邻年,而在非大流行年它们通常较小.