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Whole-proteome based phylogenetic tree construction with inter-amino-acid distances and the conditional geometric distribution profiles

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Molecular phylogenetics and evolution 2015年 89卷 37-45页

作者： Xian-Hua Xie Zu-Guo Yu Guo-Sheng Han Wei-Feng Yang Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 PR China School of Mathematics and Computer Science Gannan Normal University Jiangxi 341000 PR China. Electronic address: xxianhua@***. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QLD 4001 Australia. Electronic address: yuzuguo@***. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 PR China. Electronic address: korea10282003@***. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 PR China. Electronic address: yangweifeng09@***. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QLD 4001 Australia. Electronic address: v.anh@qut.edu.au.

There has been a growing interest in alignment-free methods for whole genome comparison and phylogenomic studies. In this study, we propose an alignment-free method for phylogenetic tree construction using whole-proteome sequences. Based on the inter-amino-acid distances, we first convert the whole-proteome sequences into inter-amino-acid distance vectors, which are called observed inter-amino-acid distance profiles. Then, we propose to use conditional geometric distribution profiles (the distributions of sequences where the amino acids are placed randomly and independently) as the reference distribution profiles. Last the relative deviation between the observed and reference distribution profiles is used to define a simple metric that reflects the phylogenetic relationships between whole-proteome sequences of different organisms. We name our method inter-amino-acid distances and conditional geometric distribution profiles (IAGDP). We evaluate our method on two data sets: the benchmark dataset including 29 genomes used in previous published papers, and another one including 67 mammal genomes. Our results demonstrate that the new method is useful and efficient.

关键词： Alignment-free whole-proteome comparison Conditional geometric distribution profile Inter-amino-acid distances Phylogenetic tree

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Current Bioinformatics 2014年第3期9卷 218-227页

作者： Chen, Xiao-Su Yu, Zu-Guo Zheng, Juan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 BrisbaneQ 4001 Australia School of Information and Engineering Xiangtan University Hunan411105 China

Whole genome sequences are generally accepted as excellent tools for studying evolutionary relationships. Due to the problems caused by the uncertainty in alignment, existing tools for phylogenetic analysis based on multiple alignments could not be directly applied to the whole-genome comparison and phylogenomic studies. There has been a growing interest in alignment-free methods for phylogenetic analysis using complete genome data. The "distances" used in these alignment-free methods are not proper distance metrics in the strict mathematical sense. In this study, we first review them in a more general frame — dissimilarity. Then we propose some new dissimilarities for phylogenetic analysis. Last three genome datasets are employed to evaluate these dissimilarities from a biological point of view. © 2014 Bentham Science Publishers.

关键词： Alignment

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Determination of multifractal dimensions of complex networks by means of the sandbox algorithm

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Chaos 2015年第2期25卷 023103页

作者： Liu, Jin-Long Yu, Zu-Guo Anh, Vo Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

Complex networks have attracted much attention in diverse areas of science and technology. Multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we employ the sandbox (SB) algorithm proposed by Tél et al. (Physica A 159, 155-166 (1989)), for MFA of complex networks. First, we compare the SB algorithm with two existing algorithms of MFA for complex networks: the compact-box-burning algorithm proposed by Furuya and Yakubo (Phys. Rev. E 84, 036118 (2011)), and the improved box-counting algorithm proposed by Li et al. (J. Stat. Mech.: Theor. Exp. 2014, P02020 (2014)) by calculating the mass exponents ?(q) of some deterministic model networks. We make a detailed comparison between the numerical and theoretical results of these model networks. The comparison results show that the SB algorithm is the most effective and feasible algorithm to calculate the mass exponents ?(q) and to explore the multifractal behavior of complex networks. Then, we apply the SB algorithm to study the multifractal property of some classic model networks, such as scale-free networks, small-world networks, and random networks. Our results show that multifractality exists in scale-free networks, that of small-world networks is not obvious, and it almost does not exist in random networks. © 2015 AIP Publishing LLC.

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Secondary structure element alignment kernel method for prediction of protein structural classes

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Current Bioinformatics 2014年第3期9卷 253-257页

作者： Han, Guo-Sheng Yu, Zu-Guo Anh, Vo Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q 4001 Australia

In this paper, we aim at predicting protein structural classes for low-homology data sets based on predicted secondary structures. We propose a new and simple kernel method, named as SSEAKSVM, to predict protein structural classes. The secondary structures of all protein sequences are obtained by using the tool PSIPRED and then a linear kernel on the basis of secondary structure element alignment scores is constructed for training a support vector machine classifier without parameter adjusting. Our method SSEAKSVM was evaluated on two low-homology datasets 25PDB and 1189 with sequence homology being 25% and 40%, respectively. The jackknife test is used to test and compare our method with other existing methods. The overall accuracies on these two data sets are 86.3% and 84.5%, respectively, which are higher than those obtained by other existing methods. Especially, our method achieves higher accuracies (88.1% and 88.5%) for differentiating the α+ β class and the α/β class compared to other methods. This suggests that our method is valuable to predict protein structural classes particularly for low-homology protein sequences. The source code of the method in this paper can be downloaded at http://***/myphp/math/research/source/SSEAK_source_***. © 2014 Bentham Science Publishers.

关键词： Support vector machines

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Multifractal analysis of weighted networks by a modified sandbox algorithm

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Scientific reports 2015年第1期5卷 17628页

作者： Yu-Qin Song Jin-Long Liu Zu-Guo Yu Bao-Gen Li Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China. College of Science Hunan University of technology Zhuzhou Hunan 412007 China. School of Mathematical Sciences Queensland University of Technology Brisbane Q4001 Australia.

Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks. First, we use the SBw algorithm to study the multifractal property of two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor dust" WFNs. We also discuss how the fractal dimension and generalized fractal dimensions change with the edge-weights of the WFN. From the comparison between the theoretical and numerical fractal dimensions of these networks, we can find that the proposed SBw algorithm is efficient and feasible for MFA of weighted networks. Then, we apply the SBw algorithm to study multifractal properties of some real weighted networks - collaboration networks. It is found that the multifractality exists in these weighted networks, and is affected by their edge-weights.

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Laplacian normalization and random walk on heterogeneous networks for disease-gene prioritization

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Computational biology and chemistry 2015年 57卷 21-8页

作者： Zhi-Qin Zhao Guo-Sheng Han Zu-Guo Yu Jinyan Li Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China. Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia. Electronic address: yuzg1970@***. Advanced Analytics Institute & Centre for Health Technologies University of Technology Sydney Broadway NSW 2007 Australia. Electronic address: jinyan.li@uts.edu.au.

Random walk on heterogeneous networks is a recently emerging approach to effective disease gene prioritization. Laplacian normalization is a technique capable of normalizing the weight of edges in a network. We use this technique to normalize the gene matrix and the phenotype matrix before the construction of the heterogeneous network, and also use this idea to define the transition matrices of the heterogeneous network. Our method has remarkably better performance than the existing methods for recovering known gene-phenotype relationships. The Shannon information entropy of the distribution of the transition probabilities in our networks is found to be smaller than the networks constructed by the existing methods, implying that a higher number of top-ranked genes can be verified as disease genes. In fact, the most probable gene-phenotype relationships ranked within top 3 or top 5 in our gene lists can be confirmed by the OMIM database for many cases. Our algorithms have shown remarkably superior performance over the state-of-the-art algorithms for recovering gene-phenotype relationships. All Matlab codes can be available upon email request.

关键词： Disease genes and phenotypes Heterogeneous network Laplacian normalization Leave-one-out cross-validation Random walk with restart Shannon information entropy

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Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

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Physical Review E 2014年第3期89卷 032814-032814页

作者： Jin-Long Liu Zu-Guo Yu Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2−H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic

关键词： TOPOLOGICAL property FRACTAL analysis BROWNIAN motion CORRELATION (Statistics) RECURSIVE sequences (Mathematics) COMPUTER networks

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Fractal and complex network analyses of protein molecular dynamics

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Physica A: Statistical Mechanics and its Applications 2014年 416卷 21-32页

作者： Yuan-Wu Zhou Jin-Long Liu Zu-Guo Yu Zhi-Qin Zhao Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China Civil Construction Engineering Department Guangxi University of Science and Technology Liuzhou 545006 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

Based on protein molecular dynamics, we investigate the fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuation analysis (MF-DFA) and the topological and fractal properties of their converted horizontal visibility graphs (HVGs). The energy parameters of protein dynamics we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. The shape of the h ( q ) curves from MF-DFA indicates that these time series are multifractal. The numerical values of the exponent h ( 2 ) of MF-DFA show that the series of total energy and potential energy are non-stationary and anti-persistent; the other time series are stationary and persistent apart from series of pressure (with H ≈ 0.5 indicating the absence of long-range correlation). The degree distributions of their converted HVGs show that these networks are exponential. The results of fractal analysis show that fractality exists in these converted HVGs. For each energy, pressure or volume parameter, it is found that the values of h ( 2 ) of MF-DFA on the time series, exponent λ of the exponential degree distribution and fractal dimension d B of their converted HVGs do not change much for different proteins (indicating some universality). We also found that after taking average over all proteins, there is a linear relationship between 〈 h ( 2 ) 〉 (from MF-DFA on time series) and 〈 d B 〉 of the converted HVGs for different energy, pressure and volume.

关键词： Protein molecular dynamics Multifractal detrended fluctuation analysis Horizontal visibility graph Fractal analysis Degree distribution

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Fractal and multifractal properties of a family of fractal networks

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Journal of Statistical Mechanics: Theory and Experiment 2014年第2期2014卷

作者： Li, Bao-Gen Yu, Zu-Guo Zhou, Yu Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan HUNAN 411105 China School of Mathematical Sciences Queensland University of Technology Brisbane GPO Box 2434 Q4001 Australia

In this work, we study the fractal and multifractal properties of a family of fractal networks introduced by Gallos et al (2007 Proc. Nat. Acad. Sci. USA 104 7746). In this fractal network model, there is a parameter e which is between 0 and 1, and allows for tuning the level of fractality in the network. Here we examine the multifractal behavior of these networks, the dependence relationship of the fractal dimension and the multifractal parameters on parameter e. First, we find that the empirical fractal dimensions of these networks obtained by our program coincide with the theoretical formula given by Song et al (2006 Nature Phys. 2 275). Then from the shape of the τ(q) and D(q) curves, we find the existence of multifractality in these networks. Last, we find that there exists a linear relationship between the average information dimension D(1) and the parameter e. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

关键词： network dynamics networks random graphs

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A directed continuous time random walk model with jump length depending on waiting time

The Scientific World Journal

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The Scientific World Journal 2014年第1期2014卷 182508页

作者： Shi, Long Yu, Zuguo Mao, Zhi Xiao, Aiguo Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China Institute of Mathematics and Physics Central South University of Forest and Technology Changsha Hunan 410004 China School of Mathematical Sciences Queensland University of Technology Brisbane QLD 4001 G.P.O. Box 2434 Australia

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P (x, t) of finding the walker at position x at time t is completely determined by the Laplace transform of the probability density function (t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived. © 2014 Long Shi et al.

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