An Inhomogeneous Markov Model to Fit the Migration Process

In this paper we study the migration process considering an inhomogeneous Markov model. This is a certain condition to investigate age-dependent population distributions, where the transition probabilities are not constant. We consider also a death process for a population alive in a region at age t and, as a result of this, combined transition probabilities between the states of the concerning Markov chain. The model has non-stationary distribution for t →∞, because the condition of ergodicity does not hold.     

变时滞SIS流行病模型的稳定性分析

研究了一类时滞SIS流行病模型,分析了该模型无病平衡点和地方平衡点的存在性,得到了无病平衡点全局指数渐近稳定和地方病平衡点局部指数渐近稳定的充分条件,同时给出了地方病平衡点吸引区域的估计。     

KL距离的变长马尔可夫模型识别人类剪接位点

针对传统基因剪接位点识别方法具有所用到的序列长,且参数多的问题,论文提出了一种基于KL距离的变长马尔可夫模型(Kullback Leibler divergence-variable length Markovmodel,KL-VLMM)。该模型在变长马尔可夫模型的基础上进行改进,由KL距离代替原来的概率比值来判断序列扩展的方向,有效地提高了特征序列的识别能力,且模型阶数由二阶降为一阶,降低了算法的空间复杂度。利用人类剪接位点数据库N269,对该模型和其他传统方法的识别性能进行了比较。实验结果表明,采用KL-VLMM方法预测人类基因剪接位点的预测效果更好。     

The Effect of Parameters Change of a Semi-Markov Model on Interval Transition Probabilities

This paper examines the changes in parameters of a Semi-Markov model and its impact on interval transition probabilities. Computational techniques are used to illustrate that the model is sensitive enough to depict changes in the interval transition probabilities if the paramters of the model are modified.     

HumGene:一个基于GHMM的人类基因预测软件

HumGene是一个采用广义隐Markov模型(GHMM)的人类基因预测软件.利用人类基因的结构特点,采用概率模型为基因结构中各个特定区域建立了独立的子模型,能够获得全局统一的评价指数,使得系统整体框架具有一定的扩展性.采用一种新的简化算法,有效地降低了计算的复杂度.介绍了软件的构成,对软件进行了测试,给出了与其它类似软件的结果比较.     

Bias in Markov models of disease

We examine bias in Markov models of diseases, including both chronic and infectious diseases. We consider two common types of Markov disease models: ones where disease progression changes by severity of disease, and ones where progression of disease changes in time or by age. We find sufficient conditions for bias to exist in models with aggregated transition probabilities when compared to models with state/time dependent transition probabilities. We also find that when aggregating data to compute transition probabilities, bias increases with the degree of data aggregation. We illustrate by examining bias in Markov models of Hepatitis C, Alzheimer’s disease, and lung cancer using medical data and find that the bias is significant depending on the method used to aggregate the data. A key implication is that by not incorporating state/time dependent transition probabilities, studies that use Markov models of diseases may be significantly overestimating or underestimating disease progression. This could potentially result in incorrect recommendations from cost-effectiveness studies and incorrect disease burden forecasts.     

A Markov Chain Model of Population Growth with an Application in Epidemiology

This paper is concerned with a class of population growth processes in discrete time; the simple epidemic process is considered as a specific example. A Markov chain model is constructed and standard Markov methods are used to study the main biological concepts. A simple and explicit formula is obtained for the transient distribution of the population size. Then, the cost of the process is defined and the joint probability generating function of its components is derived. Finally, the results are extended to the case where the inter-transition periods are bounded i.i.d. random variables.     

MicroRNA target prediction based on second-order Hidden Markov Model

MicroRNAs are one class of small single-stranded RNA of about 22 nt serving as important negative gene regulators. In animals, miRNAs mainly repress protein translation by binding itself to the 3′ UTR regions of mRNAs with imperfect complementary pairing. Although bioinformatics investigations have resulted in a number of target prediction tools, all of these have a common shortcoming—a high false positive rate. Therefore, it is important to further filter the predicted targets. In this paper, based on miRNA:target duplex, we construct a second-order Hidden Markov Model, implement Baum-Welch training algorithm and apply this model to further process predicted targets. The model trains the classifier by 244 positive and 49 negative miRNA:target interaction pairs and achieves a sensitivity of 72.54%, specificity of 55.10% and accuracy of 69.62% by 10-fold cross-validation experiments. In order to further verify the applicability of the algorithm, previously collected datasets, including 195 positive and 38 negative, are chosen to test it, with consistent results. We believe that our method will provide some guidance for experimental biologists, especially in choosing miRNA targets for validation.     

Detection of Short Protein Coding Regions within the Cyanobacterium Genome: Application of the Hidden Markov Model

The gene-finding programs developed so far have not paid muchattention to the detection of short protein coding regions (CDSs).However, the detection of short CDSs is important for the studyof photosynthesis. We utilized GeneHacker, a gene-finding programbased on the hidden Markov model (HMM), to detect short CDSs(from 90 to 300 bases) in a 1.0 mega contiguous sequence ofcyanobacterium Synechocystis sp. strain PCC6803 which carriesa complete set of genes for oxygenic photosynthesis. GeneHackerdiffers from other gene-finding programs based on the HMM inthat it utilizes di-codon statistics as well. GeneHacker successfullydetected seven out of the eight short CDSs annotated in thissequence and was clearly superior to GeneMark in this rangeof length. GeneHacker detected 94 potentially new CDSs, 9 ofwhich have counterparts in the genetic databases. Four of thenine CDSs were less than 150 bases and were photosynthesis-relatedgenes. The results show the effectiveness of GeneHacker in detectingvery short CDSs corresponding to genes.     

Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors

In many cell types, the inositol trisphosphate receptor (IPR) is one of the important components that control intracellular calcium dynamics, and an understanding of this receptor (which is also a calcium channel) is necessary for an understanding of calcium oscillations and waves. Recent advances in experimental techniques now allow for the measurement of single-channel activity of the IPR in conditions similar to its native environment, and these data can be used to determine the rate constants in Markov models of the IPR. We illustrate a parameter estimation method based on Markov chain Monte Carlo, which can be used to fit directly to single-channel data, and determining, as an intrinsic part of the fit, the times at which the IPR is opening and closing. We show, using simulated data, the most complex Markov model that can be unambiguously determined from steady-state data and show that non-steady-state data is required to determine more complex models.     

An approach to determine myocardial ischemia by hidden Markov models

A hidden Markov model (HMM) of electrocardiogram (ECG) signal is presented for detection of myocardial ischemia. The time domain signals that are recorded by the ECG before and during the episode of local ischemia were pre-processed to produce input sequences, which is needed for the model training. The model is also verified by test data, and the results show that the models have certain function for the detection of myocardial ischemia. The algorithm based on HMM provides a possible approach for the timely, rapid and automatic diagnosis of myocardial ischemia, and also can be used in portable medical diagnostic equipment in the future.     

广义隐Markov模型在基因识别中的应用

广义隐Markov模型(GHMM)是基因识别的一种重要模型,但是其计算量比传统的隐Markov模型大得多,以至于不能直 接在基因识别中使用。根据原核生物基因的结构特点,提出了一种高效的简化算法,其计算量是序列长度的线性函数。在此 基础上,构建了针对原核生物基因的识别程序GeneMiner,对实际数据的测试表明,此算法是有效的。     

Comparison of glycosyltransferase families using the profile hidden Markov model

In order to investigate the relationship between glycosyltransferase families and the motif for them, we classified 47 glycosyltransferase families in the CAZy database into four superfamilies, GTS-A, -B, -C, and -D, using a profile Hidden Markov Model method. On the basis of the classification and the similarity between GTS-A and nucleotidylyltransferase family catalyzing the synthesis of nucleotide-sugar, we proposed that ancient oligosaccharide might have been synthesized by the origin of GTS-B whereas the origin of GTS-A might be the gene encoding for synthesis of nucleotide-sugar as the donor and have evolved to glycosyltransferases to catalyze the synthesis of divergent carbohydrates. We also suggested that the divergent evolution of each superfamily in the corresponding subcellular component has increased the complexities of eukaryotic carbohydrate structure.     

The analysis of disease biomarker data using a mixed hidden Markov model (Open Access publication)

A mixed hidden Markov model (HMM) was developed for predicting breeding values of a biomarker (here, somatic cell score) and the individual probabilities of health and disease (here, mastitis) based upon the measurements of the biomarker. At a first level, the unobserved disease process (Markov model) was introduced and at a second level, the measurement process was modeled, making the link between the unobserved disease states and the observed biomarker values. This hierarchical formulation allows joint estimation of the parameters of both processes. The flexibility of this approach is illustrated on the simulated data. Firstly, lactation curves for the biomarker were generated based upon published parameters (mean, variance, and probabilities of infection) for cows with known clinical conditions (health or mastitis due to Escherichia coli or Staphylococcus aureus). Next, estimation of the parameters was performed via Gibbs sampling, assuming the health status was unknown. Results from the simulations and mathematics show that the mixed HMM is appropriate to estimate the quantities of interest although the accuracy of the estimates is moderate when the prevalence of the disease is low. The paper ends with some indications for further developments of the methodology.     

Weighted relative entropy for phylogenetic tree based on 2-step Markov Model

The degree of similarity of DNA sequences can be concluded according to the comparison of DNA sequences, which helps to speculate their relationship in respect of the structure, function and evolution. In this paper, we introduce the fundamental of the weighted relative entropy based on 2-step Markov Model to compare DNA sequences. The DNA sequence, consisted of four characters A, T, C, G, can be considered as a Markov chain. By taking state space I = {A, T, C, G} and describe the DNA sequences with 2-step transition probability matrix we can get the eigenvalue of the DNA sequence to define the similarity metric. Therefore, we find a new method to compare the DNA sequences, which is used to classify chromosomes DNA sequences obtained from 30 species. The phylogenetic tree built by the alignment-free method of the distance matrix resulted from the weighted relative entropy has clearer and more accurate division.     

Prediction of Translation Initiation Sites on the Genome of Synechocystis sp. Strain PCC6803 by Hidden Markov Model

We developed a computer program, GeneHackerTL, which predictsthe most probable translation initiation site for a given nucleotidesequence. The program requires that information be extractedfrom the nucleotide sequence data surrounding the translationinitiation sites according to the framework of the Hidden MarkovModel. Since the translation initiation sites of 72 highly abundantproteins have already been assigned on the genome of Synechocystissp. strain PCC6803 by amino-terminal analysis, we extractednecessary information for GeneHackerTL from the nucleotide sequencedata. The prediction rate of the GeneHackerTL for these proteinswas estimated to be 86.1%. We then used GeneHackerTL for predictionof the translation initiation sites of 24 other proteins, ofwhich the initiation sites were not assigned experimentally,because of the lack of a potential initiation codon at the amino-terminalposition. For 20 out of the 24 proteins, the initiation siteswere predicted in the upstream of their amino-terminal positions.According to this assignment, the processed regions representa typical feature of signal peptides. We could also predictmultiple translation initiation sites for a particular genefor which at least two initiation sites were experimentallydetected. This program would be e.ective for the predictionof translation initiationsites of other proteins, not only inthis species but also in other prokaryotes as well.     

Markov Model of Haploid Random Mating with Given Distribution of Population Size

An exact Markov chain model is formulated and computed for random mating in a haploid gamete pool. There are two versions of the gamete, and there is a finite number of diploid monoecious organisms. The founder population is given, and the subsequent generations allow a prescribed statistical distribution over different population sizes. The non-homogeneous Markov chain works on the haploid gamete level provided the probability of self-fertilization is 1/n, where n is the number of diploid individuals. Standard deviations of gamete frequencies and fixation probabilities are calculated. Effective population sizes for different population size distributions are estimated, including periodic bottlenecks.     

基于序列拓扑和二阶隐马尔可夫模型的跨膜蛋白亚细胞定位预测

现有蛋白质亚细胞定位方法针对水溶性蛋白质而设计,对跨膜蛋白并不适用。而专门的跨膜拓扑预测器,又不是为亚细胞定位而设计的。文章改进了跨膜拓扑预测器TMPHMMLoc的模型结构,设计了一个新的二阶隐马尔可夫模型;采用推广到二阶模型的Baum-Welch算法估计模型参数,并把将各个亚细胞位置建立的模型整合为一个预测器。数据集上测试结果表明,此方法性能显著优于针对可溶性蛋白设计的支持向量机方法和模糊k最邻近方法,也优于TMPHMMLoc中提出的隐马尔可夫模型方法,是一个有效的跨膜蛋白亚细胞定位预测方法。