Polymerase chain reaction: a Markov process approach

A probabilistic approach to the kinetics of the polymerase chain reaction (PCR) is developed. The approach treats the primer extension step of PCR as a microscopic Markov process in which the molecules of deoxy-nucleoside triphosphate (dNTP) are bound to the 3' end of the primer strand one at a time. The binding probability rates are prescribed by combinatorial rules in accord with the microscopic chemical kinetics. As an example, a simple model based on this approach is proposed and analysed, and an exact solution for the probability distribution of lengths of synthesized DNA strands is found by analytical means. Using this solution, it is demonstrated that the model is able to reproduce the main features of PCR, such as extreme sensitivity to the variation of control parameters and the existence of an amplification plateau. A multidimensional optimization technique is used to find numerically the optimum values of control parameters which maximize the yield of the target sequence for a given PCR run while minimizing the overall run time.     

Polymerase chain reaction and its applications: special emphasis on its role in embryo sexing

The polymerase chain reaction (PCR) has developed into one of the most promising methods for in vitro enzymatic amplification of DNA and has found widespread application in DNA cloning, sequencing and mutagenesis related studies. This innovative technique can selectively amplify a single target DNA molecule a billion-fold in a span of a few hours. Amplification of specific DNA sequences by PCR is useful in identification of sex, novel genes, pathogens and diseases. PCR has facilitated the establishment of evolutionary relationships among species and in revealing structural intricacies of single cells. In this article we review some of the major advances and applications of PCR, especially, its role in embryo sexing.     

Bayesian restoration of a hidden Markov chain with applications to DNA sequencing.

Hidden Markov models (HMMs) are a class of stochastic models that have proven to be powerful tools for the analysis of molecular sequence data. A hidden Markov model can be viewed as a black box that generates sequences of observations. The unobservable internal state of the box is stochastic and is determined by a finite state Markov chain. The observable output is stochastic with distribution determined by the state of the hidden Markov chain. We present a Bayesian solution to the problem of restoring the sequence of states visited by the hidden Markov chain from a given sequence of observed outputs. Our approach is based on a Monte Carlo Markov chain algorithm that allows us to draw samples from the full posterior distribution of the hidden Markov chain paths. The problem of estimating the probability of individual paths and the associated Monte Carlo error of these estimates is addressed. The method is illustrated by considering a problem of DNA sequence multiple alignment. The special structure for the hidden Markov model used in the sequence alignment problem is considered in detail. In conclusion, we discuss certain interesting aspects of biological sequence alignments that become accessible through the Bayesian approach to HMM restoration.     

A ratio-dependent food chain model and its applications to biological control

While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics. Two trophic level Michaelis-Menten type ratio-dependent predator-prey system was globally and systematically analyzed in details recently. A distinct and realistic feature of ratio-dependence is its capability of producing the extinction of prey species, and hence the collapse of the system. Another distinctive feature of this model is that its dynamical outcomes may depend on initial populations levels. Theses features, if preserved in a three trophic food chain model, make it appealing for modelling certain biological control processes (where prey is a plant species, middle predator as a pest, and top predator as a biological control agent) where the simultaneous extinctions of pest and control agent is the hallmark of their successes and are usually dependent on the amount of control agent. Our results indicate that this extinction dynamics and sensitivity to initial population levels are not only preserved, but also enriched in the three trophic level food chain model. Specifically, we provide partial answers to questions such as: under what scenarios a potential biological control may be successful, and when it may fail. We also study the questions such as what conditions ensure the coexistence of all the three species in the forms of a stable steady state and limit cycle, respectively. A multiple attractor scenario is found.     

One-pot fusion polymerase chain reaction for combinatorial synthesis of DNA from several cassettes

The fusion of DNA fragments is becoming increasingly more important. The ability to work without being constrained by restriction sites enables DNA fusion to be applied to a much broader range of fragments. Therefore, we describe a simplified polymerase chain reaction (PCR)-based method for fusion of DNA fragments in one step. In a single PCR, two templates, an overlapping primer, and template-specific forward and reverse primers are used. After a few cycles, the fusion DNA is assembled and is amplified. The ratio of overlapping primer to forward/reverse primers and template DNA is essential for the success of the reaction.     

Recent applications of olefin metathesis to combinatorial chemistry

Olefin metathesis has emerged as a versatile technology for the synthesis of combinatorial libraries with regard to both scaffold creation and embellishment. The incessant pursuit of 'next-generation' catalysts continues to raise the bar in terms of efficiency, functional group tolerability, diminished reaction times and temperatures and has helped foster both diversity-oriented and target-directed efforts. This report summarizes recent contributions in the area of olefin cross-metathesis and ring-closing metathesis as applied to combinatorial and parallel synthesis. These examples include generation of dimeric benzo[b]furans as novel probes for protein-protein interaction, a cross-metathesis approach to 'traceless linkers' for azide-containing sugars, stereo-diversified synthesis of 1,4- and 1,5-enediols, a novel mannitol derived combinatorial scaffold, parallel synthesis strategies for aza-sugars, as well as the synthesis of dehydro-Freidinger lactams.     

任意引物PCR及其应用研究进展

任意引物PCR技术又称为随机扩增多态性DNA技术,它是在PCR技术基础上发展起来的一项分子检测技术。它具有简便、快速,一套引物可用于多个物种的分析,不需预知分析对象的核酸序列,可以显示差异表达基因等特点,已广泛应用于病原微生物的分型鉴定、物种亲源关系分析、遗传育种研究和特异表达基因的克隆与鉴定等方面。     

耐热DNA连接酶介导的TLCR技术在简化DNA重组实验中的应用

传统的DNA重组方法Type Ⅱ型限制酶技术受到片段纯化的限制,无法做到复杂混合体系中DNA片段的特异性连接。为解决这个问题,本研究将耐热连接酶链式反应(Thermostable ligase chain reaction, TLCR)引入DNA片段的连接与捕获。该技术利用耐热型DNA连接酶的特性,在热循环反应中配合针对目的片段末端序列设计的单链寡核苷酸连接模板--Helper,实现目的片段的特异性连接和产物数量的指数性增长。两个质粒构建实验被用于验证TLCR技术的可行性和应用效果。首先利用TLCR技术从一个未经纯化的含有7种不同大小片段的混杂体系中特异性地将一段1.5 kb的片段捕获进载体,随机抽取的克隆样品经检验准确率达到80%,验证TLCR技术在复杂混合体系中特异性连接DNA片段的可行性和准确性。在另一个质粒构建实验中,TLCR技术从λ噬菌体基因组Hind消化物中将两段总长达27 kb的片段按顺序捕获进载体,随机抽取的克隆样品经检验同样达到了80%的准确率。结果表明,TLCR技术能够简化DNA重组实验的操作,并且适用于多片段和大片段的连接,可以为生物学研究提供便利。     

An improved hidden Markov model for transmembrane protein detection and topology prediction and its applications to complete genomes

MOTIVATION: Knowledge of the transmembrane helical topology can help identify binding sites and infer functions for membrane proteins. However, because membrane proteins are hard to solubilize and purify, only a very small amount of membrane proteins have structure and topology experimentally determined. This has motivated various computational methods for predicting the topology of membrane proteins. RESULTS: We present an improved hidden Markov model, TMMOD, for the identification and topology prediction of transmembrane proteins. Our model uses TMHMM as a prototype, but differs from TMHMM by the architecture of the submodels for loops on both sides of the membrane and also by the model training procedure. In cross-validation experiments using a set of 83 transmembrane proteins with known topology, TMMOD outperformed TMHMM and other existing methods, with an accuracy of 89% for both topology and locations. In another experiment using a separate set of 160 transmembrane proteins, TMMOD had 84% for topology and 89% for locations. When utilized for identifying transmembrane proteins from non-transmembrane proteins, particularly signal peptides, TMMOD has consistently fewer false positives than TMHMM does. Application of TMMOD to a collection of complete genomes shows that the number of predicted membrane proteins accounts for approximately 20-30% of all genes in those genomes, and that the topology where both the N- and C-termini are in the cytoplasm is dominant in these organisms except for Caenorhabditis elegans. AVAILABILITY: http://liao.cis.udel.edu/website/servers/TMMOD/     

Hydrazine-induced post-chemiluminescence phenomenon of permanganate-luminol reaction and its applications.

The post-chemiluminescence phenomenon arising from the permanganate-luminol reaction induced by hydrazine and isoniazid was investigated. When hydrazine or isoniazid was injected into the mixture after the end of the reaction of permanganate with alkaline luminol, a new chemiluminescence (CL) reaction was initiated and strong CL signal was detected. A possible CL mechanism is suggested, based upon the studies of the kinetic characteristics of the CL reaction, the UV-visible spectra, the CL spectra and some other experiments. The present reactions allow the determination of 0.1-10.0 mg/L hydrazine and 0.02-1.0 mg/L isoniazid, with detection limits of 0.03 mg/L and 0.006 mg/L, respectively. The method was applied to the determination of isoniazid in pharmaceutical preparations.     

Kullback-Leibler Markov chain Monte Carlo--a new algorithm for finite mixture analysis and its application to gene expression data

In this paper, we study Bayesian analysis of nonlinear hierarchical mixture models with a finite but unknown number of components. Our approach is based on Markov chain Monte Carlo (MCMC) methods. One of the applications of our method is directed to the clustering problem in gene expression analysis. From a mathematical and statistical point of view, we discuss the following topics: theoretical and practical convergence problems of the MCMC method; determination of the number of components in the mixture; and computational problems associated with likelihood calculations. In the existing literature, these problems have mainly been addressed in the linear case. One of the main contributions of this paper is developing a method for the nonlinear case. Our approach is based on a combination of methods including Gibbs sampling, random permutation sampling, birth-death MCMC, and Kullback-Leibler distance.     

Drifting Markov models with polynomial drift and applications to DNA sequences

In this article, we introduce the drifting Markov models (DMMs) which are inhomogeneous Markov models designed for modeling the heterogeneities of sequences (in our case DNA or protein sequences) in a more flexible way than homogeneous Markov chains or even hidden Markov models (HMMs). We focus here on the polynomial drift: the transition matrix varies in a polynomial way. To show the reliability of our models on DNA, we exhibit high similarities between the probability distributions of nucleotides obtained by our models and the frequencies of these nucleotides computed by using a sliding window. In a further step, these DMMs can be used as the states of an HMM: on each of its segments, the observed process can be modeled by a drifting Markov model. Search of rare words in DNA sequences remains possible with DMMs and according to the fits provided, DMMs turn out to be a powerful tool for this purpose. The software is available on request from the author. It will soon be integrated on seq++ library (http://stat.genopole.cnrs.fr/seqpp/).     

Microsatellite mutations during the polymerase chain reaction: mean field approximations and their applications

We develop a novel mathematical model for microsatellite mutations during polymerase chain reaction (PCR). Based on the model, we study the first- and second-order moments of the number of repeat units in a randomly chosen molecule after n PCR cycles and their corresponding mean field approximations. We give upper bounds for the approximation errors and show that the approximation errors are small when the mutation rate is low. Based on the theoretical results, we develop a moment estimation method to estimate the mutation rate per-repeat-unit per PCR cycle and the probability of expansion when mutations occur. Simulation studies show that the moment estimation method can accurately recover the true mutation rate and probability of expansion. Finally, the method is applied to experimental data from single-molecule PCR experiments.     

A stochastic Markov chain model to describe lung cancer growth and metastasis

A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.