Mathematics analysis of polymerase chain reaction kinetic curves

The paper reviews different approaches to the mathematical analysis of polymerase chain reaction (PCR) kinetic curves. The basic principles of PCR mathematical analysis are presented. Approximation of PCR kinetic curves and PCR efficiency curves by various functions is described. Several PCR models based on chemical kinetics equations are suggested. Decision criteria for an optimal function to describe PCR efficiency are proposed.     

Automated polymerase chain reaction product sample preparation for capillary electrophoresis analysis

The analysis of crude polymerase chain reaction (PCR) products by capillary electrophoresis (CE) is often compromised due to the presence of a high concentration of salt. Salt interferes with the electrokinetic injection and induces localized heating within the column; hence, PCR products must be desalted or cleaned-up prior to CE analysis. A variety of commercial clean-up systems are available that have been traditionally used to prepare PCR products for cloning, sequencing and digestion with restriction enzymes. These systems were tested for their effectiveness in preparing PCR products for CE analysis and were evaluated based on CE resolution, salt removal, DNA recovery, processing time and cost. One particularly effective clean-up system, membrane dialysis, was automated using a robotic workstation.     

Automated polymerase chain reaction in capillary tubes with hot air.

We describe a simple, compact, inexpensive thermal cycler that can be used for the polymerase chain reaction. Based on heat transfer with air to samples in sealed capillary tubes, the apparatus resembles a recirculating hair dryer. The temperature is regulated via thermocouple input to a programmable set-point process controller that provides proportional output to a solid state relay controlling a heating coil. For efficient cooling after the denaturation step, the controller activates a solenoid that opens a door to vent hot air and allows cool air to enter. Temperature-time profiles and amplification results approximate those obtained using water baths and microfuge tubes.     

The polymerase chain reaction

The polymerase chain reaction (PCR) is a powerful new method for 'in vitro cloning'. It can selectively amplify a single molecule of template DNA several millionfold in a few hours and has made possible new approaches to problems in molecular genetics, evolutionary biology, and development.     

The polymerase chain reaction

This essay on the polymerase chain reaction is one of a series developed as part of FASEB's efforts to educate the general public, and the legislators whom it elects, about the benefits of fundamental biomedical research-particularly how investment in such research leads to scientific progress, improved health, and economic well-being.     

Miniaturization of polymerase chain reaction

Polymerase chain reaction (PCR) is one of the most widely used analytical tool and is an important module that would benefit from being miniaturized and integrated onto diagnostic or analytical chips. There are potentially two different approaches for the miniaturization of the PCR module: chamber-type and flow-type micro-PCR. These miniaturized PCRs have distinct characteristics and advantages. In this article, we review the necessity of micro-PCR, the materials for the chip fabrication, the surface modification, and characteristics of the two types of micro-PCR. The motivation underlying the development of micro-PCR, the advantages and disadvantages of the various materials used in fabrication and the surface modification methods will be discussed. And finally, the precise features of the two different types of micro-PCR will be compared.     

Computing by polymerase chain reaction

A mathematical notation is introduced to represent, at a symbolic level, different mechanisms of DNA recombination, and a 'PCR lemma' is proven by analytically describing the combinatorial properties of the polymerase chain reaction process. This approach led to the discovery of novel techniques, based on a form of PCR which we called cross pairing PCR (briefly XPCR). They were mathematically analyzed and already experimentally proven in different contexts, such as DNA extraction and recombination. Thus, a mathematical analysis of standard methodologies may highlight novel mechanisms of DNA recombination and this can provide new technologies for DNA manipulation.     

The real-time polymerase chain reaction

The scientific, medical, and diagnostic communities have been presented the most powerful tool for quantitative nucleic acids analysis: real-time PCR [Bustin, S.A., 2004. A-Z of Quantitative PCR. IUL Press, San Diego, CA]. This new technique is a refinement of the original Polymerase Chain Reaction (PCR) developed by Kary Mullis and coworkers in the mid 80:ies [Saiki, R.K., et al., 1985. Enzymatic amplification of beta-globin genomic sequences and restriction site analysis for diagnosis of sickle cell anemia, Science 230, 1350], for which Kary Mullis was awarded the 1993 year's Nobel prize in Chemistry. By PCR essentially any nucleic acid sequence present in a complex sample can be amplified in a cyclic process to generate a large number of identical copies that can readily be analyzed. This made it possible, for example, to manipulate DNA for cloning purposes, genetic engineering, and sequencing. But as an analytical technique the original PCR method had some serious limitations. By first amplifying the DNA sequence and then analyzing the product, quantification was exceedingly difficult since the PCR gave rise to essentially the same amount of product independently of the initial amount of DNA template molecules that were present. This limitation was resolved in 1992 by the development of real-time PCR by Higuchi et al. [Higuchi, R., Dollinger, G., Walsh, P.S., Griffith, R., 1992. Simultaneous amplification and detection of specific DNA-sequences. Bio-Technology 10(4), 413-417]. In real-time PCR the amount of product formed is monitored during the course of the reaction by monitoring the fluorescence of dyes or probes introduced into the reaction that is proportional to the amount of product formed, and the number of amplification cycles required to obtain a particular amount of DNA molecules is registered. Assuming a certain amplification efficiency, which typically is close to a doubling of the number of molecules per amplification cycle, it is possible to calculate the number of DNA molecules of the amplified sequence that were initially present in the sample. With the highly efficient detection chemistries, sensitive instrumentation, and optimized assays that are available today the number of DNA molecules of a particular sequence in a complex sample can be determined with unprecedented accuracy and sensitivity sufficient to detect a single molecule. Typical uses of real-time PCR include pathogen detection, gene expression analysis, single nucleotide polymorphism (SNP) analysis, analysis of chromosome aberrations, and most recently also protein detection by real-time immuno PCR.     

Real-time quantitative polymerase chain reaction

In Charcot-Marie-Tooth type 1A disease (CMTIA), heterozygosity for the peripheral myelin protein 22 (PMP22) duplication increases the gene dose from two to three, whereas, in hereditary neuropathy with liability to pressure palsies (HNPP), heterozygosity for the PMP22 deletion reduces the gene dose from two to one. Thirty-eight Norwegian patients with CMT1, 4 patients with HNPP, 15 asymptomatic family members, and 45 normal controls were studied using the ABI 7700 sequence detection system and the TaqMan method of real-time quantitative polymerase chain reaction (PCR). Using a comparative threshold cycle (Ct) method and albumin as reference gene, the gene copy number by PMP22 gene duplication or deletion on chromosome 17p11.2-12 was quantified. The PMP22 duplication ratio ranged from 1.50 to 2.21, the PMP22 deletion ratio ranged from 0.44 to 0.55, and the PMP22 ratio in normals ranged from 0.82 to 1.27. All samples were run in triplicate, with a mean standard deviation of 0.07 (range 0.01-0.17). Thirty-four of thirty-eight CMT1 patients (89.6%) had the PMP22 duplication and the four HNPP patients had the PMP22 deletion. This was not found in any of the asymptomatic family members or the controls. Real-time quantitative PCR is a sensitive, specific, and reproducible method for diagnosing PMP22 duplication and deletion. The method is fast, allowing 13 patients to be diagnosed in 2 h. It involves no radioisotopes and requires no post-PCR handling. In our opinion, real-time quantitative PCR is the first method of choice in diagnosing PMP22 duplication and deletion.     

Rapid differentiation of Old World Leishmania species by LightCycler polymerase chain reaction and melting curve analysis

A LightCycler real-time polymerase chain reaction (PCR) assay has been developed to detect and differentiate four of the main Leishmania species of the Old World. The assay is based on fluorescence melting curve analysis of PCR products generated from the minicircles of kinetoplast DNA. According to the melting temperature, which is a function of GC/AT ratio, length and nucleotide sequences of the amplified product, Leishmania major was differentiated from L. donovani and from L. tropica and L. infantum. Melting curves analysis offers a rapid alternative for identification of species in diagnostic or epidemiological studies of leishmaniasis or asymptomatic parasitism.     

Inhibitors of the polymerase chain reaction

The information on the applied aspects of the polymerase chain reaction (PCR) is updated. In particular, the main inhibitor of PCR, considerably decreasing the sensitivity of the method both at the lysis stage of the tested material and due to the degradation of the DNA matrix and primers and/or to the direct inhibition of the activity of DNA polymerase, are described. The compounds, most frequently distorting the course of the reaction while testing clinical blood samples, bioptic samples, sputum, etc., are characterized. Testing concrete clinical material with the use of PCR was shown to require differentiated approach both at the stage of choosing the adequate method for the preparation of samples and at all other stages, including, e.g., the corresponding DNA polymerases or at the stage of heating for decreasing endonuclease activity or for IgG denaturation. Information on the causes of false negative results of PCR and the variants of their elimination, useful under practical laboratory conditions, is given.     

Quantitative analysis of total mitochondrial DNA: competitive polymerase chain reaction versus real-time polymerase chain reaction

An efficient and effective method for quantification of small amounts of nucleic acids contained within a sample specimen would be an important diagnostic tool for determining the content of mitochondrial DNA (mtDNA) in situations where the depletion thereof may be a contributing factor to the exhibited pathology phenotype. This study compares two quantification assays for calculating the total mtDNA molecule number per nanogram of total genomic DNA isolated from human blood, through the amplification of a 613-bp region on the mtDNA molecule. In one case, the mtDNA copy number was calculated by standard competitive polymerase chain reaction (PCR) technique that involves co-amplification of target DNA with various dilutions of a nonhomologous internal competitor that has the same primer binding sites as the target sequence, and subsequent determination of an equivalence point of target and competitor concentrations. In the second method, the calculation of copy number involved extrapolation from the fluorescence versus copy number standard curve generated by real-time PCR using various dilutions of the target amplicon sequence. While the mtDNA copy number was comparable using the two methods (4.92 +/- 1.01 x 10(4) molecules/ng total genomic DNA using competitive PCR vs 4.90 +/- 0.84 x 10(4) molecules/ng total genomic DNA using real-time PCR), both inter- and intraexperimental variance were significantly lower using the real-time PCR analysis. On the basis of reproducibility, assay complexity, and overall efficiency, including the time requirement and number of PCR reactions necessary for the analysis of a single sample, we recommend the real-time PCR quantification method described here, as its versatility and effectiveness will undoubtedly be of great use in various kinds of research related to mitochondrial DNA damage- and depletion-associated disorders.     

Development of melting temperature-based SYBR Green I polymerase chain reaction methods for multiplex genetically modified organism detection

Commercialization of several genetically modified crops has been approved worldwide to date. Uniplex polymerase chain reaction (PCR)-based methods to identify these different insertion events have been developed, but their use in the analysis of all commercially available genetically modified organisms (GMOs) is becoming progressively insufficient. These methods require a large number of assays to detect all possible GMOs present in the sample and thereby the development of multiplex PCR systems using combined probes and primers targeted to sequences specific to various GMOs is needed for detection of this increasing number of GMOs. Here we report on the development of a multiplex real-time PCR suitable for multiple GMO identification, based on the intercalating dye SYBR Green I and the analysis of the melting curves of the amplified products. Using this method, different amplification products specific for Maximizer 176, Bt11, MON810, and GA21 maize and for GTS 40-3-2 soybean were obtained and identified by their specific Tm. We have combined amplification of these products in a number of multiplex reactions and show the suitability of the methods for identification of GMOs with a sensitivity of 0.1% in duplex reactions. The described methods offer an economic and simple alternative to real-time PCR systems based on sequence-specific probes (i.e., TaqMan chemistry). These methods can be used as selection tests and further optimized for uniplex GMO quantification.     

Estimation of the reaction efficiency in polymerase chain reaction

Polymerase chain reaction (PCR) is largely used in molecular biology for increasing the copy number of a specific DNA fragment. The succession of 20 replication cycles makes it possible to multiply the quantity of the fragment of interest by a factor of 1 million. The PCR technique has revolutionized genomics research. Several quantification methodologies are available to determine the DNA replication efficiency of the reaction which is the probability of replication of a DNA molecule at a replication cycle. We elaborate a quantification procedure based on the exponential phase and the early saturation phase of PCR. The reaction efficiency is supposed to be constant in the exponential phase, and decreasing in the saturation phase. We propose to model the PCR amplification process by a branching process which starts as a Galton-Watson branching process followed by a size-dependent process. Using this stochastic modelling and the conditional least-squares estimation method, we infer the reaction efficiency from a single PCR trajectory.     

Selective suppression of polymerase chain reaction]

The selective suppression of the polymerase chain reaction and methods based upon it (construction of cDNA libraries from low amounts of biological material, subtractive hybridization and differential display of mRNA, fast cloning of full-size cDNA, chromosome walking, cloning in vitro, and others) are reviewed. These methods display a high effectiveness and, taken together, enable intricate DNA analyses to be performed--from the search for nontrivial sequences to the total sequencing of the corresponding genes.