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Simulation of Kinetic Curves of Polymerase Chain Reaction Obtained Using Fluorescent Oligonucleotide Probes
Abstract
At present, many polymerase chain reaction models have been proposed for exact quantitative estimation of the reaction results. In most models, kinetics of product accumulation and kinetics of fluorescent reporter are assumed to be identical. A model of the polymerase chain reaction is proposed to study the difference of such functions in the system in which a hybridization probe serves as the source of the detected fluorescence signal. Adequacy of the model is verified, and significant possible difference of the accumulation kinetics of product and probe reporter is demonstrated.
Campylobacter is one of the four most important pathogens that cause foodborne disease in humans, with symptoms as fever, diarrhea, abdominal cramps, and vomiting. In some cases, the illness can evolve toward more severe pathologies or leads to patient death. The main source of transmission is generally believed to be via contaminated undercooked meat, meat products, and raw milk. Food safety is fundamental to assure consumers safety. A risk control could be achieved using analysis methods that can reduce the time required for results still maintaining specificity and sensitivity. Here we describe advanced methods for Campylobacter detection that reduce the time needed for a response which may reduce risks of foodborne outbreaks.
Recently, a number of models of polymerase chain reaction (PCR) have been proposed. In such models, the kinetics of a reaction product and a fluorescence reporter used are usually identified. An intercalation dye is one of the two ways for “real time” detection of reaction product accumulation. In this work a PCR model is proposed, with using of intercalation dye to obtain a PCR curve. The concentration of bound intercalation dye was calculated at the end of each PCR cycle. This calculation is based on an equilibrium equation for intercalation dye binding with DNA. An analysis of simulation results demonstrates a significant difference between the accumulation kinetics of the reaction product and the fluorescent signal of the bound intercalation dye.
While many decisions rely on real time quantitative PCR (qPCR) analysis few attempts have hitherto been made to quantify bounds of precision accounting for the various sources of variation involved in the measurement process. Besides influences of more obvious factors such as camera noise and pipetting variation, changing efficiencies within and between reactions affect PCR results to a degree which is not fully recognized. Here, we develop a statistical framework that models measurement error and other sources of variation as they contribute to fluorescence observations during the amplification process and to derived parameter estimates. Evaluation of reproducibility is then based on simulations capable of generating realistic variation patterns. To this end, we start from a relatively simple statistical model for the evolution of efficiency in a single PCR reaction and introduce additional error components, one at a time, to arrive at stochastic data generation capable of simulating the variation patterns witnessed in repeated reactions (technical repeats). Most of the variation in [Formula: see text] values was adequately captured by the statistical model in terms of foreseen components. To recreate the dispersion of the repeats' plateau levels while keeping the other aspects of the PCR curves within realistic bounds, additional sources of reagent consumption (side reactions) enter into the model. Once an adequate data generating model is available, simulations can serve to evaluate various aspects of PCR under the assumptions of the model and beyond.
Linear regression of efficiency or LRE introduced a new paradigm for conducting absolute quantification, which does not require standard curves, can generate absolute accuracies of +/-25% and has single molecule sensitivity. Derived from adapting the classic Boltzmann sigmoidal function to PCR, target quantity is calculated directly from the fluorescence readings within the central region of an amplification profile, generating 4-8 determinations from each amplification reaction.
Based on generating a linear representation of PCR amplification, the highly visual nature of LRE analysis is illustrated by varying reaction volume and amplification efficiency, which also demonstrates how LRE can be used to model PCR. Examining the dynamic range of LRE further demonstrates that quantitative accuracy can be maintained down to a single target molecule, and that target quantification below ten molecules conforms to that predicted by Poisson distribution. Essential to the universality of optical calibration, the fluorescence intensity generated by SYBR Green I (FU/bp) is shown to be independent of GC content and amplicon size, further verifying that absolute scale can be established using a single quantitative standard. Two high-performance lambda amplicons are also introduced that in addition to producing highly precise optical calibrations, can be used as benchmarks for performance testing. The utility of limiting dilution assay for conducting platform-independent absolute quantification is also discussed, along with the utility of defining assay performance in terms of absolute accuracy.
Founded on the ability to exploit lambda gDNA as a universal quantitative standard, LRE provides the ability to conduct absolute quantification using few resources beyond those needed for sample preparation and amplification. Combined with the quantitative and quality control capabilities of LRE, this kinetic-based approach has the potential to fundamentally transform how real-time qPCR is conducted.
We examined five nucleic acid binding fluorescent dyes, propidium iodide, SYBR Green I, YO-PRO-1, TOTO-3, and TO-PRO-3, for nuclear DNA staining, visualized by fluorescence and laser confocal microscopy. The optimal concentration, co-staining of RNA, and bleaching speeds were examined. SYBR Green I and TO-PRO-3 almost preferentially stained the nuclear DNA, and the other dyes co-stained the cytoplasmic RNA. RNAse treatment completely prevented the cytoplasmic RNA staining. In conventional fluorescence microscopy, these dyes can be used in combination with fluorescence-labeled antibodies. Among the dyes tested, TOTO-3 and TO-PRO-3 stained the DNAs with far-red fluorescence under red excitation. Under Kr/Ar-laser illumination, TOTO-3 and TO-PRO-3 were best suited as the nuclear staining dyes in the specimens immunolabeled with fluorescein and rhodamine (or Texas red).
The course of the real-time polymerase chain reaction (PCR) is determined by the temperature dependence of the kinetics of the component reactions, particularly the DNA strand hybridization. To investigate the effect of thermal processes on the reaction behavior, a mathematical model in which the variable rate constant of dissociation of “primer–single strand” complexes depends on temperature was proposed. The reaction medium temperature, which depends on time, was also introduced into the model. The proposed model of real-time PCR makes it possible to analyze different aspects of the reaction, which are important for the development of instruments and reagents for PCR.
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.
Polymerase chain reaction (PCR) is an important molecular biological tool for the amplification of nucleic acids. PCR process can be divided into three phases according to the amplification rate: exponential, quasi-linear, and plateau. We investigated the cause of the plateau phenomenon through real-time monitoring of the amplification profile and computerized simulation. Possible limiting components, such as Taq DNA polymerase, primer pair, and dNTPs were added during quasi-linear phase, after which the differences in the amplification profiles were monitored. Modeling and computerized simulations were performed to look into the complex mechanism of the reactions, such as renaturation of templates during temperature transition from denaturation to annealing step and effective enzyme concentration profiles within the cycle progress. The decrease of effective polymerase concentration due to heat inactivation and product accumulation caused the PCR plateau. Addition of polymerase during the quasi-linear phase could increase the final product amount; however, the PCR process still reached the plateau phase in spite of polymerase addition. Simulation results suggest that renaturation of templates before competitive annealing reaction and decrease of effective enzyme concentration by non-specific binding of polymerase to double-stranded DNA is the main contribution to plateau forming.
Real-time reverse transcription (RT) PCR is currently the most sensitive method for the detection of low-abundance mRNAs. Two relative quantitative methods have been adopted: the standard curve method and the comparative C(T) method. The latter is used when the amplification efficiency of a reference gene is equal to that of the target gene; otherwise the standard curve method is applied. Based on the simulation of kinetic process of real-time PCR, we have developed a new method for quantitation and normalization of gene transcripts. In our method, the amplification efficiency for each individual reaction is calculated from the kinetic curve, and the initial amount of gene transcript is derived and normalized. Simulation demonstrated that our method is more accurate than the comparative C(T) method and would save more time than the relative standard curve method. We have used the new method to quantify gene expression levels of nine two-pore potassium channels. The relative levels of gene expression revealed by our quantitative method were broadly consistent with those estimated by routine RT-PCR, but the results also showed that amplification efficiencies varied from gene to gene and from sample to sample. Our method provides a simple and accurate approach to quantifying gene expression level with the advantages that neither construction of standard curve nor validation experiments are needed.
Several real-time PCR (rtPCR) quantification techniques are currently used to determine the expression levels of individual genes from rtPCR data in the form of fluorescence intensities. In most of these quantification techniques, it is assumed that the efficiency of rtPCR is constant. Our analysis of rtPCR data shows, however, that even during the exponential phase of rtPCR, the efficiency of the reaction is not constant, but is instead a function of cycle number. In order to understand better the mechanisms belying this behavior, we have developed a mathematical model of the annealing and extension phases of the PCR process. Using the model, we can simulate the PCR process over a series of reaction cycles. The model thus allows us to predict the efficiency of rtPCR at any cycle number, given a set of initial conditions and parameter values, which can mostly be estimated from biophysical data. The model predicts a precipitous decrease in cycle efficiency when the product concentration reaches a sufficient level for template-template re-annealing to compete with primer-template annealing; this behavior is consistent with available experimental data. The quantitative understanding of rtPCR provided by this model can allow us to develop more accurate methods to quantify gene expression levels from rtPCR data.