Sources of PCR-induced distortions in high-throughput sequencing data sets

PCR permits the exponential and sequence-specific amplification of DNA, even from minute starting quantities. PCR is a fundamental step in preparing DNA samples for high-throughput sequencing. However, there are errors associated with PCR-mediated amplification. Here we examine the effects of four important sources of error—bias, stochasticity, template switches and polymerase errors—on sequence representation in low-input next-generation sequencing libraries. We designed a pool of diverse PCR amplicons with a defined structure, and then used Illumina sequencing to search for signatures of each process. We further developed quantitative models for each process, and compared predictions of these models to our experimental data. We find that PCR stochasticity is the major force skewing sequence representation after amplification of a pool of unique DNA amplicons. Polymerase errors become very common in later cycles of PCR but have little impact on the overall sequence distribution as they are confined to small copy numbers. PCR template switches are rare and confined to low copy numbers. Our results provide a theoretical basis for removing distortions from high-throughput sequencing data. In addition, our findings on PCR stochasticity will have particular relevance to quantification of results from single cell sequencing, in which sequences are represented by only one or a few molecules.     

基于数字PCR的单分子DNA定量技术研究进展

数字PCR是一项针对单分子目标DNA的绝对定量技术．该技术是将含有DNA模板的反应溶液分配到大量独立的反应室中并且发生扩增反应,通过统计反应室中的阳性信号来定量DNA的拷贝数．DNA样品在反应室中随机和独立分布是单分子成功扩增和准确定量DNA拷贝数的关键因素．本文综述了数字PCR的发展历史、数字PCR与实时荧光定量PCR的区别,以及数字PCR在临床诊断、转基因成分定量、单细胞基因表达、环境微生物检测和下一代测序等方面的最新进展,并展望了该技术的应用前景．     

Stepwise Kinetic Equilibrium Models of Quantitative Polymerase Chain Reaction

ABSTRACT: BACKGROUND: Numerous models for use in interpreting quantitative PCR (qPCR) data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. Even so, they have not been thoroughly investigated and are rarely used for interpretation of qPCR data. New results for kinetic modeling of qPCR are presented. RESULTS: Two models are presented in which the efficiency of amplification is based on equilibrium solutions for the annealing phase of the qPCR process. Model 1 assumes annealing of complementary targets strands and annealing of target and primers are both reversible reactions and reach a dynamic equilibrium. Model 2 assumes all annealing reactions are nonreversible and equilibrium is static. Both models include the effect of primer concentration during the annealing phase. Analytic formulae are given for the equilibrium values of all single and double stranded molecules at the end of the annealing step. The equilibrium values are then used in a stepwise method to describe the whole qPCR process. Rate constants of kinetic models are the same for solutions that are identical except for possibly having different initial target concentrations. Analysis of qPCR curves from such solutions are thus analyzed by simultaneous non-linear curve fitting with the same rate constant values applying to all curves and each curve having a unique value for initial target concentration. The models were fit to two data sets for which the true initial target concentrations are known. Both models give better fit to observed qPCR data than other kinetic models present in the literature. They also give better estimates of initial target concentration. Model 1 was found to be slightly more robust than model 2 giving better estimates of initial target concentration when estimation of parameters was done for qPCR curves with very different initial target concentration. Both models may be used to estimate the initial absolute concentration of target sequence when a standard curve is not available. CONCLUSIONS: It is argued that the kinetic approach to modeling and interpreting quantitative PCR data has the potential to give more precise estimates of the true initial target concentrations than other methods currently used for analysis of qPCR data. The two models presented here give a unified model of the qPCR process in that they explain the shape of the qPCR curve for a wide variety of initial target concentrations.     

Potential influence of the first PCR cycles in real-time comparative gene quantifications

There is an underlying assumption in real-time PCR that the amplification efficiency is equal from the first cycles until a signal can be detected. In this study, we evaluated this assumption by analyzing genes with known gene copy number using real-time PCR comparative gene quantifications. Listeria monocytogenes has six 23S rRNA gene copies and one copy of the hlyA gene. We determined 23S rRNA gene copy numbers between 0.9 and 1.6 relative to hlyA when applying the comparative gene quantification approach. This paper focuses on the first cycles of PCR to explain the difference between known and determined gene copy numbers. Both theoretical and experimental evaluations were done. There are three different products (types 1-3) dominating in the first cycles. Type 1 is the original target, type 2 are undefined long products, while type 3 are products that accumulate during PCR. We evaluated the effects of type 1 and 2 products during the first cycles by cutting the target DNA with a restriction enzyme that cuts outside the boundaries of the PCR products. The digestion resulted in a presumed increased amplification efficiency for type 1 and 2 products. Differences in the amplification efficiencies between type 1, 2, and 3 products may explain part of the error in the gene copy number determinations using real-time PCR comparative gene quantifications. Future applications of real-time PCR quantifications should account for the effect of the first few PCR cycles on the conclusions drawn.     

Strand specific PCR amplification of low copy number DNA.

A method for the amplification of a single DNA strand at low copy number is described. It is a wholly PCR based approach which involves an initial linear amplification of the target using a tagged strand specific primer. This is followed by classical PCR amplification of the progeny using a pair of primers, one specific for the sequence tagged onto the 5' end of the first round primer, the second specific for the target sequence. Given the protocol used the ratio of the two strands in the final amplification product was 50:1.     

Validation and estimation of parameters for a general probabilistic model of the PCR process.

Earlier work rigorously derived a general probabilistic model for the PCR process that includes as a special case the Velikanov-Kapral model where all nucleotide reaction rates are the same. In this model, the probability of binding of deoxy-nucleoside triphosphate (dNTP) molecules with template strands is derived from the microscopic chemical kinetics. A recursive solution for the probability function of binding of dNTPs is developed for a single cycle and is used to calculate expected yield for a multicycle PCR. The model is able to reproduce important features of the PCR amplification process quantitatively.With a set of favorable reaction conditions, the amplification of the target sequence is fast enough to rapidly outnumber all side products. Furthermore, the final yield of the target sequence in a multicycle PCR run always approaches an asymptotic limit that is less than one. The amplification process itself is highly sensitive to initial concentrations and the reaction rates of addition to the template strand of each type of dNTP in the solution. This paper extends the earlier Saha model with a physics based model of the dependence of the reaction rates on temperature, and estimates parameters in this new model by nonlinear regression. The calibrated model is validated using RT-PCR data.     

Simultaneous measurement of multiple mRNAs with a single control by quantitative competitive reverse transcriptase-polymerase chain reaction: glucose transporters Glut1 and Glut4

Theoretical considerations for extending the application of quantitative competitive polymerase chain reaction (qc-PCR) to include the simultaneous measurement of multiple mRNAs, specifically the mammalian glucose transporters Glut1 and Glut4, are presented with experimental data in which the accuracy and flexibility of the system are examined. This method reliably measures changes in the initial concentration for each of three target DNA sequences. The reaction is not acutely sensitive to variations in either the primer sites or internal sequence, and although the initial concentrations of the target DNAs did affect the relative amplification efficiencies, the effect was limited and did not prohibit quantification. This PCR system was able to reliably detect differences as little as 50% in the initial concentration of the Glut1 target DNA sequence. Therefore, with the appropriate controls, PCR can be extended to include the simultaneous quantification of more than one target DNA with a single internal control.     

Calibration-curve-free quantitative PCR: a quantitative method for specific nucleic acid sequences without using calibration curves

We have developed a simple quantitative method for specific nucleic acid sequences without using calibration curves. This method is based on the combined use of competitive polymerase chain reaction (PCR) and fluorescence quenching. We amplified a gene of interest (target) from DNA samples and an internal standard (competitor) with a sequence-specific fluorescent probe using PCR and measured the fluorescence intensities before and after PCR. The fluorescence of the probe is quenched on hybridization with the target by guanine bases, whereas the fluorescence is not quenched on hybridization with the competitor. Therefore, quench rate (i.e., fluorescence intensity after PCR divided by fluorescence intensity before PCR) is always proportional to the ratio of the target to the competitor. Consequently, we can calculate the ratio from quench rate without using a calibration curve and then calculate the initial copy number of the target from the ratio and the initial copy number of the competitor. We successfully quantified the copy number of a recombinant DNA of genetically modified (GM) soybean and estimated the GM soybean contents. This method will be particularly useful for rapid field tests of the specific gene contamination in samples.     

同步PCR技术及其在植物核酸分子定量中的应用

同步PCR是一种集生化、光电和计算机技术于一体的封闭式DNA扩增系统,采用荧光染料将扩增与检测过程结合在一起,实现了在PCR过程中在线显示PCR反应,通过检测荧光强度来绝对定量起始模板的拷贝数。该技术大大简化和加速了核酸分子的定量过程,不仅快速、灵敏、准确、重复性好,而且很容易计算出待测样品中核酸分子的绝对起始拷贝数。同微阵列等分子生物技术一起,同步PcR技术将会在功能基因解析和病害分子诊断等方面发挥重要作用。本综述除了介绍同步．PCR技术的原理和应用外,还介绍了定量拟南芥,Aux／正4,4基因的转录水平的实验,并就同步PCR操作过程中的问题进行了讨论。     

同步PCR技术及其在植物核酸分子定量中的应用

同步PCR是一种集生化、光电和计算机技术于一体的封闭式DNA扩增系统,采用荧光染料将扩增与检测过程结合在一起,实现了在PCR过程中在线显示PCR反应,通过检测荧光强度来绝对定量起始模板的拷贝数.该技术大大简化和加速了核酸分子的定量过程,不仅快速、灵敏、准确、重复性好,而且很容易计算出待测样品中核酸分子的绝对起始拷贝数.同微阵列等分子生物技术一起,同步PCR技术将会在功能基因解析和病害分子诊断等方面发挥重要作用.本综述除了介绍同步PCR技术的原理和应用外,还介绍了定量拟南芥Aux/IAA基因的转录水平的实验,并就同步PCR操作过程中的问题进行了讨论.     

Retrieval of entire genes from environmental DNA by inverse PCR with pre-amplification of target genes using primers containing locked nucleic acids

We had been unsuccessful to amplify desired nucleotide sequences from various environmental DNA samples by using the inverse polymerase chain reaction (IPCR) technique, most probably because the copy numbers of target DNA sequences had been quite low. To enrich the target DNA sequences prior to IPCR, a rolling-circle amplification was used with a site-specific primer containing locked nucleic acids (LNAs). This pre-amplified IPCR (PAI-PCR) method increased the sensitivity of PCR almost 10 000 times compared with the standard IPCR in model experiments using Escherichia coli . We then applied the PAI-PCR method to isolate glycosyl hydrolase genes from DNAs extracted from vermiform appendixes of horses and termite guts. The flanking sequences of the target genes were amplified and cloned successfully using PAI-PCR, whereas standard IPCR resulted in no amplification.     

Prevention of pre-PCR mis-priming and primer dimerization improves low-copy-number amplifications.

A Hot Start Polymerase Chain Reaction (PCR) entails the withholding of at least one reagent from the reaction mixture until the reaction tube temperature has reached 60-80 degrees C. Hot Start amplification with an AmpliWax vapor barrier uses a layer of solid wax to separate the retained reagent(s) and the test sample from the bulk of the reagents until the first heating step of automated thermal cycling melts the wax and convectively mixes the two aqueous layers. Wax-mediated Hot Start PCR greatly increases the specificity, yield, and precision of amplifying low copy numbers of three HIV targets. In the presence of 1 microgram of human placental DNA (1.6 x 10(5) diploid genomes) the specificity improvement entails considerable to complete reduction in the amplification of mis-primed sequences and putative primer oligomers. When mis-priming is negligible, the procedural improvement still suppresses putative primer oligomerization. Hot Start PCR with an AmpliWax vapor barrier permits routine amplification of a single target molecule with detection by ethidium stained gel electrophoresis; nonisotopically visualized probing suffices for confirmation. The improved amplification performance is evident for target copy numbers below approximately 10(3).     

Real-time quantification of wild-type contaminants in glyphosate tolerant soybean

Background

Trait purity is a key factor for the successful utilization of biotech varieties and is currently assessed by analysis of individual seeds or plants. Here we propose a novel PCR-based approach to test trait purity that can be applied to bulk samples. To this aim the insertion site of a transgene is characterized and the corresponding sequence of the wild-type (wt) allele is used as diagnostic target for amplification. As a demonstration, we developed a real-time quantitative PCR method to test purity of glyphosate tolerant (Roundup Ready^®, RR) soybean.

Results

The soybean wt sequence at the RR locus was characterized and found to be highly conserved among conventional genotypes, thus allowing the detection of possibly any soybean non-trait contaminant. On the other hand, no amplification product was obtained from RR soybean varieties, indicating that the wt sequence is single copy and represents a suitable marker of conventional soybean presence. In addition, results obtained from the analysis of wt-spiked RR samples demonstrate that it is possible to use the real-time PCR assay to quantify the non-trait contamination with an acceptable degree of accuracy.

Conclusion

In principle this approach could be successfully applied to any transgenic event, provided that the wild-type sequence is conserved and single copy. The main advantages of the assay here described derive from its applicability to bulk samples, which would allow to increase the number of single seeds or plants forming the analytical sample, thus improving accuracy and throughput while containing costs. For these reasons this application of quantitative PCR could represent a useful tool in agricultural biotechnology.     

Estimating number of transgene copies in transgenic rapeseed by real-time PCR assay with<Emphasis Type="Italic">HMG I/Y</Emphasis> as an endogenous reference gene

In transgenic plants, the number of transgene copies can greatly influence the level of expression and genetic stability of the target gene. Transgene copy numbers are estimated by Southern blot analysis, which is laborious and time-consuming, requires relatively large amounts of plant materials, and may involve hazardous radioisotopes. Here we report the development of a sensitive, convenient real-time PCR technique for estimating the number of transgene copies in transgenic rapeseed. This system uses TaqMan quantitative real-time PCR and comparison with a novel, confirmed single-copy endogenous reference gene, high-mobile-group protein I/Y (HMG I/Y), to determine the numbers of copies of exogenous β-glucuronidase (GUS) and neomycin phosphotransferase II (nptII) genes. TheGUS andnptII copy numbers in primary transformants (T₀) were calculated by comparing threshold cycle (C _T) values of theGUS andnptII genes with those of the internal standard,HMG I/Y. This method is more convenient and accurate than Southern blotting because the number of copies of the exogenous gene could be directly deduced by comparing itsC _T value to that of the single-copy endogenous gene in each sample. Unlike other similar procedures of real-time PCR assay, this method does not require identical amplification efficiencies between the PCR systems for target gene and endogenous reference gene, which can avoid the bias that may result from slight variations in amplification efficiencies between PCR systems of the target and endogenous reference genes.     

Self-sustained sequence replication (3SR): an alternative to PCR

 The amplification of target nucleic acids before hybridization is one of the most powerful approaches for the detection of low copy number RNA and DNA. The best known amplification reaction is PCR which has many applications. However, certain drawbacks of the PCR reaction provide a role for alternative amplification methods. One of these methods is the self-sustained sequence replication (3SR) reaction, which is an isothermal method for RNA amplification depending on the action of three enzymes. 3SR has been used in several in vitro applications and has also been modified for in situ use (IS-3SR). We have studied IS-3SR with the measles virus as a model and have found that it can significantly amplify the amount of intracellular RNA. Such a level of amplification could raise the amount of single copy RNA to the level of detection by conventional in situ hybridization. Although careful controls to insure its specificity must be carried out, IS-3SR has several advantages, including ease of use, preserved cell morphology, and specificity for RNA amplification, which make it an attractive alternative to the in situ PCR method. Accepted: 27 June 1997     

Molecular clocks reduce plasmid loss rates: the R1 case

Plasmids control their replication so that the replication frequency per plasmid copy responds to the number of plasmid copies per cell. High sensitivity amplification in replication response to copy number deviations generally reduces variation in copy numbers between different single cells, thereby reducing the plasmid loss rate in a cell population. However, experiments show that plasmid R1 has a gradual, insensitive replication control predicting considerable copy number variation between single cells. The critical step in R1 copy number control is regulation of synthesis of a rate-limiting cis-acting replication protein, RepA. De novo synthesis of a large number of RepA molecules is required for replication, suggesting that copy number control is exercised at multiple steps. In this theoretical kinetic study we analyse R1 multistep copy number control and show that it results in the insensitive replication response found experimentally but that it at the same time effectively prohibits the existence of only one plasmid copy in a dividing cell. In combination with the partition system of R1, this can lead to very high segregational stability. The R1 control mechanism is compared to the different multistep copy number control of plasmid ColE1 that is based on conventional sensitivity amplification. This implies that while copy number control for ColE1 efficiently corrects for fluctuations that have already occurred, R1 copy number control prevents their emergence in cells that by chance start their cycle with only one plasmid copy. We also discuss how regular, clock-like, behaviour of single plasmid copies becomes hidden in experiments probing collective properties of a population of plasmid copies because the individual copies are out of phase. The model is formulated using master equations, taking a stochastic approach to regulation, but the mathematical formalism is kept to a minimum and the model is simplified to its bare essence. This simplicity makes it possible to extend the analysis to other replicons with similar design principles.     

Accuracy in copy number calling by qPCR and PRT: a matter of DNA

The possible implication of copy number variation (CNV) in the genetic susceptibility to human disease needs to be assessed using robust methods that can be applied at a population scale. In this report, we analyze the performance of the two major techniques, quantitative PCR (qPCR) and paralog ratio test (PRT), and investigate the influence of input DNA amount and template integrity on the reliability of both methods. Analysis of three genes (PRELID1, SYNPO and DEFB4) in a large sample set showed that both methods are prone to false copy number assignments if sufficient attention is not paid to DNA concentration and quality. Accurate normalization of samples is essential for reproducible qPCR because it avoids the effect of differential amplification efficiencies between target and control assays, whereas PRT is generally more sensitive to template degradation due to the fact that longer amplicons are usually needed to optimize sensitivity and specificity of paralog sequence PCR. The use of normalized, high quality genomic DNA yields comparable results with both methods.     

Detection of small sequence differences using competitive PCR: molecular monitoring of genetically improved, mercury-reducing bacteria

A quantitative PCR approach is presented to detect small genomic sequence differences for molecular quantification of recombinant DNA. The only unique genetic feature of the mercury-reducing, genetically improved Pseudomonas putida KT2442::mer73 available to distinguish it from its native mercury-resistant relatives is the DNA sequence crossing the border of the insertion site of the introduced DNA fragment. The quantification assay is a combination of specific PCR amplification and temperature gradient gel electrophoresis (TGGE). Gene quantification is provided by a competitively co-amplified DNA standard constructed by point mutation PCR. After computing the denaturation behavior of the target DNA stretch, a single base difference was introduced to achieve maximum migration difference in TGGE between the original target DNA and the modified standard without altering the PCR amplification efficiency. This competitive PCR strategy is a highly specific and sensitive way to detect small sequence differences and to monitor recombinant DNA in effluxes of biotechnological plants.