A mathematical model and a computerized simulation of PCR using complex templates

Positive feedback drives a secondary nonlinear product burst during a biphasic DNA amplification reaction

Isothermal DNA amplification reactions are used in a broad variety of applications, from diagnostic assays to DNA circuits, with greater speed and less complexity than established PCR technologies. We recently reported a unique, high gain, biphasic isothermal DNA amplification reaction, called the Ultrasensitive DNA Amplification Reaction (UDAR). Here we present a detailed analysis of the UDAR reaction pathways that initiates with a first phase followed by a nonlinear product burst, which is caused by an autocatalytic secondary reaction. The experimental reaction output was reproduced using an ordinary differential equation model based on detailed reaction mechanisms. This model provides insight on the relative importance of each reaction mechanism during both phases, which could aid in the design of product output during DNA amplification reactions.

Modeling bias and variation in the stochastic processes of small RNA sequencing

The use of RNA-seq as the preferred method for the discovery and validation of small RNA biomarkers has been hindered by high quantitative variability and biased sequence counts. In this paper we develop a statistical model for sequence counts that accounts for ligase bias and stochastic variation in sequence counts. This model implies a linear quadratic relation between the mean and variance of sequence counts. Using a large number of sequencing datasets, we demonstrate how one can use the generalized additive models for location, scale and shape (GAMLSS) distributional regression framework to calculate and apply empirical correction factors for ligase bias. Bias correction could remove more than 40% of the bias for miRNAs. Empirical bias correction factors appear to be nearly constant over at least one and up to four orders of magnitude of total RNA input and independent of sample composition. Using synthetic mixes of known composition, we show that the GAMLSS approach can analyze differential expression with greater accuracy, higher sensitivity and specificity than six existing algorithms (DESeq2, edgeR, EBSeq, limma, DSS, voom) for the analysis of small RNA-seq data.

Computational analysis of stochastic heterogeneity in PCR amplification efficiency revealed by single molecule barcoding

The polymerase chain reaction (PCR) is one of the most widely used techniques in molecular biology. In combination with High Throughput Sequencing (HTS), PCR is widely used to quantify transcript abundance for RNA-seq, and in the context of analysis of T and B cell receptor repertoires. In this study, we combine DNA barcoding with HTS to quantify PCR output from individual target molecules. We develop computational tools that simulate both the PCR branching process itself, and the subsequent subsampling which typically occurs during HTS sequencing. We explore the influence of different types of heterogeneity on sequencing output, and compare them to experimental results where the efficiency of amplification is measured by barcodes uniquely identifying each molecule of starting template. Our results demonstrate that the PCR process introduces substantial amplification heterogeneity, independent of primer sequence and bulk experimental conditions. This heterogeneity can be attributed both to inherited differences between different template DNA molecules, and the inherent stochasticity of the PCR process. The results demonstrate that PCR heterogeneity arises even when reaction and substrate conditions are kept as constant as possible, and therefore single molecule barcoding is essential in order to derive reproducible quantitative results from any protocol combining PCR with HTS.

FastPCR software for PCR, in silico PCR, and oligonucleotide assembly and analysis

This chapter introduces the software FastPCR as an integrated tools environment for PCR primer and probe design. It also predicts oligonucleotide properties based on experimental studies of PCR efficiency. The software provides comprehensive facilities for designing primers for most PCR applications and their combinations, including standard, multiplex, long-distance, inverse, real-time, group-specific, unique, and overlap extension PCR for multi-fragment assembly in cloning, as well as bisulphite modification assays. It includes a program to design oligonucleotide sets for long sequence assembly by the ligase chain reaction. The in silico PCR primer or probe search includes comprehensive analyses of individual primers and primer pairs. It calculates the melting temperature for standard and degenerate oligonucleotides including LNA and other modifications, provides analyses for a set of primers with prediction of oligonucleotide properties, dimer and G/C-quadruplex detection, and linguistic complexity, and provides a dilution and resuspension calculator. The program includes various bioinformatics tools for analysis of sequences with CG or AT skew, of CG content and purine-pyrimidine skew, and of linguistic sequence complexity. It also permits generation of random DNA sequence and analysis of restriction enzymes of all types. It finds or creates restriction enzyme recognition sites for coding sequences and supports the clustering of sequences. It generates consensus sequences and analyzes sequence conservation. It performs efficient and complete detection of various repeat types and displays them. FastPCR allows for sequence file batch processing, which is essential for automation. The FastPCR software is available for download at http://primerdigital.com/fastpcr.html and online version at http://primerdigital.com/tools/pcr.html .

Simulation of between repeat variability in real time PCR reactions

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 C(q) 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.

Java web tools for PCR, in silico PCR, and oligonucleotide assembly and analysis

The polymerase chain reaction is fundamental to molecular biology and is the most important practical molecular technique for the research laboratory. We have developed and tested efficient tools for PCR primer and probe design, which also predict oligonucleotide properties based on experimental studies of PCR efficiency. The tools provide comprehensive facilities for designing primers for most PCR applications and their combinations, including standard, multiplex, long-distance, inverse, real-time, unique, group-specific, bisulphite modification assays, Overlap-Extension PCR Multi-Fragment Assembly, as well as a programme to design oligonucleotide sets for long sequence assembly by ligase chain reaction. The in silico PCR primer or probe search includes comprehensive analyses of individual primers and primer pairs. It calculates the melting temperature for standard and degenerate oligonucleotides including LNA and other modifications, provides analyses for a set of primers with prediction of oligonucleotide properties, dimer and G-quadruplex detection, linguistic complexity, and provides a dilution and resuspension calculator.

Experimental Validation of a Fundamental Model for PCR Efficiency

Recently a theoretical analysis of PCR efficiency has been published by Booth et al., (2010). The PCR yield is the product of three efficiencies: (i) the annealing efficiency is the fraction of templates that form binary complexes with primers during annealing, (ii)the polymerase binding efficiency is the fraction of binary complexes that bind to polymerase to form ternary complexes and (iii)the elongation efficiency is the fraction of ternary complexes that extend fully. Yield is controlled by the smallest of the three efficiencies and control could shift from one type of efficiency to another over the course of a PCR experiment. Experiments have been designed that are specifically controlled by each one of the efficiencies and the results are consistent with the mathematical model. The experimental data has also been used to quantify six key parameters of the theoretical model. An important application of the fully characterized model is to calculate initial template concentration from real-time PCR data. Given the PCR protocol, the midpoint cycle number (where the template concentration is half that of the final concentration) can be theoretically determined and graphed for a variety of initial DNA concentrations. Real-time results can be used to calculate the midpoint cycle number and consequently the initial DNA concentration, using this graph. The application becomes particularly simple if a conservative PCR protocol is followed where only the annealing efficiency is controlling.

Efficiency of the Polymerase Chain Reaction

The polymerase chain reaction (PCR) has found wide application in biochemistry and molecular biology such as gene expression studies, mutation detection, forensic analysis and pathogen detection. Increasingly quantitative real time PCR is used to assess copy numbers from overall yield. In this study the yield is analyzed as a function of several processes: (1) thermal damage of the template and polymerase occurs during the denaturing step, (2) competition exists between primers and templates to either anneal or form dsDNA, (3) polymerase binding to annealed products (primer/ssDNA) to form ternary complexes and (4) extension of ternary complexes. Explicit expressions are provided for the efficiency of each process, therefore reaction conditions can be directly linked to the overall yield. Examples are provided where different processes play the yield-limiting role. The analysis will give researchers a unique understanding of the factors that control the reaction and will aid in the interpretation of experimental results.

Improved assay-dependent searching of nucleic acid sequence databases

Nucleic acid-based biochemical assays are crucial to modern biology. Key applications, such as detection of bacterial, viral and fungal pathogens, require detailed knowledge of assay sensitivity and specificity to obtain reliable results. Improved methods to predict assay performance are needed for exploiting the exponentially growing amount of DNA sequence data and for reducing the experimental effort required to develop robust detection assays. Toward this goal, we present an algorithm for the calculation of sequence similarity based on DNA thermodynamics. In our approach, search queries consist of one to three oligonucleotide sequences representing either a hybridization probe, a pair of Padlock probes or a pair of PCR primers with an optional TaqMan™ probe (i.e. in silico or ‘virtual’ PCR). Matches are reported if the query and target satisfy both the thermodynamics of the assay (binding at a specified hybridization temperature and/or change in free energy) and the relevant biological constraints (assay sequences binding to the correct target duplex strands in the required orientations). The sensitivity and specificity of our method is evaluated by comparing predicted to known sequence tagged sites in the human genome. Free energy is shown to be a more sensitive and specific match criterion than hybridization temperature.

Delivery and mechanistic considerations for the production of knock-in mice by single-stranded oligonucleotide gene targeting

Single-stranded oligodeoxynucleotide (ssODN) gene targeting may facilitate animal model creation and gene repair therapy. Lipofection of ssODN can introduce point mutations into target genes. However, typical efficiencies in mouse embryonic stem cells (ESC) are <10(-4), leaving corrections too rare to effectively identify. We developed ESC lines with an integrated mutant neomycin resistance gene (Tyr22Ter). After targeting with ssODN, repaired cells survive selection in G418. Correction efficiencies varied with different lipofection procedures, clonal lines, and ssODN designs, ranging from 1 to 100 corrections per million cells plated. Uptake studies using cell sorting of Cy5-labelled ssODN showed 40% of the corrections concentrated in the best transfected 22% of cells. Four different basepair mismatches were tested and results show that the base-specificity of the mismatch is critical. Dual mismatch ssODN also showed mismatch preferences. These ESC lines may facilitate development of improved ssODN targeting technologies for either animal production or ex vivo gene therapy.

Information theory-based algorithm for in silico prediction of PCR products with whole genomic sequences as templates

Background

A new algorithm for assessing similarity between primer and template has been developed based on the hypothesis that annealing of primer to template is an information transfer process.

Results

Primer sequence is converted to a vector of the full potential hydrogen numbers (3 for G or C, 2 for A or T), while template sequence is converted to a vector of the actual hydrogen bond numbers formed after primer annealing. The former is considered as source information and the latter destination information. An information coefficient is calculated as a measure for fidelity of this information transfer process and thus a measure of similarity between primer and potential annealing site on template.

Conclusion

Successful prediction of PCR products from whole genomic sequences with a computer program based on the algorithm demonstrated the potential of this new algorithm in areas like in silico PCR and gene finding.

Numeric definition of the clinical performance of the nested reverse transcription-PCR for detection of hematogenous epithelial cells and correction for specific mRNA of non-target cell origin as evaluated for prostate cancer cells

BACKGROUND

Inappropriate quality management of reverse transcription-PCR (RT-PCR) assays for the detection of blood-borne prostate cancer (PCa) cells hampers clinical conclusions. Improvement of the RT-PCR methodology for prostate-specific antigen (PSA) mRNA should focus on an appropriate numeric definition of the performance of the assay and correction for PSA mRNA that is not associated with PCa cells.

METHODS AND RESULTS

Repeated (RT-)PCR tests for PSA mRNA in single blood specimens from PCa patients and PCa-free controls, performed by four international institutions, showed a large percentage (approximately equal to 50%) of divergent test results. The best estimates of the mean, lambda (SD), of the expected Poisson frequency distributions of the number of positive tests among five replicate assays of samples from PCa-free individuals were 1.0 (0.2) for 2 x 35 PCR cycles and 0.2 (0.1) for 2 x 25 PCR cycles. Assessment of the numeric value of the mean can be considered as a new indicator of the performance of a RT-PCR assay for PSA mRNA under clinical conditions. Moreover, it determines the required number of positive test repetitions to differentiate between true and false positives for circulating prostate cells. At a predefined diagnostic specificity of > or = 98%, repeated PCRs with lambda of either 1.0 or 0.2 require, respectively, more than three or more than one positive tests to support the conclusion that PSA mRNA-containing cells are present.

CONCLUSIONS

Repeated nested PCR tests for PSA and appropriate handling of the data allow numeric quantification of the performance of the assay and differentiation between analytical false and true positives at a predefined accuracy. This new approach may contribute to introduction of PSA RT-PCR assays in clinical practice.

Comparison of competitively primed and conventional allele-specific nucleic acid amplification

A simulation of competitively primed allele-specific DNA amplification has been constructed and its behavior examined. This has shown that when the ratio of the amount of homoduplex misprime product to the total amount of amplimer is low, it increases by approximately one-fourth of the mispriming frequency with each doubling of the total amount of amplimer. When the ratio is high and reverse mispriming becomes significant, it asymptotes toward a value <0.5. An analogous simulation was carried out on conventional allele-specific DNA amplification. As expected, the ratio of the amount of amplimer in the positive and negative reactions closely approximates the mispriming frequency provided that amplification is exponential in both cases. This suggests that conventional allele-specific amplification has somewhat higher inherent specificity than competitively primed amplification. However, conventional allele-specific reactions are subject to a "catch-up" phase in which the positive reaction slows or stops, thus reducing the specificity. It was hypothesized that competitively primed reactions may be easier to optimize than conventional allele-specific reactions. This conjecture was supported experimentally. In addition, it was shown that the specificity of competitively primed reactions is a function of the degree of amplification.

Consensus-degenerate hybrid oligonucleotide primers for amplification of distantly related sequences

We describe a new primer design strategy for PCR amplification of unknown targets that are related to multiply-aligned protein sequences. Each primer consists of a short 3' degenerate core region and a longer 5' consensus clamp region. Only 3-4 highly conserved amino acid residues are necessary for design of the core, which is stabilized by the clamp during annealing to template molecules. During later rounds of amplification, the non-degenerate clamp permits stable annealing to product molecules. We demonstrate the practical utility of this hybrid primer method by detection of diverse reverse transcriptase-like genes in a human genome, and by detection of C5DNA methyltransferase homologs in various plant DNAs. In each case, amplified products were sufficiently pure to be cloned without gel fractionation. This COnsensus-DEgenerate Hybrid Oligonucleotide Primer (CODEHOP) strategy has been implemented as a computer program that is accessible over the World Wide Web (http://blocks.fhcrc.org/codehop.html) and is directly linked from the BlockMaker multiple sequence alignment site for hybrid primer prediction beginning with a set of related protein sequences.

Direct amplification of length polymorphisms (DALP), or how to get and characterize new genetic markers in many species

Direct amplification of length polymorphisms (DALP) uses an arbitrarily primed PCR (AP-PCR) to produce genomic fingerprints and to enable sequencing of DNA polymorphisms in virtually any species. Oligonucleotide pairs were designed to each produce a specific multi-banded pattern and all the fragments thus generated can be directly sequenced with the same two universal M13 sequencing primers. This strategy combines the advantages of a high resolution fingerprint technique and the possibility of characterizing the polymorphisms. The use of family members as templates in the multi-locus detection step allows a direct test of allele transmission, as well as early mapping of the markers or selection of loci associated with some traits or diseases. We used this method to detect micro-deletions/insertions and microsatellite DNA loci useful in population genetics studies, but it could be applied in many other fields of biology, such as genome mapping for definition of polymorphic sequence tagged sites, directly localized on a genetic map.

Theoretical studies on the mobility-shift assay of protein-DNA complexes

The theory of mass transport coupled to reversible macromolecular interactions under chemical kinetic control forms the basis for computer simulation of the electrophoretic mobility-shift behavior of protein-DNA complexes. Model systems include (i) specific binding of a univalent protein molecule to a single site on the DNA molecule; (ii) the putative cage effect; (iii) cooperative binding to multiple sites; (iv) formation of looped complexes of 1:1 and 2:1 stoichiometry; (v) noncooperative and cooperative, nonspecific binding modes; and (vi) binding of dimerizing transcriptional factors to response elements of target genes. Favorable comparison of simulated with experimental mobility-shift behavior indicates that the phenomenological mechanisms, whereby observed mobility-shift patterns are generated during electrophoresis, are embodied in the theory. These studies have provided guidelines for definitive interpretation of mobility-shift assays and for the design of experiments to develop a detailed understanding of the particular system under investigation.

Abortive gap repair: underlying mechanism for Ds element formation

The mechanism by which the maize autonomous Ac transposable element gives rise to nonautonomous Ds elements is largely unknown. Sequence analysis of native maize Ds elements indicates a complex chimeric structure formed through deletions of Ac sequences with or without insertions of Ac-unrelated sequence blocks. These blocks are often flanked by short stretches of reshuffled and duplicated Ac sequences. To better understand the mechanism leading to Ds formation, we designed an assay for detecting alterations in Ac using transgenic tobacco plants carrying a single copy of Ac. We found frequent de novo alterations in Ac which were excision rather than sequence dependent, occurring within Ac but not within an almost identical Ds element and not within a stable transposase-producing gene. The de novo DNA rearrangements consisted of internal deletions with breakpoints usually occurring at short repeats and, in some cases, of duplication of Ac sequences or insertion of Ac-unrelated fragments. The ancient maize Ds elements and the young Ds elements in transgenic tobacco showed similar rearrangements, suggesting that Ac-Ds elements evolve rapidly, more so than stable genes, through deletions, duplications, and reshuffling of their own sequences and through capturing of unrelated sequences. The data presented here suggest that abortive Ac-induced gap repair, through the synthesis-dependent strand-annealing pathway, is the underlying mechanism for Ds element formation.