Simultaneous fitting of real-time PCR data with efficiency of amplification modeled as Gaussian function of target fluorescence

<p>Abstract</p> <p>Background</p> <p>In real-time PCR, it is necessary to consider the efficiency of amplification (EA) of amplicons in order to determine initial target levels properly. EAs can be deduced from standard curves, but these involve extra effort and cost and may yield invalid EAs. Alternatively, EA can be extracted from individual fluorescence curves. Unfortunately, this is not reliable enough.</p> <p>Results</p> <p>Here we introduce simultaneous non-linear fitting to determine – without standard curves – an optimal common EA for all samples of a group. In order to adjust EA as a function of target fluorescence, and still to describe fluorescence as a function of cycle number, we use an iterative algorithm that increases fluorescence cycle by cycle and thus simulates the PCR process. A Gauss peak function is used to model the decrease of EA with increasing amplicon accumulation. Our approach was validated experimentally with hydrolysis probe or SYBR green detection with dilution series of 5 different targets. It performed distinctly better in terms of accuracy than standard curve, DART-PCR, and LinRegPCR approaches. Based on reliable EAs, it was possible to detect that for some amplicons, extraordinary fluorescence (EA > 2.00) was generated with locked nucleic acid hydrolysis probes, but not with SYBR green.</p> <p>Conclusion</p> <p>In comparison to previously reported approaches that are based on the separate analysis of each curve and on modelling EA as a function of cycle number, our approach yields more accurate and precise estimates of relative initial target levels.</p

Enhanced analysis of real-time PCR data by using a variable efficiency model: FPK-PCR

Current methodology in real-time Polymerase chain reaction (PCR) analysis performs well provided PCR efficiency remains constant over reactions. Yet, small changes in efficiency can lead to large quantification errors. Particularly in biological samples, the possible presence of inhibitors forms a challenge. We present a new approach to single reaction efficiency calculation, called Full Process Kinetics-PCR (FPK-PCR). It combines a kinetically more realistic model with flexible adaptation to the full range of data. By reconstructing the entire chain of cycle efficiencies, rather than restricting the focus on a ‘window of application’, one extracts additional information and loses a level of arbitrariness. The maximal efficiency estimates returned by the model are comparable in accuracy and precision to both the golden standard of serial dilution and other single reaction efficiency methods. The cycle-to-cycle changes in efficiency, as described by the FPK-PCR procedure, stay considerably closer to the data than those from other S-shaped models. The assessment of individual cycle efficiencies returns more information than other single efficiency methods. It allows in-depth interpretation of real-time PCR data and reconstruction of the fluorescence data, providing quality control. Finally, by implementing a global efficiency model, reproducibility is improved as the selection of a window of application is avoided.JRC.I.3-Molecular Biology and Genomic

Real-time PCR Machine System Modeling and a Systematic Approach for the Robust Design of a Real-time PCR-on-a-Chip System

Chip-based DNA quantification systems are widespread, and used in many point-of-care applications. However, instruments for such applications may not be maintained or calibrated regularly. Since machine reliability is a key issue for normal operation, this study presents a system model of the real-time Polymerase Chain Reaction (PCR) machine to analyze the instrument design through numerical experiments. Based on model analysis, a systematic approach was developed to lower the variation of DNA quantification and achieve a robust design for a real-time PCR-on-a-chip system. Accelerated lift testing was adopted to evaluate the reliability of the chip prototype. According to the life test plan, this proposed real-time PCR-on-a-chip system was simulated to work continuously for over three years with similar reproducibility in DNA quantification. This not only shows the robustness of the lab-on-a-chip system, but also verifies the effectiveness of our systematic method for achieving a robust design

Characterizing variability in fluorescence-based forensic DNA measurement and developing an electrochemical-based quantification system

A reliable and robust laboratory method is essential for the forensic analysis of deoxyribonucleic acid (DNA), particularly for low-template samples. Electropherogram peak heights are important to the identification of STR alleles, and these peak heights are prone to error. Since error can be introduced into the process during sample preparation, quantification, amplification, or analysis, validation studies are performed in an attempt to characterize the signal variation associated with the process. While current practices assess aspects of a method, such as sensitivity and reproducibility, the effects of daily laboratory alterations are often not considered. Additionally, samples used in a validation study may be prepared using serial dilutions. Therefore, understanding the extent to which error is propagated through the series and the effect it has on the results could help improve validation practices. This work aimed to assess the effect daily laboratory modifications have on the signal in a forensic electropherogram. Specifically, the variability in signal when different capillary and amplification kit lots were used was evaluated against the variability observed when a single sample was either injected or amplified multiple times. The variability was determined via the examination of peak heights, peak height ratios, stutter, and drop-out. The effect of serially diluting samples was examined via an in silico model of the dilution process, polymerase chain reaction (PCR), and capillary injection. The peak heights from simulated serially diluted samples using the concentration of a stock DNA were compared to the peak heights from simulated samples that were quantified after the dilution series was generated and prior to amplification. The different capillary lots and amplifications were found to result in greater variation compared to the multiple injections. Additionally, when the stutter percentages obtained from using multiple kit lots were compared to those obtained using the same kit lot, differences in stutter percentage deviations resulted in different stutter thresholds. Drop-out rates were also different between the samples amplified with one kit versus the same samples amplified with multiple kit lots. Therefore, at a minimum, multiple amplifications should be run on multiple capillary lots during validation. Further, if available, the use of multiple kit lots is recommended, particularly in cases where stutter thresholds or drop-out models are used during interpretation. Creating validation samples via serial dilutions was also found to increase the variation observed in peak height in the simulated samples, suggesting that samples should be quantified post-dilution. In addition to characterizing the variability of several components of DNA analysis, an alternative quantification method was investigated in order to decrease the overall variability associated with the quantification process. This work sought to develop an electrochemical biosensor using a single-stranded DNA (ssDNA) probe chemically adsorbed to a gold electrode. This would allow for the direct quantification of DNA and eliminate the need for qPCR and fluorescent-based oligonucleotide detection systems. The DNA probe was successfully adsorbed to the surface of the gold disk electrode, hybridized to a single-stranded complementary DNA sequence, and detected using square wave voltammetry. Additionally, the ability to control the amount of DNA chemisorbed to the electrode surface was investigated by varying the incubation time in the probe solution. The measured current increased as the incubation time increased from 15 minutes to one hour, after which it plateaued. The use of an electrochemical biosensor is a promising alternative to qPCR for the quantification of DNA, with one hour being the optimal incubation time in the probe solution

Unaccounted uncertainty from qPCR efficiency estimates entails uncontrolled false positive rates

BACKGROUND: Accurate adjustment for the amplification efficiency (AE) is an important part of real-time quantitative polymerase chain reaction (qPCR) experiments. The most commonly used correction strategy is to estimate the AE by dilution experiments and use this as a plug-in when efficiency correcting the ΔΔC(q). Currently, it is recommended to determine the AE with high precision as this plug-in approach does not account for the AE uncertainty, implicitly assuming an infinitely precise AE estimate. Determining the AE with such precision, however, requires tedious laboratory work and vast amounts of biological material. Violation of the assumption leads to overly optimistic standard errors of the ΔΔC(q), confidence intervals, and p-values which ultimately increase the type I error rate beyond the expected significance level. As qPCR is often used for validation it should be a high priority to account for the uncertainty of the AE estimate and thereby properly bounding the type I error rate and achieve the desired significance level. RESULTS: We suggest and benchmark different methods to obtain the standard error of the efficiency adjusted ΔΔC(q) using the statistical delta method, Monte Carlo integration, or bootstrapping. Our suggested methods are founded in a linear mixed effects model (LMM) framework, but the problem and ideas apply in all qPCR experiments. The methods and impact of the AE uncertainty are illustrated in three qPCR applications and a simulation study. In addition, we validate findings suggesting that MGST1 is differentially expressed between high and low abundance culture initiating cells in multiple myeloma and that microRNA-127 is differentially expressed between testicular and nodal lymphomas. CONCLUSIONS: We conclude, that the commonly used efficiency corrected quantities disregard the uncertainty of the AE, which can drastically impact the standard error and lead to increased false positive rates. Our suggestions show that it is possible to easily perform statistical inference of ΔΔC(q), whilst properly accounting for the AE uncertainty and better controlling the false positive rate

Measurements of DNA Damage and Repair in Bacillus anthracis Sterne Spores by UV Radiation

Spores of Bacillus anthracis (Ba) sterne were irradiated with 267nm UV light using small light emitting diodes. The pRB373 plasmid with a red fluorescent protein was transformed into Ba sterne cells prior to irradiation. Following irradiation, germination media was added and the spores were incubated for various times, to allow for DNA repair. The pRB373 plasmid was isolated and analyzed using real-time PCR. Primers were designed across the RFP in the plasmid yielding two amplicons, 245bp and 547bp long. PCR amplification was not achieved for germinated samples. Spore samples isolated using bead beating methods were amplified. Results indicate a quicker amplification (lower Ct) for irradiated samples then for un-irradiated. Lack of PCR amplification in germinated samples is attributed to too damaging an extraction method for Ba cells. This observation was not expected. Ba Survival Curves were also developed using the quadratic fit y = alpha x + beta x squared. Averaging results form 3 experiments, alpha is reported as -0.0144 + or - 0.008 and beta as -0.00001 + or - 0.0002. Actinometry experiments corrected for the efficiency of the LEDs in all experimentation. Fluorescence measurements monitored germination and outgrowth; they indicated a delay in germination of irradiated spores. AFM images showed morphological changes in irradiated spores

Improving Thermodynamic Models of Transcription by Combining ChIP and Expression Measurements of Synthetic Promoters

Regulation of gene expression is a fundamental process in biology. Accurate mathematical models of the relationship between regulatory sequence and observed expression would advance our understanding of biology. I developed ReLoS, a regulatory logic simulator, to explore mathematical frameworks for describing the relationship between regulatory sequence and observed expression and to explore methods of learning combinatorial regulatory rules from expression data. ReLoS is a flexible simulator allowing a variety of formalisms to be applied. ReLoS was used to explore the question of how complex rules of combinatorial transcriptional regulation must be to explain the complexity of transcriptional regulation observed in biology. A previously published dataset was analyzed for regulatory elements that explained the behavior of regulatory modules for 254 genes in 255 conditions. I found that ReLoS was able to recapitulate a reasonable fraction of the variation: mean gene-wise correlation of 0.7) with only twelve combinatorial rules comprising 13 cis-regulatory elements. This result suggested that learning the combinatorial rules of transcriptional regulation should be possible. State ensemble statistical thermodynamic models are a class of models used to describe combinatorial transcriptional regulation. One way to parameterize these models is measuring the expression of a reporter gene driven by many similar promoters . Models parameterized in this fashion do better at explaining the sequence to expression relationship, but fail to distinguish between multiple biological mechanisms that give rise to equivalent expression results in the synthetic promoters, thus limiting the generalizability of the models. I developed a ChIP-based strategy for quantitatively measuring the relative occupancy of transcription factors on synthetic promoters. This data complements existing methods for obtaining expression data from the same promoters. Comparison of models parameterized with only expression, only occupancy, or expression and occupancy reveals specific biological details that are missed when considering only expression data. In particular, the occupancy data suggests that differential regulatory effects of Cbf1 in glucose versus amino acid are a function of how it interacts with polymerase rather than changes in concentration or binding affinity. Additionally, the occupancy data suggests that Gcn4 binds in a cooperative manner and that Gcn4 occupancy is adversely affected by the presence of a nearby Nrg1 site. Finally, the occupancy data and expression data taken together suggest that Gcn4 binds in competition with another transcription factor. Synthesizing disparate sources of information resulted in an improved understanding of the mechanics of transcriptional regulation of the synthetic promoters and was ultimately largely successful in decoupling the DNA binding energies from the TF interactions with polymerase. However, it suggests that more sophisticated models of the relationship between occupancy and expression may be required in at least some cases. Incorporating different sources of data into models of regulation will continue to be important for learning the biological specifics that drive expression changes