An analysis of quantitative PCR reliability through replicates using the Ct method

ABSTRACT

There is considerable interest in quantitatively measuring nucleic acids from single cells to small populations. The most commonly employed laboratory method is the real-time polymerase chain reaction (PCR) analyzed with the crossing point or crossing threshold (Ct) method. Utilizing a multiwell plate reader we have performed hundreds of replicate reactions each at a set of initial conditions whose initial number of copies span a concentration range of ten orders of magnitude. The resultant Ct value distributions are analyzed with standard and novel statistical techniques to assess the variability/reliability of the PCR process. Our analysis supports the following conclusions. Given sufficient replicates, the mean and/or median Ct values are statistically distinguishable and can be rank ordered across ten orders of magnitude in initial template concentration. As expected, the variances in the Ct distributions grow as the number of initial copies declines to 1. We demonstrate that these variances are large enough to confound quantitative classi?cation of the initial condition at low template concentrations. The data indicate that a misclassi?cation transition is centered around 3000 initial copies of template DNA and that the transition region correlates with independent data on the thermal wear of the TAQ polymerase enzyme. We provide data that indicate that an alternative endpoint detection strategy based on the theory of well mixing and plate ?lling statistics is accurate below the mis- classi?cation transition where the real time method becomes unreliable.

There is considerable interest in quantitatively measuring nucleic acids from single cells to small populations. The most commonly employed laboratory method is the real-time polymerase chain reaction (PCR) analyzed with the crossing point or crossing threshold (Ct) method. Utilizing a multiwell plate reader we have performed hundreds of replicate reactions each at a set of initial conditions whose initial number of copies span a concentration range of ten orders of magnitude. The resultant Ct value distributions are analyzed with standard and novel statistical techniques to assess the variability/reliability of the PCR process. Our analysis supports the following conclusions. Given sufficient replicates, the mean and/or median Ct values are statistically distinguishable and can be rank ordered across ten orders of magnitude in initial template concentration. As expected, the variances in the Ct distributions grow as the number of initial copies declines to 1. We demonstrate that these variances are large enough to confound quantitative classi?cation of the initial condition at low template concentrations. The data indicate that a misclassi?cation transition is centered around 3000 initial copies of template DNA and that the transition region correlates with independent data on the thermal wear of the TAQ polymerase enzyme. We provide data that indicate that an alternative endpoint detection strategy based on the theory of well mixing and plate ?lling statistics is accurate below the mis- classi?cation transition where the real time method becomes unreliable.

Cite this paper

nullStowers, C. , Haselton, F. and Boczko, E. (2010) An analysis of quantitative PCR reliability through replicates using the Ct method.*Journal of Biomedical Science and Engineering*, **3**, 459-469. doi: 10.4236/jbise.2010.35064.

nullStowers, C. , Haselton, F. and Boczko, E. (2010) An analysis of quantitative PCR reliability through replicates using the Ct method.

References

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[15] Matsubara, Y., Kerman, K., Kobayashi, M., Yamamura, S., Morita, Y. and Tamiya, E. (2004) Microchamber assay based DNA quantification and specific sequence detection from a single copy via PCR in nanoliter volumes. Journal of Biosensors and Electronics, 20(1), 1482-1490.

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[18] Williams, R., Peisajovish, S., Miller, O., Magdassi, S., Tawﬁk, D. and Griths, A. (2006) Ampliﬁcation of complex gene libraries by emulsion PCR. Nature Methods, 3(7), 545-550.

[19] Karsai, A., Muller, S., Platz, S. and Hauser, T. (2002) Evaluation of a home-made SYBR Green 1 reaction mixture for real-time PCR quantification of gene expression. Biotechniques-Short Technical Reports, 32(4), 790- 796.

[20] Neubert, K. and Brunner, E. (2007) A studentized permutation test for the non-parametric Behrens-Fisher problem. Computational Statistics & Data Analysis, 51(10), 5192-5204.

[21] Reiczigel, J., Zakarias, I. and Rozsa, L. (2005) A bootstrap test of stochastic equality of two populations. Ame- rican Statistical Association, 59(2), 156-161.

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[23] Stowers, C. and Boczko, E.M. (2008) Platescale: The birthday problem applied to single molecule PCR. Biocomp’08, Las Vegas. http://www.ucmss.com/cr/main/ papersNew/papersAll/BIC9135.pdf

[24] Cook, P., Fu, C., Hickey, M., Han, E. and Miller, K. (2004) SAS programs for real-time RT-PCR having multiple independent samples. Biotechniques, 37(6), 990- 995.

[1] Freeman, W., Walker, S. and Vrana, K. (1999) Quantitative rt-PCR: Pitfalls and potential. Biotechniques, 26(1), 124-125.

[2] Larionov, A., Krause, A. and Miller, W. (2005) A standard curve based method for relative real time PCR data processing. BMC Bioinformatics, 6(1), 62-66.

[3] Yuan, J., Reed, A., Chen, F. and Stewart, C. (2006) Statistical analysis of real-time PCR data. BMC Bioinformatics, 7(S6), 85-90.

[4] Abramov, D., Troﬁmov, D. and Rebrikov, D. (2006) Accuracy of a real-time polymerase chain-reaction assay for quantitative estimation of genetically modified food sources in food products. Applied Biochemistry and Microbiology, 42(4), 485-488.

[5] Diehl, F., Li, M., Dressman, D., Yiping, H., Shen, D., Szabo, S., Diaz, L., Goodman, S., David, K., Juhl, H., Kinzler, K. and Vogelstein, B. (2005) Detection and quantification of mutations in the plasma of patients with colorectal tumors. Proceedings of the National Academy of Sciences, 102(45), 16368-16373.

[6] Roussel, Y., Harris, A., Lee, M. and Wilks, M. (2007) Novel methods of quantitative real-time PCR data analysis in murine HelicobaCter pylori vaccine model. Vaccine, 25(15), 2919-2929.

[7] Jagers, P. and Klebaner, K. (2003) Random variation and concentration effects in PCR. Journal of Theoretical Biology, 224(3), 299-304.

[8] Lalam, N., Jacob, C. and Jagers, P. (2004) Modeling the PCR ampliﬁcation process by a size-dependent branching process and estimation of the efficiency. Advanced Applied Probability, 36(2), 602-615.

[9] Liu, W. and Saint, D. (2002) A new quantitative method of real time reverse transcription polymerase chain reaction assay based on simulation of polymerase chain reaction kinetics. Analytical Biochemistry, 302(1), 52-59.

[10] Nedelman, J., Haegerty, P. and Lawrence, C. (1992) Quantitative PCR: Procedures and precision. Bulletin of Mathematical Biology, 54(4), 477-502.

[11] Vaerman, J., Saussoy, P. and Inargiola, I. (2004) Evaluation of real-time PCR data. Journal of Biological Regulators and Homeostatic Agents, 18(2), 212-214.

[12] Pfaffl, M. (2001) A new mathematical model for relative quantification in real-time PCR. Nucleic Acid Research, 29(9), e00.

[13] DeGroot, M.H. (1986) Probability and statistics. 2nd Edition, Addison Wesley Reading MA, Massachusetts.

[14] Cady, N., Stelick, S., Kunnavakkam, M., Lui, Y. and Batt, C. (2004) A microchip-based DNA purification and real-time PCR biosensor for bacterial detection. Proceedings of IEEE Sensors, Vienna, 1191-1194.

[15] Matsubara, Y., Kerman, K., Kobayashi, M., Yamamura, S., Morita, Y. and Tamiya, E. (2004) Microchamber assay based DNA quantification and specific sequence detection from a single copy via PCR in nanoliter volumes. Journal of Biosensors and Electronics, 20(1), 1482-1490.

[16] Mitra, R. and Church, G. (1999) In situ localized ampliﬁcation and contact replication of many individual DNA molecules. Nucleic Acids Research, 27(24), e34.

[17] Samatov, T., Chetverina, H. and Chetverin, A. (2006) Real-time monitoring of DNA colonies growing in a polyacrylamide gel. Analytical Biochemistry, 356(2), 300- 302.

[18] Williams, R., Peisajovish, S., Miller, O., Magdassi, S., Tawﬁk, D. and Griths, A. (2006) Ampliﬁcation of complex gene libraries by emulsion PCR. Nature Methods, 3(7), 545-550.

[19] Karsai, A., Muller, S., Platz, S. and Hauser, T. (2002) Evaluation of a home-made SYBR Green 1 reaction mixture for real-time PCR quantification of gene expression. Biotechniques-Short Technical Reports, 32(4), 790- 796.

[20] Neubert, K. and Brunner, E. (2007) A studentized permutation test for the non-parametric Behrens-Fisher problem. Computational Statistics & Data Analysis, 51(10), 5192-5204.

[21] Reiczigel, J., Zakarias, I. and Rozsa, L. (2005) A bootstrap test of stochastic equality of two populations. Ame- rican Statistical Association, 59(2), 156-161.

[22] Wilcox, R.R. (2006) Comparing medians. Computational Statistics & Data Analysis, 51(3), 1934-1943.

[23] Stowers, C. and Boczko, E.M. (2008) Platescale: The birthday problem applied to single molecule PCR. Biocomp’08, Las Vegas. http://www.ucmss.com/cr/main/ papersNew/papersAll/BIC9135.pdf

[24] Cook, P., Fu, C., Hickey, M., Han, E. and Miller, K. (2004) SAS programs for real-time RT-PCR having multiple independent samples. Biotechniques, 37(6), 990- 995.