Student: Jana Gevertz Undergraduate Institution: Rutgers University, Mathematics Dept. Graduate Institution: Princeton University, Program in Applied and Computational Mathematics Email: jgevertz@princeton.edu janag@dimax.rutgers.edu Research Area(s): Mathematical Biology Project Name: Mathematical model of real-time PCR kinetics Faculty Advisors: Dr. Stanley Dunn, Professor of Biomedical Engineering Dr. Charles Roth, Assisstant Professor of Biochemical and Biomedical Engineering Rutgers University

### Project Description

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.

### References

[1] Freeman, W. M., S. J. Walker and K. E. Vrana. 1999. Quantitative RTPCR: pitfalls and potential. Biotechniques 26(1): 112-22, 124-5.
[2] Goidin, D., A. Mamessier, M. J. Staquet, D. Schmitt and O. Berthier-Vergnes. 2001. Ribosomal 18S RNA prevails over glyceraldehyde-3-phosphate dehydrogenase and beta-actin Genes as internal standard for quantitative comparison of mRNA levels in invasive and noninvasive human melanoma cell subpopulations. Anal Biochem 295(1): 17-21.
[3] Halford, W. P., V. C. Falco, B. M. Gebhardt and D. J. Carr. 1999. The inherent quantitative capacity of the reverse transcription-polymerase chain reaction. Anal Biochem 266(2): 181-91.
[4] Hsu, J. T., S. Das and S. Mohapatra. 1997. Polymerase chain reaction engineering. Biotechnol Bioeng 55: 359-366..
[5] Jayaraman, A., M. L. Yarmush and C. M. Roth. 2000. Dynamics of gene expression in rat hepatocytes under stress. Metabolic Eng 2: 239-251.
[6] Kainz, P. 2000. The PCR plateau phase - towards an understanding of its limitations. Biochim Biophys Acta 1494(1-2): 23-7.
[7] Peirson, S. N., J. N. Butler and R. G. Foster. 2003. Experimental validation of novel and conventional approaches to quantitative real-time PCR data analysis. Nucleic Acids Res 31(14): e73.
[8] Pfaffl, M. W. 2001. A new mathematical model for relative quantification in real-time RTPCR. Nucleic Acids Res 29(9): e45.
[9] Plum, G. E., K. J. Breslauer and R. W. Roberts (1999). Thermodynamics and kinetics of nucleic acid association/dissociation and folding processes. Comprehensive Natural Products Chemistry. Oxford, UK, Elsevier Science Ltd. 7, ch. 2: 15-33.
[10] Qiagen (2002). HotStar Taq PCR Handbook. Valencia, CA.
[11] Roth, C. M. 2002. Quantifying gene expression. Curr Issues Mol Biol 4(3): 93-100.
[12] Rutledge, R. G. and C. Cote. 2003. Mathematics of quantitative kinetic PCR and the application of standard curves. Nucleic Acids Res 31(16): e93.
[13] Sambrook, J. and D. W. Russell (2001). Molecular Cloning: A Laboratory Manual. Cold Spring Harbor, New York, Cold Spring Harbor Laboratory Press.
[14] Schmittgen, T. D. and B. A. Zakrajsek. 2000. Effect of experimental treatment on housekeeping gene expression: validation by real-time, quantitative RTPCR. J Biochem Biophys Methods 46(1-2): 69-81.
[15] Schnell, S. and C. Mendoza. 1997. Theoretical description of the polymerase chain reaction. J Theor Biol 188(3): 313-8.
[16] Stagliano, K. E., E. Carchman and S. Deb. 2003. Real-time polymerase chain reaction quantitation of relative expression of genes modulated by p53 using SYBR Green I. Methods Mol Biol 234: 73-91.
[17] Tinoco, I., K. Sauer, J. C. Wang and J. D. Puglisi (2001). Physical Chemistry: Principles and Applications in Biological Sciences. Upper Saddle River, NJ, Prentice Hall.

### Project Results

Project results can be found in:

Gevertz, J., Dunn, S., Roth, C.M. 2005. Mathematical model of real-time PCR kinetics. Biotechnology and Bioengineering 92(3): 346-355.

### Project Presentations

 7/1/04: First Project Presentation 7/21/04: Final Project Presentation 10/15/04: Poster Presentation at Biomedical Engineering Society Annual Meeting