A quantitative approach for polymerase chain reactions based on a hidden Markov model |
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Authors: | Nadia Lalam |
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Institution: | 1.Department of Mathematical Statistics,Chalmers University of Technology,G?teborg,Sweden |
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Abstract: | Polymerase chain reaction (PCR) is a major DNA amplification technology from molecular biology. The quantitative analysis
of PCR aims at determining the initial amount of the DNA molecules from the observation of typically several PCR amplifications
curves. The mainstream observation scheme of the DNA amplification during PCR involves fluorescence intensity measurements.
Under the classical assumption that the measured fluorescence intensity is proportional to the amount of present DNA molecules,
and under the assumption that these measurements are corrupted by an additive Gaussian noise, we analyze a single amplification
curve using a hidden Markov model(HMM). The unknown parameters of the HMM may be separated into two parts. On the one hand,
the parameters from the amplification process are the initial number of the DNA molecules and the replication efficiency,
which is the probability of one molecule to be duplicated. On the other hand, the parameters from the observational scheme
are the scale parameter allowing to convert the fluorescence intensity into the number of DNA molecules and the mean and variance
characterizing the Gaussian noise. We use the maximum likelihood estimation procedure to infer the unknown parameters of the
model from the exponential phase of a single amplification curve, the main parameter of interest for quantitative PCR being
the initial amount of the DNA molecules. An illustrative example is provided.
This research was financed by the Swedish foundation for Strategic Research through the Gothenburg Mathematical Modelling
Centre. |
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Keywords: | Data analysis Hidden Markov model Molecular biology Monte Carlo expectation maximization algorithm Polymerase chain reaction |
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