Limits of Performance of Quantitative Polymerase Chain Reaction Systems

Estimation of the DNA copy number in a given biological sample is an important problem in genomics. Quantitative polymerase chain reaction (qPCR) systems detect the target DNA molecules by amplifying their number through a series of thermal cycles and measuring the amount of created amplicons in each cycle. Ideally, the number of target molecules doubles at the end of each cycle. However, in practice, due to biochemical noise the efficiency of the qPCR reaction - defined as the fraction of the target molecules which are successfully copied during a cycle - is always less than
1
. In this paper, we formulate the problem of the joint maximum-likelihood estimation of the qPCR efficiency and the initial DNA copy number. Then, we analytically determine the limits of performance of qPCR by deriving the Cramer-Rao lower bound on the mean-square estimation error. As indicated by simulation studies, the performance of the proposed estimator is superior compared to competing statistical approaches. The proposed approach is validated using experimental data.