Distributions of positive signals in pyrosequencing

Pyrosequencing is one of the important next-generation sequencing technologies. We derive the distribution of the number of positive signals in pyrograms of this sequencing technology as a function of flow cycle numbers and nucleotide probabilities of the target sequences. As for the distribution of sequence length, we also derive the distribution of positive signals for the fixed flow cycle model. Explicit formulas are derived for the mean and variance of the distributions. A simple result for the mean of the distribution is that the mean number of positive signals in a pyrogram is approximately twice the number of flow cycles, regardless of nucleotide probabilities. The statistical distributions will be useful for instrument and software development for pyrosequencing and other related platforms.