Multitype PCR branching processes

TL;DR

This paper introduces a multitype PCR branching process model to better understand DNA amplification in PCR, extending previous models with new limit theorems for multiple DNA types.

Contribution

It generalizes existing PCR branching process models to multiple DNA types and proves new limit theorems for this multitype case.

Findings

Extended the PCR branching process model to multiple DNA types.

Proved two new limit theorems for the multitype PCR process.

Abstract

To model amplification Polymerase Chain Reaction (PCR) techniques targeting DNA sequences of several types, we introduce a multitype PCR branching process as a generalized version of the Michaelis-Menten-based branching process model introduced in Jagers-Klebaner, 2003. We establish two limit theorems extending the results of Chigansky-Jagers-Klebaner, 2018 to the multitype case.