Statistical inference for a quasi birth–death model of RNA transcription

Abstract

Background: A birth–death process of which the births follow a hypoexponential distribution with L phases and are controlled by an on/off mechanism, is a population process which we call the on/off-seq-L process. It is a suitable model for the dynamics of a population of RNA molecules in a single living cell. Motivated by this biological application, our aim is to develop a statistical method to estimate the model parameters of the on/off-seq-L process, based on observations of the population size at discrete time points, and to apply this method to real RNA data. Methods: It is shown that the on/off-seq-L process can be seen as a quasi birth–death process, and an Erlangization technique can be used to approximate the corresponding likelihood function. An extensive simulation-based numerical study is carried out to investigate the performance of the resulting estimation method. Results and conclusion: A statistical method is presented to find maximum likelihood estimates of the model parameters for the on/off-seq-L process. Numerical complications related to the likelihood maximization are identified and analyzed, and solutions are presented. The proposed estimation method is a highly accurate method to find the parameter estimates. Based on real RNA data, the on/off-seq-3 process emerges as the best model to describe RNA transcription.