A Model-Based Bayesian Estimation of the Rate of Evolution of VNTR Loci in Mycobacterium tuberculosis

Variable numbers of tandem repeats (VNTR) typing is widely used for studying the bacterial cause of tuberculosis. Knowledge of the rate of mutation of VNTR loci facilitates the study of the evolution and epidemiology of Mycobacterium tuberculosis. Previous studies have applied population genetic models to estimate the mutation rate, leading to estimates varying widely from around to per locus per year. Resolving this issue using more detailed models and statistical methods would lead to improved inference in the molecular epidemiology of tuberculosis. Here, we use a model-based approach that incorporates two alternative forms of a stepwise mutation process for VNTR evolution within an epidemiological model of disease transmission. Using this model in a Bayesian framework we estimate the mutation rate of VNTR in M. tuberculosis from four published data sets of VNTR profiles from Albania, Iran, Morocco and Venezuela. In the first variant, the mutation rate increases linearly with respect to repeat numbers (linear model); in the second, the mutation rate is constant across repeat numbers (constant model). We find that under the constant model, the mean mutation rate per locus is (95% CI: ,)and under the linear model, the mean mutation rate per locus per repeat unit is (95% CI: ,). These new estimates represent a high rate of mutation at VNTR loci compared to previous estimates. To compare the two models we use posterior predictive checks to ascertain which of the two models is better able to reproduce the observed data. From this procedure we find that the linear model performs better than the constant model. The general framework we use allows the possibility of extending the analysis to more complex models in the future. Author Summary: Genetically typing the bacterium responsible for tuberculosis is useful for understanding the evolutionary and epidemiological characteristics of the disease. Typing methods based on variable number tandem repeat (VNTR) loci are increasingly being used. These loci, which are composed of repeated units, mutate by increasing or decreasing in the number of these repeats. Knowledge of the mutation rate of molecular markers facilitates the epidemiological interpretation of the observed genetic variation in a sample of bacterial isolates. Few studies have examined the rate of mutation at these markers and estimates to date have varied considerably. To address this problem we develop a stochastic model of evolution of these markers and then estimate their mutation rate using approximate Bayesian computation. We examine two alternative forms of the mutation process. The observed data are from four published data sets of tuberculosis bacterial isolates sampled in Albania, Iran, Morocco and Venezuela. We find that these markers have fairly high rates of mutation compared with estimates from previous studies.