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

R. Zachariah Aandahl, Josephine F. Reyes, Scott A. Sisson, Mark M. Tanaka

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 10⁻⁵ to 10⁻² 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 10⁻²·⁰⁶ (95% CI: 10⁻²·⁶¹,10⁻¹·⁵⁸)and under the linear model, the mean mutation rate per locus per repeat unit is 10⁻²·⁴⁵ (95% CI: 10⁻³·⁰⁷,10⁻¹·⁹⁴). 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.