Bayesian approach to model CD137 signaling in human M. tuberculosis in vitro responses

Immune responses are qualitatively and quantitatively influenced by a complex network of receptor-ligand interactions. Among them, the CD137:CD137L pathway is known to modulate innate and adaptive human responses against Mycobacterium tuberculosis. However, the underlying mechanisms of this regulation remain unclear. In this work, we developed a Bayesian Computational Model (BCM) of in vitro CD137 signaling, devised to fit previously gathered experimental data. The BCM is fed with the data and the prior distribution of the model parameters and it returns their posterior distribution and the model evidence, which allows comparing alternative signaling mechanisms. The BCM uses a coupled system of non-linear differential equations to describe the dynamics of Antigen Presenting Cells, Natural Killer and T Cells together with the interpheron (IFN)-γ and tumor necrosis factor (TNF)-α levels in the media culture. Fast and complete mixing of the media is assumed. The prior distribution of the parameters that describe the dynamics of the immunological response was obtained from the literature and theoretical considerations Our BCM applies successively the Levenberg-Marquardt algorithm to find the maximum a posteriori likelihood (MAP); the Metropolis Markov Chain Monte Carlo method to approximate the posterior distribution of the parameters and Thermodynamic Integration to calculate the evidence of alternative hypothesis. Bayes factors provided decisive evidence favoring direct CD137 signaling on T cells. Moreover, the posterior distribution of the parameters that describe the CD137 signaling showed that the regulation of IFN-γ levels is based more on T cells survival than on direct induction. Furthermore, the mechanisms that account for the effect of CD137 signaling on TNF-α production were based on a decrease of TNF-α production by APC and, perhaps, on the increase in APC apoptosis. BCM proved to be a useful tool to gain insight on the mechanisms of CD137 signaling during human response against Mycobacterium tuberculosis.