Global sensitivity analysis of a single-cell HBV model for viral dynamics in the liver

Abstract

The predictive accuracy of mathematical models representing anything ranging from the meteorological to the biological system profoundly depends on the quality of model parameters derived from experimental data. Hence, robust sensitivity analysis (SA) of these critical model parameters aids in sifting the influential from the negligible out of typically vast parameter regimes, thus illuminating key components of the system under study. We here move beyond traditional local sensitivity analysis to the adoption of global SA techniques. Partial rank correlation coefficient (PRCC) based on Latin hypercube sampling is compared with the variance-based Sobol method. We selected for this SA investigation an infection model for the hepatitis-B virus (HBV) that describes infection dynamics and clearance of HBV in the liver [Murray & Goyal, 2015]. The model tracks viral particles such as the tenacious and nearly ineradicable covalently closed circular DNA (cccDNA) embedded in infected nuclei and an HBV protein known as p36. Our application of these SA methods to the HBV model illuminates, especially over time, the quantitative relationships between cccDNA synthesis rate and p36 synthesis and export. Our results reinforce previous observations that the viral protein, p36, is by far the most influential factor for cccDNA replication. Moreover, both methods are capable of finding crucial parameters of the model. Though the Sobol method is independent of model structure (e.g., linearity and monotonicity) and well suited for SA, our results ensure that LHS-PRCC suffices for SA of a non-linear model if it is monotonic.

Keywords

• Latin hypercube sampling
• Partial rank correlation coefficient (PRCC)
• Sobol method
• HBV
• Liver