Modeling neutralization of Shiga 2 toxin by A-and B-subunit-specific human monoclonal antibodies

A mathematical model for Shiga 2 toxin neutralization by A-and B-subunit-specific human monoclonal antibodies initially delivered in the extracellular domain is presented, taking into account toxin and antibodies interaction in the extracellular domain, diffusion of toxin, antibodies, and their reaction products toward the cell, the receptor-mediated toxin and complex composed of toxin and antibody to A-subunit internalization from the extracellular into the intracellular medium and excretion of this complex back to the extracellular environment via recycling endosomal carriers. The retrograde transport of the intact toxin to the endoplasmic reticulum and its anterograde movement back to the vicinity of the plasma membrane with its subsequent exocytotic removal to the extracellular space via the secretory vesicle pathway is also taken into account. The model is composed of a set of coupled PDEs. A mathematical model based on a system of ODEs for Shiga 2 toxin neutralization by antibodies in the absence of cell is also studied. Both PDE and ODE systems are solved numerically. Numerical results are illustrated by figures and discussed.