The receptor-toxin-antibody interaction: Mathematical model and numerical simulation

TL;DR

This paper develops a reaction-diffusion mathematical model and numerical simulations to evaluate the protective effectiveness of antibodies against toxins at the cellular level, aiding in antibody selection.

Contribution

It introduces a refined RTA interaction model with numerical simulations tailored to realistic parameters, enhancing evaluation of antibody protection and timing.

Findings

Model demonstrates different intracellular transport regimes.

Simulation results inform optimal timing for antibody application.

Refined model improves prediction of antibody protective potential.

Abstract

A reaction-diffusion model of receptor-toxin-antibody (RTA) interaction is studied numerically. The protective properties of an antibody against a given toxin are evaluated for a spherical cell placed into a toxin-antibody solution. The selection of parameters for numerical simulation approximately corresponds to the practically relevant values reported in the literature (ricin and monoclonal antibody 2B11) with the significant ranges in variation to allow demonstration of different regimes of intracellular transport. The proposed refinement of the RTA model may become important for the consistent evaluation of protective potential of an antibody and for the estimation of the time period during which the application of this antibody becomes the most effective. It can be a useful tool for in vitro selection of potential protective antibodies for progression to in vivo evaluation.