Systems biology and the mathematical modelling of antibody-directed enzyme prodrug therapy (ADEPT)

Antibody-directed enzyme prodrug therapy (ADEPT) can generate highly localised concentrations of cytotoxic agents directly in a tumour, thereby reducing the collateral toxicity associated with normal tissue exposure. ADEPT is a two-component approach. First, a non-toxic antibody-enzyme fusion protein is localised in the tumour matrix by binding a specific antigen expressed only on the surface of a cancer cell. Once the fusion protein is bound, an inert small molecule prodrug is administered which is the substrate for the enzyme bound to the tumour surface. When the prodrug comes into contact with the bound enzyme, an active cytotoxic agent is generated. A multiple length-scale model of ADEPT therapy in solid tumours is presented. A four-compartment pharmacokinetic (PK) model is formulated where the tumour is comprised of interstitial and cell-surface subcompartments. The macroscopic PK model which describes the biodistribution of antibody-enzyme conjugate, prodrug and active drug at the largest length scale is coupled to a reaction-diffusion tumour model. The models are qualitatively validated against current literature and experimental understanding. The relationship between tumour localisation and the affinity of the antibody-enzyme conjugate for its surface antigen is explored by simulation. The influence of pharmacokinetic and biophysical parameters such as renal elimination rate and permeability of the tumour vasculature upon tumour uptake and retention of the fusion protein are also explored. Lastly, a technique for establishing an optimal prodrug dosing schedule is formulated and initial simulation results are presented.