A mathematical analysis of rebound in a target-mediated drug disposition model: I.Without feedback

Abstract

We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after one or more applications of an antibody drug using a target-mediated drug disposition model. Using geometry and dynamical systems analysis, we show that rebound will occur if and only if the elimination rate of the drug-receptor product is slower than the elimination rates of the drug and of the receptor. We also analyse the magnitude of rebound through approximations and simulations and demonstrate that it increases if the drug dose increases or if the difference between the elimination rate of the drug-receptor product and the minimum of the elimination rates of the drug and of the receptor increases.

A mathematical analysis of rebound in a target-mediated drug disposition model: II. With feedback

“…2014), we considered a one-compartment TMDD model based on the original work of Levy (1994) where the ligand L binds reversibly with the receptor R to form a receptor-ligand complex P as shown in Fig. 2.…”

“…Adding the bolus injection gives the initial conditionsAfter the ligand is added to the system in its baseline state, initially the receptor level decreases, but after a while it goes up again and returns to its baseline value, since the steady state is globally asymptotically stable (Aston et al. 2014). Rebound occurs if, in the return to the baseline value, the receptor level increases to values above the baseline .…”

“…In Aston et al. (2014), we determined precise conditions for the existence and non-existence of rebound. Our main result was the following.…”

“…In our previous paper (Aston et al. 2014), we showed that if no homeostatic feedback is present, rebound will occur if and only if the elimination rate of the target-drug complex is slower than both the elimination rate of the drug and the elimination rate of the target. Binding to cell-surface receptors typically results in accelerated turnover of the anti-body and hence complex, so it can be expected that rebound will occur in rare cases only.…”

“…3, after a review of the main results of our first paper (Aston et al. 2014) on rebound in the basic TMDD model without feedback in Sect. 2.…”