Interplay between Diffusion and Bond Cleavage Reaction for Determining Release in Polymer-Drug Conjugates

In conjugated polymeric drug delivery systems, both the covalent bond degradation rate and the diffusion of the freely moving drug particles affect the release profile of the formulation. Using Monte Carlo simulations in spherical matrices, the release kinetics resulting from the competition between the reaction and diffusion processes is discussed. For different values of the relative bond cleavage rate, varied over four orders of magnitude, the evolution of (i) the number of bonded drug molecules, (ii) the fraction of the freely moved detached drug within the polymer matrix, and (iii) the resulting fractional release of the drug is presented. The characteristic release time scale is found to increase by several orders of magnitude as the cleavage reaction rate constant decreases. The two extreme rate-limiting cases where either the diffusion or the reaction dominates the release are clearly distinguishable. The crossover between the diffusion-controlled and reaction-controlled regimes is also examined and a simple analytical formula is presented that can describe the full dependence of the release time on the bond cleavage rate constant. This simple relation is provided simply by the sum of the characteristic time for purely diffusional release and the bond cleavage decay time, which equals the inverse of the reaction rate constant.