(29e) Stochastic and Deterministic Analysis of Reaction Kinetics in the Partially Reversible Copolymerization of Lactide and Glycolide

Poly(lactide-co-glycolide) (PLGA) is an important component in many pharmaceutical applications, including as an excipient in long-acting drug formulations. Several factors are relevant for PLGA’s use as an excipient including molecular weight, composition, end group, and backbone lactyl/glycolyl repeat unit sequencing. Gaps in our understanding of the polymer chemistry surrounding PLGA repeat unit sequencing have hindered regulation of PLGA-containing pharmaceuticals, particularly approval of generic products. A detailed understanding of repeat unit ordering in PLGA is complicated by depolymerization and transesterification reactions that result in broad variability of repeat unit sequencing, which can affect PLGA properties. The established copolymerization models apply only to irreversible copolymerization and new models are required to relate reactivity ratios to repeat unit sequence for copolymers such as PLGA. The central difficulty lies in the prohibitively large number (> 10³⁰) of equations required for a complete deterministic mathematical description of a reversible copolymerization. Initial observations from kinetic experiments demonstrated that glycolide was consumed early in the copolymerization and did not exhibit reversibility, whereas lactide did. Based on these observations, we combined a simplified deterministic model and full stochastic model to extract forward reactivity ratios (r_G, r_L) and a third parameter to account for lactide reversibility (r_R) from experimental time-evolution data taken at several initial feed compositions. The stochastic model was used to verify that the reactivity ratios provided an accurate description of the partially reversible copolymerization by comparison of the fully parameterized model against experimental data. The important effects of transesterification on copolymer sequence are not captured by reactivity ratios. These effects can be modeled stochastically and observed experimentally through the presence of isolated lactyl or glycolyl units in the chain and randomization of the molecular weight distribution. A more complete understanding of PLGA repeat unit sequencing will expand its usefulness as an excipient, promote effective regulation and generic drug development, and advance understanding of reversible copolymerizations.