Optimization of ion exchange sigmoidal gradients using hybrid models: Implementation of quality by design in analytical method development.

Thorough product understanding is one of the basic tenets for successful implementation of Quality by Design (QbD). Complexity encountered in analytical characterization of biotech therapeutics such as monoclonal antibodies (mAbs) requires novel, simpler, and generic approaches towards product characterization. This paper presents a methodology for implementation of QbD for analytical method development. Optimization of an analytical cation exchange high performance liquid chromatography (CEX-HPLC) method utilizing a sigmoidal gradient has been performed using a hybrid mechanistic model that is based on Design of experiment (DOE) based studies. Since sigmodal gradients are much more complex than the traditional linear gradients and have a large number of input parameters (five) for optimization, the number of DOE experiments required for a full factorial design to estimate all the main effects as well as the interactions would be too large (243). To address this problem, a mechanistic model was used to simulate the analytical separation for the DOE and then the results were used to build an empirical model. The mechanistic model used in this work is a more versatile general rate model in combination of modified Langmuir binding kinetics. The modified Langmuir model is capable of modelling the impact of nonlinear changes in the concentration of the salt modifier. Further, to get the input and output profiles of mAb and salts/buffers, the HPLC system, consisting of the mixer, detectors, and tubing was modelled as a sequence of dispersed plug flow reactors and continuous stirred tank reactors (CSTR). The experimental work was limited to calibration of the HPLC system and finding the model parameters through three linear gradients. To simplify the optimization process, only three peaks in the centre of the profile (main product and the adjacent acidic and basic variants) were chosen to determine the final operating condition. The regression model made from the DoE data yielded a R2 >0.97 which made it possible to predict and choose the design space where the optimal resolution between the acidic/main peaks and the basic/main peaks could be achieved (>1.2 and >2.5, respectively). The optimal operating condition was validated using experimental runs and was found to give the same resolution as what was predicted by the simulation. The proposed approach aims to significantly reduce the time required for method optimization as well as the extent of experimentation.