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Mechanistic chromatography models

Mathematical models based on natural science

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Mechanistic chromatography models

Liquid chromatography is a complex superposition of different effects: general flow and transport patterns, mass transfer phenomena in microporous materials and adsorption. Creating a predictive model of your downstream process requires a profound consideration of these effects.

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How do mechanistic models work?

Mechanistic downstream models consider physical and biochemical effects in the chromatography system by means of natural laws. Outside the adsorber beads, the injected components are transported by convection, which is induced by a connected pump. Dispersion comprises, among other effects, molecular diffusion and non-ideal flow. Inside the pores of the adsorbing particle, diffusion dominates their movement. Finally, the component is adsorbed onto the inner surface of the particle.

Depiction of the key principles of mechanistic chromatography models.

Building a predictive chromatography model

In order to predict a bioprocess, the governing natural principles are described in mathematical model equations. In fact, column chromatography systems comprise three individual but coupled models: a fluid dynamics model, describing general flow and transport patterns in the in the column; a model to describe the fluid phase within the beads’ pores and an adsorption isotherm that models the adsorption process via thermodynamics. A large variety of such models are known in literature, describing different chromatography and interaction modes. Given the model and corresponding model parameters, the resulting chromatogram can be predicted by means of computer simulation.

Chromatography model equations

Few experiments are needed to calibrate your chromatography model

Within mechanistic model equations a number of model parameters are inherent, such as column dimensions or flow rates. Unknown parameters such as diffusivity coefficients, protein charge or mass transfer parameters must be derived from experimental data. Since each model parameter has a unique purpose and effect on the chromatogram, the required data is limited and experiments usually range from three to ten. These do not require purified components but can be performed with impure feedstock. The measured chromatograms are then processed in silico using numerical optimization to derive the unknown parameters by inverse curve fitting.

Once calibrated, downstream models are a fully equivalent digital representation of your real chromatography system. A simulated experiment can thereby replace a real experiment. The most obvious application of simulation is therefore to optimize existing processes. In conjunction with Process Analytical Technologies (PAT) and real-time information on the composition of raw materials, downstream models can be expanded to become digital twins of running production processes.

Hand dropping testube in laptop, ChromX then calibrates model

Downstream models can predict new bioprocesses

As they are based on natural principles, mechanistic models include all elementary information of the system dynamics. This also allows the extrapolation and examination of a wide range of process options without any further experimentation. Even completely different scenarios can be simulated with no additional experimental effort: overloaded conditions, flow-through operations or continuous chromatography. This opens a wide range of mechanistic model applications, enabling a cheap and fast replacement of lab experiments with computer simulation.

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