Samuel Leweke

Mechanistic modeling of ion-exchange process chromatography of charge variants of monoclonal antibody products

Ion-exchange chromatography (IEX) is universally accepted as the optimal method for achieving process scale separation of charge variants of a monoclonal antibody (mAb) therapeutic. These variants are closely related to the product and a baseline separation is rarely achieved. The general practice is to fractionate the eluate from the IEX column, analyze the fractions and then pool the desired fractions to obtain the targeted composition of variants. This is, however, a very cumbersome and time consuming exercise. A mechanistic model that is capable of simulating the peak profile will be a much more elegant and effective way to make a decision on the pooling strategy. This paper proposes a mechanistic model, based on the general rate model, to predict elution peak profile for separation of the main product from its variants. The proposed approach uses inverse fit of process scale chromatogram for estimation of model parameters using the initial values that are obtained from theoretical correlations. The packed bed column has been modeled along with the chromatographic system consisting of the mixer, tubing and detectors as a series of dispersed plug flow and continuous stirred tank reactors. The model uses loading ranges starting at 25% to a maximum of 70% of the loading capacity and hence is applicable to process scale separations. Langmuir model has been extended to include the effects of salt concentration and temperature on the model parameters. The extended Langmuir model that has been proposed uses one less parameter than the SMA model and this results in a significant ease of estimating the model parameters from inverse fitting. The proposed model has been validated with experimental data and has been shown to successfully predict peak profile for a range of load capacities (15-28mg/mL), gradient lengths (10-30CV), bed heights (6-20cm), and for three different resins with good accuracy (as measured by estimation of residuals). The model has been also validated for a two component mixture consisting of the main mAb product and one of its basic charge variants. The proposed model can be used for optimization and control of preparative scale chromatography for separation of charge variants.

Fast arbitrary order moments and arbitrary precision solution of the general rate model of column liquid chromatography with linear isotherm

Abstract Algorithms and software are presented for efficiently computing reference solutions of the general rate model with proven error bounds. Moreover, algorithms and software are presented for efficiently computing moments of arbitrary order. The methods are based on numerical inverse Laplace transform, and support both quasi-stationary and dynamic linear binding models. The inlet concentration profiles are treated in a most general way using piecewise cubic polynomials. Algorithmic differentiation obviates manual derivation of the required derivatives. Arbitrary precision arithmetics are applied for minimizing numerical roundoff errors, and several convergence acceleration techniques are evaluated. The implemented software package is freely available as open source on GitHub.

To be certain about the uncertainty: Bayesian statistics for 13C metabolic flux analysis

13C Metabolic Fluxes Analysis (13C MFA) remains to be the most powerful approach to determine intracellular metabolic reaction rates. Decisions on strain engineering and experimentation heavily rely upon the certainty with which these fluxes are estimated. For uncertainty quantification, the vast majority of 13C MFA studies relies on confidence intervals from the paradigm of Frequentist statistics. However, it is well known that the confidence intervals for a given experimental outcome are not uniquely defined. As a result, confidence intervals produced by different methods can be different, but nevertheless equally valid. This is of high relevance to 13C MFA, since practitioners regularly use three different approximate approaches for calculating confidence intervals. By means of a computational study with a realistic model of the central carbon metabolism of E. coli, we provide strong evidence that confidence intervals used in the field depend strongly on the technique with which they were calculated and, thus, their use leads to misinterpretation of the flux uncertainty. In order to provide a better alternative to confidence intervals in 13C MFA, we demonstrate that credible intervals from the paradigm of Bayesian statistics give more reliable flux uncertainty quantifications which can be readily computed with high accuracy using Markov chain Monte Carlo. In addition, the widely applied chi‐square test, as a means of testing whether the model reproduces the data, is examined closer.

Efficient numerical simulation of simulated moving bed chromatography with a single-column solver

Abstract We present four different numerical methods for the numerical simulation of simulated moving bed chromatography. Two approaches use fixed-point iteration for computing cyclic steady states, and two other approaches use operator splitting for computing complete system trajectories. All methods are based on weak coupling of individual column models and can easily be implemented using any existing single-column solver. Simulation software is implemented based on the CADET project and published as open source code. The numerical performance is compared using five case studies. For both fixed-point iteration and operator-splitting, an alternative approach is found to be more efficient than the standard approach. Namely, the one-column analog saves time in computing the cyclic steady state, while lag-aware operator-splitting yields more detailed information on the system trajectory. The presented methods can be combined with other models, for example to consider hold-up volumes, and have applications beyond simulated bed chromatography.

Multi-state steric mass action model and case study on complex high loading behavior of mAb on ion exchange tentacle resin

Tentacle resins for IEX are increasingly applied in preparative chromatography for their higher selectivity and higher capacities in comparison to IEX resins without tentacles. However, tentacle resins are often observed to cause unusual elution behavior of monoclonal antibodies under high loading conditions. Understanding this elution behavior is important for a quality by design approach, as it is now mandated by regulatory agencies. A model-based analysis of load, wash and gradient elution is performed for a monoclonal antibody (mAb) on Fractogel SO3-. Four experiments with increasing loaded mass show complex peak shapes and formation of a shoulder under overloaded conditions. We hypothesize that the observed peak shapes are caused by mAbs binding in multiple states on the tentacle ion-exchange resin. A new multi-state SMA binding model is used for testing this hypothesis. A two-state binding model is found to quantitatively reproduce all four experiments. An in-depth analysis reveals that the shoulder formation under overloaded conditions can be explained by multi-state binding that particularly manifests in rapid but weak re-adsorption of eluting molecules near the column end. The introduced multi-state SMA model combines features of the so-called spreading model (multiple bound states) and of the standard SMA model (salt dependency). It is by no means limited to ion-exchange chromatography on tentacle resins, but the same concept can be applied for studying systems that are based on other physical mechanisms. The new model can potentially improve mechanistic understanding and facilitate quantitative simulation of various phenomena, such as caused by reorientation, reconformation or unfolding of bound species. Similar concepts can be applied for studying surface-induced aggregation and denaturation.