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Adaption of Retention Models to Allow Optimisation of Peptide and Protein Separations Patrik Petersson, 1 Jette Munch, 1 Mel Euerby, 2 Andrey Vazhentsev, 3 Michael McBrien, 3 and Karim Kassam 3 1 Novo Nordisk A/S, Måløv, Denmark. 2 Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, Glasgow, UK. 3 Advanced Chemistry Development (ACD/Labs), Toronto, Canada. Introduction Proteins and peptides are becoming analytes of increasing importance within the pharmaceutical industry. This poster describes the adaption and validation of the retention models necessary to accurately model and optimise analytical scale Reverse Phase Chromatography (RPC) and Ion Exchange Chromatography (IEC) separations of peptides and proteins. Retention modelling has successfully been used for the optimisation of analytical scale separations of small molecules for approximately 30 years. A large number of articles have been published on this topic by L. Snyder, P. Janderra, P. Schoenmakers et al. and several commercial software are available, i.e., DryLab, ACD/LC Simulator, ChromSword, and Osiris. When defining a method development strategy for peptides and proteins involving retention modelling, investigated commercially available software packages were not capable of accurately modelling the retention of proteins. This collaboration with ACD/Labs resulted in models that can be utilized within ACD/LC Simulator to accurately model retention times of proteins and peptides. Isocratic Retention Models As described by Snyder and Dolan 1 the following isocratic relationships are required when numerically determining the retention of proteins in gradient elution: lnk = a + b x (1) where k is the isocratic retention factor, a and b are system and analyte specific constants and x the fraction of the strong solvent. Eqn. 1 is valid for reversed phase (RPC) and hydrophobic interaction chromatography (HIC). Often it is extended with a 2nd order term to account for non-linearity. lnk = a + b x + c x 2 (2) In order to account for ion exchange chromatography (IEC) and hydrophilic interaction chromatography (HILIC) the following equation is needed. lnk = d + e lnx (3) where d and e are system and analyte specific constants and x the fraction of the strong solvent. RPC Reversed phase chromatography IEC Ion exchange chromatography HILIC hydrophilic interaction chromatography HIC hydrophobic interaction chromatography NPC Normal phase chromatography Temperature Retention Models For small molecules it has been found to be very effective to simultaneously model gradient shape and temperature. However, the relationship which is normally used, eqn. 4 below, was found to be insufficient for proteins. lnk = f + g / T (4) f and g are analyte and system specific constants and T the column temperature. In order to accurately account for the retention of proteins (Fig.1.) it was necessary to add a second order term. lnk = f + g / T + h / T 2 (5) Figure 1. Retention of small molecules and proteins as function of temperature. UK Office: +44 (0) 1344 668030 Head Office: +1 416 368-3435 Email: [email protected] www.acdlabs.com This can probably be explained by the fact that the structure of the protein changes when heated. At low temperature the protein is folded, at intermediate temperature the protein unfolds and the retention increases with increasing temperature as the number of sites which can interact with the stationary phase increase. When the protein, at high temperature, is completely unfolded it starts to behave as a small molecule, i.e., the retention starts to decrease with increasing temperature (Fig. 2). 3 3.1 3.2 3.3 3.4 x 10 -3 2 2.05 2.1 2.15 1/T [1/K] ln(k) Temperature 20°C 60°C Figure 2. Potential explanation to the retention behaviour of proteins at different temperatures. Method To create models for proteins we used isocratic retention models in combination with numerical solutions in order to calculate retention times for gradient conditions. In this study six proteins with a MW of approx. 25 000 Da were chromatographed and modelled by RPC and IEC. An alpha version of ACD/LC Simulator 2 was provided, which allowed gradient modelling employing the RPC/HIC model (Eqn. 2) and the IEC/HILC model (Eqn. 3) in combination with the 2nd order temperature model (Eqn. 5). t G [min] T [°C] 45 35 25 30 40 50 10 20 40 50 30 60 70 55 Δ t R [%] Δ w [%] A 1.6 22 B 1.7 22 C 2.2 -11 D 2.2 -9 E 2.1 -1 F 2.3 5 Δ t R [%] Δ w [%] A -0.3 21 B -0.3 20 C -0.4 6 D -0.4 8 E -0.4 10 F -0.4 16 Δ t R [%] Δ w [%] A 0.6 -5 B 0.6 -4 C -0.1 1 D -0.1 -1 E 0.0 -1 F -0.1 -3 Δ t R [%] Δ w [%] A 0.7 -6 B 0.8 -5 C 0.6 4 D 0.6 1 E 0.6 -1 F 0.6 3 Figure 3. Experiments used for building (green circles) and validating the model (red dots). The green circles in the illustration above represent experimental data that was used to fit the model while the red dots represent conditions for evaluation of predicted retention times and peak widths. For a simple linear gradient, the accuracy of prediction is Dt R <2% and systematic, whereas Dw <20% (Fig.3). Extrapolation to approximately 20% seems to be reasonable. An evaluation of predictions made for more complex, multi step gradients using the models fitted to one step gradients were found to give very similar accuracy, i.e., Dt R <2% and systematic, whereas Dw <20% (Fig.4). 0 10 20 30 40 50 60 70 0 5 10 15 20 25 30 time [min] %ACN Δ t R [%] Δ w [%] A 1.0 9 B 0.9 8 C 0.0 -1 D 0.0 -1 E 0.0 3 F 0.0 11 Δ t R [%] Δ w [%] A 1.9 15 B 1.8 15 C 0.7 -6 D 0.7 -5 E 0.7 0 F 0.7 8 Δ t R [%] Δ w [%] A 0.5 8 B 0.4 8 C -0.5 -4 D -0.5 -2 E -0.5 1 F -0.4 9 Δ t R [%] Δ w [%] A 1.9 0 B 1.9 1 C 0.5 -2 D 0.5 -4 E 0.4 -2 F 0.4 -8 Figure 4. Evaluation of predictions made for multi step gradients using models built with single step gradients (Fig.3). While 20% error in peak width predictions may sound like a serious problem, as shown below it is quite acceptable for optimisation purposes (Fig.5). There is no difference in the accuracy of peak width predictions between small molecules and proteins. -50 0 50 100 150 200 250 300 350 400 450 500 1.9 2.4 2.9 3.4 3.9 4.4 t [min] S [-] -50 0 50 100 150 200 250 300 350 400 1.9 2.4 2.9 3.4 3.9 4.4 t [min] Figure 5. Illustration of the impact of a 20% error in peak width. ACD/LC Simulator Interface The figure below depicts the ACD/LC Simulator user interface. Figure 6. The ACD/LC Simulator user interface. Conclusion It can be concluded that RPC and IEC gradient chromatography at different temperatures can be modeled with the same accuracy for proteins as for small molecules. Most likely due to the unfolding of proteins at higher temperature, a 2nd order temperature model is needed. As previously described by Snyder et al. 1 also HILIC and HIC should be possible to model using the same models. References 1 L.R. Snyder, J.W. Dolan, High-Performance Gradient Elution: The Practical Application of the Linear-Solvent-Strength Model, Wiley, Hoboken, NJ, 2007. 2 ACD/LC Simulator, version 12 (12.02), Advanced Chemistry Development, Inc., Toronto, On, Canada, www.acdlabs.com, 2013. ) ln( ln + = b a k + = b a k ln ) ln( ln + = b a k ) ln( ln + = b a k + = b a k ln Request a reprint of this poster
