17


Figure 3. Experimental design used for generation (green circles) and validation (red dots) of combined solvent strength and temperature models for six proprietary proteins A - F. T corresponds to the column temperature, tG


gradient time for a linear gradient, ∆tR error for peak width.


experimental retention time were less than 1% for both RPC and IEC. This is comparable to what previously has been reported for small molecules [12,13]. For extrapolation to shorter gradient times, the retention error increased up to 2% for RPC and 10% for IEC. As previously reported, it is important to have a certain difference in retention time between the gradients used to build the retention models. A ratio in gradient time between the longest and shortest gradient of three to four has been proposed by Snyder et al [14], e.g., 20 and 60 min gradients.


prediction error for retention time, and ∆w prediction


The deviation between calculated and experimental peak width is less than 22% for both RPC and IEC. This is similar to what previously has been reported in the literature for small molecules [4, 15, 16]. A deviation in peak width of up to 20% may appear excessive but for peaks of similar size, the impact on resolution should be perfectly acceptable as illustrated in Figure 4.


Figure 4. An illustration of the impact of a 20% prediction error in peak width. For symmetric peaks of similar size the impact on resolution is perfectly acceptable for optimisation purposes.


The RPC and IEC models fi tted to data from the linear gradients described above were subsequently challenged by the prediction of retention time and peak width for more complex, multi-step gradients. Figure 5 depicts the gradients evaluated for RPC. Similar gradients were evaluated for IEC. For both RPC and IEC the prediction errors for retention time and peak width were similar to what was obtained for linear gradients (i.e., error in retention time and peak width were less than 2% and 15% respectively). It should be stressed, however, that it is important to start the gradient at a solvent strength that results in a strong retention of the analytes. If not, signifi cant errors in peak width can be expected due to poor focusing of the sample.


3. Conclusions


Figure 5. Evaluation of predictions made for multi-step RPC gradients using models built with single step gradients for six proprietary proteins A – F (Figure 3). ∆tR


tion time and peak width respectively.


concentration, temperature, pH, and more). It provides a unifi ed environment for processing chromatographic data from different vendor instruments and formats; predicts retention times, carries out automatic peak matching, and predicts chromatograms based on method conditions.


Results The combination of the 1st order solvent strength models (Eqn. 1 or 3) with the 2nd


order temperature model (Eqn. 5) were found to give similar results for RPC and IEC. For the current dataset the 2nd


order solvent


) and peak width (w). For interpolations, the deviation between calculated and


strength model (Eqn. 2) did not increase the accuracy for predictions. Figure 3 shows the design used for generation and evaluation of models for RPC. A similar design was used for IEC. Green circles represent experimental data used to build the model. Red dots represent conditions for evaluation of predicted vs. experimental retention (tR


and∆w corresponds to prediction errors for reten-


It can be concluded that RPC and IEC gradient chromatography at different temperatures can be modelled with the same accuracy for proteins as for small molecules. Presumably due to the unfolding of proteins at higher temperature, a 2nd order temperature model is needed in order to correctly model the retention behaviour of proteins as a function of temperature.


Since proteins respond much more strongly to small changes in solvent strength than small molecules [6], we believe that the use of retention modelling will facilitate the development of chromatographic methods for proteins not only in order to fi nd an optimal selectivity but also to quickly and conveniently fi nd a gradient that gives a suitable retention.


The potential to defi ne custom gradient models in combination with 2nd


order temperature models is now available in


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