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The Consultant
Every issue we'll address a practical topic in downstream processing, on which we'll share insights and technical tips we've developed from over 15 years of hands-on idustrial process development. There will be a strong emphasis on the steps required to achieve the best results, along with whatever theory is necessary for it all to make sense. We welcome follow-up discussion, which we will post in the next issue. Our topic for this issue is:

Linear and Step Gradient Elution; Data versus Dogma
Pete Gagnon, VBI

The relative value of linear and step gradients remains a point of controversy in purification process design. Like most such controversies, its persistence reflects incomplete articulation of the merits and limitations of the two formats. In this article we'll discuss some of the major process parameters affecting or affected by gradient format, with the goal of revealing how the 2 formats can be applied most productively.

Product concentration
Step gradients have a reputation for eluting product at higher concentrations than linear gradients. They do so in many contexts, but not all, and there are limits to their concentrating ability in any case. Figures 1 and 2 contrast peak volume as a function of step or linear gradient interval. As shown, gradient format is a minor determinant of peak volume. The key factor is the magnitude of the step or slope. Depending on sample composition and resolution requirements, peak volume from linear gradients can be competitive with peak volume from steps.



As implied by the above Figures, there is an inverse relationship between peak concentration and resolution (Figures 3,4). The sacrifice of resolution to achieve a high product concentration is generally more severe with step gradients. Within a linear gradient, the relative relationships among the eluting proteins tend to be well-preserved. In a step gradient, setting a broader interval to achieve higher product concentration automatically compromises purity. Such intervals are feasible with step gradients only when the requirement for resolution is low.



It is important to look beyond the method at hand when evaluating resolution requirements. If the contaminants flanking the product in one method are easily removed by another method in the same process, then resolution requirements for method at hand are low, despite the flanking contaminants (Figure 5). Broad gradient steps can be employed to elute the product at high concentration without imparing overall process performance.



Figure 6 illustrates the opposite situation where flanking contaminants are shaired by a pair of separation methods. Linear gradients would be challenged by such a situation, but step gradients would be wholly unsuitable. This highlights the point that the foundation of a good process is built on complementarity of separation methods. High resolution linear gradients can be used to maximize the degree of complementarity, but they are not a substitute for the lack of it.



When developing gradient specifications for step gradients, set the broadest interval that doesn't compromise overall process performance. With linear gradients, set the steepest slope. These actions will yield the highest eluting product concentration for whichever format you use.

Eluted product concentration is limited by a number of other factors, regardless of gradient setpoints. One of the most important is diffusional limitations. The slow diffusion constants of proteins makes peak volume a function of media particle and pore size distribution. No matter how extreme your elution step, a given gel will always have a fixed minimum peak width, as a function of particle and pore size distribution. Packing quality will have an effect and dependency on diffusion makes peak width strongly dependent on flow rate as well. Figure 7 illustrates increasing peak width in a linear gradient as a function of flow rate for BSA on a HIC matrix and an anion exchanger. The differences in the relative response, despite column dimensions, sample load, particle and pore size distribution all being identical, demonstrate the influence of other factors. In this case, the higher viscosity of the high-salt HIC buffer was judged to be the dominant cause. However, differential kinetics of the respective elution mechanisms cannot be discounted.



Product purity and recovery
Product purity within a given method is seldom as good with step gradients as with linear gradients, and when it is, it's usually is achieved at the expense of recovery. Narrowing the gradient intervals to partition out flanking contaminants almost always requires sacrificing the leading or trailing fractions of the product peak (Figure 8). This re-emphasizes the importance of maximizing complementarity among process methods as the foundation to process development.



Where high resolution is required, linear gradients are the best option. Figure 9 illustrates a frequent pattern in linear gradient development. As gradient slope is reduced, initially, resolution increases more than peak volume. This reflects the rate of change in mobile phase composition coming into phase with the kinetic limitations of the ligand:protein interaction. With further slope reduction, peak volume increases more than resolution. This doesn't mean that resolution won't continue to improve, just that you will pay an increasingly high price for it. The transition point in resolving efficiency versus peak volume can be estimated by comparing the ratio of product peak height to adajcent valley height among chromatograms with different gradient slopes.



Process reproducibility
Linear gradients have the ability to buffer minor process variations. So long as the product elutes near gradient center, and the gradient amplitude exceeds the range of process variation, external variations cause little more than a modest deviation of gradient slope. The relative relationships among the eluting proteins remain relatively unchanged. If uncontrolled external process variation is high, maintaining the slope while extending the gradient start and endpoints increases its insulating capability. Even substantial variances are absorbed with little consequence. This is important because the sources of variation are diverse and many of them are substantial.

One such source is variation in the fluidics architecture of process chromatographs, especially as they compare with process development systems. Systems vary with respect to accuracy of both flow and solvent proportioning. Equally important, they vary with respect to the amount of internal solvent mixing that occurs between the proportioning valve and the column. Each systems has a characteristic "dispersion volume" -- the volume of solvent required for complete transition from one gradient setpoint to another. The larger the dispersion volume, the larger the volume of solvent required to achieve a programmed setpoint. The effects on step gradients can be devastating.

Figure 10 illustrates process variation resulting from differences in dispersion volume relative to column volume. The process was developed with a small column on a chromatograph with a high dispersion volume. During development, the wash step never reached target concentration within the programmed volume. When the process was scaled to a larger column on the same system, the dispersion to column volume ratio diminished, the wash step did reach its programmed value, and the product eluted prematurely.



Degree of column loading also has disproportionate importance for step gradients. Figure 11 illustrates variation in peak width and elution position as a function of column load. Not only does the peak become wider with increasing load, it elutes earlier. Step specifications set at a given column load are valid only at that load. This is a particular problem in situations where the product concentration and its proportion to contaminants in the feedstream vary from lot to lot.



This is also an impediment to process development. Development columns must be loaded to their intended process capacity throughout process development. This is a circular trap since capacity varies according to the run conditions. Setpoints for linear gradients, on the other hand, can be set preliminarily with low subcapacity column loads, then adjusted to compensate for the load-shift after other process specifications have been set. This is much simpler and it conserves sample.

Other external variations also have significant impact on the efficacy of step gradient setpoints. Hydrophobic interaction and protein A separations are very sensitive to temperature. Variations of a few degrees can render steps invalid, sacrificing purity, recovery, or both. Ion exchange is sensitive to minor variations in conductivity. As with column load, these effects have process development as well as reproducibility ramifications. The process must be modeled, and setpoints validated across the range of process variation that may affect the process. If resolution requirements are very permissive then broad steps pose no serious reproducibility concern. Otherwise, the "buffering capacity" of linear gradients makes their use essential.

Process sequencing
Step gradients offer process sequencing opportunities that linear gradients rarely match. For example, you can often elute product from a HIC column with a low salt buffer, and proceed directly to an ion exchanger with little intermediate sample re-equilibration. Products eluting within a linear gradient are likely to have a higher salt content, requiring either a higher degree of dilution or complete buffer exchange. The same principle applies to other process sequences.

Process control
Step gradients on ion exchangers can cause gross pH aberrations within the column. With anion exchangers, a large step in chloride concentration can liberate a sufficient concentration of hydroxide to raise the local pH to 12 and potentially denature the product. Acidification by hydronium ion displacement can occur on cation exchangers. This puts more constraints on buffer formulation to ensure adequate pH control. The gradual increase of salt in linear gradients avoids this problem.

Process monitoring
Steps provide no information as to the composition of a peak. Three gradient steps taken on a column loaded with a complex mixture will produce 3 peaks, regardless of the gradient intervals. This makes extensive secondary testing essential during process development, and also means that large-scale process failures can be masked. Even linear gradients can't indicate the complete composition of a peak, but the relationship among eluting peaks does provide an index that allows immediate visual assessement as to whether or not the process is within specified control limits. Linear gradient profiles also make it possible to abbreviate the requirement for secondary testing during method devlopment.

Process simplicity
The purported simplicity of step gradient applies to mechanical simplicity only. When large-scale chromatography systems were limited to simple switch valves this was an overiding factor, but no longer. Virtually all of the current generation large scale systems have linear gadient capability equivalent to the most sophisticated HPLCs.

With the wide availability of large-scale linear gradient chromatography systems, step gradients have become more -- not less -- complicated than linear gradients. The complications begin in development, as noted above, where setting reproducible specifications requires comprehensive full-load scale modeling. Accommodating all of the factors requires tedious balancing and rebalancing of the step intervals to support the best combination of purity, recovery, product concentration, and reproducibility. With linear gradients, once the slope is defined, accommodating external process variation is a simple matter of extending the start and endpoints sufficiently to insulate the "core" segment.

Process economy
The higher resolution supported by linear gradients frequently allows purifications to be conducted with fewer methods. A pair of linear methods will often support purification performance equivalent or better than a triplet of step methods, and triplets of linear gradient methods consistently outperform quads of steps. This is an important distinction for process economics. It reduces media requirements. It reduces column hardware requirements. It reduces labor. It reduces storage space requirements. It means that expensive manufacturing space is tied up for shorter periods per product -- thereby increasing facility capacity -- and it reduces validation requirements. The economic advantage is amplified by simpler development and better reproduciblity.

Conclusions
Gradient elution is the means by which the inherent complementarity among separation methods is exploited to its greatest advantage. Step gradients may be preferable where the relative selectivities among separation methods make high resolution fractionation unnecessary. The more permissive the fractionation requirements for a given method, the steeper the steps, the higher the eluted product concentration, and the less the results will be affected by external process variation. This tends to favor steps in processes with more methods, and where external sources of process variability are tightly controlled, as with manufacture of injectable products.

Linear gradients are generally a stronger option where resolution requirements are high, where external process variables are poorly controlled, where time pressure requires accelerating the development cycle, and where there is economic pressure to minimize the number of fractionation methods. This combination of requirements is more characteristic of in vitro reagent manufacturing environments and preparation of investigational materials.

In practice, every purification represents a unique challenge, as well as a unique set of opportunities. No preconceived philosophy about gradient modes is going to give you the flexibility you need to achieve the best process performance. Evaluate both formats, and apply them as they serve you best.