h reality it is not uncommon for the product and impurity o f a chromatographic reparation to be expressed in different units and for there to be no mass equivalence, fo r example, in the separation o f an enzyme from total protein the enzyme level is often expressed in terms o f enzymatic activity whilst total protein is expressed in rormal concentration units i.e. m gm f'; in the purification o f plasmid DNA for gene fierapy the DNA level is often expressed in m g m f’ whereas that o f a major contaminants, endotoxin, is expressed in EU (endotoxin unit). Conversion to consistent units is often not straightforward. In the case where mass equivalency is not known, the generation o f the fractionation diagram will encounter a problem as the total mass o f the materials, including product and impurity, is required to plot the graph. If the product and impurity are expressed in different units, then they cannot be summed up while calculating the total mass.
For such systems the fractionation diagram is replaced by a plot where the relative change in the cumulative fractional amount o f impurity with the corresponding fractional mass o f product eluted is shown (Figure 3.9).
Having defined the basis for a modified fractionation diagram it is now possible to examine the process insight such a plot revels. The first observation is that the plot enables a contamination index (Cl) to be defined as the amount o f impurity remaining in a unit o f product:
t- . r-r X- X- j- total amount o f impurity
Cl = gradient o f fractionation diagram x ------- (-^ • i z) total amount o f product
As with the continual form of the fractionation diagram it is possible to operate at any positions along the modified fractionation curve that satisfy the following criterion: the horizontal distance between any two points gives the yield; the slope of the tangent between these two points leads to the calculation o f the contamination index corresponding to that yield. By varying the position o f the collection points a plot o f contamination index against yield can then be produced. Again, similar to the
C hapters: Development of Fractionation Diagram Approach In Chromatography
PF vs. yield diagram illustrated previously, the plot obtained in this case represents the set o f all the possible values o f the eontamination index achievable for any yield (Figure 3.10).
Y,
0
1
X, 9
Figure 3.9; Fractionation diagram for the system where product and impurity are expressed in different units. X ’ and Y ’ are the cumulative fraction of target product and impurity respectively eluted at any time. Subscripts 1 and 2 denote the start and end points of product collection on the fractionation curve.
Contamination Index
CI,„i„ Boundary
Yield (%)
Figure 3.10: Theoretical plot of contamination index against product yield. For any value of product yield, there exist a number of possible values of contamination index. The minimum contamination index (CCm) is usually of most interest. This exists at the lower bound of the contamination index. Points A is the minimum value in first interval, point B in the second and so on.
C hapter 3: D evelopm ent o f Fractionation Diagram A pproach in Chrom atography
For the case o f impurity removal the objective is to maximise the removal o f impurity. In the new notation that is equivalent to minimising the contamination index for a specified product yield. In order to obtain the minimum contamination index (CI„,j„) the same incremental-searching-type computer algorithm as was used for the generation o f PF versus yield plots was implemented. However in this case the algorithm was employed to search through all the contamination index values achievable for each product yield, and to select the minimum value. This enables a plot o f minimum contamination index versus product yield to be generated. For example, in Figure 3.10, point A is the minimum contamination index for the first value o f yield, and point B for the second, C for the third and so on.
Similarly, having specified a desired value o f product yield and/or minimum contamination index, the retention time or volume for the sample collection can be determined by retrieving the corresponding data points generated and stored during the simulation o f the contamination index versus yield plot.
3.4
Concluding Remarks
The background to the fractionation diagram approach has been explained. The extension and modification o f the framework, originally developed for protein precipitation, to chromatographic separations have been discussed. The development o f a contamination index for the purpose o f indicating the degree o f contamination in the chromatographic fractions has been defined. The resultant diagrams: fractionation diagram, maximum purification factor versus product yield diagram and minimum contamination index versus product yield diagram will now be used in a series o f case studies in the following chapters (Chapter 4, 5 and 6) in order to establish the utility o f the approaches and to demonstrate the nature o f the process insight gained from such a method o f data analysis. The robustness o f the approach will be demonstrated through application to two sets o f simulated results (Chapter 4 and 6) and three sets o f experimental results and industrial data (Chapter 5).