Is Your Chromatography in Control, or in Transition?

By Dr. Scott Rudge

While chromatography continues to be an essential tool in pharmaceutical manufacturing, it remains frustratingly opaque and resistant to feedback control of any kind.  Once you load your valuable molecule, and insufferable companion impurities, onto the column, there is little that you can do to affect the purification outcome that waits you some minutes to hours later.

Many practitioners of preparative and manufacturing scale chromatography perform “Height Equivalent to a Theoretical Plate” testing prior to putting a column into service, and periodically throughout the column’s lifetime.  Others also test for peak shape, using a measurement of peak skewness or Asymmetry.  However, these measurements can’t be made continuously or even frequently, and definitely cannot be made with the column in normal operation.  More over, the standard methods for performing these tests leave a lot of information “on the table” so to speak, by making measurements at half peak height, for example.

To address this shortcoming, many have started to use transition analysis to get more frequent snapshots of column suitability during column operation.  This option has been made possible by advances in computer technology and data acquisition.

Transition analysis is based on fairly old technology called moment theory.  It was originally developed to describe differences in population distributions, and applied to chromatography after the groundbreaking work of Martin and Synge (Biochem. J. 35, 1358 (1941)).  Eugene Kucera (J. Chromatog. 19, 237, (1965) derived the zeroth through fifth moments based on a linear model for chromatography that included pore diffusion in resins, which is fine reading for the mathematically enlightened.  Larson et al. (Biotech. Prog. 19, 485, (2003)) applied the theory to in-process chromatography data.  These authors examined over 300 production scale transitions resulting from columns ranging from 44 to 140 cm in diameter.  They found that the methods of transition/moment analysis were more informative than measurements of HETP and Asymmetry traditionally applied to process chromatography.

What is transition analysis, and how is it applied?  Any time there is a step change in conditions at the column inlet, there will occur, some time later, a transition in that condition at the column outlet.  For example, when the column is taken out of storage and equilibrated, there is commonly a change in conductivity and pH.  Ultimately, a wave of changing conductivity, or pH, or likely both, exits the column.  The shape of this wave gives important information on the health of the column, as described below.  Any and all transitions will do.  When the column is loaded, there is likely a transition in conductivity, UV, refractive index and/or pH.  When the column is washed or eluted, similar transitions occur.  As with HETPs, the purest transitions are those that don’t also have thermodynamic implications, such as those in which chemicals are binding to or exchanging with the resin.  However, the measurements associated with a particular transition should be compared “intra-cycle” to the same transition in subsequent chromatography cycles, not “inter-cycle” to different transitions of different natures within the same chromatography cycle.

Since transition analysis uses all the information in a measured wave, it can be very sensitive to effects that are observed any where along the wave, not just at, for example, half height.  For example, consider the two contrived transitions shown below:

In Case 1, a transition in conductivity is shown that is perfectly normally distributed.  In Case 2, an anomaly has been added to the baseline, representing a defect in the chromatography packing, for example.  Transition analysis consists of finding the zeroth, first and second moments of the conductivity wave as it exits the column.  These moments are defined as:

These are very easy calculations to make numerically, with appropriate filtering of noise in the data, and appropriate time steps between measurements.  The zeroth moment describes the center of the transition relative to the inlet step change.  It does not matter whether or not the peak is normally distributed.  The zeroth moments are nearly identical for Case 1 and Case 2, to several decimal places.  The first moment describes the variance in the transition, while the second moment describes the asymmetry of the peak.  These are markedly different between the two cases, due to the anomaly in the Case 2 transition.  Values for the zeroth, first and second moments are in the following table:

	Case 1	Case 2
Zeroth moment	50.0	50.0
First moment	1002	979.6
Second moment	20,300	19,623

It would be sufficient to track the moments for transitions from cycle to cycle.  However, there is a transformation of the moments into a “non-Gaussian” HETP, suggested by McCoy and Goto (Chem. Eng. Sci., 49, 2351 (1994)):

Where

Using these relationships the variance and non-Gaussian HETP are shown in the table below for Case 1 and Case 2:

Using this method, a comparative measure of column performance can be calculated several times per chromatography cycle without making any chemical additions, breaking the column fluid circuit, or adding steps.  The use of transition analysis is still just gaining foothold in the industry, are you ahead of the curve, or behind?