INTRODUCTION

Broadly, chromatography refers to a number of separation techniques where molecules are distributed between two phases: a stationary phase, often a chromatography resin, and a mobile phase or eluent, which in the case of protein separation, is a solvent such as water or chloroform.

For commercial purifications, chromatography is always carried out as column Chromatography due to scale considerations. But other techniques, such as thin layer chromatography or paper chromatography, also exist.

COLUMN CHROMATOGRAPHY

In column chromatography, the mobile phase, or eluent, is pumped through the column filled with a stationary chromatography resin.

In the simplest form of operation, the components to be separated travel through the column at different speeds and are collected at different times at the outlet of the column.

Molecules that are more attracted to the stationary phase move more slowly through the system than those that are more attracted to the mobile phase. For biopharmaceutical manufacturing, only column chromatography is capable of operating at commercial scale.

There are a number of different types of chromatography used in the purification of proteins:

• Gel permeation chromatography, which separates molecules by size
• Ion exchange chromatography, which separates molecules based on differences in their charge density
• Hydrophobic interaction chromatography, which separates molecules based on differences in hydrophobicity
• Affinity chromatography, which separates molecules based on differences in their affinity for a target ligand attached to the chromatography resin

MAIN CALCULATIONS

Since the eluent is pumped through the column at a defined flow rate, this also means that molecules will elute after different volumes of eluent have passed through the column. This is captured in a chromatogram, which is a plot of the concentration exiting the column versus time or volume. The retention volume, V_R, for a molecule is the volume that has passed through the column since the target molecule was introduced onto the column.

We can determine how well a molecule is retained by the column by calculating the retention factor, k

Here V₀ is the void volume, or the total volume of the mobile phase within the column.

The larger the retention factor, the less the molecule is associated with the mobile phase and the more it is associated with the stationary phase.

The goal for any chromatographic operation is the separation of two or more species. The measure of the ability of a column to separate species is known as the peak resolution, R_S. It is defined by the following equation:

Here, V_R2 and V_R1 are the retention volumes for two different molecules with V_R2 > V_R1 and w_b1 and w_b2 are the widths of each chromatographic peak at its base.

To completely separate two molecules, R_S must equal at least 1.5.

The shape of a chromatographic peak is also indicative of how efficient the column is.

The column efficiency N, also known as the number of theoretical plates, can be calculated using this equation.

Because all symmetrical peaks should have roughly the same value of N, N is a property of the column. The larger N is, the narrower the peaks, and the better the column.

All other things being equal, a longer column will have more theoretical plates than a shorter one. So it's often useful to calculate the height of a theoretical plate H by dividing the length of the column by the number of plates.

Here, the smaller the plate height, the better the column.

The peak resolution can also be related to N, and with some algebra, we get this equation.

 Here, k bar is the mean of the retention factors for the two peaks, k1 plus k2 divided by 2. And alpha is the relative retention or separation factor, k2 divided by k1. The resolution depends on three key factors, the selectivity, the retention, and the plate number.

The selectivity alpha has the largest impact on resolution.

The selectivity depends on both the resin and the molecules to be separated.

Therefore, correctly choosing the chromatography resin has the largest impact on our ability to separate two different molecules