Table of Contents
Chromatography is the collective term for a set of separation techniques that operate based on the differential partitioning of mixture components between a mobile and a stationary phase. The mobile phase (a liquid or a gas) travels through the stationary phase (a liquid or a solid) in a defined direction. The distribution of components between the two phases depends on adsorption, ionic interactions, diffusion, solubility or, in the case of affinity chromatography, specific interactions. Depending on the experimental design, the separation in a liquid mobile phase may be carried out via column or planar chromatography, on analytical or preparative scales.
Chromatographic methods are important in the analytical and preparative separation of biological samples. Gel filtration chromatography (size exclusion chromatography) is often the method of choice to purify macromolecules, taking advantage of their different sizes and shapes. Ion exchange chromatography is also useful for the separation of macromolecules, operating based on the various net charges on their surface, which can be tuned via the pH of the medium. Biological specificity in enzyme-substrate, enzyme-inhibitor, receptor-ligand, antigen-antibody (and other) interactions is utilised in affinity chromatography. In this method, one interaction partner is immobilised on a solid surface (stationary phase) and can selectively bind its interacting partner from a mixture in the mobile phase. The other components of the mixture can then be removed by replacing the mobile phase (washing). The pure material is then eluted by applying a mobile phase that disrupts the specific interaction.
Of the quasi-infinite possibilities of analytical applications of liquid chromatography, only a few relevant ones will be mentioned in this chapter. The analysis of amino acid mixtures and that of the products of Edman degradation in the process of amino acid sequencing are both carried out using chromatography. Chromatographic methods coupled to on-line mass spectrometry are instrumental in current proteomics research.
Quantification of separation
(1) Resolution (RS)
Resolution is a number describing the separation of chromatographic peaks. By definition, resolution is the distance between peak maxima (elution volumes) divided by the average of peak widths (Figure 6.1). The elution volumes and the peak widths are to be measured in identical units. RS is therefore a dimensionless number. In the case of a constant flow rate, the quantification of volumes can be replaced with the more convenient measurement of time.
The RS value defines the extent of separation. The larger the RS between two peaks, the more ideal the separation (Figure 6.2). (Note that even perfectly separated peaks may comprise impure materials. In many cases, two or more components may co-elute under a given set of chromatographic conditions.)
The chromatographic separation, the behaviour of the different peaks, and the efficiency of the chromatographic column can be described using the following parameters.
The retention factor or capacity factor, k`n, is defined for the extent of retention of a compound under a given set conditions. The retention factor can be calculated for each peak.
k’n = Vn –V0 /V0 or k’n = tR – t0 / t0
where Vn is the elution volume of component n, V0 is the elution volume of a component proceeding through the column without any interaction, and tR and t0 are the corresponding times, respectively (Figure 6.3).
The retention factor is characteristic of a component in a given composition of the mobile phase, in a given type of column, and at a given temperature. It is independent of the size of the column and of the flow rate of the mobile phase.
(3) Efficiency (N)
The efficiency, N, or in other words, the number of theoretical plates characterises the spreading of the eluted compound. It can be calculated as follows:
N = (Ve/σ )2 = 16(Ve/w)2 = 5,54*(Ve/w1/2)2
N = (tR/σ )2 = 16(tR/w)2 = 5.54*(tR/w1/2)2
where Ve and tR are the elution volume and the retention time of the peak, respectively; σ is band broadening (to be determined by measuring the peak width, W = 4σ); W is peak width measured at the baseline; W1/2 is peak width measured at 50 % of the maximal peak depth. The sign * marks a coefficient calculated from the ratio of W and W1/2 if the peak follows a Gaussian distribution.
The value of N is used to characterise the chromatographic column. As N largely depends on the experimental conditions including the flow rate of the mobile phase, the quantity and quality of the loaded sample, the determination of N is carried out in a standardised manner.
The main reason behind the spreading of a compound and the broadening of chromatographic bands is the longitudinal diffusion of molecules within the column. The effect of diffusion may be decreased by using smaller chromatographic beads and by enhancing the homogeneity of their size distribution.
Besides the particle size, efficiency is significantly influenced by the method of packing of the chromatographic media, especially when the column is home-made. Any inhomogeneity in the sedimented matrix (e.g. due to air bubbles or tunnels) will result in poorer efficiency and, in consequence, imperfect separation.
(4) Selectivity (α)
The selectivity (α) for two neighbouring elution peaks at V1 and V2 is characterised by the quotient of their retention factors:
α = k’2/k’1
The overall quality of the chromatographic separation is influenced by both selectivity and efficiency. Nevertheless, selectivity is more definitive (Figure 6.4).
The chromatographic medium for gel filtration is a hydrophilic gel made up from porous, fine-grain spheres of 10-300 µm diameter. This type of medium defines two solution compartments within the column: one is the freely moving mobile phase outside the gel particles, while the other is the restricted liquid compartment inside the porous particles (Figure 6.5).
When a solution is moving through the gel filtration column, the movement of the solutes depends on two factors: the flow rate of the mobile phase and diffusion. Diffusion enables the molecules to explore the inside of the gel particles if their size so permits. The separation of a molecular mixture is based on the phenomenon that some molecules are excluded from the inside of the gel particles due to their size. These molecules travel quickly in the mobile phase of the column, which is the only compartment available to them. Smaller molecules, on the other hand, spend various amounts of time inside the particles (stationary phase) and flow through the column slower (Figure 6.6).
The result of a gel filtration experiment is usually depicted as an elution diagram. In this diagram, the concentration of the eluted compound is plotted against the volume of the eluent. The appearance of a given compound occurs at its elution volume (Ve). As in other distribution chromatographic methods, the elution of a compound is best characterised by its distribution coefficient (Kd):
where Vo equals the exclusion volume, i.e. the elution volume of a molecule that is larger than the largest pore size of the separating gel. Such a molecule therefore explores only the mobile phase, and is entirely excluded from the gel. Vs equals the volume of the stationary phase, i.e. the volume of the liquid inside the gel particles that is fully accessible only to molecules small enough to travel smoothly even through the smallest pores of the gel. Vs itself is difficult to determine. Therefore, in practice, it is replaced by the Vt-Vo term, also accounting for the non-negligible volume of the gel itself. As a result, a constant pertinent to an apparent volume (Kav) is used instead of Kd (the latter would be valid only for real liquid volumes):
Kav = (Ve-Vo )/(Vt-Vo)
where Kav represents the portion of the gel volume that is accessible to a molecule of a given size. For a totally excluded macromolecule, Kav = 0; whereas, for small molecules diffusing freely in the entire volume of the gel, Kav = 1.
Planning a gel filtration experiment
(1) Choosing the gel type
Several different gel filtration media are available, which should be chosen according to the substance to be separated. These media differ in the chemical properties of the gel matrix, the pore size, the particle size, as well as the physical and chemical stability of the gel. The first developed and still widely used gel matrix is made of crosslinked dextran. Polymer beads made of dextran are known by the trade name Sephadex.
The pore size of the various Sephadex media is controlled by the number of crosslinks. The most popular ones are the entirely hydrophilic G-type gels. Numbers accompanying the G-type mark refer to the pore size and indicate the approximate molecular mass of excluded molecules in kDa. For example, Sephadex G-25 is used to separate relatively small molecules in the molecular mass range of 1000-5000 Da, including peptides. Alternatively, it can also be used to desalt larger proteins. To fractionate larger macromolecules up to 200-300 kDa, the G-150 or G-200 Sephadex gels are to be used. The mechanical properties of dextran gels having large pores are unfavourable due to the low density of crosslinks. These gels are easily compressible. Therefore, more rigid gels made of synthetic polymers are used to separate very large or elongated molecules.
If the size difference between the compounds to be separated is relatively large, e.g. during desalting of a macromolecule, it is practical to choose a gel in which the large-sized compound is eluted in the excluded volume (Vo; thus Kav = 0), while the small component elutes around Vt (thus Kav = 1). In this case, the fraction containing the macromolecules appears sharply, with minimal band broadening and dilution, in the shortest possible elution time.
In case of fractionating macromolecules and if the molecular weight of the compound of interest is known, the gel should be chosen so that the component of interest will elute approximately at the half of the entire fractionation range. For example, if a 100-kDa protein is to be isolated from a protein mixture, the use of a gel that spans the 10-250 kDa fractionation range is recommended.
(2) Choosing the particle size of the gel
Fine-sized beads fill the available space within the chromatographic column more efficiently. Therefore, the volume of the mobile phase will be reduced. This will result in a similar reduction in dilution and band broadening and, in turn, will yield a better resolution. On the other hand, the flow rate in a compact gel column is also reduced. Therefore, larger pressure should be applied when using super-fine beads. Indeed, special pumps are needed below a particle size of 10 µm. Naturally, only rigid, non-compressible gel types can be used in these cases.
For most purposes, the Fine and Medium type particle sizes (20-150 µm) are suitable. For preparative purposes and desalting, where high flow rates are required and the compounds of interest separate well even at a poor resolution, Coarse type gels can be used too.
(3) Choosing the size of the column
During gel filtration, the distance between two zones of separation increases proportionally to the square root of the column length. Long columns (> 100 cm) are used when a high resolution is required, while shorter (< 50 cm) columns are more practical when the aim is desalting or the separation of compounds that can be eluted at markedly different volumes.
Columns with diameters of around 1 cm are used for analytical purposes. By increasing the diameter, the amount of the applied sample, i.e. the capacity of the column, can be increased.
(4) Choosing the sample volume
A narrow start zone (relative to the column length) is sought if maximal resolution is to be achieved, e.g. for analytical purposes or in the case of compounds whose separation is difficult. Therefore, the sample volume in this case should be chosen to be 1-5 % of the column volume. The resolution cannot be further increased using smaller sample volumes, while the dilution will be greater. The sample volume can be increased to as much as 15-20 % of the column volume if the compounds are readily separable, especially when working on a large scale.
(5) Choosing the eluent
The composition of the eluent does not directly influence the resolution of gel filtration. However, all components that have an effect on the molecules to be separated may influence the separation. The pH, ionic strength or the presence of detergents may influence the molecular state of the solutes. For instance, changes in molecular shape or the dissociation of multimeric proteins and enzyme-inhibitor complexes will change their chromatographic behaviour. In general, dilute (0.01-0.1 M) buffers are used that do not influence the structure of the compounds to be separated, but restrict the unwanted adsorption interactions between the gel matrix and the molecules of interest.
When the fractions containing the separated compounds are to be later concentrated, volatile buffers (e.g. ammonium bicarbonate) are practical to use that easily disappear during lyophilisation or film evaporation. The same considerations apply when the salt content of the gel filtration buffer should be subsequently eliminated.
(6) Choosing the flow rate of the eluent
During gel filtration, increasing the flow rate will deteriorate the resolution, because it prevents the formation of equilibrium between the mobile and the stationary phases. Generally, 5-10 mL/cm2x hour is recommended as an optimal flow rate, but in most cases, a several times excess of this will not deteriorate the separation significantly. When doing preparative work, or if the operation must be performed quickly for some reason, the advantage conferred by the higher flow rate may compensate for the deterioration of separation.
To achieve a higher flow rate, of course, a larger pressure must be applied. Therefore, in these cases, the mechanical stability of the gel matrix must be taken into consideration. Non-rigid gels may be compressed at pressures higher than allowed, which may lead to the complete clogging of the chromatographic column.