What is Gel filtration?

Gel filtration (GF) is a chromatography technique that separates molecules according to size.
Within the fractionation range chosen, molecules are eluted in order of decreasing size.

The separation mechanism is non-adsorptive and independent on the eluent system used and thus very gentle. Recoveries are very high both on the basis of mass and biological activity.

Since GF is non-adsorptive and eluted under isocratic conditions (no gradients or steps) the sample is not concentrated during the separation, but slightly diluted, a fact that limits the applicable sample volume.

The fact that the separation depends solely on molecular size makes the selectivity unique and high overall resolutions are obtained when gel filtration is combined with other LC techniques.

Since large molecules elute earlier than small ones, proteins and peptides will elute in the buffer used to equilibrate the gel filtration column, regardless of the original sample solvent.
GF can thus be used for desalting, buffer exchange and removal of low Mr contaminants.
Compared to other LC techniques the resolution in GF may be judged as relatively low. However, its unique selectivity allows dimers and larger polymeric forms of the target molecule to be separated from monomers and denatured forms may be separated from native ones.

All this together makes GF especially well-suited to so-called polishing.

Gel filtration is commonly used in two different modes:
1. High resolution mode to separate large molecules like proteins, peptides oligonucleotides, polysaccharides etc (Figures. 1 and 2).

Fig 1. High resolution mode - Peptides separated on Superdex™ Peptide

Fig 2. High resolution mode for polishing - Removal of polymers.

2. Group separation mode (Fig 3) to separate large molecules (Mr >5000) as a group from small molecules like salts and buffer ions.

Fig 3. Group separation mode - Desalting a protein on a PD-10 column.

Group separation mode accepts much larger sample volumes than high resolution mode and can be performed at considerably higher flow rates.
Simple small gravity-driven columns are normally used to desalt samples with volumes ~1ml. So-called spin columns, used e.g. for post-PCR clean-ups or for clean up after labelling oligos are examples on chromatography driven by centrifugation. The great advantage with centrifugation-driven columns is that a very large number of samples can be dealt with in parallel.

The gel filtration experiment

The typical gel filtration experiment consists of three phases as illustrated below:

Explanation of the symbols

Symbolic representation of a
section of a gel filtration bead
surface. The light parts represent
pores of various sizes.

Sample molecule with no access to the pores.	Sample molecule with partial access to the pores (the larger ones in the bead section!)	Sample molecule with full access to the pores.

.1. Equilibration.
The column is equilibrated with the buffer intended for the separation.

2. Sample application.
The sample is added as a sharp narrow zone at the top of the column. For good resolution the sample volume should be restricted to 0.5 % - 5% of the column volume.

3. Elution.
Elution buffer (normally the same type buffer as that used for equilibration) is pumped through the column to make the sample components separate by continuous re-partitioning.

.

The separation mechanism

The ability of gel filtration to separate molecules according to size resides with the highly porous structure of gel filtration media and is basically a question of accessible volumes.

In a column all sample molecules have access to the liquid between the beads . This volume is called the void volume in gel filtration and equals ~30% of the column volume.

Gel filtration media contain pores allowing the sample molecules to penetrate into the gel filtration beads to different degrees depending on size. Size, together with the volume of these pores determines the pore volume.

The non-porous part of the beads is called the backbone and is inaccessible for the sample molecules. For a good GF matrix the volume of the backbone is around 3% - 5% of the column volume of a well- packed column.

Fig 1.1. Scanning electron micrograph
of an agarose gel. Magnification x 50,000.
Ref. Anders S. Medin,PhD Thesis,
Uppsala University 1995.

Fig 1.2. The different volumes accessible to
sample molecules.

Partitioning between the mobile and the stationary phase

In the gel filtration column, sample molecules are partitioned between the eluent (the mobile phase) and the accessible pores of the gel filtration beads (the stationary phase). This partitioning acts to establish a dynamic equilibrium of sample molecules between the mobile and the stationary phases and is driven exclusively by diffusion (Fig 1.3).

Fig 1.3

Transport along the column
The mobile phase transports the sample molecules down the column, but acts only on the sample molecules present in the mobile phase. The molecules present in the pores are "stationary" and escape this type of transportation.
However, this transport creates an uneven distribution of “stationary” and “mobile” sample molecules, which the partitioning mechanism tries to correct. The effect of this is a mass transfer of sample molecules from the mobile phase to the pores at the front of the sample zone (Fig 1.4), a mass transfer in the opposite direction at the rear end of the zone (Fig 1.5) and an apparent retardation of the sample zone.

The larger the part of sample molecules in the pores, the larger the retardation.

Fig 1.4

Fig 1.5

A certain deviation from equilibrium is needed in order to make the sample zone move down the column.
This, however, is unavoidably associated with broadening of the sample zone.

Elution volumes

The migration rate of a sample zone in any chromatographic situation depends on the fraction of the sample molecules present in the mobile phase.

Molecules excluded from the pores of the stationary phase (100% in the mobile phase) move down the column at the same speed as the mobile phase. They will consequently leave the column after one void volume ( V₀ ) of mobile phase has passed through the column.

Molecules with partial access to the pores will be retarded in relation to their respective degree of access to the pores: in other words they will elute from the column in order of decreasing sizes.

Molecules with full access to the pores will all move down the column at the same speed and remain unseparated from each other. Using a GF medium with a backbone volume of ~5% they leave the column after slightly less than one column volume of mobile phase has passed through the column.

Fig 1.6. The three categories of accessible volumes are used for different purposes.

Separation modes

High resolution mode is used to separate individual macromolecules. This can only be achieved for molecules with partial access to the pores of the gel filtration medium. To help in selection of the proper medium for any given problem, gel filtration media are categorized according to fractionation range. The fractionation range reflects the pore size distribution of a given gel filtration medium by stating the range of molecular masses with partial access to the pores. A wide variety of gel filtration media are available today and together they cover a molecular mass range from 100 to 8000000 i.e. from small peptides to very large proteins.

Applicable sample volume is restricted in high resolution mode, since no concentrating effect is active in gel filtration. Sample volumes of ~0.5 -5 % of the column volume will provide sample zones narrow enough to avoid unacceptable overlap between closely spaced peaks.

Flow rate is kept low to avoid peak broadening due to incomplete mass transfer and columns are long to provide optimum resolution (see under Resolution in gel filtration below).

A _{280 nm}

Fig 3.1. High resolution mode - high resolution run of peptides on Superdex™ peptide.

Group separation mode is used to remove small molecules from macromolecules.
The fractionation range is chosen to elute the macromolecules in the void volume and the small molecules as late as possible. Being completely excluded from the pores, macromolecules will not separate from each other but elute as a group at an elution volume equal to the void volume.

GF will not discriminate between small molecules having full access to the pores (neutral salts, buffer salts, low M_r additives etc.). These molecules will instead elute as a group after approximately one column volume of eluent has passed the column. The effect of this is that the macromolecules "move" into the buffer used for equilibrating the column, while the low M_r components of the original sample buffer lag behind. In other words a buffer exchange has been achieved.

The large difference in elution volumes for macromolecules and for "salts" allows sample volumes up to 30% of the column volume to be applied.

In a group separation like this the degree of overlap caused by zone broadening effects is far less important than in the high resolution mode.

Higher flow rates can consequently be applied and a broader and shorter column may be used.
Simple small gravity-driven columns are normally used to desalt samples with volumes ~1ml. Spin columns, used for example post-PCR clean-ups or for clean up after labelling oligos are examples on chromatography driven by centrifugation. The great advantage with centrifugation-driven columns is that a very large number of samples can be dealt with in parallel

Fig 3.2. Group separation mode -
desalting albumin on a PD-10 column.

Characterisation of gel filtration media

The selectivity of a gel filtration medium depends solely on its pore size distribution and a selectivity curve is used to describe this.

Selectivity curves, independent of the conditions used, are obtained by plotting Kd or Kav vs log M_r for series of macromolecules with different sizes (Fig 4.1).

Fig 4.1 Selectivity curve where Kav
is plotted against log M_r.

Kd is the distribution coefficient for the partitioning of a sample molecule between the mobile and stationary phases and is defined by the following expression:

K_d is linearly related to V_r and represents the fraction of the pores available to a given sample molecule. It depends only on the gel filtration medium used and the size of the sample molecule.
Since V_i is difficult to measure it is usual to substitute the term (V_c-V_o) for V_i in the partition equation and call the result Kav instead of Kd.

Though not a true partition coefficient, K_av is also linearly related to V_r for a given GF medium.
K_av varies between 0 (V_r = V₀) and slightly less than 1 (V_r approximately = V_c). Selectivity curves are usually fairly linear over the range Kav = 0.1 to Kav = 0.7. This part of the curve is used to define the fractionation range (Fig 4.2).

Fig 4.2. Definition of fractionation range and
exclusion limit for a gel filtration medium.

Another important characteristic of a GF medium is the M_r of the smallest molecule excluded from the pores called the exclusion limit. The exclusion limit is defined by conventional as the M_robtained from the intercept of the extrapolated linear part of the selectivity curve with the log M_r axis (Fig 4.2).

Figure 4.3 shows the linear parts of the selectivity curves for Superdex™ and Sephacryl™ media. Together they cover a M_r range from 100 to 8,000,000 for peptides and globular proteins.
As can be, Superdex has very steep selectivity curves and should be chosen for applications requiring the highest resolution.

Fig 4.3. Fractionation ranges for Superdex and Sephacryl gel filtration media.
The steeper the curve, the higher the resolution.

Resolution in Gel filtration

The success of high resolution separations in gel filtration depend, primarily on:

Choosing conditions that provide enough space between the relevant sample zones i. e. achieving a sufficient selectivity.
Counteracting the zone broadening effects i.e. achieving a sufficient efficiency in the chromatographic process.

As exemplified in Figure 5.1 these two parameters are interdependent with regard to resolution. In the chromatogram to the left the two peaks show no overlap when the peaks are kept narrow i.e. when the zone broadening effects are effectively counteracted [blue trace]. However, when the peak width is doubled (red trace) the overlap becomes massive. In fact, a doubling of the distance between the centers of the peaks is necessary to restore the non-overlap situation (chromatogram to the right).

Figure 5.1. The dependence of resolution on the selectivity
and the counteraction of zone broadening.

To describe phenomena as shown in Figure 5.1, resolution (Rs) is defined by the following expression:

(V_r2 - V_r1) thus represents the distance between the peaks and 1/2 (W₁ + W₂) the mean peak width of the two peaks (Fig 5.2).

Fig 5.2. Parameters used for defining resolution (Rs).

The distance between the peaks (V_r2 - V_r1) (the selectivity) is determined by two factors in GF:

The selectivity curve of the medium.
The steeper the slope of the selectivity curve, the larger the Kav and consequently (V_r2 - V_r1) (Fig 5.3).

Fig 5.3. Relation between elution difference and
difference in M_r for two proteins.

Observe however, that (V_r2 - V_r1) is not linearly related to the difference in M_r, but to the ratio between the respective M_r or to be more precise (V_r2 - V_r1) is proportional to log(M_r1 / M_r2) for globular proteins.
.

Figure 5.4 Examples of how to match fractionation
range and M_r of sample molecules.
The length of the column.
GF is an isocratic technique meaning that elution conditions are constant throughout the entire experiment (no gradients or steps). Each sample component will thus move down the column with its own specific and constant speed . Consequently distance between the peaks increases steadily with travel distance and the longer the column, the larger the (V_r2 - V_r1). However, the sample zones broaden during their passage through the column and the longer the column, the broader the zones. This zone broadening will in part counteract what is gained in separation by the larger (V_r2 - V_r1).
In reality one need to increase the column length four-fold to double the resolution.

One HR 10/300 GL column
Column length: 30 cm
Two 10/300 GL columns in series column
Column length: 60 cm

ddddddddddddddddddd
Figure 5.5. Column length and resolution - effect of using two columns in series.

Peak width is affected by the following factors:

Uniformity of the beads and of the packed bed.

These factors influence the uniformity of the flow through the column and thus the shape of the sample zones. When the stationary phase consists of irregular, non-uniform beads or when the gel bed in the column contains irregularities, the path length for the sample may vary in different parts of the column. As a result, broad asymmetric sample zones will be formed when passing the column (Fig 5.6). This type of effect is assigned the term eddy diffusion and is independent of time and flow rate.
Eddy diffusion should not be confused with the type of effects described below which depend on diffusion rather than cause it.

Figure 5.6. Eddy diffusion -
Zone broadening caused by bed irregularities.
Bead size and flow rate.

Bead size and flow rate both influence the efficiency (the ability to keep peaks narrow) of the chromatographic process though in different ways.

Consider a zone of sample molecules moving down a GF column and involved in a continuous partitioning process between the mobile and the stationary phases (Fig 5.7) The mobile phase transports the sample molecules down the column, but acts only on the sample molecules present in the mobile phase. The molecules present in the pores of the stationary phase escape this type of transportation.
.

Figure 5.7 Mass transfer directions
in a travelling sample zone.

However, the transport creates an uneven distribution of “stationary” and “mobile” sample molecules in that the concentration profile in the mobile phase will always be slightly ahead of that in the stationary phase.
The partitioning mechanism strives to correct this resulting in a mass transfer of sample molecules from the mobile phase to the pores at the front of the sample zone and a mass transfer in the opposite direction at the rear end of the zone.

This positional discrepancy in concentration profiles causes broadening of the sample zone and is a consequence of the chromatographic process itself i.e. the continuous re-partitioning.

Though always present, the extent of this type of zone broadening depends on:
1. Mass transfer rate.
2. Mobile phase flow rate.
To minimize it, mass transfer must be allowed time enough for equilibration (figure 5.8):

The flow rate has to be balanced against the mass transfer rate.
.
.

Figure 5.8. Zone broadening caused
by incomplete mass transfer.

However, zone broadening caused by diffusion along the column (axial diffusion) in the mobile phase increases with the time the zone spends in the column.
Since zone broadening due to incomplete mass transfer and to axial diffusion react in opposite ways on flow rate, there exists a flow rate where the sum of these effects is at a minimum.

The diagrams in Figure 5.9 illustrate the flow rate dependence of the three different zone broadening effects discussed above for small and large molecules:
- Incomplete mass transfer dominates zone broadening at high flow rates (2). This is less pronounced for small molecules, since they diffuse faster than large molecules.
- Axial diffusion dominates at low flow rates (4). This time the effect is more pronounced for small molecules due to their higher diffusion rates.
- Eddy diffusion reflecting heterogeneities of the gel bed is independent on flow rate (3).
- The sum total zone broadening shows a minimum (1).
Three important conclusions can be drawn:

1. Excessively high flow rates should be avoided with large molecules, while low flow rates are less detrimental.
2. With small molecules on the other hand, flow rates lower than the optimal one (minimum of curve 1 in Figure 5.9) should be avoided.
3. The optimal flow rate (minimum of curve 1) is lower for large molecules than for small ones. Moreover, curve 1 for small molecules is rounder around the minimum than that for large molecules.

Figure 5.10. Peak width and bead size -
shows the practical consequences of the effects
explanied above for three molecules with wide differing Mr.

The effects of flow rate on zone broadening discussed above applies to all chromatographic techniques based on re-partitioning.

One can facilitate the mass transfer by reducing the bead size. This will shorten distances between the beads and above all increase the "active" surface of the stationary phase, all circumstances that aid in increasing the mass transfer rate in the re-partitioning process.
The higher the mass transfer rate, the closer you get to equilibrium conditions and the lesser the zone broadening (figure 5.11). (For a given molecule the efficiency is inversely proportional to the square of the bead diameter, all other conditions being constant !)

Figure 5.11. Peaks are narrower with smaller beads
and higher flow rates may be used.

In fact, modern HPLC techniques capitalizes mainly on facilitating mass transfer by employing small beads.

The chromatograms in Figure 5.12 demonstrate the effect of employing smaller beads. As seen in Figure 5.11, not only will the peaks provided by 10 µm beads be narrower than those provided by 100 µm beads, they are also far less sensitive to higher flow rates.
.

Figure 5.12. Effect of bead size on resolution.

The effect of bead size on zone broadening discussed above applies to all chromatographic techniques based on re-partitioning.

Gel Filtration in practice

Use of gel filtration

High resolution mode	Group separation
Separates macromolecules according to size.	Desalting macromolecular samples.
Suitable for polishing in multi-step purification protocols.	Buffer exchange of macromolecular samples.
Separates macromolecular polymers from monomers.	Removal of low and high Mr contaminants.
Separates de-natured forms of proteins from native ones.
Separates conformers.

Experimental

	High resolution mode	Group separation
GF chromatograpy medium	Select fractionation range to embrace target molecule. For best resolution select steepest selectivity curve. For narrow peaks select small bead size.	Use Sephadex™ G-25 or equivalent.
Column	Use long and narrow columns. Typical length: 30-100 cm. Column volume should be 20 - 200 times sample volume.	Column length less important.
Eluent	Any eluent may be used provided it is compatible with sample and medium.	Any eluent may be used provided it is compatible with stability of sample and medium.
Flow rate	Use low flow rates to prevent peak broadening.	Accepts flow rates considerbly higher than those used in high resolution mode.
Sample volume	For high resolution restrict sample volume to 0,5 % to 5% of column volume.	Desalting and buffer exchange will accept sample volumes up to 30% of the column volume.

Before applying the sample:

Check the viscosity.
Filter or spin to remove particles.

To increase resolution:

Keep within the optimal fractionation range.
Reduce the sample volume.
Change to a chromatography medium with smaller beads.
Connect two columns in series.
Reduce the flow rate.

Sample viscosity must not drastically deviate from that of the eluent or distorted sample zones will form. Avoid viscosities larger than 4 cP or protein concentrations above 70mg/ml.

Non-specific adsorption rarely occurs with agarose or dextran-based GF media. However, if peaks are unexpectedly retarded, show tailing or if poor recovery is experienced, ionic or hydrophobic interactions may be suspected.

Buffer should contain > 0.05M NaCl or equiv. to avoid ionic interactions
Hydrophobic interactions may be avoided by adding 25% acetonitrile; or 5 % isopropopanol. Alternatively add 10% etyleneglycol.