C) top five unique and symmetric complexes of perlucin (without calcium ions)
3.4. Size-‐exclusion chromatography of perlucin
3.4.1. Principles of size-‐exclusion chromatography
Back in 1959 Porath and Flodin (Porath & Flodin [1959], Porath [1960]) introduced “a method for desalting and group separation” of macromolecular solutions, which they called “gel filtration”. They filled columns with liquid-‐soaked beads of cross-‐linked dextran under wet conditions. Dextran is a polymer of glucose that can be cross-‐linked with epichlorohydrin in small beads (see e.g. Porath [1960], Flodin [1967] and Arshady [1991a] for a review on the manufacturing of beaded gel filtration media). Porath and Flodin (Porath & Flodin [1959]) applied a solution of polysaccharides of different molecular weights and a monosaccharide on top of a bed of hydrated dextran beads as described above. After the solution had entered the bed the column was continuously purged with distilled water at approximately 2 𝑚𝑚𝑚𝑚/𝑚𝑚𝑚𝑚𝑚𝑚. The eluated solution from the column was fractionated and analysed for carbohydrate content. It turned out that the components of the saccharide solution were separated and those molecules with larger molecular weight were found in the fractions corresponding to a smaller elution volume.
This observed effect – the separation of components with different molecular weight in such a manner that heavier substances have a lower elution volume compared to lighter molecules – can be explained by the following basic mechanism (see e.g.
Tiselius et al. [1963] or Hagel [2011] as well as Yau et al. [1979] for a general introduction to SEC). Depending on the “effective size” (“effective” in this context shall denote those size of the molecules that takes effect in SEC) of the molecules in the solvent that is used during the chromatographic analysis, different volumes inside the polymer beads are accessible for them. The smaller the molecules the larger the space inside the beads consisting of (cross-‐linked) polymers they can occupy and vice versa.
This separation principle is illustrated schematically in Fig. 3.4.1. This easily drawn picture of the operation principle of SEC assumes that an equilibrium between the concentrations of the molecules inside the polymer beads and in the void volume is established fast with respect to the solvent flow rate.
Fig. 3.4.1. Principle of size-‐exclusion chromatography. A dissolved sample A consisting of several constituents of different sizes (red, green and blue dots) is brought into a tube between a buffer solution reservoir B and a SEC column C. Through continuous pumping of the buffer solution the sample is applied on top of the SEC bed (orange circles). The beads consist of a (cross-‐linked) polymer network schematically illustrated by black entangled lines inside the orange circles. The polymer beads consist of pores of different sizes. Due to the different size of the sample molecules (red, green, blue dots) different volumes inside the polymer beads are accessible for these molecules. This is indicated in the figure as follows. The red particles are large and cannot enter the polymer beads. The green particles are smaller than the red particles and can enter parts of the polymer beads. In contrast the smallest blue particles of the injected sample can access most of the space inside the polymer beads. This leads to a size-‐
dependent separation of the injected sample. The different molecules leave the column in different elution volumes 𝑉𝑉!. When the separated molecules leave the SEC column they can be detected by a photometer D operating at the appropriate wavelength. The output of the photometer is a graph of the absorbance dependent on the elution time or volume. Finally the solution that passed the photometer is fractionated in E. An important parameter in SEC is the (extra-‐particle) void volume 𝑉𝑉!. The void volume is shown in this figure in dark grey. It is the space inside the SEC column that is not occupied by polymer beads (orange). Particles that cannot penetrate the polymer beads (or interact with them) leave the SEC column in an elution volume that is equivalent to the void volume. Note that in this illustration the buffer solution pump and the valve for the sample injection is not shown for simplicity. Figure prepared with Inkscape (http://inkscape.org). Similar figures can be found e.g. in Yau et al. [1979] as well as Hagel [2011].
This assumption was tested with at least two approaches (see also Yau et al. [1979], chapter 2.3. therein). Little et al. (Little et al. [1969]) found no flow rate dependency of
the elution volume of acetonitrile and polysterene in the flow rate range between0.1 and 12.5 𝑚𝑚𝑚𝑚/𝑚𝑚𝑚𝑚𝑚𝑚. Yau (Yau [1969]) incubated dry SEC media directly with different solutions of molecules of different molecular weight each for 24 ℎ. Then he determined the concentration of the corresponding molecules in the volume outside of the swollen SEC media. The concentrations of the molecules in solution before and after the addition of SEC media were measured. A relationship between these concentrations and the elution volume of the corresponding substance on the corresponding SEC media could be derived if the ideal case of instantaneous equilibration during SEC was assumed. For Yau the experimental values obeyed the expected relationship sufficiently to conclude that “the exclusion effect plays the primary role in GPC peak separation” (Yau [1969], p. 491). However Yau noted that other processes can affect the separation of macromolecules on a SEC column as well. In particular lateral diffusion can have an influence on the separation depending on the substances to be separated and the experimental conditions. The effect of diffusion can be expected being more pronounced at higher flow rates and substances with low diffusion coefficients.
To allow a comparison of the results of SEC experiments with different column geometries not the elution volume 𝑉𝑉! of a substance is usually stated but its
“distribution coefficient” (also termed “partition coefficient” or “exclusion coefficient”) 𝐾𝐾! (see e.g. Gelotte [1960]). It is given by
𝐾𝐾! =𝑉𝑉!− 𝑉𝑉!
𝑉𝑉! (3.4.1.a)
and includes the (extra-‐particle) void volume 𝑉𝑉! and the accessible inner (intra-‐
particle) pore volume 𝑉𝑉! of the SEC media. Introducing the total liquid volume 𝑉𝑉! inside a SEC column the distribution coefficient can be written as (see e.g. Hagel [2011])
𝐾𝐾! =𝑉𝑉!− 𝑉𝑉!
𝑉𝑉!− 𝑉𝑉! (3.4.1.b)
Note that usually 𝑉𝑉! is not equal to the geometrical SEC column volume 𝑉𝑉! due to the volume occupied by the cross-‐linked hydrated polymers of the SEC media. The distribution coefficient of a substance can be interpreted as the fraction of the volume
of the SEC media that is available to the corresponding substance during the SEC (Laurent & Killander [1964]). Under ideal conditions the distribution coefficient has values between 0 (substance is completely excluded from the SEC media) and 1 (the SEC media is completely accessible to the substance).
Obviously there are at least two important parameters relevant to the separation of substances with SEC. One parameter is the pore shape inside the polymer beads that constitute the media inside the SEC column. The other parameter is the “effective size”
of the molecules to be analysed under the conditions during the SEC. Knowledge of both parameters would be necessary to derive a theoretical relationship between the distribution coefficient of a given substance and a molecular property like molecular weight.
The pore size distribution of dry SEC media can be determined experimentally for example with mercury intrusion porosimetry (see Grimaud et al. [1978] for an example study and Adamson [1990] for a brief introduction to mercury intrusion porosimetry). Many different pore shape models for SEC media can be found in the literature, for example: simple pore geometries like cylinders or spheres (e.g. Yau et al.
[1979] or Knox & Scott [1984]), a normal distribution of the accessible volume fraction (Ackers [1967]), SEC media as a network of randomly oriented rods (Laurent &
Killander [1964]), or the accessible volume is designed as the space between random-‐
sized touching spheres (Knox & Scott [1984]). Hagel et al. (Hagel et al. [1996]) stated that “many materials have a rather complicated structure which may not be described accurately by a few parameters” (p. 34). They used experimentally obtained SEC data to calculate “apparent size-‐exclusion pore dimensions” (p. 42) for a given SEC media.
These dimensions were obtained from a fit of the experimental data to the following model. The authors assumed on the one hand that the SEC media consists of pores (cylindrical, spherical or slab geometry) with a normal distribution of radii (the mean and the standard deviation were fit parameters) and on the other hand that the molecules to be separated are hard spheres. Dependent on the chosen pore geometry (cylindrical, spherical or slab geometry) different apparent pore dimensions were calculated for the same set of experimental values.
It seems that for the SEC media used in this thesis – cross-‐linked copolymer of allyldextran and bisacrylamide (Sephacryl S-‐100 HR, Hagel et al. [1989], see also Fig.
10 in Arshady [1991b] for a chemical structure) – a simple pore geometry cannot be
inferred from scanning electron microscopy images given by Hagel et al. (Hagel et al.
[1989], Fig. 2 therein for Sephacryl S-‐500 HR).
A determination of the apparent pore dimensions as described by Hagel et al. (Hagel et al. [1996]) was beyond the scope of this thesis. In principal this would require a sufficient number of well characterized dextran standards.
The reason why dextran standards are used in several different studies as calibration – because they are flexible polymers – leads to the second important parameter involved in the separation of substances with SEC: the “effective size” of the molecules to be separated.
It seems to be reasonable to assume that the “effective size” is the hydrated volume of the substance. The hydrated volume 𝑉𝑉! of a molecule of this substance can be expressed as (Cantor & Schimmel [1980], Chapter 10-‐2)
𝑉𝑉! = 𝑀𝑀
𝑁𝑁! 𝜈𝜈!+ 𝛿𝛿!" 𝜈𝜈!" ≈ 𝑀𝑀
𝑁𝑁! 𝜈𝜈!∗ + 𝛿𝛿!" 𝜈𝜈! (3.4.2.)
Here 𝑀𝑀 is the molecular weight of the substance, 𝜈𝜈! is the specific volume of the hydrated substance, 𝛿𝛿!" is the ratio of the masses of the solvent bound to the hydrated substance and the substance itself and 𝜈𝜈!" is the specific volume of the bound solvent.
Assuming that the substance is diluted and its concentration does not affect its hydration then the sum in the brackets in 3.4.2. can be approximated: 𝜈𝜈!∗ is the partial specific volume of the substance and 𝜈𝜈! the specific volume of the (pure bulk) solvent.
The partial specific volume of a substance expresses the change of the volume of a (liquid) system when a certain mass of the substance is added to the solvent (see also IUPAC Gold Book, http://goldbook.iupac.org/P04422.html, last access 07/03/14).
Some illustrative values for proteins quoted from Cantor and Schimmel (Cantor &
Schimmel [1980]) are given. The partial specific volume of proteins is in the order of 0.73 𝑐𝑐𝑚𝑚!/𝑔𝑔 and the hydration is in the order of 0.4 𝑔𝑔 H!O 𝑔𝑔 protein.
There are at least two easier approaches to determine the hydrated volume of a solvated molecule. One exploits the diffusion of molecules in solution. If the diffusion constant 𝐷𝐷 of a molecule in a given solution with viscosity 𝜂𝜂 is known, one can calculate its frictional coefficient with the Einstein-‐Smoluchowski relation. In a second
step Stokes law can be used to calculate the (Stokes) radius 𝑟𝑟!" of a sphere with the same diffusion and friction coefficient
𝑟𝑟!" = 3 4 𝜋𝜋 𝑉𝑉!
!!
= 𝑘𝑘! 𝑇𝑇 𝐷𝐷
1
6 𝜋𝜋 𝜂𝜂 (3.4.3.)
Here 𝑘𝑘! and 𝑇𝑇 are the Boltzmann constant and the Temperature. An ellipsoidal molecule shape can be considered by shape parameters (see for example Cantor &
Schimmel [1980]).
Following Cantor and Schimmel (Cantor & Schimmel [1980], Chapter 12-‐1) another possibility to determine the hydrated volume exploits the intrinsic viscosity [𝜂𝜂] of a solvated substance. It is defined as
𝜂𝜂 = lim!→!
𝜂𝜂𝜂𝜂!− 1
𝑐𝑐 (3.4.4.)
If a (macro)molecular substance is solvated in a liquid with viscosity 𝜂𝜂! then one can expect an concentration 𝑐𝑐 dependent increase in the solution´s viscosity 𝜂𝜂(𝑐𝑐). The limiting value – at infinite dilution – of the relative change in viscosity divided by concentration is the intrinsic viscosity. Note that 𝜂𝜂 has the units of the inverted concentration 𝑐𝑐, e.g. volume per mass. This volume can be associated with the hydrated volume of the solute
𝜂𝜂 = σ 𝑉𝑉!𝑁𝑁!
𝑀𝑀 (3.4.5.)
where σ is a shape factor considering the geometry of the molecule. It is σ ≥ 2.5 where the lower bound corresponds to a spheric molecule.
In terms of SEC both parameters – the Stokes radius as well as the intrinsic viscosity [𝜂𝜂] – were proposed amongst others as parameter that describes the separation of different substances (see Hagel [2011]). Potschka (Potschka [1987]) proposed the viscosity radius obtained from the intrinsic viscosity as universal calibration principle.
Frigon et al. (Frigon et al. [1983]) observed that dextrans and native proteins with
similar value of the product 𝜂𝜂 ⋅ 𝑀𝑀 had similar elution volumes. Less agreement was found when Stokes radii were used. Dubin and Principi (Dubin & Principi [1989]) found the use of 𝜂𝜂 ⋅ 𝑀𝑀 only meaningful for flexible polymers and globular proteins since rod-‐like molecules show an elution volume deviating from the one expected from the intrinsic viscosity. It might be important that the latter two studies used silica based SEC media whereas Potschka used agarose-‐based, silica-‐based and cross-‐linked polymer SEC fillings.
It could be observed that the elution volume of proteins can depend on the ionic strength (for example Frigon et al. [1983]) and pH value (for example Golovchenko et al. [1992]) of the buffer solution as well as on the explicit column material (for example Agrawal & Goldstein [1965]).
The ionic strength and pH-‐value dependency of the elution volume of proteins during SEC can be attributed at least to two effects. As summarised by Hagel (Hagel [2011]) between the samples and the SEC media electrostatic, van der Waals and repulsive interactions can occur. Those interactions can be influenced by the choice of the buffer solutions pH value and ionic strength (see also Ruckenstein & Lesins [1986]).
Additionally the buffer solution composition can influence the conformation of proteins. A drastic example is the pH dependent interaction between β-‐lactoglobulin (β-‐Lg) molecules: at pH 2.6 it is a monomer and at near neutral pH values it forms a dimer (Uhrínová et al. [2000]). Additionally between pH 6 and 8 conformational changes – e.g. a change of the solvent accessible surface area – occur in the protein (Qin et al. [1998]).
Finally it must be pointed out that some proteins can interact with the SEC media if it is composed of structures similar to native ligands of the protein. Agrawal and Goldstein (Agrawal & Goldstein [1965]) observed that the lectin concanavalin A can bind to the cross-‐linked dextran of a SEC medium. This must be kept in mind since perlucin as a C-‐
type lectin might show a similar behaviour. As it is stated above the SEC media used in this thesis consist also of a cross-‐linked dextran and it was reported by Hagel et al.
(Hagel et al. [1989]) that a lectin from lentil show affinity for this particular SEC medium. Such behaviour might be beneficial for purification and separation of proteins from protein mixtures but is definitely unwanted for size estimation.
The information provided so far is only a very brief summary of the fundamentals of the separation principle of SEC and the influence of the buffer solution. Nonetheless it is considered to be sufficient in the scope of this thesis. It will become clear in the next sections that the main challenge was the determination of suitable buffer solution conditions for the perlucin elution from the SEC media. The systematic variation of the buffer conditions had to be left for future research. The provided background is therefore considered sufficient to estimate the apparent size/molecular weight of perlucin. Four proteins of known molecular weight were used as reference substances.
As it was shown for example by Andrews (Andrews [1964]) the elution volume of native proteins during SEC can be correlated to the molecular weight of those proteins – at least under the conditions given in this study. In a certain range – that depends in particular on SEC media – the elution volume varied nearly linear with the logarithm of the molecular weight.
In the following section the results of the SEC with the reference substances and perlucin are shown. Detailed information on the used reference substances and the experimental set-‐up will be given in the next section.