Chromatography

I. Partition Between Two Phases

A. Separatory Funnel

1. two immiscible liquids -- solutes soluble in both
2. Partition Coefficient, K = C_U / C_L after equilibration
3. K depends upon:
   1. solute -- polarity, ionization, etc.
   2. 2 liquid phases -- polarity etc.
4. If K >> 1 or K << 1 for a particular solute ==> can purify the solute pretty well with a single extraction (or relatively few extractions). But what if K is approximately equal to 1?

B. Multiple Extractions

1. Let's look at two cases: (a) K = 1 (b) K = 3
2. if K > 1 ==> more material in right most vessels --> peak moves to right quickly
   if K < 1 == > more material in leftmost vessels --> peak moves to right more slowly
   (In the diagrams below, lower phase stays in place while the upper phase is transferred to the next vessel to the right with fresh lower phase.)
   

   a.	K = 1					b.	K = 3
   1/2						3/4
   1/2						1/4
   1/4	1/4					3/16	9/16
   1/4	1/4					1/16	3/16
   1/8	1/4	1/8				3/64	18/64	27/64
   1/8	1/4	1/8				1/64	6/64	9/64
   1/16	3/16	3/16	1/16			3/256	27/256	81/256	81/256
   1/16	3/16	3/16	1/16			1/256	9/256	27/256	27/256
   1/32	1/8	3/16	1/8	1/32		3/1024	36/1024	162/1024	324/1024	243/1024
   1/32	1/8	3/16	1/8	1/32		1/1024	12/1024	54/1024	108/1024	81/1024

   
   
   

3. How can this be done many times automatically?
   ==> Craig Counter Current Distribution Apparatus -- special separatory funnel

The two phases are equilibrated in chamber B by rocking the tube back and forth around pivot point, P. After equilibration, the apparatus is rotated 90º so the upper phase goes into D while the lower phase remains in B. When the apparatus is rotated back (counterclockwise) 90º, the upper phase flows into the next vessel via tube E. More upper phase can be added to this vessel through tube A

The power of this apparatus lies in the fact that one can assemble 100's of these vessels (flasks) together to do 100's of extractions (transfers). These were very elaborate and expensive apparati.

There are now better much less expensive methods, but they're based upon the same principle of partition of a solute between two phases.

II. Column Chromatography

A. Partition of solute(s) between two phases

1. Stationary Phase -- column packing materia
2. Mobile Phase -- fluid which passes through

B. Plate Theory

1. Column is divided (conceptually) into consecutive zones called plates
   1. Each plate is a length of column sufficient to effect one equilibrium distribution between the two phases ==> Height Equivalent to a Theoretical Plate (HETP)
   2. bhe size of a plate is determined by: column packing material (surface area etc.), rate of flow, etc.
2. One Plate = One Transfer in a Separatory Funnel ==> the longer the column, the more plates it contains and the better the resolution.

C. Cellulose Chromatography -- Paper Chromatography

1. Cellulose has many hydroxyl groups which are polar and bind H₂O. The bound H₂O is the Stationary Phase.
2. Flow another solvent past the cellulose/ H₂O ==> it becomes the Mobile Phase. The mobile phase solvent will be less polar than H₂O; it is usually a mixture of organic solvents (alcohols, ketones, aldehydes etc.) and possibly water.
3. Solutes partition between H₂O in the stationary phase and the solvent of the mobile phase. One can change the characteristics of separation by changing the polarity of the mobile phase (i.e. adjust the composition).
4. Paper Chromatography -- most common form of cellulose chromatography
   1. solute is "spotted" on "dry" paper (still contains H₂O)
   2. chromatograph is "developed by dipping one end in the mobile phase. Two modes: Ascending and Descending
   3. The solvent moves through the paper, drawn by capillary action
   4. Solutes move as spots with a rate depending upon how much time they spend in the staionary phase vs. the mobile phase--determined by their partition coefficient--measured as an Rf value.
   5. may be combined with paper electrophoresis ==> 2-dimensional technique often used to separate peptides produced by trypsin digestion ==> Peptide Fingerprint

D. Gel Permeation Chromatography -- Molecular Sieve Chromatography

1. Column Packing -- spherical porous beads of defined size
   1. crosslinked dextrans -- Sephadex (Pharmacia)
   2. crosslinked polyacrylamide -- Bio-Gel P (Bio-Rad)
   3. crosslinked agarose -- Sepharose (Pharmacia) or Biogel A (Bio-Rad). Agarose beads have very large pores and are, therefore, good for separating very large molecules
   4. other materials developed by other companies
2. Gel beads are designed to have a distribution of pore sizes around a mean pore size. The mean pore size and the distribution determines the size range of molecules which can be separated.
3. Total Volume (volume of gel bed): V_T = V_o + V_g + V_i
   [V_o is the volume of space between the beads, the void volume; V_g is the volume of gel material in the beads; V_i is the volume of the pores within the beads, the included volume]
   1. Solute will partition between V_o and V_i: m_i = s V_i c where s is the partition coefficient and c is the solute concentration in V_o.
   2. Each type of molecule has a characteristic partition coefficient, s, related to the fraction of the included volume V_i, accessible to that molecule (how many pores are large enough for the molecule to enter).
   3. limits of s:
      • s = 0 ==> solute molecules can't enter the gel beads at all (excluded) because the pores are too small
      • s < 1 ==> solute molecules are less likely to be in the beads than in the void volume, V_o, because some pores are too small
      • s = 1 ==> solute molecules partition equally between the void volume, V_o, and the included volume, V_i.
      • s > 1 ==> solute molecules adsorb to the gel material (undesirable, usually, but does occur sometimes)
   4. The volume of bead accessible to solute molecules is: V_p = s V_i ==> s = V_p / V_i
4. Elution of the Gel Column -- sample is applied as a thin band and rinsed through (eluted) with buffer.
   1. Each type of sample molecule must pass through the entire volume available to them displacing a volume of buffer equal to the volume available to the molecules.
   2. Elution volume: V_e = V_o + s V_i Thus, for....
      • s = 0 ==> V_e = V_o <-- very large molecules
      • s < 1 ==> V_e = V_o + s V_i <-- intermediate sized molecules
      • s = 1 ==> V_e = V_o + V_i <-- small molecules
5. Elution volume is a measure of molecular size
   1. normalize elution by expressing V_e as s = V_p / V_i
   2. s = -A' log r_h + B' ==> r_h = radius of hydrated sphere (Stokes radius)
   3. for a homologous series of molecules (similar shape, V, etc.)
      r_h is proportional to M^1/3 thus, s = -A log M + B <-- the equation has the same form with a new slope and intercept ==> Gel Permeation Chromatography can be used to "estimate" MW

Other types of Partition Chromatography

E. Gas / Liquid Chromatography

1. Mobile Phase is a gas -- usually inert (He, Ar, N₂)
2. Stationary Phase is a liquid coating on an inert solid support.
   1. open tube or capillary operation -- coat the inside surface of a long thin tube (30 - 100 m long)
   2. packed column -- larger diameter column is packed with an inert support -- commonly diatomaceous earth, teflon powder, or glass beads .
   3. coating may be solid at room temp (e.g. polyethylene glycol) bu the column is run at higher temperature where the coating melts.
3. Sample usually injected as a liquid which is then heated to vaporize it ==> sample must be somewhat volatile and stable at higher temperature.
4. Can provide very high resolution by making very long columnes
5. Detectors: various types. Most powerful detector is a mass spectrometer (GC/Mass Spec.) which give mass spectrum that can be used to identify and quantitate samples as them come off the column.

F. Reversed Phase Chromatography

1. Stationary Phase -- apolar (hydrophobic) ==> reversed with respect to cellulose chromatography
   1. hydrocarbon chains -- bound to an inert matrix; hydrophobicity varied by changing the hydrocarbon chain length
   2. aromatic groups
2. Mobile Phase -- depends upon hydrophobicity of stationary phase. Commonly use a more polar organic solvent: acetonitrile, DMSO, EtOH, ethylene glycol, propanol, or mixtures of these with H₂O. Also may use gradients.
3. Use of shorter hydrocarbon chains less densely packed is called
   Hydrophobic Interaction Chromatography

G. Ion Exchange Chromatography

1. Stationary Phase -- chemically bound charged groups
   1. Must have counter ions bound
   2. really is classified as Absorption Chromatography because the stationary phase contains a specific number of sites to which solutes can bind reversibly.
2. Mobile Phase -- an aqueous buffer solution characterized by: pH and ionic strength
3. Properties of Ion Exchangers:
   1. Nature of the solid support:
      • polystyrene/divinyl benzene -- Dowex -- mechanically very strong
      • other plastics -- acrylic, phenolic, epoxy
      • cellulose
      • dextrans -- Sephadex
      • agarose -- Sepharose <-- The latter two are commonly used for gel permeation chromatography but can be modified to contain charged groups for ion exchange chromatography.
   2. Nature of the Charged Groups:
   3. Cation Exchangers -- have negative charge
   4. Anion Exchangers -- have positive charge
4. Strong Ion Exchangers: based upon strong acids or bases and are charged over a wide range of pH
   1. strong cation exchangers: Sulfonic Acid (or derivatives) R-SO₃^-
   2. strong anion exchangers: quaternary ammonium salts R-N (CH₃)⁺
5. Weak Ion Exchangers: based upon weak acids or bases which are charged only over a limited pH range
   
   1. weak anion exchangers: Diethyl-amino-ethyl (DEAE); tertiary amines
   2. weak cation exchangers: carboxy methyl (CM); phosphoryl
   3. These may be bonded to a variety of supports: e.g. DEAE-cellulose; DEAE-Sephadex; DEAE-Sepharose; CM-Cellulose; CM-Sephadex; CM-Sepharose
6. Choosing an Ion Exchanger
   1. Charge -- cation or anion exchanger -- depends upon the charge of the molecules to be separated. This will also depend upon pH.
   2. Weak Exchanger -- for labile molecules such as proteins.
   3. Strong Exchanger -- for more stable molecules such as nucleotides, amino acids, peptides etc.
      
7. Eluting Ion Exchange Columns -- molecules usually adsorb tightly in the buffer in which they're applied ==> must weaken this interaction.
   1. Increase ionic strength (most common method): F = q₁ q₂ / D r²
      q₁and q₂ are the charges on 2 groups, r is the distance between the groups, and D is the dielectric constant of the solvent which is increased with higher ionic strength thus weakening the force between the solute and the ion exchanger. Another way to look at this is that other ions in the buffer compete for the ion exchanger binding site.
   2. change pH -- changes the charges on the molecules being separated; also can change the charge of a weak ion exchanger
   3. These changes can be made stepwise by changing the buffer reservoir (step gradient) or as gradient -- by mixing two buffers

III. Variations in Apparatus -- most of these modes can be run in the following ways.

A. Thin Layer Chromatography

1. Solid/Stationary Phase is a thin layer on a flat support
2. Developed like a paper chromatogram (dip into mobile liquid phase)

B. HPLC -- High Pressure (Performance) Liquid Chromatography

1. Increase resolution of liquid chromatography by...
   1. use very small particles to get the larges possible surface area -- 3 - 20 µ diameter
   2. high pressure (up to 400 atmospheres) needed to get acceptable flow rates -- requires very strong particles to resist bed compression and crushing of particles
   3. tens of thousands of "plates" per meter of column length provides excellent resolution
2. Used in most of the common modes discussed above although reversed phase is probably the most common type of HPLC
3. Advantages: very high resolution (replaces paper chromatography / electrophoresis in most applications) and short run times.