VII. Electrophoresis

A. Macromolecule is accelerated by a force (like sedimentation)

1. F = q E
   [q is the net charge on the molecule; E is the electric field strength experienced by the molecule]
2. This causes an acceleration until the velocity, v, causes a frictional force equal to but opposite in direction to the applied force F = q E = f v
3. Like sedimentation, we can define a mobility per unit field, U
   

4. For a spherical molecule of radius, r, and charge z e (e = elementatry charge, the charge on 1 electron)

F is the Perrin shape factor; r_h is the radius of a sphere of equal volume.

B. Rigorous quantitative treatment is very difficult because the electric field actually felt by the macromolecule is difficult to evaluate due to the fact that the macromolecule is a very large ion in solution with many small counterions. 2 extreme situations:

1. Very Low Ionic Strength
   
   Once the macromolecule is separated slightly from its counterions, it takes enormous energy to pull them further apart ==> charge separation counteracts the external field resulting in little or no molecular transport.
2. Very High Ionic Strength -- overcomes the problem of charge separation (the macromolecule will always have enough counterions around). But this creates an ion cloud around the particle partially shielding it from the external field. This does not prevent electrophoretic movement, but it does complicate rigorous analytical treatment.
3. Most electrophoretic experiments (whether preparative or analytical) are analyzed semi-empirically.

C. Experimental Approaches -- Boundary and Zonal (just like sedimentaiton)

1. Boundary: Analogous to Boundary Sedimentation -- measure the rate of movement of the boundary and calculate U from E and v -- hardly ever used anymore
   
2. Zonal: Analogous to Zonal Sedimentation in density gradients
   1. sample is applied in a zone (small region: a spot on moistened paper or a band on a gel) and an applied field causes the molecules to separate into zones based upon different U's.
   2. Like Zonal sedimentation, need some way of stabilizing the zones to prevent mechanical mixing (from vibrations) or convection mixing (from temperature differences -- a particularly severe problem with resistance heating caused by the electric field).
3. Paper Electrophoresis:
   1. a strip of paper is kept moist with buffer to make it electrically conductive; ends are dipped into buffer solutions containing electrodes across which an electric potential is applied
   2. Used primarily for separation of small molecules ==> must use a high voltage, otherwise they diffuse too rapidly ==> paper must be cooled (usually by water)

D. Gel Electrophoresis Media -- Three types

1. Starch Gel -- swollen potato starch granules (little used now except for prep isoelectric focusing)
2. Agarose Gel -- purified large MW polysaccharide (from agar) ==> very open (large pore) gel used frequently for large DNA molecules
3. Polyacrylamide Gels -- most commonly used gel because they are very stable and can be made at a wide variety of concentrations or even with a gradient of concentrations ==> large variety of pore sizes
   
4. Acrylamide Concentrations -- typically 5-20% by weight (5%, 7.5%, 10%, 12.5%, 15%, 20% are commonly used values) ==> gel is mostly water. Acrylamide polymerizes in head-to-tail fashion to form long polymers which form a complex network held together by bis-acrylamide crosslinks. The cris-crossing polymers create pores in the gel; the size of pores is determined by the acrylamide concentraion.
5. Acrylamide can be polymerized into any desired shape -- two shapes used for electrophoresis
   1. Tube Gels -- polymerize in glass tubing ==> cylindrical shape
   2. Slab Gels -- polymerize between glass plates

G. Nucleic Acids -- How does a gel affect mobility?

Let's consider simple (conformationally) molecules moving free in solution in the presence of an electric field.

1. Structure -- Random coil of...
   Thus: Z is proportional to M, the molecular weight
   Recall that for an ellipsoid: f = 6 p h r_h F and:
   ==> f is proportional to M (for molecules with similar shapes)
   --> both numerator and denomenator contain terms which are directly proportional to M ==> M terms cancel out and the electrophoretic mobility, U, should be independent of the size of the nucleic acid.
   N. Davidson at CalTech measured U for nucleic acids without a supporting gel, and found that it is constant from 1 nucleotide up to 1.7 x 10⁵ nucleotides.
2. How can we use electrophoresis to separate molecules? Electrophoresis in a gel matrix -- the gel sieves the molecules
   1. large molecules move slowly because they have difficulty going through the pore
   2. small molecules move rapidly, their freedon is not restricted
3. from Physical Chemistry:
   1. a. h becomes a function of the particle size (r_h) because large particles "feel" the gel matrix more than small particles--they more often come in contact with the gel matrix. Thus, since f = 6 p h r_h ==> h is larger when r_h is large and f increases ==> U decreases because
      

   2. for a 7.5% polyacrylamide gel--average pore size is ~50Å
      • How is pore size related to gel concentration?
      • s₁ = pore size for gel concentration 1 -- c₁
      • s₂ = pore size for gel concentration 2 -- c₂
      • d = diameter of the hydrated polymer
        
        e.g. for a 7.5% gel s₁ = 50Å =; d = 10 Å ==> for a 30% gel: s₂ = 20Å
        Thus, we can adjust the gel concentration to produce a pore size appropriate for the sizes of molecules we wish to separate.
4. U is measured as the "relative" distance traveled, R_f = R / R_max
   Find that R_f depends upon log M ==> R_f = b - a log M where "a" and "b" are constants determined (primarily) by the gel; they're measured empirically by plotting R_f for molecules of known M and making a calibration curve. Note: the relationship is linear only over a limited range of log M determined by the pore size of the gel and by the polymer length. This is because h is a logarithmic function of molecule radius, r_h over a limited range (see above).
5. Choice of Gel
   1. Agarose: 0.2 % for Nucleic Acids up to M = 150 x 10⁶
      0.8 % for Nucleic Acids up to M = 50 x 10⁶
   2. Polyacrylamide: for smaller Nucleic Acids; choose % acrylamide to produce correct size pores

H. Electrophoresis of Proteins

1. Less straightforward because charge on proteins is much more variable -- it depends upon:
   1. amino acids composition
   2. pH;
   3. net charge can be + or - or 0
2. Electrophoresis of "native" proteins is relatively rare except for Isoelectric Focusing described later. What is needed is a way of modifying proteins so that z is proportional to M as is the case with nucleic acids.
3. SDS PolyAcrylamide Gel Electrophoresis -- SDS PAGE
   1. Sodium Dodecyl Sulfate = Sodium Lauryl Sulfate: CH₃(CH₂)₁₁SO₃^- Na⁺
      This is a detergent because it contains a hydrophobic region, the CH₃(CH₂)₁₁ tail, attached to a hydrophilic group, SO₃^- Na⁺, making it amphipathic. It is a very strong detergent which denatures proteins by binding to the polypeptide backbone.
   2. Measurements show that most proteins bind 1.4 gm SDS/gm protein with very little variation (except for some membrane proteins; membrane proteins are very hydrophobic and may bind more SDS) ==> The charge on an SDS-protein complex is determined almost entirely by SDS --> -1 charge for each SDS. Since the amount of SDS bound is determined by the size of the protein and all protein/SDS micelles are anionic ==> z is directly proportional to M
   3. Hydrodynamic studies show that the shape of an SDS/protein complex is a rod or prolate ellipsoid--called a micelle--of ~18Å diameter and a length proportional to M
   4. U in solution is independent of M, just like Nucleic Acids
   5. Thus, electrophoresis of SDS/protein micelles through a polyacrylamide gel should separate them according to M as with nucleic acids ==> R_f = b - a log M
   6. If one plots the mobility for different proteins as a function of gel concentration, a Ferguson Plot, one finds that the mobilities of all proteins extrapolate to the same value at [gel conc.] = 0 as expected. The slope of the mobility of a single protein provides another more accurate method of estimating its molecular weight from SDS PAGE.

I. Discontinuous Electrophoresis (Disc): Most common type of SDS-PAGE

1. Buffers--2 layers: upper layer contains low mobility ions; lower layer contains high mobility ions
2. The two zones move down with a sharp boundry between them. Why? Faster lower buffer ions should move faster leaving slow ones behind.
   1. They experience different potentials: V_U and V_L
   2. Ohms Law: V = R i: i = current and is the same for both layers, R is the resistance. The resistance of the upper zone, R_U, is greater than the resistance of the lower zone, R_L, because:
      
      where c_i = concentration; m_i = mobility; z_i= charge on the ith ion. ==> R_U will be larger than R_L because m_U is smaller than m_L
   3. Thus, if c_U and c_L are chosen appropriately, V_U will be enough larger than V_L to compensate for lower mobility of ions in the upper zone ==> 2 zones move at the same speed with a sharp boundry between them.
      .
   4. Why a sharp boundry? (1) if a mobile lower zone ion drifts into the upper zone, it immediately experiences a higher potential, V_U, and speeds up until it reaches the lower zone where the lower potential, V_L, causes it to slow down again. (2) if a low mobility upper zone ion drifts into the lower zone, it immediately experiences a lower potential, V_L, which causes it to slow down until it drifts back into the upper zone.
3. What about proteins? Choose upper and lower zone ions so that m_U < m_proteins < m_L
   ==> proteins will be concentrated at the interface into thin zones stacked in order of protein mobility. Note: all this assumes electrophoresis in a "stacking" gel with large pores which do not inhibit protein movement.

When the thin bands of proteins reach the separating gel, their mobility decreases dramatically and the upper buffer ions pass them. At this point, the proteins are separated according to their individual mobilities (sizes). The whole point of this buffer system is to concentrate the proteins into very thin zones before separating them.

J. IsoElectric Focusing:

All protein charges vary from a net positive charge at low pH (-COOH and -NH₃⁺ forms of acidic and basic functional groups) through 0 at some intermediate pH to a net negative charge (-COO^- and -NH₂ forms) at high pH.

1. pI - IsoElectric Point: pH at which a protein has a net 0 charge (positive and negative charges balance). Depends mostly on the amino acid composition and a little on the tertiary structure
2. Create a pH gradient in a gel: Can be done on a slab (vertical or horizontal) or a tube.
   This is analogous to Equilibrium Density Gradient Centrifugation (IsoPycnic Centrifugation); the final positions of each band depend only on an intrinsic property of the proteins, their pI's, and not on where they started in the gel
3. How to make a stable pH gradient? Must have a buffer for each pH along the gradient
   ==> Ampholytes (various commercial names) are small organic molecules with different combinations of acidic and basic groups so that each one has a different pKa. If one electrophoreses a mixture of ampholytes (polyampholytes) with H₃PO₄ in the Anode buffer reservoir (to buffer it at very low pH) and NaOH in the Cathode buffer reservoir (to buffer it at very high pH), each ampholyte will migrate to a pH equal to its pKa and buffer the pH at that point.

K. Two-Dimensional Electrophoresis: There are many variations; all basically combine 2 types of electrophoresis

1. Most common combines Isoelectric Focusing in tube gels and SDS-PAGE in slab gels
   Final gel has a complex mixture or proteins separated by pI along the horizontal axis and by log M along the vertical axis. Can resolve thousands of spots (proteins) by this technique. Analysis is now automated by computer so that one can do 2D gels on whole cell extracts and monitor how each protein changes during: a) Development; b) Transformation; c) Excitation -- e.g. by a hormone etc.
2. Other Variations
   1. SDS-PAGE -- non-reducing conditions (-S--S- bonds intact) + reducing conditions
   2. SDS-PAGE -- proteins X-linked + X-links broken
   3. Native Gel (non-denatured proteins ) + SDS-PAGE

VIII. pH Measurement

A. Glass Electrode

1. H⁺ inside have a higher chemical potential, µH⁺, than H⁺ outside because their concentration is higher. The difference in µH⁺ (free energy due to different concentrations) is given by the
   
   F is called the Faraday const. and converts to Volts
2. H⁺ diffuse out of the bulb creating a charge separation or voltage across the glass, DV.
   H⁺ ions will continue to diffuse across the glass until:
   
   ==> if we can measure ÆV we can detemine [H⁺]_out since we already know R, T, F and [H⁺]_in
   
3. Calomel Electrode -- a convenient reference electrode; ÆV across the glass electrode is compared with the reference ==> reference electrode must be pH independent. KCl is used to make contact between the solution and the reference electrode through a fiber capillary or a fibrous plug.
4. Other Types of Reference Electrodes
   1. Ag-AgCl -- for high temperatures
   2. Hg-HgSO₄ -- for Cl-free electrode
5. Combination Electrode -- Glass electrode + reference electrode combined into one unit --> more compact for measuring pH of small volumes.6. In addition to the ÆV's across the glass electrode and across the reference electrode, there are also ÆV's across:
   1. the AgCl-coated wire in the glass electrode;
   2. an asymmetry potential across the H+-permeable glass when the pH is the same on both sides
   3. liquid-junction potential of the reference electrode due to the fact that KCl is used to conduct current and K+ and Cl- don't diffuse at the same rate. Fortunately, all of these are pH-independent (like the reference electrode) and can be corrected by calibration.

B. Complications of pH measurement

1. Dependence on concentrations of ions
   one is really measuring the H⁺ activity. This is related to concentrations and is approximately equal to concentration in dilute solutions but can be significantly different than concentration when concentrations of other ions are very high ==> measure pH at approximately the same concentrations as those at which the buffer will be used or take the change due to dilution into account.
2. Electrode contamination
   1. foreign material -- e.g. protein film -- may coat the glass electrode -->should remove with detergent or acid
   2. Tris reacts with some commercial electrodes --> see that your electrode gives correct results with Tris if you use this buffer.
3. Sodium Error: many glass electrodes are somewhat permeable to Na⁺ ==> pH can appear to be lower ([H⁺] greater) than it actually is! Most noticeable at high pH where the error can be as much as 1-2 pH units
   1. use special Na⁺ impermeable electrodes when measuring high pH's of buffers containing high concentrations of Na+
   2. use K⁺ salts instead of Na⁺ salts
4. Temperature: there are 2 variations with temperature
   1. in Nernst Equation: <-- this temperature variation is corrected with the
      temperature compensation control on the pH meter.
   2. buffer equilibrium may shift with a change in temperature -- this will be different for different buffers and can go in different directions depending upon whether dissociation is exothermic or endothermic. This is a problem with Tris buffers whose pH decrease approximately 0.03 pH units for every degree change from 25°C --> 5°C.

C. Ion Specific Electrodes:

can be constructed for other ions by changing the composition of the glass in the glass electrode. The principles of operation will be exactly the same as the pH electrode. There are 3 basic ways of altering the electrode.

1. Change the glass:

• SiO2, Na₂O, CaO ==> H⁺ electrode
• SiO2, Al₂O₃,Li₂O ==> Na⁺ electrode
• SiO₂ + other components ==> Li+, K+, Rb+, Cs+, Ag+, Cu+, Ti+, NH₄+ electrodes-

1. Thinly Sliced Crystals:

• LaF₃ ==> F- electrode
• Ag₂S ==> S-2 electrode
• AgX ==> X- electrode (X is a halide)

1. Liquid Membrane (inorganic salt dissolved in an organic solvent and held in porous glass or plastic: Ca(C₁₀H₂₁O)PO₂ ==> Ca⁺⁺electrode