Method III:  pK Determination and Isoelectric Focusing

1.  Acids and Bases

     According to Brönstedt, acids are proton donors and bases are proton acceptors. By giving up a proton, an acid becomes its conjugate base. Similarly, a base becomes its conjugate acid when it accents a proton. Each of these is called an acid base pair. The charge of the acid can be positive, neutral, or negative (in the case of polyprotic acids). In the case of water, the equation of the constant at 25°C is

pH is defined as the negative log of hydrogen concentration:

The dissociation of an acid HA is given by the general equation

with the constant being calculated by [products]/[reactants].

From these equations, we can get the pK of an acid, which is defined as the negative log of the acid dissociation constant:

There are a bunch more equations involved that I'm not going to waste time typing because this is generic 1st year acid/base chem. We end up with the Henderson-Hasselbalch equation. (Look it up.) The pK of an acid thus tells us the pH: At the equivalence point, half the acid has dissociated its A^- form, giving us both in equal concentrations. When pH = pK, the log of the base:acid ratio is 0. This equation can also be used to calculate the pH of a solution from a mixture of acids and its salt, assuming the pK (Check tables at the back of any book.) or the base:acid ratio is known. Near the pK value, the pH is extremely stable and will only very slightly change upon addition of protons or hydroxide ions. This is known as the buffer zone. On a titration curve, this is in the middle of the flattest region, where the pH is a function of the amount of acid or base added. The buffer zone essentially means DpH = pK_a ± 1. For optimal buffer effects, use this area wisely!

2.  Amino Acids

     Amino acids have at least 2 ionizable groups, the a-carboxyl group and the protonated a-amino group. Of the 20 acids, 7 have ionizable R groups. As an example, the titration curve for aspartic acid (aspartate) is shown in figure 1 with the 3 pK values marked. At the pK values, we find the inflection points of the curve, where the slope of the tangent is at its lowest. The isoelectric point (IEP), where the net molecular charge is 0, lays at the average of the first 2 pK values ([pK₁ + pK₂] / 2). This is the first equivalence point - this is where the curve has the largest slope.

[Fig 1. Titration curve of aspartic acid.]

3.  Isoelectric Focusing

     Proteins and peptides differ in their composition/amino acid sequence. The net charge of the molecule is determined by the number of ionizable groups (D, E, H, C, T, K, and R for eg), the terminal carboxyl and amino groups, and the pH of the solution they're in. In a strongly acidic range, we get -COOH and -NH₃⁺, so everything is positively charged. The pH at which the protein has a completely neutral net charge is called the isoeletric point and depends not only on the sequence, but on the types of protein interactions too. Migration in an electric field is only possible if the protein possesses a charge due to the pH in its immediate environment. At an average pH, proteins with many basic groups, like cytochrome c, will go towards the cathode while proteins with many acidic groups will migrate towards the anode. These are the specific characteristics of acids and bases upon which isoelectric focusing are based. This method has been highly improved by the development of high resolution analytical lab methods in recent years.

[Fig 2. Isoelectric focusing of 2 proteins.]

     This method is special because it builds a stable pH gradient using a low-molecular ampholyte matrix in a gel (agarose or polyacrylamide) in an electric field; the area around the cathode will be basic and that around the anode acidic. Due to this gradient, a protein in the basic area where the pH is over its IEP will travel towards the anode; thus the pH in the immediate environment doesn't matter. If the local pH of the gel is the same as the IEP, the protein won't migrate. Using this method, you can get a highly resolved protein band within 0.01 pH unit. You have to get to a point where the total charge is zero! When the pH is anywhere close to a pK_a of one of the amino acids or the terminal ends, it will become ambiguous as to whether the molecule is protonated or not - it flips between states. Thus, when the pk_a and pH are the same, the ratio between protonated and non- states will be 50/50; as you move away in either direction, it will become tilted in one direction, depending on which way you go. There is only a tiny range in which you can actually hit the IEP, but that's part of the beauty of this method - just leave it all hooked up to the current and the system will find equilibrium on its own.

     The example in the figure illustrates the isoelectric focusing of a mixture of 2 proteins, A and B, once in an alkali gel and once in an acidic. In both cases, the proteins were focused at their characteristic IEPs. In the lab however, just be careful that you don't use too extreme a pH range, lest your proteins be denatured. The pH gradient will be established using a low-molecular mixture ampholyte medium. This is a buffer-type substance, whose IEP can be used to determine the pH of a certain area. (See notes at end.) Chemically, it's a matter of polyamino-polycarboxylic acids, which are avaiable commercially, fixed at wide and narrow pH ranges. In the set ampholyte mixture, aka gel, the pH gradient forms first because of the electric field - the determining factors are the reactions at the respective electrodes: the solution will become acidic at the anode and basic at the cathode.

The ampholyte matrix tries to put itself into these local pH gradients according to their IEPs, similarly to the proteins, such that the many partial overlappings result in the formation of a continuous pH gradient.

4.  Questions

1. Predict whether the following peptides will migrate towards the cathode or anode or just focus at pH = 2.0, 3.0, 6.5, and 10.0:
   1. K-G-A-G
   2. E-G-A-E
   3. F-G-A-V
   4. T-E-D-W
2. What will the the pH of a 0.17 M sodium acetate solution?  (pK_{acetic acid} = 4.75)
3. A 0.17M solution of acetic acid is to be neutralized with 0.1M NaOH. Using the Henderson-Hasselbalch equation, calculate the pH of the mixture after 15%, 45%, and 90% neutralization.
4. The [H⁺] of a solution is 4.2x10^-5. What's the pH?  If the pH was 1.93, find [H⁺] and [OH^-].
5. Given 10mL 0.5M sodium acetate solution, how much 0.1M acetic acid (pK 4.75) must be added to get a final pH of 4.0?
6. In what area of the titration curve do amino acids have the highest buffer capacity? What happens at the equivalence point?

5.  Procedure

Prelim tasks

• Take the titration curve of an amino acid.
• Calculate the IEP of hemoglobin in cow and pig blood. Determine the pK of the acid.
  1. L-histidine:  1mmol L-his hydrocloride monohydrate (MW = 209.63 g/mol) in 60mL H₂O_dist
  2. L-glutamate:  1mmol L-glu (MW = 147.14 g/mol) in 60mL H₂O_dist

How to use a digital biuret
- Turn it on. The monitor will light up.
- Push "add".
- Turn the knobs till no more bubbles come out.
- Turn the knob up till the equipment is charged.
- Turn the knob down till you hit equilibrium
- Push "titr".
- Zero it. The button's on the left.
- Now the monitor should show an amount.
- Feck.
     Add 0.1M NaOH in 0.25mL increments. If the DpH < 0.1, hike it up to 0.5mL increments - ideally, u want a DpH of 0.2. Stop after about 24-25 mL.

Calculations
     The pH is a function of the volume of NaOH added. Calculate the equivalence point and the pK then assign them to the aa groups. Find the values for the titration curve of the other group and analyze this too.

Isoelectric Focusing
Come in the day before to make the gel; it takes a long time, more than can be wasted the day of the experiment.

1. 90 mg Agarose IEF + 8.3 mL water in a 100mL Erlenmeyer. Secure the flask and heat in a waterbath to boiling (add magnetic stirrer to flask and thermometer to water bath). Once the agarose is dissolved, let the the temperature of the waterbath cool to 75°C. Now add the matrix (700µL Ampholine, pH 7-10). While the agarose solution is heating, clean the 2 glass plates with soap and a brush; rinse with distilled water then ethanol. See step 4.
   
2. Mold prep:  Put a few mLs water on the longer glass plate. Roll the gel bond foil with the hydrophilic side up (hydrophobic side on the glass plate). Run a lint-free rubber roll over foil for the entire length of the glass plate to get rid of bubbles. The sides of the foil can be identified using drops of water:  on the hydrophilic side, a wide surface will smooth edges will develop, while the droplet will stay as is on the hydrophobic side.
   
3. Lay the clean and dry plate (spacer-side down) on the longer plate so that there's anout 1 cm free on each end. Clamp them together along the longer side and shift the clamps till they're as far apart as possible. Put them like so into the drying oven for 15 mins (75°C).
   
4. Be well-prepped for the following steps and do them as quickly as possible!  Mix the Ampholine at 75°C into the agarose solution from step 1. Take the mold out of the drying oven (step 3). Get one person to pour the gel while the other holds the mold at a 30°C angle, jiggling to help settle the solution. There should always be a clump of solution over the brim of the glass plates in order to stop formation of bubbles in the gel. The mold should fill completely due to capillary action. As soon as the level of agarose solution reaches just under the rim of the glass plates, put the mold immediately into a horizontal position. Let cool at room temperature for an hour.
   
5. Once cooled, whick off the excess agarose from the ends of the mold with a spatula and remove the clamps. Wedge the spatula between the foil and the bottom plate and separate. Remove the top plate, leaving you with the foil and the gel. Put the gel (with foil) into a dish lined with a moistened paper and store at 2-8°C.
   
6. Start here on lab day!Electrophoresis chamber prep:  Join the horizontal electrophoresis chamber with the thermostat and cool to +10°C (15°C for hemoglobin). For the water, get a flow rate of at least 10 L/min going. On the cooling plate, add a bit of of decane (or another long-chain hydrocarbon) (we used mineral oil) and lay the (bubblefree) gel on top. Avoid bubbles between the cooling plate and the foil in order to ensure a clean and cold application.
   
7. Soak the electrodes in the electrode solution. Remove excess electrolyte solution by application of a 2nd electrode strap. Cut off the ends of the straps if they stick out of the gel. (?)
   
8. The sample can be applied in 2 ways:  Pipette 15µL of the sample solution (1-4 mg prot/mL). For most proteins, it's best if you do it 2-4 cm away from teh cathode. High-molecular proteins should be close enough to their IEP without adding filterpaper. Avoid putting the sample less than 5 mm away from the end of the gel. To double check the pH gradient, add 15 µL of a mixture of a marker protein with characteristic IEPs as a tracer.
   
9. Lay the glass plates (with electrodes) in such a manner than the wires are positioned approximately in the middle of the electrode straps and have good contact over the entire length of the gel. Put the lid on and hook up the electrodes with the red wire. Hook the chamber up to the main adapter with the cable.
   
10. Run conditions for a pH gradient of 4-10:

    Spannung (voltage): Strom (current): Leistung (power): Laufzeit:

    maximum maximum generally around 500V; push the "read" button 45-90 minutes

    Note:  After half the run time, remove the sample.
11. After the focusing, remove the electrodes - Take the pincer in the middle and pull away horizontally to the gel. Immediately lay the gel in a fixing solution for 10 minutes. Work quickly to avoid further protein diffusion.
    
12. After the fixing solution, incubate 10 mins in 300 mL 80-95% EtOH, then 5 mins in 300mL colouring solution. leave over night. Dry with a hair dryer or leave under a fume hood for awile. Check the linearity of the marker protein and find the IEP of the focused protein.
    

     To separate blood components from serum, add 10mL 150mM NaCl to each 1mL blood. Mix and centrifuge for 5 minutes at level 9. Suction off and dispose of the clear supernatant. Do this twice more to more fully separate the serum proteins from the solid blood parts.

     Resuspend the red sediment with water, fill to 5x the original volume, and cool for 15 minutes - this puts the RBCs in a hypotonic medium. Centrifuge the sample in the SS34 Rotor (Sorvall cool centrifuge) at 15000rpm for 20 minutes. The clear red hemolysate will separate from the white sediment - take it off with a pipette and cool it for photometric analysis and IEF later. To determine the Hb content (g/L) in the sample, we're going to measure the hemolysate spectrum between 500 and 600 nm. The samples will be diluted so that the absoprtion will ahve no wavelength longer than 1.0. Now determine the Hb concentration using the following absorption coefficients for oxyhemoglobin:

6.  Literature

• Allen, R.C. and B. Budowlw (1994). Gel electrophoresis of proteins and nucleic acids: selected techniques. de Gruyter: Berlin.
• Stryer, L.L. (1995). Biochemistry, 4th Edition.  Freeman & Co.: New York. 48
• Karger, B.L. and W.S. Hancock (1996). Methods in Enzymology: High resolution separation and analysis of biological macromolecules, Fundamentals. Academic Press: San Diego. 270, 49-56.

Kyra's stuff

• In a pH gradient, under the influence of an electric field a protein will move to the position in the gradient where its net charge is zero.
• amphoteric - able to possess a positive, negative, or 0 net charge; Having the characteristics of an acid and a base and capable of reacting chemically either as an acid or a base. (American Heritage Dict, 4th ed.)
• Carrier ampholytes are small, soluble, amphoteric molecules with a high buffering capacity near their pI - what we use is a mixture so that there's a span of different ampholytes across the entire gel, arranged according to their pIs, thus buffering their immediate region --> pH gradient!
• IEF can be run either native or denaturing - native is generally preferred.
  Amersham Biosciences
• Buffers used in this system require 2 fundamental properties: amphoterism so they can reach an equilibrium position along the separation column and "carrier" ability. Any ampholyte isn't necessarily suited for IEF; it must be able to carry a current as well as a pH (ie, good conductor and buffer).
• Important note! The pH gradient is built into the gel and immobilized! This involves a substance called Immobiline and it's very vague and confusing - I think it's an additive to the PAG solution before it sets; there's Immobilie and Ampholine.
            Righetti, P.G. and E. Gianazza. (1987). "Isoelectric Focusing in Immobilized pH Gradients." Methods of Biochemical Analysis. John Wiley & Sons, Inc.: Chichester. v.32, p.215-278.

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