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Basic Instructions for Calculating Calcium-Binding Constants Using the Competitive Chelator Method

Written by: Melanie Nelson, spring 1999

Please note: these are only sketchy instructions, and no guarantee is made about their completeness or accuracy. Please consult the literature for more information about the details of the method. One good paper to look at is:
Linse, S., C. Johansson, P. Brodin, T. Grundstrom, T. Drakenberg, S. Forsen. Electrostatic contributions to the binding of Ca2+ in calbindin D9k (1991) Biochemistry, 30, 154-162.

This document contains skeletal instructions for calculating the calcium-binding constants of a protein using the competitive chelator method. This method was taught to me by Sara Linse, at Lund University in Sweden. However, any errors are purely my own. People in Walter Chazin's lab can consult my Wetlab and NMR notebook #1, starting on page 58, for my notes on this technique.

Collect the raw data

You should choose a competitive chelator that has a calcium affinity in the range of that of the protein whose constants you want to measure. Quin-2 and BAPTA are two common competitive chelators. The chelator must have a difference in absorbance or fluorescence between the apo and calcium-loaded states. The following instructions are for the Quin-2 chelator:

1. Make a 25-30 micromolar solution of Quin-2 in a calcium-free buffer. We use 2mM Tris-HCl, pH 7.5. Note that most of these chelators are light sensitive, so wrap the container with your stock solution in foil.
2. Determine the exact concentration of Quin-2 in your solution by measuring the absorbance at 239.5 nm of a small aliquot in the presence of calcium:
   • Take a tiny amount of Quin-2 and dissolve it in 5 ml of buffer. This is the stock solution.
   • In a quartz cuvette, mix: 200 ul of the Quin-2 stock, 1800 ul of buffer, 5 ul 1 M CaCl₂
   • Measure the absorbance at 239.5 of the mixture in the cuvette
   • Calculate the concentration of Quin-2 in the stock solution:
     C = A/E x 10
     A = absorbance at 239.5
     E = the extinction coefficient of calcium-loaded Quin-2 at 239.5 (4.2 E4)
     multiply by 10 because we want the concentration in the stock, not in the dilution made in our cuvette.
3. Calculate the required dilution of the stock solution to get ~28 uM Quin-2 in 20 ml of total solution. For example, if my stock solution has a concentration of 371 uM Quin-2:
   0.02 L sol'n x (28 umol Quin-2/1 L sol'n) x (L stock/371 umol Quin-2) = 0.00151 L stock
   So I would use 1.5 ml of the Quin-2 stock in 18.5 ml of calcium-free buffer.
4. Take 2.5 ml of the new, diluted Quin-2 solution, and put it in a cuvette with 5 ml of 1 M CaCl₂, and measure the absorbance. Use this to calculate the true concentration fo Quin-2, using the C = A/E equation described above.
5. Now we need to determine the residual calcium concentration in the chelator stock solution.
   • Switch to measuring the absorbance at 263 nm
   • Let the cuvette sit for a few minutes with a little EDTA and (calcium-free) water in it, then rinse it with water.
   • Put 2.5 ml diluted Quin-2 solution in the cuvette, and measure the absorbance (A1)
   • Add 5 ul 0.1 M EDTA, and measure the absorbance (A0)
   • Add 5 ul of 1 M CaCl₂, and measure the absorbance (A2)
   • Use the following equation to calculate the Ca2+-concentration in the chelator solution:
     [(A1 - A0)/A2-A0)] x CQ
     CQ = the conentration of Quin-2 in the chelator solution
6. Now we can begin the titration of our protein. Dissolve 0.7 - 0.8 mg of the protein in 2.5 ml of the (dilute) Quin-2 solution. Record the actual weight you added.
7. Read the absorbance at 263
8. Titrate in calcium. Add 5 ul of 3 mM CaCL₂ at each step, and measure and record the absorbance at 263 nm after each addition. Wait ~30 seconds after adding the calcium before taking the measurment, to let the system equilibrate. Repeat until there is no change in the absorbance for approximately 5 additions.

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   Calculate an Estimate of the Calcium Concentration in Your Protein Solution

   You can use the data from the titration to calculate a rough estimate of the concentration of the residual calcium in the protein preparation. Use the following equation:
   [Ca] = [ 1 - ( (AS - AE)/(A0 - A2) )] x CQ
   AS = the absorbance of the protein/Quin-2 solution before any calcium was added
   AE = the absorbance of the protein/Quin-2 solution after the last calcium addition
   A0 = absorbance of the Quin-2 solution alone, in presence of EDTA (from step 5 of the previous section)
   A2 = absorbance of Quin-2 solution alone, in presence of calcium (from step 5 of the previous section)
   CQ = concentration of the Quin-2 solution (from step 4 of the previous section)

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   Calculate the Calcium-Binding Constants of the Protein using the BAPTAFIL2 Program

   This program was written by Sara Linse, at Lund University in Sweden. Contact her if you want to obtain a copy. It runs on Macintosh computers.

   In order to run the program, you will need to know:

   • The binding constant of your chelator (K_D for Quin-2 is 5.2 E-9)
   • The concentration of the chelator in your titration solution (see step #4 of the section on collecting the data)
   • The concentration of your protein in the titration solution (calculate this from the weight measured in step #6 of the section on collecting the data)
   • The total volume of the titration solution (in this example, it was 2.5 ml)
   You also need to know the values for the following parameters:
   • Number of addition types: in most cases, this will be 2 (the first measurement, without any calcium, and all of the subsequent measurements after the addition of a calcium aliquot)
   • CAPORT = the aliquot size (in this example, 5 ul)
   • CACONC = the concentration of the CaCl₂ solution used in the titration (in this example, 3 mM)
   The program will ask you for additional information, including the following values, for which you provide a guess:
   • The initial calcium concentration (in uM): guess something relatively low, like 3 or 4. If you don't get a good fit, try changing this guess and running the program again.
   • Calcium constants: guess something reasonable, based on what you know about your protein. For instance, for my calbindin D9k mutants, I usually guessed the wildtype constants initially.
   • A(max): absorbance in the absence of calcium. Guess something a little higher than the first absorbance point, measured before any calcium was added)
   • A(min): absorbance when protein is fully calcium-loaded, in the absence of any dilution. Guess something a little bit higher than the absorbance at the last titration point.
   • factor: the factor to compensate for errors in weighing the protein, etc. I think I started with a guess of 1 for this.
   You will be asked to supply a value for a "vary" factor for some of the parameters. Set this to a non-zero value if you want this parameter to vary, and to zero if you want it to be kept fixed. You want you initial calcium concentration, you calcium constants, and the compensatory factor. It is not clear from my notes, but you may need to tell the program to let the A(max) and A(min) values vary, as well.

   Iterate through the program until the difference between A(max) and A(min) is approximately 1.023 (the same range as for Quin-2. If you are using a different chelator, change this target appropriately). The program will also provide you with a value called "E.S.S." This is the error square sum, and is a measure of the quality of the fit. A good fit has an E.S.S. value of less than 0.0001.