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

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

Written by: Melanie Nelson, spring 1999 and Anders Malmendal, spring 2001

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. The expert on this method is Sara Linse at Fysikalisk Kemi 2, Lund University in Sweden. 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. People in the Chazin lab can consult Melanie's Wetlab and NMR notebook #1, starting on page 58, for notes on this technique. Click here for Melanie's original version of this page.

Measurement

Getting binding constants using kjell

Getting binding constants using BAPTAFIL2

Measurement

You should choose a competitive chelator with a calcium affinity in the similar to protein you study. 5N-BAPTA, 5,5'Br₂-BAPTA and Quin-2 are good choices. The absorbance of the chelator must change when it binds calcium. Note that you use different wavelengths for determining the chelator concentration and the calcium titration.

chelator	Extinction coeff. (Ca²⁺-loaded)	Wavelength
Quin-2	4.2 10⁴ l mol^-1 cm^-1	239.5 nm
5,5'Br₂-BAPTA	1.6 10⁴ l mol^-1 cm^-1	239.5 nm
5N-BAPTA	? 10⁴ l mol^-1 cm^-1	?

Make a 25-30 micromolar solution of chelator.

Make a stock solution by taking a tiny amount of chelator (a qouple of flecks on the tip of a spatula) and dissolve it in 5 ml of calcium-free buffer, e.g chelex-treated XX mM KCl, 2 mM Tris-HCl, pH 7.5. Note that most of these chelators are light sensitive, so wrap the container with your stock solution in foil.
Make a 5X dilutioned sample of your chelator stock in your buffer with 2 ul 1 M CaCl₂ (per ml soln.) in a quartz cuvette.
Determine the exact concentration of chelator in your solution by measuring the absorbance at the appropriate wavelength (239.5 for 5,5'Br₂-BAPTA and Quin-2). If the absorbance is outside the linear range adjust the chelator concentration.
Calculate the required dilution of the stock solution to get ~28 uM chelator. Make the required amount and check the concentration as above. This is your chelator solution.

chelator	K_D (low salt) /M	K_D (150 mM KCl) /M	Wavelength
Quin-2	5.26 10^-9	1.19 10^-7	263 nm
5,5'Br₂-BAPTA	1.0 10^-7	2.27 10^-6	263 nm
5N-BAPTA		2.45 10^-5	430 nm

Determine the residual calcium concentration in the chelator stock solution.

Switch wavelength to that used for calcium titration (430 nm for 5N-BAPTA, and 263 nm for 5,5'Br₂-BAPTA and Quin-2).
Let the cuvette sit for a few minutes with a little EDTA and (calcium-free) water in it, then rinse it with (chelex) water.
Measure the absorbance (A1) of your chelator solution
Add 2 ul 0.1 M EDTA (per ml soln.) and measure the absorbance (A0)
Add 2 ul of 1 M CaCl₂ (per ml soln.) and measure the absorbance (A2)
Calculate the Ca2+-concentration in the chelator solution:

((A1 - A0)/A2-A0)) x

Check the affinity of your chelator by following its absorbance while you add calcium. (If you use standard conditions this may not be necessary, but it is a good check.)

Measure the absorbance of your sample at the calcium titration wavelength.
Follow the absorbance as you add aliquots of CaCl₂. Mix thoroughly, but be careful to minimize sample loss. Start with 1 ul of 1 mM (per ml soln.), when the decrease in absorbance is smaller than 0.015 absorbance units switch to 1 ul of 3 mM, then 10 mM, 1 ul of 100 and then finally 1 M till the absorbance is constant.

Mix your protein (lyophilized or concentrated solution) with the chelator solution to a protein concentration of about 25 to 30 uM. If you are going to make more than one titration with the same protein, make one stock solution with protein and chelator. Make sure that your protein solution has the right pH.
Measure the binding constants of your protein by following its absorbance while you add calcium.

Measure the absorbance of your sample at the calcium titration wavelength.
Follow the absorbance as you add aliquots of CaCl₂. Mix thoroughly, but be careful to minimize sample loss. Start with 1 ul of 1 mM (per ml soln.), when the decrease in absorbance is smaller than 0.015 absorbance units switch to 1 ul of 3 mM, then 10 mM, 1 ul of 100 and then finally 1 M till the absorbance is constant.

Estimation of the calcium concentration in the protein solution

The data from the titration can be used to roughly calculate a lower limit of the residual calcium concentration in the protein preparation as follows:

[Ca] = [ 1 - ( (AS - AE)/(A0 - A2) )] x CQ
AS = the absorbance of the protein/chelator solution before any calcium was added
AE = the absorbance of the protein/chelator solution after the last calcium addition
A0 = absorbance of the chelator solution alone, in presence of EDTA (from step 2 of the previous section)
A2 = absorbance of chelator solution alone, in presence of calcium (from step 2 of the previous section)
CQ = concentration of the chelator solution (from step 1 of the previous section)

Calcium-binding constants calculation using the kjell and kjell_ator programs

These AWK scripts are written by Anders. They run under UNIX (and probably need some modifications to run under LINUX). In order to obtain the best result you need to explore the function of the different parameters in the headers of these programs.

kjell calculates two macroscopic binding constants from a chelator titration using monte-carlo type fitting procedure. It finds the optimal fit by randomly choosing values of the parameters within an N-dimensional cube. The cube shrinks until the error sum improvement is smaller than mindiff. If your protein has a number of sites different from two you need to slightly modify the equations.

Usage:kjell inputfile logk1_est logk2_est tries denominator

inputfile can look as follows:

kdchel 2.493e-5chelator kd in M
cchel 28.8chelator concentration in uM
cprot 25.3protein concentration in uM
naapo 0.375start value for absorption in apo chelator
naholo 0.048start value for absorption in holo chelator
c_0 1initial ion concentration in uM
v_0 2500volume in uL
0 5added vol in uL and concentration in mM (for each of the following rows)
0.5379absorbance
5 2.35added vol in uL and concentration in mM (for each of the following rows)
0.4514absorbance
0.3678absorbance
0.2915Calabsorbance
.
.
.

logk1_est and logk2_est are starting values for the macroscopic binding constants in 10logs (in log(M-1)).
tries is the number of random values used
denominator is the shrinkage factor of the cube

In a similar way kjell_ator calculates the chelator binding constant.

Usage: kjell_ator inputfile kd_est tries denominator

the inputfile can look as follows:
cchel 28.8chelator concentration in uM
c_0 1initial ion concentration in uM
v_0 2500volume in ul
0 5added vol in ul and concentration in mM (for each of the following rows)
0.5379absorbance
5 2.35added vol in ul and concentration in mM (for each of the following rows)
0.4514absorbance
0.3678absorbance
0.2915absorbance
.
.
.
kd_est is a starting value for kd in M
tries is the number of random values used
denominator is the shrinkage factor of the cube

Calcium-binding constants calculation 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. The concentration of the chelator in your titration solution (see step #2 of the measurement section)
The concentration of your protein in the titration solution (calculate this from the weight measured in step #4 of the measurement section)
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 Melanie's 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 Melanie's 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 chelator. If you are using a different chelator, change this target appropriately). The program will also provide you with a measure of the quality of the fit "E.S.S." the error square sum. A good fit has an E.S.S. value of less than 0.0001.

Last updated February 12, 2001 by Anders Malmendal