About measurement of Protein-Ligand binding equilibria by the Ultrafiltration method

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Introduction

Ultrafiltration is one of the conventional methods for indirect measurement of the energetics of protein-ligand binding. In this method, the protein and ligand are incubated together and allowed to attain binding equilibrium at a constant temperature and pressure. Subsequently, the bound and unbound ligand (smaller molecule) are separated by filtration through an ultrafiltration membrane. By quantifying the amount of free ligand, the equilibrium constant may be determined, thereby yielding the standard free energy change (G0) for the biomolecular pair. By designing experiments that provide data, on the temperature dependence of the equilibrium constant, it is possible to determine the standard enthalpy change and the standard entropy change. Thus, one may obtain a complete set of thermodynamic data on a biomolecular pair using this method. Although widely used in biochemical research and clinical laboratories, this method suffers from a few drawback. The major concern involves the stability of the binding equilibrium during the ultrafiltration step. This problem may be overcome by using a sufficiently short analysis time, which differs between different binding pairs. Theory The figure shown below, illustrates the ultrafiltration method. The protein and ligand are placed in the upper chamber of the filter cartridge and allowed to come to equilibrium. The equilibrium mixture of bound and unbound protein and ligand is filtered in a centrifuge. The solution retained in the upper chamber after the filtration is called the retentate, and contains the bound ligand and free protein. The filtrate, which collects in the lower chamber, contains the unbound ligand. Measurement of the unbound ligand concentration may be made using a suitable method such as fluorescence or absorbance. The method for calculating the equilibrium constant is described below.

Consider the following binding strategy for the protein (BSA) and ligand (phenylbutazone):

BSA+PBBSA_PB

where: PB Phenylbutazone, MW = 308.38 Da BSA Bovine serum albumin, MW = 66 kDa At equilibrium, the equilibrium dissociation constant,

_D^* = [][]/[] -----------------Eq (1)

Let, n= no. of binding sites, [BSA]₀ = total BSA, [PB]₀ = total PB. Let the fraction of PB that is bound to BSA be, _e^* Then,

_D^* ={[]₀ (1_e^*)([]₀ /[]_{0 e}^*) }/ _e^* -------------Eq(2)

Experimental Procedure There are three main steps in this experiment.

1. Generate phenylbutazone absorbance calibration curve.

2. Perform phenylbutazone-BSA binding assay using the ultrafiltration method.

3. Determine _D^* of the binding from data obtained in (1) and (2) above, and calculate G0.

Materials You will be given:

1. Phosphate-buffered saline solution

2. BSA protein as a lyophilized powder (around 2mg)

3. 1mL of 400M Phenylbutazone in NaOH stock solution

4. Vivaspin 500 (3 kDa MWC O) ultrafiltration cartridges.

Phenylbutazone absorbance calibration curve. 1. Dilute the stock solution with PBS to make the three standard phenylbutazone solutions (A C in Table-1).

2. Take two measurements of each sample's absorbance at 254 nm. For each reading, use the same amount.

3. Before measuring the absorbance of each standard, auto zero the Nanodrop spectrophotometer using standard (D). 4. Plot a graph of the absorbance at 254 nm vs the concentration of phenylbutazone.

Phenylbutazone-BSA binding assay.

1. Each 500 mL binding assay reaction mix contains phenylbutazone in PBS solution, with or without BSA.

2. The final concentrations of phenylbutazone and BSA in the reaction mix are [PB]0 and [BSA]0, respectively. Prepare the reaction mixtures according to the instructions in Table 2.

3. Allow the reaction mixtures to sit at room temperature for a few hours. For 30 minutes, slowly agitate on the shaker at 120 rpm.

4. Fill a Vivaspin 500 cartridge with all 500 liters of each reaction mix. The cartridge should be labeled.

5. Place the cartridges in the centrifuge so that the marks are on the bottom.

6. Centrifuge the reaction mixtures for 10 minutes at 15, 000 rcf.

7. If desired, dilute 400 liters of each filtrate in 600 liters of PBS.

8. Use the control to auto-zero the Nanodrop spectrophotometer (C-2). Calculating the absorbency of each diluted filtrate was measured twice at 254 nm. Make the necessary adjustments for the dilution.

Table1

Standard	Final Concentration	Volume of preceding standard (L)	Volume of PBSA (L)	Absorbance 1	Absorbance 2
A	100	25	75	0.048	0.042
B	50	12.5	87.5		0.033
C	25	6.25	93.75	0.016	0.015
D	0	0	100	0	0

Table2

	[]0	[]0	Volume of PB stock (L)	Weight of BSA (mg)	Volume of PBSA (L)	Absorbance (2 readings avg)
Sample	50.00	55.00	62.5	1.828	437.5	0.014
Control-1	50.00	0	62.5	0	437.5	0.0085
Control-2	0	0	0	0	0	0

Questions

Estimate the fraction of PB that is bound to BSA, and Calculate _D^* and G0, assuming the temperature to be 22o C and n = 1.