Determination of Protein-Ligand Binding Constants Using a Spectroscopy

Protein-ligand interactions are studied across many scientific disciplines. Understanding these interactions allows one to further understand how many systems within the human body works. When a protein binds to a ligand, a change occurs that alters a reaction and results in a cascade. An example would be the interactions involved in the uptake of 02 by hemoglobin, where binding inaugurates the transport of molecular oxygen throughout the vascular system (2).

Optimal conditions are considered when studying protein-ligand interactions because different conditions are known to be more ideal than others for the reaction. To determine what the optimal condition is, protein-ligand constants are calculated and compared. Using spectrophotometric methods, a protein-ligand binding constant was calculated under five pH environments within five studies in order to evaluate the ideal pH conditions for this protein to find to the ligand. For this report, BSA acts as the protein and MO acts as the ligand.

There are multiple binding sites for a ligand within a protein molecule (3). The affinity of a binding site for a specific ligand depends on whether or not the other sites are occupied (3). To appropriately evaluate the differences in these protein-ligand equilibria constants for each protein, the concept of multiple bind sites must be accounted for.

We can first take the formula for equilibria where P and L stand for the ligand (L) and free protein (P):
P + L ? PL

(1)
K is the binding constant that can be defined as:
K =
PL

(2)
P x L
The following equation us used to accommodate for the proteins and ligands that do not bind to each other (for in this case, the concentration of protein is much larger than that of ligand, i.e. [P] >>> [L]):

Pt = P + PL or P = Pt - PL

(3)
Lt = L + PL or L = Lt - PL

(4)
These two equations can be substituted into the original equation for K so that:

K =

PL

(5)
(Pt - PL)( Lt - PL)

In evaluation of Beer's Law (which will be used because the method in this report is spectrophotometric and therefore requires Beer's Law. Absorbance is defined as:
A = ?bc

(6)
Where ? is the molar absorbtivity, b is the path length, and c is the concentration.
As derived by Örstan in a similar study (3), absorbance can also be defined in the follow formula:

A = ?f[L] + ?i [PL]

(7)
= ?f (Lt - PL) + ?i [PL]

(8)
= ?f [Lt] - ?f [PL] + ?i [PL]

(9)
Expanding (8), then setting (8) equal to (9) determines that the change in absorbance (?A) is:

?A = PL(ai-?f)

(10)
From here, B (PL) can also be derived as:

B = -(- Pt Lt + ¼ (Lt + Pt + 1/K2)1/2 + ½( Lt + Pt + 1/K)

(11)

To solve for the unknowns, Microsoft? Excel's "solver" function was utilized in order to calculate a "brute-force" least-squares curve-fitting procedure (3).

Experimental

Five individual smaller experiments that contributed to the overall lab with different pH values were analyzed (Table 1). Although each of the studies prepared the appropriate solutions with a pH, the protocol for making the solutions was executed in a similar fashion. The phosphate buffer solutions were prepared using deionized (DI) water.

Five solutions were created in 50.00 mL volumetric flasks for the absorption measurements. The five solutions contained 6.10 x 10-6 M of MO that was prepared using deionized water. BSA solutions made by using the pH buffer were distributed into five aloquots in the range of 8.0 x 10-6 M to 4.0 x 10-6 M. Each solution was filled to volume with buffer solution. A standard solution of MO and BSA was prepared and filled to volume with buffer.

Absorbance measurements were obtained on a Hewlett-Packard HP 8453 Diode Array Spectrophotometer. Quartz cuvettes were used for the analysis of absorptions at 490 nm during all five individual studies. The data was then transferred and analyzed in Microsoft Excel with a best-fit line.

Results and Discussion

A previous experiment by Klotz et al. noted that the largest change in absorbance of MO as a result of binding to BSA occurred at 490 nm (4). The change in absorbance for pH 7 is illustrated in Figure 1. Two of the six K values (1.1 X 105 and 2.5 x 104) produced questionable data because these two were fit with only four data points instead of five.

The constant at pH 5.5 was considerably higher than the constant at pH 8 (Table 1).

General conclusions can be made based on the results of the experiment. The data acquired showed a correlation between the pH and binding constant values. As the pH increased, so did the values for the constant- exception of the two points in question that were mentioned earlier. This data indicates that the protein-ligand interactions of BSA to MO is at lower pH levels rather than high pH levels and that binding is favored at a neutral pH. There were hydrophobic and electrostatic interactions of the BSA molecules to the MO during the experiment in which was determined by binding constant measurements. The validity of equations 3 and 4 are confirmed by the lowest BSA concentration being higher than the MO concentration (2).

Future experiments should involve further analysis of the true optimal conditions of such a system by using the neutral pH in this experiment and much more acidic pH than those included in this experiment. For instance, a similar method used by Klotz, Walker, and Pivan to quantitatively investigate the binding of alzosulfonic acids (1) to BSA could be incorporated. The individual studies for the two constants that only had four data points should be repeated and compared to the other three values acquired in this experiment.

References
(1) Klotz, I.M.; Walker, F. M.; Pivan, R. B. J. Am. Chem. Soc. 1946, 68, 1486.
(2) Klotz, I.M.; Acc. Chem. Res. 1974, 7, 162.
(3) Örstan, A.; Wojcik, J.F. J. Chem. Ed. 1987, 64, 814.