Determination of dissociation constants for protein-ligand complexes by

In this study we present a fully automated biophysical assay based on non-denaturing ESI-MS for the determination of the dissociation constants (KD) between proteins and low molecular mass compounds. When measuring dissociation constants with ESI-MS the difference in complex stability between the gas phase and solution must be considered. While dissociation of polar or ionic interactions in the gas phase can be neglected, nonpolar interactions tend to dissociate in the gas phase. Thus, the dissociation constant must be determined so that it reflects the complexes in the solution. We demonstrate that quantitative studies on complex formation by ESI-MS are not limited to polar or ionic interacting molecules, but it is also valid for nonpolar interactions. This is achieved by using the MS response data of the protein-ligand complex only (and not relative MS responses of the protein and the protein-ligand complexes), and by introducing a response factor. The response factor R normalizes the measured intensities to the situation in the solution for a given experimental condition. The response factor is also a measure of the stability of the complex in the gas-phase.

As a model system we used the 24 kDa extracellular soluble domain of the human growth hormone receptor, a drug target for the treatment of growth hormone disorders. The binding between this protein and the ligands used are mostly based on hydrophobic interactions. The binding affinities presented are determined from direct binding experiments and from competition experiments with a reference ligand. The obtained affinities reflect the situation in the solution phase. In the analysis of competition binding experiments, the response factor is canceled out, since relative changes in intensities of the protein-reference ligand complex were used.

The experimental conditions were optimized for noncovalent binding: Non-organic solvent at neutral pH, i.e. 10 mM ammonium acetate pH 7, was used. The source temperature and the desolvation temperature were low; 45 and 60ºC, respectively. In order to preserve the noncovalent complexes in the gas phase, an increased pressure was applied in the source region in order to make the gradient in the athmosphere-vacuum interface less steep (see 2.2.3).

The introduction of a response factor, R, makes our assay valid both for polar and nonpolar interactions. The MS response, S, is proportional to the concentration of the complex in solution, [ML].

S=R[ML]

The dissociation constant is defined as:

KD = [M][L]/[ML]

The total concentrations of the reactants are:

Mt = [M]+[ML]; Lt = [L]+[ML]

[ML] is a function of K_D, Mt, and Lt:

r + X + 1 – (r + X + 1)²– 4r 2

½ [ML] = M_t r + X + 1 – (r + X + 1)²– 4r

2

r + X + 1 – (r + X + 1)²– 4r ½ 2

r + X + 1 – (r + X + 1)²– 4r ½ r + X + 1 – (r + X + 1)²– 4r

2

½ [ML] = M_t

r = molar ratio Lt/Mt (in solution); X= K_D/Mt

From direct binding ESI-MS experiments where Mt is kept constant and Lt is varied, the response factor, R, and the affinity, K_D, are solved by non-linear regression (Fig.

10).

0 10 20 30 40 50 60

0 200 400 600 800 1000 1200

Kd 0.97549 ± 0.23895 factor 1177.12403 ± 37.19578 Protein Conc. 4 µM

Std error of point 17

Concentration/µM

S

-100 -50 0 50 100

Residuals

Figure 10. Direct K_D determination. Amount protein is kept constant and the amount ligand is increased. The MS responses (S) corresponding to the protein-ligand complex are plotted as a function of ligand concentration. K_D was solved by non-linear regression and was estimated to 0.97 µM.

The response factor should be regarded as a system- and instrument-dependent fitting parameter. However, it is equal to the maximum response of the complex. A complex that dissociates in the gaseous phase will have a low R while a complex that is intact in the gaseous phase will have a high R.

For the competition binding experiments, the change in the MS response of the protein-reference ligand complex, MA, due to competition by a second ligand, B, gives information of the affinity of the competing ligand KD,B. An increased concentration of B will lead to partially displacement of A from the complex with M.

The degree of displacement will be dependent on the binding constants and the concentrations of A and B.

In the mass spectra the observed MS response of the MA complex when ligand B is present is compared with the MS response of the MA complex of the solution free from B (Fig 11). In the single point determination (Fig, 11A) only one concentration of B is used, while in the dose response curve (Fig. 11B), several concentrations of B

are used, giving a more accurate KD measurement. KD,B is solved by nonlinear regression.

238000 23900 24000 24100 24200 24300 24400 24500 24600 100

% 0 100

%

MA

MB M

M

[B]= 0 µM

[B]= 60 µM MA

mass

Relative change

KDof competing ligand

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.001 0.01 0.1 1

K_D,Bca 1.

Ratio: 0.488

238000 23900 24000 24100 24200 24300 24400 24500 24600 100

% 0 100

%

MA

MB M

M

[B]= 0 µM

[B]= 60 µM MA

238000 23900 24000 24100 24200 24300 24400 24500 24600 mass

100

% 0 100

%

MA

MB M

M

[B]= 0 µM

[B]= 60 µM MA

mass

Relative change

KDof competing ligand

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.001 0.01 0.1 1

K_D,Bca 1.

Ratio: 0.488

Relative change

K_Dof competing ligand

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.001 0.01 0.1 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.001 0.01 0.1 1

K_D,Bca 1.

Ratio: 0.488

24300 24400 24500 24600 24700

[B]= 0 µM [B]= 30 µM

[B]= 60 µM [B]= 120 µM [B]= 300 µM MA

MB

0 50 100 150 200 250 300

0.0 0.2 0.4 0.6 0.8 1.0

[MB] (uM)

S/Sref

K_D,B= 1.2 ± 0.06 µM

24300 24400 24500 24600 24700

[B]= 0 µM [B]= 30 µM

[B]= 60 µM [B]= 120 µM [B]= 300 µM MA

MB

24300 24400 24500 24600 24700

[B]= 0 µM [B]= 30 µM

[B]= 60 µM [B]= 120 µM [B]= 300 µM MA

MB

0 50 100 150 200 250 300

0.0 0.2 0.4 0.6 0.8 1.0

[MB] (uM)

S/Sref

K_D,B= 1.2 ± 0.06 µM

0 50 100 150 200 250 300

0.0 0.2 0.4 0.6 0.8 1.0

[MB] (uM)

S/Sref

K_D,B= 1.2 ± 0.06 µM

B

A

10 10 10 10

Figure 11. Competition experiment using A) One-point calibration. The ESI-MS response of the protein-ligand complex MA is determined before and after addition of ligand B. The concentration for ligand A is constant and K_D,A is known. KD,B is estimated by non-linear regression to ca 1.4 µM. B) Dose-response curve. The concentration of ligand A is constant and K_D,A is known. The concentration of ligand B is varied from 0 to 300 µM. The ESI-MS responses of MA is determined, and K_D,B

is calculated from non-linear regression to 1.2 ± 0.06 µM.

The flexibility of the ESI-MS method makes it possible to produce reliable KD values of low-affinity ligands, even if the solubilities of the ligands are poor. In the

“reversed” procedure of KD measurements we increased the amounts of the reference ligand A and allowed the amount of the competing ligand B (the low-affinity ligand) to be fixed.

A software enabling automated MS data processing has reduced the data process time from approximately 4 min to 20 s per sample. By using a simple sample preparation procedure and automation of the MS analysis as well as automation of the MS data processing, it is possible to screen 100 different compounds per day against the protein using the single point competition experiment.

The ESI-MS assay has some limitations. Many buffers (e.g. phosphate buffers, TBS buffers etc) are not compatible with ESI-MS. High salt concentrations and detergents can also affect the MS signal negatively. For the best MS results, the protein should be possible to dissolve in ammonium acetate (10-50 mM), pH 7.

The stability of the protein upon ligand binding must be carefully studied prior to KD

measurements. If the ligand induces denaturation or aggregation on the protein, the total MS response will decrease and the KD measurements could become incorrect.

Furthermore, the protein must be fairly homogenous in order to provide enough resolution between the peak corresponding to the protein-ligand complex and the peak of the free protein. Finally, nonspecific binders can be hard to distinguish from low affinity binders, especially if the interaction is polar or ionic. In this case complementary techniques are recommended.

4.4 MECHANISM OF ACTION OF PYRIDAZINE ANALOGUES ON