Ligand Binding Inhibitors Sodium Sucrose Octasulfate

An analysis of the inhibitor effectiveness is conducted based on steady-state data acquisition with two independent first-order reactions occurring in solution.

where P is E-HS, L is the growth factor (bFGF), C1 is the binding complex of E-HS and bFGF, S is a growth factor binding inhibitor (SOS), and C2 is the binding complex of SOS and bFGF.

Assuming conservation of mass, the following equation at the steady state can be solved for the KD value (KD2):

where C2 = 2 L( L, - C1 + 50 + Km)-i (L> - C1 + 50 + Kd2> -4S0 (L0 - Q)J

Knowing P0 and KD1 from steady-state analysis in the absence of inhibitor (see Subheading 3.2.), experiments are run at a constant level of E-HS and bFGF (L0) and various levels of inhibitor (S0). Retention is a measurement of C1. The programming to determine KD2 is outlined below.

1. Mathematica software (Version 3.0, Wolfram Research) is launched, and a new notebook page is initialized. Commands as outlined below are entered into the notebook page, and the "shift" and "enter" key are pressed simultaneously at the end of each instructional set (symbolized in the procedure by " ♦ ")

2. The statistical package must be loaded by typing (see Note 2)

<<StatisticsvNonlinearFif ♦

3. The known parameters—P0 and KD1—with both in units of nM:

4. Enter the ligand concentration, L0 (nM), the reaction volume, volume (L), the molecular weight of the inhibitor, mwl (g/mol), and the molecular weight of the growth factor, mwF (g/mol):

5. Enter the quantity of inhibitor (S0) added (ng):

s = {0, 0, 0, 0, 5, 5, 5, 25, 25, 25, 50, 50, 50, 100, 100, 100, 500, 500, 500, 750, 750, 750}; ♦

6. Enter the measured values of bFGF retained (C1) (ng):

c = {.018, .015, .022, .021, .02, .016, .013, .011, .0061, .011, .0082, .0061,

.013, .0094, .010, .0076, .0072, .0015, .0052, .0073, .0040, .0039}; ♦

7. Convert these values (S0 and Cj) to nM from ng and store as data sets A and B:

8. Enter KD1C1 as a set of data:

10. Perform the calculation for the nonlinear regression—ParameterCITable will output the KD2 value at the end, with the standard error and the confidence interval. Entering an estimate or initial guess for KD2 will aid in the fitting process (the initial guess in our example was 300; see Note 4). It should be noted that the C2 value corresponds to one of the roots of the quadratic equation (note the minus sign shown bold below)—the alternate root yielded a negative value for KD2 for this case.

ParameterCITable /. NonlinearRegress[SOS, (Po-C1)*(Lo-C1)-(Po-C1)*((Lo-C1+So+Kd2) -((Lo-C1+So+Kd2)A2-4*So*(Lo-C1))A0.5)*0.5, {So,C1}, {Kd2,300}] ♦

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