Mathematica Fitting Program for Ligand Proteoglycan Binding

« Statistics "NonlineaxFit."

volumes 0.0002;

Fadds{.05, .05, .05, .05, .05, .05, 0.10, 0.10, 0.10, 0.10, 0.10, 0.10,0.20,0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.75, 0.75, 0.75, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.5, 2.5, 2.5, 4.0, 4.0, 4.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 6.0, 6.0, 6.0, 10.0, 10.0, 10.0};

Ebound = { • 0025, .0035, .0034, .0013, .0055, .0033, .0067, .0069, .0076, .0028, .0033, .0035, .017, .020, .018, .0063, .0076, .0063, .017, .016, .018, .016, .017, .017, .079, .034, .043, .029, .034, .032, .021, .022, .020, .047, .056, .057, .080, .13, .099, .13, .071, .078, .037, .039, .086, .088, .066, .070, .21, .24, .19, .17, .16, .16, .25, .20, .22, .32, .32, .30, .17, .37, .27, .22, .20, .17, .51, .48, .45, .44, .39, .42};

datl = Fadd / (volume * mwF) ; dat2 k Fbound / (volume * mwF); data = {datl, dat2); binding = Transpose [data];

ParameterCITable /. NonlinearRegress[binding, ligand*rt/ (led + ligand), {ligand}, {rt, kd)]

rt kd

Estimate 0.228852 2.34021

Asymptotic SE

0.0385813

0.624793

Fig. 3. Mathematica program to solve for ligand-proteoglycan affinity and binding sites. The code and data are input as shown. The ; following each line suppresses output and may be eliminated if the user prefers. The output is displayed at the bottom and includes the asymptotic standard error and the asymptotic confidence intervals.

10. Perform the calculation for the nonlinear regression—ParameterCITable will output the KD1 and Rt values at the end with the standard error and the confidence interval. The units for each will be in nM:

ParameterCITable /. NonlinearRegress[binding, ligand*Rt/(Kd1+ligand),

11. KD1 is 2.3 ± 0.6 nM. RT is 0.23 ± 0.04 nM. The complete Mathematica program is shown in Fig. 3. To convert RT to sites/ng E-HS (see Note 3):

volume sites = Rt —pG— • N av where PG is the amount of E-HS added (ng), NAV is Avogadro's number <6.02 * 1023 sites mol>. Rt for this system is 7.0 ± 1.2 x 108 sites/ng.

Although similar, the specifics for the ligand-binding inhibitor and the proteoglycan binding inhibitor do differ slightly and will each be outlined below. As example inhibitors, we include data for sucrose octasulfate (ligand-binding inhibitor) and protamine sulfate (proteoglycan-binding inhibitor)

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