
420 Forsten and Nugent
3.2 Analysis
3.2.1. Ligand–Proteoglycan Binding
1. The output data will represent the amount of bFGF retained on the filter for a given added
concentration. The amount retained in the absence of E-HS should be subtracted from
that with E-HS to generate data that represent specific E–HS bound bFGF.
2. Varying the concentrations of bFGF while holding constant the concentration of E-HS
(with no inhibitor), this data set should be analyzed to determine the binding capacity
(amount of bFGF bound per unit of E-HS) and the binding affinity (K
D1
), assuming a
simple monovalent binding reaction,
which, at steady state assuming negligible ligand depletion, is described by
where R
T
is the binding capacity, and L
0
is the concentration of FGF added. The
programming to determine K
D1
and R
T
is outlined below.
3. 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” keys are pressed simultaneously at the end of each instructional set
(symbolized in the procedure by “ ♦ ”)
4. The statistical package must be loaded by typing (see Note 2):
<<Statistics`NonlinearFit` ♦
5. Enter the volume of test solution (in liters) and the molecular weight of the growth factor
(bFGF) being investigated:
volume = 0.0002; ♦
mwF = 18000; ♦
6. Enter the amount of bFGF added per test well (L
0
) 〈ng〉
Fadd = {0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 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}; ♦
7. Enter the measured values of bFGF retained (C
1
) 〈ng〉
Fbound = {.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}; ♦
8. Convert these values (L
o
and C
1
) from ng to nM and store as data sets 1 and 2:
dat1 = Fadd/(volume*mwF) ; ♦
dat2 = Fbound/(volume*mwF); ♦
C
1
R
T
L
0
K
D1
+ L
P + L
K
D1
C
1