Inhibitor effectiveness analysis is 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, PS is a proteoglycan binding inhibitor (protamine sulfate), and C3 is the binding complex of PS and bFGF.

Assuming conservation of mass, the following equation at the steady state can be solved for the KD value (KD3):

where C3 = i(Pq - C1 + PSQ + Kd3) - V (PQ - C1 + PSQ + KD3> - 4PS iPq - C1 )J

Knowing P0 and KD1 from steady-state analysis in the absence of inhibitor (see Subheading 3.2.1.), experiments are run at a constant level of E-HS and bFGF (L0) and various levels of inhibitor (PS0). Retention is a measurement of C1.

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" keys 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 are then initialized—Po 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, 40, 40, 40, 80, 80, 80, 160, 160, 160, 320, 320, 320, 600, 600, 600}; ♦

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

c = {.018, .022, .019, .014, .017, .014, .009, .013, .014, .01, .012, .003, .001, .006, .011,

7. Convert these values (PS0 and Cj) from ng to nM 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 or with the standard error and the confidence interval. Entering an estimate or initial guess for KD3 will aid in the fitting process (the initial guess in our example was 75) (see Note 4). It should be noted that the C3 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 KD3 for this case.

ParameterCITable /. NonlinearRegress[Protamine, (L0 - Cj)*(P0 - Cj) - (L0 - Cj) * ((P0 -Cj + PS + KD3) - ((P0 - C1 + PS + KD3) a 2 - 4 * PS *(P0 - C1)) A 0.5) * 0.5, {PS,C1},

3.3. Summary

Proteoglycan binding is a physiologically important means of regulating growth factor activity and availability. This chapter details a fast and simple assay for quantifying inhibitors of growth factor-proteoglycan binding. Although data and the corresponding analysis focused on inhibitors of bFGF interactions, the method should be easily transferable to other proteoglycan-binding growth factors and molecules.

1. Many protocols for isolation of proteoglycans involve the use of denaturing agents such as urea. These agents can interfere with protein-proteoglycan interactions and should be removed from proteoglycan preparation prior to binding experiments.

2. When loading the Statistics packages, it is important to use v (grave accent) as opposed to ' (open quote) in the statement: <<StatisticsvNonlinearFit\

3. In calculating the growth-factor binding sites per nanogram of proteoglycan, it is important to enter the RT value in moles per liter, volume in liters, and proteoglycan in nanogram to generate binding sites per nanogram (see Subheading 3.2.1, step 11).

4. When fitting parameters using NonlinearRegress, a warning may be issued:

NonlinearFit::lmpnocon : Warning: The sum of squares has achieved a minimum, but at least one parameter estimate fails to satisfy either an accuracy goal of 1 digit (S) or a precision goal of 1 digit (s). These goals are less strict than those for the sum of squares, specified by AccuracyGoal ->6 and PrecisionGoal ->

If this occurs, it is best to rerun your regression fit with the output KD used as your new initial guess. This may be easily done by highlighting the right sidebar and pressing ♦ . Repeat this procedure until the warning is not issued.

References

1. Conrad, E. (1998) Heparin Binding Proteins, Academic Press, San Diego, CA.

2. Rapraeger, A. C., Krufka, A., and Olwin, B. B. (1991) Requirement of heparan sulfate for bFGF-mediated fibroblast growth and myoblast differentiation. Science 252, 1705-1708.

3. Fannon, M. and Nugent, M. A. (1996) Basic fibroblast growth factor binds its receptors, is internalized, and stimulates DNA sythesis in Balb/c3T3 cells in the absence of heparan sulfate. J. Biol. Chem. 271, 17949-17956.

4. Forsten, K. E., Courant, N. A., and Nugent, M. A. (1997) Endothelial proteoglycans inhibit bFGF binding and mitogenesis. J. Cell. Physiol. 172, 209-220.

5. Dowd, C. J., Cooney, C. L., and Nugent, M. A. (1999) Heparan sulfate mediates bFGF transport through basement membrane by diffusion with rapid reversible binding. J. Biol. Chem. 274, 5236-5244.

6. Isner, J. M. (1996) The role of angiogenic cytokines in cardiovascular disease. Clin. Immunol. Immunopathol. 80, S82-S91.

7. Rapraeger, A. and Yeaman, C. (1989) A quantitative solid-phase assay for identifying radiolabeled glycosaminoglycans in crude cell extracts. Anal. Biochem. 179, 361-365.

8. Nugent, M. A. and Edelman, E. R. (1992) Kinetics of basic fibroblast growth factor binding to its receptor and heparan sulfate proteoglycan: a mechanism for cooperativity. Biochemistry 31, 8876-8883.

9. Farndale, R. W., Buttle, D. J., and Barrett, A. J. (1986) Improved quantitation and discrimination of sulphated glycosaminoglycans by use of dimethylmethylene blue. Biochim. Biophys. Acta 883, 173-177.

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