6142
Biochemistry 2001, 40, 6142-6154
An Analytical Approach to the Measurement of Equilibrium Binding Constants: Application to EGF Binding to EGF Receptors in Intact Cells Measured by Flow Cytometry† Richard A. Stein, John C. Wilkinson, Cheryl A. Guyer, and James V. Staros* Department of Biological Sciences, Vanderbilt UniVersity, NashVille, Tennessee 37235 ReceiVed December 12, 2000; ReVised Manuscript ReceiVed February 27, 2001
ABSTRACT: In ligand binding studies, ligand depletion often limits the accuracy of the results obtained. This problem is approached by employing the simple observation that as the concentration of receptor in the assay is reduced, ligand depletion is also reduced. Measuring apparent KD’s of a ligand at multiple concentrations of receptor with extrapolation to infinitely low receptor concentration takes ligand depletion into account and, depending on the binding model employed, yields a KD within the defined limits of accuracy. We apply this analysis to the binding of epidermal growth factor (EGF) to the EGF receptor expressed in intact 32D cells, using a homogeneous fluorescein-labeled preparation of EGF and measuring binding by flow cytometry. Binding isotherms were carried out at varying cell densities with each isotherm fit to the generally applied model with two independent binding sites. Examination of the variation in the KD’s versus cell density yields a high-affinity site that accounts for 18% of the sites and a lower affinity site that accounts for the remainder. However, further examination of these data suggests that while consistent with each individual isotherm, the simple model of two independent binding sites that is generally applied to EGF binding to the EGF receptor is inconsistent with the changes in the apparent KD’s seen across varying cell densities.
The epidermal growth factor receptor (1) is a member of the ErbB family (2), that includes ErbB2/HER2 (3), ErbB3 (4, 5), and ErbB4 (6), and is the prototypical member of the superfamily of transmembrane receptor tyrosine kinases. There are multiple ligands for the ErbB family of receptors (2), including EGF (7-9), TGFR (10), betacellulin (11), amphiregulin (12), epiregulin (13), HB-EGF (14), and the neuregulins 1-4 (15-20). ErbB receptor function has been proposed to rely on the formation of multiple combinations of homo- and heterodimers (21). In the cell, the extent of dimerization and the composition of dimers most likely depend on the receptors that are expressed, their level of expression, and the ligands that are present. A better understanding of the ligand binding events for the individual receptors and receptor combinations should yield insights on the function of homo- and heterodimeric receptors in signal transduction. There have been a variety of studies that have examined ligand binding to the ErbB receptors. The most extensively studied is the binding of EGF to the EGF receptor. In most cases, examination of EGF binding to the EGF receptor has suggested that two classes of receptors exist, a high- and a low-affinity class, respectively (22-25). One hypothesis is that the low-affinity class represents ligand binding to a monomer, whereas the high-affinity class represents pre† This work was supported in part by grants from the National Institutes of Health (R01 GM55056, R01 DK25489, and T32 GM08320). * Address correspondence to this author at the Department of Biological Sciences, Vanderbilt University, VU Station B 351634, Nashville, TN 37235-1634. E-mail:
[email protected]. Phone: (615) 322-4341. Fax: (615) 343-6707.
formed dimers (26). Within the framework of this hypothesis, one open question is whether the high-affinity class represents a heterodimer or a homodimer of the EGF receptor, since the cell lines that have been used in most binding studies express other members of the ErbB family, specifically ErbB2, which has been shown to be the preferred heterodimerization partner of the other three receptors (27). The hypothesis that heterodimerization of the EGF receptor with ErbB2 creates a high-affinity ligand binding site is supported by data indicating that ErbB3 alone binds neuregulin with low affinity, but in the presence of ErbB2 there is both low- and high-affinity binding of ligand (28, 29). The use of a fluorescent ligand and flow cytometry to measure ligand binding was pioneered by Bohn (30). This method of measuring ligand binding, further advanced by Sklar et al. (31), was first applied to studies of EGF binding to the EGF receptor by Chatelier et al. (32). There are several advantages to carrying out a ligand binding assay using flow cytometry. Radioactivity is not required, and it is possible to obtain a homogeneously labeled ligand. There is no need to remove free (unbound) ligand, eliminating the requirement for separation techniques, such as filter binding, gel filtration, or centrifugation, that introduce error and often perturb the binding equilibrium prior to measuring the amount of bound ligand. Lack of a washing or filtering step simplifies the assay; binding is performed in the tubes used in the flow cytometer, thus significantly reducing the time required to perform the assay, even though the equivalent amount of time is required for equilibrium binding conditions. One potential drawback is that the cells need to be in suspension,
10.1021/bi002817a CCC: $20.00 © 2001 American Chemical Society Published on Web 04/26/2001
EGF Binding to Receptors in Intact Cells requiring that adherent cells be detached prior to the assay. Like other fluorescence-based methods, a ligand that is intrinsically fluorescent or has a fluorescent moiety attached to it is required. Once a fluorescent ligand is obtained, the affinity of a panel of nonfluorescent potential ligands can, in principle, be measured by competition binding experiments.1 While our study is aimed at measuring ligand binding via flow cytometry, the data analysis is applicable to any ligand binding assay, without regard to the method of detection of bound ligand. To exploit the advantages of using flow cytometry to measure ligand binding to receptors in intact cells, a straightforward analytical approach for the determination of KD’s that takes into account ligand depletion was developed. Further, by exploring the interdependence of cell density, the number of receptors per cell, and the apparent KD’s, a method for testing the adequacy of the generally applied twoindependent-site model of EGF binding to the EGF receptor was devised. Our analysis indicates that while individual EGF-EGF receptor binding isotherms can be fit with high statistical accuracy to a model with two independent binding sites, this model does not accurately describe the behavior of the EGF-EGF receptor interactions. THEORY The derivations in this section assume either ligand depletion or no ligand depletion, and the subsequent analyses investigate the effect of fitting data affected by ligand depletion with equations that assume no ligand depletion. These analyses form the basis for the subsequent discussion on measuring ligand affinity using flow cytometry. The aim of this section is to describe the binding interaction to either a single receptor population or two independent receptor populations in the absence of any nonspecific binding and without measurement of free ligand in the assay. Discussion of the applicability of competition binding assays for both a one- and two-site model utilizing similar methods is in the Supporting Information. One-Site Ligand Binding. The binding interaction between a ligand and a single receptor site at equilibrium is described by the following:
RF + LF h RL KD )
RFLF RL
where KD is the dissociation constant, RF is the concentration of free receptor, LF is the concentration of free ligand, and RL is the concentration of ligand bound to the receptor. The equations for conservation of mass are
RT ) RF + RL LT ) LF + RL where RT and LT denote the total receptor and ligand concentration, respectively. Substituting the equations for conservation of mass into the equation describing ligand 1
See Supporting Information.
Biochemistry, Vol. 40, No. 20, 2001 6143 affinity and algebraic manipulation yields
RL2 - (LT + RT + KD)RL + RTLT ) 0 The concentration of ligand bound to receptor, RL, is then simply the solution of this quadratic equation with the negative root:
(LT + RT + KD) - x(LT + RT + KD)2 - 4RTLT RL ) 2 (1) Under most conditions, this equation is the most accurate description of equilibrium binding of a ligand to a receptor. Historically, however, eq 1 has rarely been used to analyze equilibrium binding curves. In most studies, LF has not been replaced in the derivation, yielding the equation:
RL )
RTLF LF + KD
This method relies on the accuracy with which the concentration of free ligand is known; however, the concentration of free ligand is not frequently measured; rather it is assumed that LF ) LT, based on the routine assumption that the concentration of receptor-bound ligand, RL, is negligible compared to the amount of ligand added, LT. When the assumption LF ) LT is made, it is assumed that there is no ligand depletion, and
RL )
RTLT LT + KD,app
(2)
where KD,app, is not the true dissociation constant, KD, but an apparent dissociation constant. Even under experimental conditions in which the concentration of receptor is less than 10% of the dissociation constant, RT e KD/10, the dissociation constant obtained is still an approximation, but it will be within 10% of the true KD. This equation is useful in that the concentration of ligand-receptor complex is proportional to the total concentration of receptor present, with the proportionality determined by KD,app and the concentration of ligand added, LT; however, binding experiments rarely approach ideal conditions and are often performed without consideration of these inherent assumptions. Two-Site Ligand Binding. Many ligand binding studies have suggested the presence of multiple classes of ligand binding sites. The presence of multiple classes of binding sites is often revealed by the nonlinear plots of data transformed and plotted by the method of Scatchard (bound vs bound/free) (33). Several authors have discussed appropriate methods and potential difficulties in obtaining binding parameters from these nonlinear plots (34-37). There are several modes of ligand binding that could lead to nonlinear Scatchard plots. One of the simpler models consists of two noninteracting receptor classes, described by
RF + LF h RL, SF + LF h SL KDR )
RFLF SFLF , KDS ) RL SL
where R and S denote two independent receptor classes:
6144 Biochemistry, Vol. 40, No. 20, 2001
Stein et al.
either two different receptors that both bind the ligand, or the same receptor that binds the ligand with two different and independent affinities. While these are considered independent binding sites in relation to their ligand binding properties, the fraction bound for each class is not independent, but will depend on the amount of each receptor class present and on the amount of ligand added. This can be seen by accounting for mass balance:
R T ) RF + RL ST ) SF + SL LT ) LF + RL + SL One can solve for RL and SL:
RL )
STLF RTLF and SL ) LF + KDR LF + KDS
(3)
and substitute into the equation for LT to obtain an equation for LF. This equation is a cubic equation like the one obtained for the one-site competition case (see Supporting Information) and can be solved similarly (38) to yield:
a 2 θ LF ) - + cos xa2 - 3b 3 3 3
()
θ ) arc cos
(3a)
-2a3 + 9ab - 27c 2x(a2 - 3b)3
a ) KDR + KDS + RT + ST - LT b ) KDS(RT - LT) + KDR(ST - LT) + KDRKDS c ) -KDRKDSLT Equation 3a can then be used to solve for RL and SL to obtain the concentration of receptor-bound ligand. The above derivation makes no assumptions about the extent of ligand depletion. Assuming that there is no ligand depletion, LT ) LF, the total bound reduces to
BOUND ) RL + SL )
RTLT STLT + (4) LT + KDR,app LT + KDS,app
This equation is simply the sum of independent binding sites (cf. eq 2), and the amount bound to each subclass is independent of the presence of the other class of receptor. These two derivations can be used to examine the effect of ligand depletion on the determination of the dissociation constants for ligand binding to two independent classes of receptors. METHODS Simulations and Fitting. To ascertain the effects of fitting experimental data assuming that there is no ligand depletion, data were simulated with the equations in which ligand depletion is taken into account and then fit with equations in which it is assumed that there is no ligand depletion. Theoretical data were generated using eqs 1 and 3 in the spreadsheet Quatro Pro (Corel). These data were then imported into Prism (GraphPad Software) and fit using builtin functions corresponding to eqs 2 and 4.
Materials. Restriction enzymes and T4 DNA ligase were from New England Biolabs. pCDNA3.1(-) was from Invitrogen. Sequanase Kit 2.0 was from U.S. Biochemical, and Sequitherm EXCEL II sequencing kit was from Epicenter Technologies. G418 sulfate was from Mediatech. Protein A-Sepharose CL-4B, enhanced chemiluminescence (ECL) reagents, and horseradish peroxidase (HRP)-conjugated donkey anti-rabbit IgG were from Amersham Pharmacia Biotech. Fetal bovine serum (FBS) was from Gibco BRL. Ab 528 and Ab 1005, both directed against the EGF receptor, were from Santa Cruz Biotechnology. Glycerol was from Fisher. Sodium dodecyl sulfate (SDS) was from Serva. Nitrocellulose membranes were from Schleicher & Schuell. Fluorescein isothiocyanate (FITC)-conjugated goat antimouse IgG2a was from Southern Biotechnology Associates. Paraformaldehyde was from Electron Microscopy Sciences. All other reagents were ACS reagent grade or better. Construction of H22Y-mEGF. A plasmid, pIN-II-ompA3H22Y-mEGF, encoding H22Y-mEGF was constructed using the approach previously described for Y3K,H22Y-mEGF (39), except that only a single synthetic oligonucleotide, 5NGGTGTTTGCTATGTACATCGAATCT-3N, was employed. Expression and Purification of H22Y-mEGF. Following transformation of E. coli HB101 with the pIN-III-ompA3H22Y-EGF plasmid, the expression and purification of H22Y-mEGF were carried out largely as previously described for Y3K,H22Y-mEGF (39). Briefly, bacteria were grown to mid-log phase, induced by addition of isopropyl β-D-thiogalactopyranoside (IPTG) to 200 µM, harvested by centrifugation, and osmotically shocked to release periplasmic proteins, including H22Y-mEGF. The osmotic shock fluid was lyophilized and dissolved in water. H22Y-mEGF was purified from other periplasmic proteins by reversedphase HPLC (RP-HPLC) using a 10 × 100 mm Poros R2/H column with 0.1% triethylamine/acetate (pH 6.0) in 95:5 water/acetonitrile (buffer A) and 0.1% triethylamine/acetate (pH 6.0) in 50:50 water/acetonitrile (buffer B) as mobile phases. The solvent delivery system consisted of a Waters 600E system, and the absorbance was monitored at 280 nm with a Waters 486 tunable absorbance detector. For each HPLC run, the column was equilibrated with 100% buffer A, and proteins were eluted using a 2 min linear gradient of 0-100% buffer B at a flow rate of 12 mL/min. The peak containing H22Y-mEGF was hand-collected and lyophilized. The lyophylized protein was redissolved in water and further purified using a 4.6 × 220 mm Brownlee Aquapore RP-300 C-8 column with 0.1% trifluoroacetic acid (TFA) in water (buffer C) and 0.1% TFA in 20:80 water/acetonitrile (buffer D) as mobile phases. The solvent delivery system consisted of two Waters 510 pumps, and the absorbance was monitored at 220 and 280 nm with a Waters 490E detector, with the system controlled from a Maxima 820 workstation. For each HPLC run, the column was equilibrated with 95:5 buffer C/buffer D, and the products were eluted with a 70 min linear gradient of 5-50% buffer D at a flow rate of 1 mL/min. The H22Y-mEGF peak was hand-collected and lyophilized. The lyophilized protein was dissolved in water and quantified by its absorbance at 280 nm [280 ) 18 700 cm-1 M-1 (40)]. Preparation and Purification of Fluorescein Isothiocyanate Labeled H22Y-mEGF (F-EGF). Labeling of H22Y-mEGF with fluorescein isothiocyanate was carried out as previously described for wt-mEGF (41). The homogeneity of the HPLC-
EGF Binding to Receptors in Intact Cells purified peak was verified in an analytical run using the same gradient. The stoichiometry of the labeled species was verified to be 1:1 by matrix-assisted laser desorption ionization time-of-flight mas spectroscopy (MALDI-TOF MS). The lyophilized F-EGF was dissolved in 5 mM Tris, pH 7.4, and the concentration was quantified from the absorbance using 280 ) 36 000 cm-1 M-1. This extinction coefficient was used to correct for the contribution of fluorescein to the absorbance at 280 nm (41). Construction of EGF Receptor Expression Plasmid. The pXER construct (gift of G. N. Gill, University of California at San Diego) was digested with XbaI and HindIII to generate a full-length EGFR cDNA fragment. This fragment was ligated into the multiple cloning site of the mammalian expression vector pCDNA3.1(-) using T4 DNA ligase to generate the pCER construct. Correct insertion of EGF receptor cDNA was confirmed by dideoxynucleotide sequencing using the SequiTherm EXCEL II sequencing kit according to the manufacturer’s instructions. Cell Culture. The IL-3-dependent cell line 32D (obtained from G. Carpenter, Vanderbilt University) was maintained in RPMI-1640 containing 15% FBS and 5% WEH1-3B conditioned medium (as a source of IL-3). Cells were grown at 37 °C in an atmosphere of 5% CO2/95% air. Transfection. 32D cells (1 × 107) were transfected by electroporation using 10 µg of circular pCER DNA. Electroporation was carried out using a BioRad GenePulser II electroporator set at 950 µF and 300 V. Cells were allowed to recover in RPMI-1640/15% FBS/5% WEH1-3B conditioned medium for 18 h prior to selection by the addition of 750 µg/mL G418. Clonal cell lines were established by serial dilution in 24-well microtiter plates to a final titer of
