INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Human interleukin (IL)-13 is a 12-kDa pleiotropic cytokine that is expressed in activated Th1 and Th2 lymphocytes (Minty et al., 1993; McKenzie et al., 1993), stimulated keratinocytes, activated mast cells and transformed B lymphocytes (Minty et al., 1993; McKenzie et al., 1993; de Waal, 1993). It inhibits proliferative activity of normal B cells and their precursors, B-CLL cells, and it protects B-CLL cells from spontaneous apoptosis (Chaouchi et al., 1996). A number of biological effects recently reported for IL-13 were previously observed for IL-4. But, in contrast to IL-4, IL-13 has not been shown to modulate growth characteristics of T lymphocytes (Zurawski and de Vries, 1994).

The effects of IL-13 are mediated by specific plasma membrane receptors (R). We have recently reported that a variety of human solid tumor cells express intermediate to high affinity IL-13R* and that their interaction with IL-13 inhibits growth of some human RCC cells (Obiri et al. 1996a). We proposed that IL-13R exists in three or four different forms in various cell types (Obiri et al., 1997). Type I IL-13R expressed in human RCC cells appear to be composed of a homodimer of p65-70 proteins [termed IL-13R₁ (or ') and ₂ (or )]. In type II IL-13R, IL-13R₁ forms a heterodimer with IL-4R p140 chain termed IL-4R. In types III and IV IL-13R, IL-13 binds IL-13R₁ and IL-4R subunits and IL-2R-chain (_c) may (type III) or may not (type IV) modulate IL-13 binding (Obiri et al., 1996b).

Although, the structure and biological properties of IL-13R are being vigorously investigated, the kinetics of IL-13 binding, dissociation, internalization, shedding, recycling, and degradation have not been studied. Knowledge of the biophysical and biochemical mechanisms of these processes is necessary for an understanding of the mechanisms of intracellular signaling and biological response of target cells. Fitting mathematical models that correspond to the kinetics of these processes may result in better understanding of the biochemical and biophysical properties of IL-13R, similar to IL-2R, IL-4R (Goldstein et al., 1992; Kuznetsov and Borisova, 1995a; Borisova and Kuznetsov, 1996) and other receptor systems (Gex-Fabry and DeLisi, 1984; Bajzer et al., 1989; Wofsy et al., 1992; Rovati et al., 1996). In this manuscript, we have studied IL-13 binding kinetics on two RCC cell lines (HL-RCC and ML-RCC) and evaluated the influence of _c gene expression on IL-13 and IL-13R interaction in ML-RCC cells transfected with _c cDNA. The kinetics of binding, dissociation, shedding of IL-13R, and ligand-induced receptor-mediated endocytosis of ligand has been investigated. We used mathematical models to analyze the kinetics of IL-13 binding to its receptors.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Cytokines and reagents

Recombinant human IL-13 was expressed in Escherichia coli and purified as described (Debinski et al., 1995).

Cells

The RCC cell lines ML-RCC and HL-RCC were established in our laboratory from primary surgical tissues and were maintained in HEPES buffered DMEM with high glucose supplemented with glutamine plus 10% fetal bovine serum (FBS) and antibiotics (penicillin, 100 U/mL and streptomycin, 100 µg/mL) (Obiri et al., 1993). The _c-cDNA, along with neomycin transferase cDNA, was transfected into ML-RCC cells as previously described (Puri et al., 1996b).

Iodination of IL-13

IL-13 was labeled with ¹²⁵I (Amersham Research Products, Arlington Heights, IL) using IODO-GEN reagent (Pierce, Rockford, IL) according to the manufacturer's instructions. The specific activity of the radiolabeled IL-13 was estimated to range from 80 to 120 µCi/µg protein (Obiri et al., 1995).

Kinetics of IL-13 binding and dissociation

All binding and dissociation experiments were performed at 4°C to prevent receptor-mediated IL-13 internalization. The association kinetic studies were performed by incubating 0.5 × 10⁶ or 1.0 × 10⁶ cells with various concentrations (10-500 pM) of ¹²⁵I-IL-13 in 120 µL binding buffer (RPMI 1640 containing 0.2% human serum albumin and 10 mM HEPES) for 3 min to 18 h at 4°C. Nonspecific binding was determined for each ¹²⁵I-IL-13 concentration and each time point by co-incubation with 50 nM unlabeled IL-13. In some cases, nonspecific binding was established by determining total ¹²⁵I-IL-13 bound to cells after a short incubation (3-6 min) with radio-labeled IL-13. Both techniques gave similar results and the average value of these data was used as the nonspecific binding. The specific fraction of bound ligand was calculated by

(1)

where y₀, and z are the initial concentration of the radio-labeled ligand in the medium and the concentration of specifically bound ligand at time t_i, respectively; z(t_i)/y₀ is the specific bound fraction of ¹²⁵I-IL-13 at time t_i, i = 1, 2, 3, ... , and cpm_i, cpm_tot, cpm_n represent cpm for bound, total, and nonspecifically bound ¹²⁵I-IL-13.

Cell-bound ¹²⁵I-IL-13 was separated from unbound ligand by centrifugation through a cushion of phthalate oils (Obiri et al., 1995). Radioactivity in the cell pellets and supernatants was counted in a gamma-counter.

For dissociation kinetic assays, aliquots were taken after 4-6 h of incubation at 4°C, which allowed time to attain a state of equilibrium at the concentration of ligand used. Cells were then centrifuged at 1500 × g for 5 min to remove free radioactive material, washed twice with cold PBS and resuspended to the initial volume with binding buffer containing 50 nM unlabeled IL-13. At different time intervals, bound and free ligand was measured as described above.

Competitive binding assays at 4°C

Two types of competitive binding experiments were performed. In the first set of experiments, the binding of a single concentration of labeled IL-13 in the presence of various concentrations of unlabeled IL-13 (from 0 to 200 nM) at 4°C was measured at fixed time points. In the second set of experiments, the binding of various concentrations of labeled IL-13 and a single concentration of unlabeled ligand was determined at various times from 2 min to 14 h.

Internalization assay

The _c negative control (ML_neo) or _c transfected (ML_c) RCC cells or HL-RCC cells were incubated in binding buffer containing 0.2 nM chloroquine at 37°C for 5 min to prevent degradation of internalized IL-13 (Obiri and Puri, 1994). Cells were then washed and 2.5 × 10⁶ cells of each type were incubated with 0.2 or 0.3 nM ¹²⁵I-IL-13 at 4°C for 4.5 h, after which unbound ligand was washed away with PBS. The cell pellets were suspended in binding buffer and then quickly brought to 37°C. At various time intervals, two duplicate sets of 50 µL aliquots were taken. One set was incubated with 100 µL glycine buffer (25 mM glycine, 125 mM NaCl, final pH = 2.0) at 4°C for 10 min. The suspension was then centrifuged through a mixture of phthalate oils and the radioactivity in the cell pellet (acid resistant or internalized (C_in) and in the supernatant (surface bound + dissociated, C_s + C_out) was measured with a gamma counter. The other set of 50 µL aliquots was directly centrifuged through phthalate oils and the radioactivity measured in the supernatant was used for dissociated ¹²⁵I-IL-13 values (C_out). Surface bound ¹²⁵I-IL-13 was determined by subtracting internalized ¹²⁵I-IL-13 values from surface bound + internalized values. Internalized, dissociated, and surface bound radioactivity values were added to obtain total bound value cpm.

Fractions of specific surface bound (C_s), internalized (C_in) and shed/dissociated (C_out) ligand were calculated by


where a = bound + internalized, b = dissociated ligand, c = internalized ligand, d = bound + dissociated ligand, a + b is the total in experiment 1 (without glycine treatment); c + d is the total in experiment 2 (after glycine treatment); c₀ is the nonspecific internalized ligand. The kinetic parameters for the internalization experiments were estimated by the two independent binding sites model (Kuznetsov, 1990).

Analysis of association kinetics by one binding site model

Kinetic binding of IL-13 was analyzed by one binding site model. According to this model,

(2)

where x, y, and z are the concentrations of unbound receptor, unbound ligand, and their bound pairs [z = (x + y)], respectively, and k₁, k₁ are the association and dissociation rate constants for reaction 2, respectively. For fitting the model to kinetic data, we used the exact solution of the differential equation which corresponds to the kinetic scheme 2 as described by Kuznetsov (1996).

A fractal analysis of IL-13 binding kinetics

The model of diffusion of a ligand in homogeneous solution to a fractal dimension surface where it forms a ligand-receptor complex was described by Havlin (1989). For analysis of binding of macromolecules to membrane receptors, this model can be rewritten as

(3)

where z is the concentrations of bound ligand-receptor pairs, y₀ is the initial concentration of the ligand in the medium far from the cell surface, N_c is the concentration of cells, and R₀ is the average number of receptor molecules per cell (R₀ = x₀/N_c), where x₀ is the initial concentration of receptor. k₁ is the binding rate of ligand to receptor, D_f is the fractal dimension (complexity) of the surface, t_c is the characteristic time when regular diffusion of ligand to the cell surface dominates. The effective binding rate by this model is _f = k₁R₀N_c. Eq. 3 indicates that, in the fractal kinetic reaction, the concentration of ligand-receptor complex on cell surfaces z(t) is proportional to t^p, where p = (3  D_f)/2 during the early reaction period (t < t_c), and p = 1/2 outside (Havlin, 1989).

Analysis of kinetic association data by a two independent binding site model

Our kinetic experiments were also analyzed using the kinetic scheme,

(4)

where y, x₁, x₂ are the concentrations of the free ligand and their two forms of independent receptors, respectively, and z₁, z₂ are the concentrations of ligand-receptor pairs. The system of ordinary differential equation corresponding to this kinetic scheme was used to evaluate the rate constants of binding (k₁, k₂) and of dissociation (k₁, k₂) by curve-fitting.

Analysis of kinetic dissociation data

Dissociation data were analyzed using both the one receptor and two independent receptor models. For the first model, the fraction of bound ligand in time was described by

(5)

where t is time in the dissociation assay,  is binding time, t > ; z() is ligand bound to the receptor after binding time ; and k₁ is the dissociation rate constant.

For the two independent receptor model, the time course of dissociation was described with the two-exponential equation,

(6)

where z_tot is the sum concentration of the fast (z₁) and slow (z₂) receptors, which differed with the rate of ligand dissociation, t is the current time of dissociation, and  is the time of IL-13 binding on the cells after which the dissociation experiment was started. z_tot(t) = z₁(t) + z₂(t) is the concentration of ligand bound to the slow (z₁) and fast (z₂) species at time t > , d() = z₂()/z_tot(). k₁, k₂ are the dissociation rates observed for each species. Other parameters are the same as defined above.

Mathematical modeling for internalization kinetics

Two simple mathematical models for processing kinetics (Kuznetsov and Borisova, 1995a) were fit to the experimental data of the internalization assay. For the first model, we presumed that a single IL-13-IL-13R complex is formed and that it follows a single pathway for internalization, dissociation, and shedding. For the second model, we assumed that two independent IL-13-IL-13R complexes are formed, each of them having a separate pathway of processing after ligand binding. Both models assume that a concentration of unbound ligand is negligibly low. For the second model, the following differential equations were used:

(7)

where z_f, z_s are the type 1 and 2 ligand-receptor complex (LRCs) on the cell surface, and z_in, z_out are the internalized and shed/dissociated LRCs, respectively. Initial conditions (at t₀ = ) are defined as z_f () = z_f0, z_s () = z_s0, z_in () = z_out () = 0; ₁, ₂ are the constant rates for shedding/dissociation of the ligand/receptor type 1 complexes and ligand/receptor type 2 complexes, respectively. _in, '_in are the constant rates for internalization of the ligand/receptor type 1 complexes and ligand/receptor type 2 complexes, respectively. Five parameters, f₀(f₀ = z_f0/(z_f0 + z_s0), _i (i = 1, 2), _in, '_in were estimated by fitting the model, Eq. 7, to the internalization assay data by the method described in Kuznetsov (1990).

Proliferation assay

ML_neo and ML_c-transfected RCC cells were harvested, washed, and resuspended in culture medium and 3.5 × 10⁴ cells were plated in 10-cm² tissue culture-treated Petri dishes (Falcon, Dickinson, Lakeridge, NJ) with culture medium and cultured for different periods of time at 37°C in a 5% CO₂ environment. After 52, 72, 96, 124, 144, and 240 h of incubation, a number of live cells was determined in duplicate dishes for each cell line by harvesting the cells with versene, washing them, and resuspending to 0.25-0.5 mL for direct cell counts using a hemacytometer.

Simulation procedure

Simulations based on the nonlinear ordinary differential equations (stiff method) corresponding to the models presented in this paper were performed using MLAB modeling system (Civilized Software, Inc.; www.civilized.com).

Procedures for fitting of nonlinear kinetic systems

For estimating parameters of the models, we used both the direct nonparametric weighted global optimization method (Kuznetsov et al., 1993) and the curve-fitting facilities of the MLAB mathematical and statistical modeling system (Knott, 1996). A goodness-of-fit analysis of the models was applied for data from association, dissociation, and displacement assays as separate sets of data and pooled together. To get more accurate and robust estimates of parameters, we used a cross-validation procedure for parameter estimation (V. A. Kuznetsov and G. D. Knott, in preparation). In this approach, each experimental curve, in turn, was eliminated from the fitting procedure. Then, the set of the best parameters was evaluated by fitting the other experimental curves, and these parameter estimates were used to calculate the sum of squared deviations of the predicted kinetic curve points from the excluded experimental points. The reciprocals of these sums were used as the weights of the set of evaluated parameters. Wilcoxon two-sample signed-rank testing and the method of Durbin and Watson for testing the null hypothesis of serial independence of residuals in the least squares analysis against the existence of positive or negative correlation were applied.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Kinetic binding of ¹²⁵I-IL-13 and dissociation kinetics at 4°C

As shown in Fig. 1 A, the binding of radiolabeled IL-13 to control ML_{neo c}-negative cells reached steady state after 1 h, and persisted for up to 10 h. Similar forms of this kinetic curve were observed when 50 nM unlabeled IL-13 was added in the reaction mixture (open circles, Fig. 1 A). The level of specific IL-13 binding was reduced in _c-transfected cells compared to control cells (Fig. 1 B). In addition, the apparent rate of binding in _c-transfected cells was slower compared to control cells. Furthermore, the steady-state level of binding was reached between 4 and 5.5 h of incubation, compared to 1 h in control ML_neo cells (Fig. 1 B). The fraction of bound ¹²⁵I-IL-13 to MI RCC cells was much smaller than in control _c-negative cells (Fig. 1 A and C).

View larger version (26K): [in this window] [in a new window]   FIGURE 1   Time-dependent binding and dissociation of 125I-IL-13 in RCC cells. 0.5 × 106 control MLneo (A), c-transfected RCC cells (B) were incubated with 200 pM 125I-IL-13 and 1 × 106 HL-RCC cells (C) were incubated with 100 pM 125I-IL-13 at 4°C with and without 50 nM of unlabeled IL-13 for indicated period of time. Cell-bound and free ligand were measured as described in Materials and Methods. Black circles, mean values of two determinations in a direct binding assay; open circles, mean values in a displacement binding assay. MLneo 106 (D) and MLc-transfected (E) RCC cells were incubated with 200 pM 125I-IL-13 and 106 HL (F) RCC cells incubated with 300 pM for 5 h at 4°C, washed from unbound radiolabeled ligand and cells were used for dissociation assays. Unlabeled IL-13 100 pM was added immediately after washing the cells to prevent rebinding of radiolabeled ligand. Data for dissociation curves were corrected for nonspecific dissociation. The SDs for experimental points were not larger than the size of symbols presented on the figure. Association and dissociation assays were performed in the same session. Data for ML- and HL-RCC cell lines were obtained in separate experiments. By trypan blue staining, 85-90% cells were alive in binding buffer after 12 h incubation at 4°C. Experiments were repeated two times with similar results.

The rate of dissociation of a small fraction (10-20%) of bound ligand was rapid in the initial phase (up to 10-20 min), but this was followed by a very slow phase in all RCC cell lines (Fig. 1 D, E, and F). Such a slow dissociation rate is unusual for cytokine receptors: most of them have half-lives of 1-30 min. The calculated half-life, t_1/2, of the slow-dissociated ligand on HL, ML_neo, and ML RCC cells was 13.3 ± 1 h, 27 ± 3 h and 43 ± 4 h, (mean ± SD), respectively. These results indicate that IL-13 binding and dissociation at 4°C in _c-transfected RCC cells is slower than control cells.

Dissociation kinetics after binding of different concentrations of IL-13 at 4°C

To determine whether dissociation kinetics vary with different concentration of bound ¹²⁵I-IL-13, we measured the rate of dissociation after preincubation of ML-RCC cells with various concentrations of ¹²⁵I-IL-13 for 3.5-5 h. As shown in Fig. 2 A-C, in control ML_neo RCC cells, ¹²⁵I-IL-13 dissociation kinetics did not vary with different amounts of bound ¹²⁵I-IL-13. The effective rate of the slow phase of dissociation, k₁, was 0.023 h¹, 0.017 h¹, 0.025 h¹, and 0.027 h¹ at 15, 70, 200, and 500 pM of ¹²⁵I-IL-13, respectively. Similar results were obtained in _c-transfected cells (Fig. 2 D-F). The effective dissociation rates at 15, 150, 200, and 300 pM ¹²⁵I-IL-13 were 0.014 h¹, 0.016 h¹, 0.017 h¹, and 0.018 h¹, respectively. Thus, the rate of the slow phase of IL-13 dissociation from its receptor did not depend on the amount of bound ligand; however, transfection of _c chain reduced this rate by 1.6 times (p < 0.05).

View larger version (25K): [in this window] [in a new window]   FIGURE 2   Dissociation kinetics of IL-13 from IL-13R on control and MLc-RCC cells. Values represent the averages of duplicate determination. Time-dependence of 125I-IL-13 dissociation at initial concentrations 15 pM (A, D), 150 pM (B, F) and 200 pM (C, E) were fitted by the one-exponential model (solid curves). The SD of mean values was not larger then 0.06. These experiments were repeated two times with similar results.

¹²⁵I-IL-13 binding in the presence of different concentrations of ¹²⁵IL-13 at 4°C

It has been reported for several ligand-receptor systems that the effective binding rate varies with the concentration of ligand (Park et al., 1987; Sadana and Beelaram, 1996b; Franco et al., 1996). We, therefore, examined whether the association rate of ¹²⁵I-IL-13 varied with the ligand concentration. We performed these experiments using 10 to 500 pM ¹²⁵I-IL-13. Additionally, in some experiments, we used two concentrations of target cells, 0.5 × 10⁶ and 1 × 10⁶.

As shown in Fig. 3, A and B, the slope of the normalized binding curves increased monotonically with the ligand concentration in control ML_neo cells, but, in contrast, the slope decreased in _c-transfected cells. These results suggest that the binding rate and/or number of available binding sites in _c-negative RCC cells increase with the concentration of ligand, and _c-transfection suppresses the positive cooperative mechanism of binding of IL-13 to its receptor(s).

View larger version (28K): [in this window] [in a new window]   FIGURE 3   Dose-dependence of specific binding of 125I-IL-13 (specific bound/total 125I-IL-13, z/y0) on MLneo (A) and MLc-transfected (B) RCC cells, integral rate binding (C) and fractal dimension parameter (D) at various ligand concentration. (A) 0.5 × 106 cells and 10 pM (), 15 pM (), and 500 pM () 125I-IL-13; (B) 106 cells and 15 pM IL-13 ( ), 106 cells and 200 pM IL-13 (), and 0.5 × 106 () 300 pM 125I-IL-13. Kinetic binding studies were performed as described in Fig. 1. Bound 125I-IL-13 was plotted as the ratio of specific bound ligand to the total radiolabeled ligand after subtraction of the nonspecifically bound fraction as described in Materials and Methods. Values represent the average of duplicate determinations: SEM values for each point are not shown to simplify presentation. The values of SD of the mean were not larger than 0.07. Experiments were repeated two times. The values of SD smaller than size of the points were not presented on the figures C and D.

Sadana and Beelaram (1996b) successfully applied kinetic fractal models to interpret the dependence of binding rate constants on ligand concentration in biosensor systems. These models describe the effect of topological complexity (fractal dimension) of the surfaces that carry the specific receptor. Surface complexity imposes 1) heterogeneity in the rate of ligand binding due to the geometric difficulty of diffusion of ligand to different surface regions, and 2) a nonuniform distribution of receptor molecules on the surfaces. We show that this type of model can be also applied to the analysis of IL-13 binding on cell surfaces. Figure 3, A and B shows that Eq. 3 fits well to the initial (transit) phase of specific IL-13 binding data. The effective rate of IL-13 binding by the fractal kinetic model, _f (_f = k₁x₀), increased from 0.41 ± 0.01 h¹ to a saturation level of 0.58 ± 0.004 h¹ in control ML_neo cells (Fig. 3 C), but it was very low (_f = 0.029 ± 0.007 h¹) and independent of an initial concentration of IL-13 in the _c-transfected cells. This analysis shows that transfection of _c chain reduces the effective rate of binding, _f, by a factor of 20.

The D_f, parameter of Eq. 3, is the fractal dimension of the cell membrane that displays how much space it occupies. This parameter is a measure of the degree of complexity of the natural or artificial surfaces, and it also characterizes the degree of irregularity of the distribution of binding sites on the surface (Havlin, 1989; Sadana and Beelaram, 1996b). Figure 3 D shows that D_f increases with increasing concentrations of IL-13 at low initial concentrations of IL-13. However, at higher concentrations of ligand, this parameter did not change. The constant level of D_f in control cells was significantly higher than in _c-transfected RCC cells.

Thus, fractal kinetic analysis exhibits an anomalous reaction order and concentration dependence of the association rate coefficient in control _c-negative cell line; however, in _c-transfected cells, these effects were not observed.

Analysis of binding/dissociation kinetics by one receptor model

The effective rate of binding of IL-13, _f, is defined as a product of the association rate constant (k₁) and the number of binding sites R₀. The rapid effective rate observed in ML_neo cells, suggests a higher rate of binding or higher number of binding sites on the cell surface or both. The kinetic fractal model described in Eq. 3 did not allow us to discriminate between these possibilities.

We used association and dissociation measurements at different initial concentrations of IL-13 to evaluate the association rate (k₁), dissociation rate (k₁) and the number of binding sites per cell. We calculated these parameters using the simple one-receptor model (Eq. 2). Dissociation and binding kinetic experiments were performed using the same experimental protocol. This model fit our binding kinetics data in both control and _c-transfected ML-RCC cells at each initial concentration of ¹²⁵I-IL-13, taken separately to fit the mathematical model. Figure 4 shows the fit of this model at low (15 pM) IL-13 concentration. The analysis shows that, following _c transfection, the number of IL-13-specific binding sites on the cell surface was reduced and the affinity of this binding site decreased. These differences were defined at different initial concentrations of IL-13 and cells. However, we found that the estimated parameters, k₁ and R₀, changed monotonically with ligand concentration in both cell lines (Fig. 5 A and B). The rate of these changes differed in control and _c-transfected cells as a function of ligand concentration. At a low concentration of IL-13 (10-15 pM), a small number (330-440 sites per cell) of super-high affinity binding sites (K_d = k₁/k₁  0.1 pM) was estimated to exist on ML_neo cells, and a small number (170 sites per cell) of very high affinity binding sites (K_d = 1.4  10 pM) on ML_c cells. At higher concentrations of IL-13, the number of binding sites increased for both RCC cell lines. These alterations of the number of binding sites and the association rate constant at various concentrations of ligand with an invariant rate of dissociation cannot be explained by a one-binding site ligand-receptor model.

View larger version (15K): [in this window] [in a new window]   FIGURE 4   Association kinetic data and theoretical curves for 125I-IL-13 binding. 15 pM 125I-IL-13 was incubated with 0.5 × 106 MLneo and 106 c-transfected RCC cells at 4°C. Association kinetics was determined as described in Material and Methods. Closed circles, MLneo RCC; open circles, MLc-RCC. Symbols represent the mean values. Theoretical curves (solid lines) were generated by the model, Eq. 2, after fitting theoretical curves to experimental points. These curves were calculated at (1) k1 = 0.36 (h pM)1, k1 = 0.023 h1, R0 = 440 sites per cell in the case of MLneo RCC cells and (2) k1 = 0.0094 (h pM)1, k1 = 0.014 h1, R0 = 170 sites per cell in the case of c-transfected RCC cells. The amounts of dissociation rate constants, k1, were determined from analysis of dissociation assay (see Fig. 2).

View larger version (25K): [in this window] [in a new window]   FIGURE 5   The 125I-IL-13 concentration dependence of k1, R0 in the MLneo (A, B) and MLc (C, D) RCC cells. The decrease of parameter k1 was fitted to the exponential model; the increase in a number of available binding sites, R0, at IL-13 concentration was fitted to a linear regression model.

Analysis of ligand concentration dependence of binding kinetics with Berg-Pursell model

The Berg-Pursell diffusion limit model (Berg and Pursell, 1977) was successfully used to explain the dependence of apparent association rate and apparent dissociation rate on the number of receptor molecules for some ligand-receptor systems (Erickson et al., 1987; Goldstein et al., 1989; Posner et al., 1992). According to the Berg-Pursell model, the ligand diffuses to a smooth spherical cell, closely approaches the cell surface, and forms a reversible complex with receptor sites. It was assumed that total concentrations of receptor and ligand does not change during the process. If the receptor has one binding site for ligand and the ligand-receptor complexes are in quasisteady state, then the apparent association rate coefficient and the apparent dissociation rate coefficient were modeled as

(8)

(9)

(10)

where R is the average number of free binding sites on the cell surface; x, y are the concentrations of free ligand and free membrane receptor at steady state, respectively; x₀, y₀ are the initial concentrations of receptor and ligand, respectively; N_c is the number of cells per mL; R₀ is the average number of binding sites per cell; and _free is the fraction of free binding sites (i.e., _free = x/x₀ = 1  (y₀  y)/x₀); k_on and k_off are the fundamental rate constants of association and dissociation; k₊ is the diffusion limited forward rate constant, and k₊ = 4Da, where a is the radius of a cell and D, is the diffusion coefficient of the ligand.

According to these equations, the effective rate of association must increase, when the initial concentration of ligand is increased. This is reasonable, because a higher concentration of ligand reduces the local concentration gradient (i.e., concentration change) of ligand near the cell surface and leads to the occupation of more receptor molecules. Furthermore, increasing the ligand concentration abolishes the diffusion limit. Therefore,
The parameter, k₁, follows the same type of dependence on y₀ as was shown for k₁: it must increase with increasing ligand concentration.

Our observations of dependence of the parameters k₁, k₁ on the initial ligand concentration disagreed with the predictions of dose-dependence for these parameters by the Berg-Pursell model. Figures 2 and 3 shows k₁ decreasing and k₁ independent of the initial concentration of IL-13. This behavior was found for both ML_neo and ML_c cells. We also observed the same behavior at much higher concentrations of ligand (50-200 pM ¹²⁵I-IL-13 and 50-100 nM unlabeled IL-13).

Numerical analysis of Eqs. 8-10 shows that the kinetic parameters k_on and k₁ are very similar for concentrations of IL-13 from 10 to 500 pM. For example, for ML_neo cells, when y₀ = 10 pM, D = 10⁶ (cm²/s), a  4 µm; then k₊ = 1.09 × 10⁴ (pM h)¹ = 5.02 × 10⁹ (cm³/s) = 3 × 10¹² (s M)¹; k₁ = 5.3 × 10⁷ (s M)¹; _free = [1  (0.25 × 10)/2.75] = 0.089; R = 330 × _free = 0.089 × 330 = 29 copies/cell; k_f × R = (5 × 10⁷)29 = 1.5 × 10⁹. Thus, k_on  5.5 × 10⁷ (s M)¹ = k₁.

Similar results were obtained for other initial concentrations of IL-13. These results suggest that ligand diffusion did not limit the binding step of the reaction. Thus, the diffusion step in two-step binding kinetics (diffusion + binding of ligand) is negligible for IL-13 binding.

A two-independent receptor model in _c-transfected ML-RCC cells

Because _c-transfection abolishes the dependence of IL-13R binding rate on the concentration of IL-13, and the dissociation curves demonstrate a very fast and a very slow phase, it was reasonable to assume that binding, dissociation, and displacement curves could be described by a two-independent binding site model (Eq. 4, Tables 1 and 2).

View this table: [in this window] [in a new window]   TABLE 1   Equations for mathematical models of IL-13 and IL-13 receptor interactions for ML-RCC cells without and with c-chain expression

Figure 6 shows that the model by Eq. 4 can fit the binding and dissociation kinetic curves at different concentrations of ligand. These results indicate that ML_c cells express intermediate-affinity (R₁₀) and high-affinity (R₂₀) binding sites. R₁₀ = 3030 ± 2300 copies/cell and R₂₀ = 560 ± 60 copies/cell. The association rate and dissociation rate constants for the first type of receptor were k₁ = 1.5 × 10³ (h pM)¹ and k₁ = 5.0 ± 4.0 h¹. The kinetic constants for the second type of receptor were k₂ = 1.9 × 10³ ± 0.2 × 10³ (h pM)¹, and k₂ = 0.015 ± 0.004 h¹. The parameters were evaluated with the fitting procedure as described in Material and Methods. The dissociation constants for intermediate-affinity and high-affinity receptors were estimated as K₁ = k₁/k₁ = 3.3 nM and K₂ = k₂/k₂ = 8 pM. We also investigated the accuracy of the estimated parameters by fitting the model with displacement assay data. Figure 6 D shows that our model agrees with the displacement assay protocol. The numerical values of the parameters of the model were the same, which was found by fitting the binding/dissociation kinetic data.

View larger version (20K): [in this window] [in a new window]   FIGURE 6   Fitting of two-independent receptor model. Association of IL-13 to the surface receptors (A, B), dissociation of IL-13 (C) from the cell membrane, and a numerical prediction of displacement curve (D) in the MLc RCC is shown. The initial conditions were: (A) y0 = 15 pM, Nc = 106 cell/mL (--); y0 = 200 pM, Nc = 1.0 × 106 cell/mL (--), y0 = 300 pM, Nc = 1 × 106 cell/mL (----); (B) y0 = 150 pM, Nc = 0.5 × 106 cells/mL (----), y0 = 200 pM, Nc = 0.5 × 106 cells/mL (--×--), (C) y0 = 15 pM, Nc = 106 cell/mL (----); y0 = 150 pM, Nc = 0.5 × 106 cell/mL (----); y0 = 200 pM, Nc = 0.5 × 106 cell/mL (--×--); y0 = 200 pM, Nc = 106 cell/mL (--);  = 4 h (D) Displacement assays were performed in separate experiments, 106 cell MLneo cells were incubated with 100 pM 125I-IL-13 in the absence or presence of different concentrations of unlabeled IL-13 (from 5 pM to 110 nM) at 3.5 h. The lines show theoretical curves.

Analysis of potential models of IL-13 binding in ML_{neo c}-negative cells

We also applied a two-binding site model to simultaneously fit binding and dissociation kinetic curves on ML_neo RCC cells at different concentrations of radiolabeled ligand. However, this model did not accurately describe the kinetic binding experiments at different concentrations of ligand (data not shown). We also tried to improve fitting by using an advanced nonsteady-state diffusion-reaction model (Goldstein and Dembo, 1995). This model took into account diffusion-controlled binding of ligand to two receptor populations and included the possibility of rebinding of ligand after dissociation from each type of receptor. However, this model was also rejected by goodness-of-fit statistical analysis.

Neither a three-independent receptor binding site model nor a model of homodimerization of IL-13R induced by ligand binding fit our set of experimental data. We also modified a two-binding site model so that a fraction of a receptor could bind to more than one IL-13 molecule. However, the goodness of fit analysis revealed a poor fit of this model (data not shown).

A model of ligand-induced coreceptor mediated binding in ML_neo RCC cells

Because neither simple one-site model or other conventional models adequately fit the set of binding and dissociation data, a cooperative binding model was tried. We postulated that the association rate is a nonlinear function of free ligand concentration, so that the binding rate is increased (or decreased) over time while binding occurs. We also proposed that a third molecule, dubbed the coreceptor subunit, exists and helps keep the ligand on the cell surface for a long period of time and causes the release of the inhibitor molecule(s). This inhibitor molecule drifts away from the cell membrane and binds to free IL-13 molecules in the medium, which are then captured so they cannot bind to receptors on the cell membrane. This last assumption is consistent with the fact that both small and large concentrations of IL-13 appear to have almost the same binding effect at the steady-state phase of reaction (Fig. 7 A and B). Based on these assumptions, we established the following model for IL-13 binding on the cell surface.

(11)

(12)

(13)

where y, x, and c are the free (unbound) ligand (IL-13), free primary binding subunit, and free coreceptor, respectively; i is the inhibitor (released or shed from cell surface molecules); z and z_c are the complex (x + y) and three-molecular complex (c + x + y); y_i is the inactivated ligand, i.e., the (y + i) complex. n₁ and n₁ are the association and dissociation constant rates of IL-13 to the primary binding subunit; n₂ and n₂ are the association and dissociation rate constants of the IL-13 bound primary receptor to the free coreceptor, respectively; n₃ and n₃ are the association and dissociation rates of the inhibitor to IL-13; and n₄ is the rate of release/shedding of the inhibitor from cells to medium.

View larger version (19K): [in this window] [in a new window]   FIGURE 7   (A, B) 125I-IL-13 binding kinetics, (C) dissociation kinetics, and (D) simulation of time course of separate variables of mathematical model. Kinetics of binding experimenters were performed at various initial concentrations of radiolabeled IL-13 such as (A) y01 = 15 pM (), y02 = 500 pM (). (B) y03 = 70 pM (), y04 = 200 pM (×). (C) Dissociation experiments were performed at y05 = 15 pM, (), y06 = 200 pM (×), y07 = 500 pM ()  = 5 h. The values of SD and mean were not larger than 0.07. Kinetic binding and dissociation studies were performed as described in Figs. 1 and 2. The lines are the theoretical kinetic curves. Kinetics of the ligand receptor complex (z = [x + y]) (solid line), three-molecular complex (zc = [y + x + c0]) (dash line) and inhibitor (i) (dot line) are shown at the initial conditions: (D) y0 = 15 pM; x0 = 5980 pM, c0 = 5587 pM; z = zc = yi = i = 0.

A small but significant amount of cooperativity is present in reaction 11 (see also Fig. 3). This is modeled by assuming that the association constant for this reaction is of the form n₁y^b with 0  b < 1, where b is the cooperative binding parameter of IL-13R expressed on the cell membrane. This parameter indicates the level of heterogeneity of binding capacity of binding sites on cell surfaces that can be correlated to the complexity (fractal dimension) of the cell surface. The complex shape of a cell membrane can impose a restraint on the binding of ligand to receptor molecules localized in inaccessible regions. The parameter b could also indicate the fraction of binding sites that pre-exist on the cell membrane in a homodimer and/or heterodimer form in the absence of external ligand. If b = 0, then the binding kinetics follows the classical mass laws kinetic reactions, if b > 0, then positive cooperativity in binding is expressed.

Table 1 contains a mathematical model of binding assays for IL-13-IL-13R interaction in control RCC cells. Note that, for the binding kinetic model, the constant y₀ is the initial concentration of ligand (pM), and x₀ (pM), and c₀ (pM) are the concentrations of primary binding sites and coreceptor copies, respectively, z(0) = z_c(0) = y_i(0) = i(0) = 0.

By fitting differential equations for reactions 11-13 to our set of binding and dissociation data (Fig. 7) at different initial concentrations of IL-13, we estimated the set of constants x₀, c₀, n₁, n₁, n₂, n₂, n₃, n₃, n₄, and b. The average number of binding sites and average number of coreceptor copies per cell was evaluated by Eqs. N_R = x₀/N_c and N_C0 = c₀/N_c, where N_c is the concentration of target cells. When we applied the fitting procedure, we found high correlations between estimated values x₀, and c₀, as well as between a few other estimated parameters. In other words, the available experimental data allowed estimation of the ratio of these parameters but not their values individually. This parametrization property often limits the predictive power of kinetic models. Therefore, to reduce the number of calculated parameters and their correlations, we fixed a mean of parameters x₀, n₁, n₂, and n₃. The number of binding sites per cell, R₀ (R₀ = x₀/N_c or concentration of IL-13 receptor (x₀)), on the control ML_neo cells have been previously evaluated using a one-receptor model (Obiri et al., 1996b). This number varied from 360 × 10³ to 620 × 10³ molecules/cell. We assumed that N_R = 360 × 10³ molecules/cell. The constant, n₁, was estimated by fitting the two-binding site model (see Eq. 6) to the set of dissociation curves. The amount of rate constants n₃ (n₃ = 4 (h pM)¹) and n₂(n₂ = 1.22 × 10⁴ (h pM)¹) were taken from the best set of constants when we applied the fitting procedure for evaluation of complete set of constants, i.e., x₀, c₀, n₁, n₁, n₂, n₂, n₃, n₃, n₄, and b. Finally, we simultaneously estimated 6 constants: c₀, n₁, n₂, n₃, n₄, and b, using about 60 duplicate experimental points of 7 kinetic curves.

Figure 7 shows the result of fitting of the mathematical model for reactions 11-13 using the best set of parameters: c₀ = 5587 ± 222 pM (or N_C0 = 336 × 10³ ± 14 × 10³ molecules/cell); n₁ = 3.36 ± 0.25 × 10⁴ (h pM)¹; n₁ = 4.8 h¹; n₂ = 1.22 × 10⁴ (h pM)¹; n₂ = 0.023 ± 0.001 h¹; n₃ = 0.23 ± 1.55 h¹; n₃ = 4 ± 8 (h pM)¹; n₄ = 0.83 ± 0.05 h¹; b = 0.09 ± 0.015.

These results show that a large number of coreceptor molecules are expressed on the cell surface of control ML_neo cells. The effective rate of ligand association to primary receptor (n₁x₀ = 2.0 h¹) is 3 times higher than the effective rate of capture of ligand-receptor complexes by coreceptor (n₂c₀ = 0.68 h¹). The dissociation constant of the primary receptor, coreceptor, and inhibitor complexes differed dramatically: K_dR = n₁/n₁ = 14.3 nM, K_dC0 = n₂/n₂ = 188 pM, K_di = n₃/n₃ = 0.06 pM, respectively.

IL-13 displacement analysis in ML_neo cells

Because our model suggested a new control mechanism mediated by the postulated coreceptor component, it was important to determine if our model was accurate, and if the parameter estimations were stable over a broad range of IL-13 concentrations. We designed binding and displacement assays simultaneously in the same experimental protocol (Fig. 8). We used 50 pM ¹²⁵I-IL-13, and the concentration of unlabeled IL-13 was varied from 5 pM to 200 nM. The model for the displacement assay was constructed from Eqs. 11-13 for radiolabeled ligand binding and by the schema

(14)

(15)

(16)

for unlabeled IL-13 binding. Where y₁ is free (unbound) unlabeled IL-13; q and q_c are the complex (x + y₁) and three-molecular complex (c + x + y₁); i is the inhibitor produced after binding of the coreceptor with ligand-receptor complex q; y_1i denotes inactivated unlabeled ligand. Corresponding mathematical model is presented in Table 1.

View larger version (13K): [in this window] [in a new window]   FIGURE 8   125I-IL-13 association and displacement assays. The association kinetic experiments were performed using 50 pM 125I-IL-13 and 0.5 × 106 MLneo cells. (A) Displacement assays were performed using 85 pM 125I-IL-13, 1 × 106 MLneo cells and various concentrations of unlabeled IL-13 (from 5 pM to 200 nM) for 2.7 h incubation at 4°C. (B) The numerical solutions were derived from the model, Eqs. 11-13, (A), 14-16 and are shown by solid lines. The values of SD of the mean were not larger than 0.07.

The five relatively sensitive parameters n₁, n₂, n₃, n₄, and b were estimated along with fixed parameters (n₁ = 4.8 h¹, n₂ = 0.023 h¹, n₃ = 0.23 h¹, x₀ = 5980 pM, c₀ = 5587 pM) by fitting the binding and displacement assays. The result of simultaneously fitting the model for the binding/dissociation reactions described in Eqs. 11-13 (Fig. 8 A) and the model for the displacement reactions Eqs. 11-16 (Fig. 8 B) demonstrates that our model agrees with these sets of observations. A mathematical model for Eqs. 11-13, and 14-16 fits data using parameters that are very similar to parameters described in Fig. 7.

Thus, we can conclude that our stoichiometric model, 11-13, can describe IL-13-IL-13R binding on cells that do not express _c, at least for concentrations of IL-13 from 10 pM to 200 nM.

Internalization of ¹²⁵I-IL-13

As shown in Fig. 9, the rate of internalization and dissociation/shedding of IL-13 at 37°C was higher for control cells. However, the relative distribution of ¹²⁵I-IL-13 on the cell surface, within cells, and in the medium were similar. Similar internalization and dissociation/shedding was observed for another RCC cell line (HL-RCC). Figure 10 shows the kinetics of ¹²⁵I-IL-13 binding on the cell surface, fraction remaining inside the cell, and unbound radiolabeled IL-13 in the cell culture medium for HL, ML_neo, and ML_c-transfected RCC cell lines. Kinetic data are shown after normalization. IL-13 internalization kinetics in all types of cell lines was similar. The solid lines show the numerical solutions according to the two-state receptor model (Kuznetsov, 1990; Kuznetsov and Borisova, 1995b). Only 15-25% and 12-17% of total bound radiolabeled ligand is internalized by control and _c-transfected RCC cells, respectively. The same fractions were dissociated or shed from cell surfaces. Internalization in these cell lines was ceased after 20-45 min. After this period, a fraction of internalized ligand stayed at the steady-state level within the cell for at least 4.5 hours. These results indicate that two types of IL-13R or conformation states of single IL-13R might exist on the surface of HL, ML_neo, and _c-transfected RCC cells, which differ in their rate of internalization and dissociation/shedding. The two-state receptor model, Eq. 4 [but not the one-state receptor model (data not shown)], provided the best fit for all experimental data (Fig. 10). The estimations of the kinetic parameter values ₁,