INTRODUCTION

Human polymorphonuclear leukocytes, or neutrophils, play a central role in immune and inflammatory responses. Neutrophils respond to injury or infection by crawling to the affected site through receptor-mediated chemotaxis and eliciting a respiratory burst to kill and remove foreign antigen and traumatized tissue. Uncontrolled activation, leading to local and systemic destruction of host tissue, is implicated in the onset of inflammatory joint and bowel diseases, adult respiratory distress syndrome, degenerative arthritis, and multiple organ failure (Anderson and Harken, 1990; Kubes, 1993; Olsson and Venge, 1980; Omann et al., 1987; and references therein). A quantitative understanding of the biochemical pathways of neutrophil activation is essential to developing therapeutic strategies for countering these diseases.

The goal of our research is to understand the quantitative relationship between receptor-mediated activation and specific responses under physiologic conditions. The first step in achieving this goal is to characterize ligand-receptor (LR)¹ dynamics at 37 °C. The most extensively studied chemoattractant receptor of neutrophils is the N-formyl peptide receptor. At 37 °C, the onset of N-formyl peptide-induced actin polymerization, a response that is characteristic of chemotaxis, occurs rapidly after exposure to ligand (<2 s). Direct quantification of the number of LR complexes at such early times is obscured by a combination of analytical limitations and dynamic cellular processes that hinder the ability to measure the size of the surface receptor pool and the capability of those receptors to bind ligand. Flow cytometry, capable of detecting as few as 1000 fluorescently labeled LR complexes, is utilized to measure real-time formation of LR complexes (reviewed in Sklar (1987) and Sklar and Finney (1982)). It has been estimated, however, that actin polymerization requires less than 0.1% receptor occupancy (Sklar et al., 1984b, 1985c; Sklar, 1985); assuming an average N-formyl peptide receptor density of 50,000 receptors/cell (Omann et al., 1987; Sklar, 1987), this translates into 50 bound receptors/cell, which is well below the threshold of detection.

It is therefore necessary to utilize binding models to predict a quantitative relationship between LR complexes and the initiation of neutrophil responses. The most frequently utilized binding model (used to estimate the 0.1% value above) is given by Reaction I.  R_sis a homogeneous, monovalent population of surface receptors (no./cell), L is the free ligand concentration (M), and LR_sis the number of ligand-receptor complexes (no./cell) which form with an association rate constant of k_f(M¹s¹) and are lost with a dissociation rate constant of k_r(s¹). Using Reaction I to fit N-formyl-norleucyl-leucyl-phenylalanyl-norleucyl-tyrosyl-lysine-fluorescein (FNLPNTL-FL) association data, similar values for rate constants have been determined at 4 °C and 37 °C. 4 °C kinetic binding assays, performed to isolate binding events from receptor trafficking events such as internalization and receptor up-regulation, have yielded k_f = 4.6-10 × 10⁶M¹s¹(Sklar et al., 1984b, 1985a) and k_r = 5.8 × 10³s¹(Sklar et al., 1985a). The 37 °C values of k_f = 1.7 × 10⁷M¹s¹and k_r = 1 × 10²s¹have been reported (Sklar et al., 1984b). Other approaches to kinetic data analysis based on Reaction I yield different values for k_ras a result of weighting different time frames of the kinetic data. For example, a half-time analysis of association data, which utilizes data from only the initial stages of binding, yielded a 4-fold larger value for k_r(Schonbrunn and Tashjian, 1978). Since different methods of data analysis can predict significantly different rate constants, the method, the associated models, and all assumptions must be critically evaluated.

A key assumption of Reaction I is that other reactions that affect R_s and LR_s can be neglected. For neutrophils at 37 °C, however, recent data have demonstrated that this assumption is not valid (Jesaitis and Klotz, 1993; Jesaitis et al., 1983, 1984, 1988a, 1988b, 1989; Norgauer et al., 1991; Sengelov et al., 1993, 1994; Sklar et al., 1987, 1989). In addition to the binding of ligand to the receptor, the number of receptor/ligand complexes on the cell surface is influenced by at least four other processes during the first few minutes of stimulation: the conversion of a low affinity ligand-receptor complex to a high affinity complex LR_x, LR_x internalization, receptor up-regulation, and quenching of internalized fluorescent ligand. Reaction II, proposed by Sklar (1985), accounts for two of these four processes. The binding of L to R_syields a low affinity complex (LR_s), which then converts to a high affinity complex (LR_x) with a rate constant of k_x(s¹). High affinity complexes are lost via endocytosis with rate constant k_in(s¹) to give internalized complexes (LR_in) or by ligand dissociation with rate constant k_r2(s¹) to give an inactivated surface receptor (R_x). R_xmay rebind ligand with rate constant k.

The existence of two receptor states for the N-formyl peptide receptor in intact cells, characterized by a difference in the rate of ligand dissociation, has been well documented (Jesaitis and Klotz, 1993; Jesaitis et al., 1983, 1984, 1988a, 1988b; Klotz et al., 1994; Klotz and Jesaitis, 1994; Koo et al., 1982; Painter et al., 1987; Sklar et al., 1987, 1989). The two receptor states arise from a conversion of a low to a higher affinity form of receptor. Evidence suggests that the association rate constant is not different for the two states. The biochemical nature of LR_x is not defined; however, it appears to be an inactive form of the receptor and is not sensitive to guanine nucleotides (Sklar et al., 1989). Using the model Reaction II to fit binding and dissociation data of FNLPNTL-FL, values of the rate constants have been estimated as follows: k_f = 2.7 × 10⁷ M¹ s¹, k_r = 0.046 s¹, k_x = 0.041 s¹, k_r2 = 0.0055 s¹ and k_in = 0.0052 s¹ (Sklar 1987). The range of values estimated for the rate constants in intact cells from several experimental protocols are listed in Table I.

Table I. Rate constants for the binding of 3 nM FNLPNTL-FL to intact cells at 37 °C Parameter Experimental data Ref. Full Reaction III fita Reduced Model III Fits Literature Values kf (M1s1) 8.4 ± 1.9  × 107 4.7 ± 0.6  × 107b 1.7  × 107 (Sklar et al., 1984b) 5.5 ± 0.4  × 107c 2.7  × 107 (Sklar, 1987) kr (s1) 3.7 ± 1.0  × 101 3.0 ± 1.0  ×101b 7  × 102d (Sklar et al., 1987) 3.4 ± 0.03  × 101c 1  × 102 (Sklar et al., 1984b) 4.6  × 102 (Sklar, 1987) kup (s1) 8 ± 2  × 104 3-7  × 103e 4  × 103 (Norgauer et al., 1991) kr2 (s1) Constantf 4.6 ± 0.7  × 103g 5  × 103d (Sklar et al., 1987) 3.6 ± 0.4  × 103c 5.5  × 103 (Sklar, 1987) kx (s1) 6.5 ± 1.0  × 102h 4.0 ± 0.3  × 102c 4  × 102 (Sklar, 1987) 7  × 102 (Sklar et al., 1989) kin (s1) Constanti,j NDk 3.3  × 103 (Sklar, 1986) 5.2  × 103 (Sklar, 1987) kq (s1) Constanti ND 3.9  × 103d (Sklar et al., 1984b) a  All determined from association data, n = 7. Rate constants given as value ± the standard error of the mean. b  Determined from association data for PhAsO-treated cells at 37 °C with 3 nM FNLPNTL-FL using the simplified Reaction IIIa, n = 3. c  Determined from association data for pertussis toxin-treated cells at 37 °C with 3 nM FNLPNTL-FL using Reaction III (without up-regulation of receptors), n = 3. d  Data were originally reported as half-times for dissociation or quenching and were converted to rate constants by assuming a first order process and using the formula k = 0.693/t1/2. e  Determined from data shown in Fig. 2B. f  Held constant at 4.6 × 103 s1, the value determined from dissociation experiments described in footnote g. g  Determined from dissociation experiments after 60 s of binding of 3 nM FNLPNTL-FL, n = 3. h  Varied with upper and lower bounds set at the two reference values given. i  Held constant at the literature values (kin = 3.3 × 103 s1; kq = 3.9 × 103 s1). j  The value found by Sklar (1986) was confirmed in our laboratory with a single timecourse, using the methods of Finney and Sklar (1983). k  ND, not determined.

To date, binding models have not addressed two other processes that affect a quantitative description of ligand binding: receptor up-regulation and an experimental phenomenon of fluorescence quenching. In this study, receptor up-regulation is defined as the increase in surface receptors over an unstimulated, steady-state level. Up-regulation is characterized by both long term and rapid changes in surface receptor number. Long term (>15 min) up-regulation can be induced by ``priming'' (a phenomenon that has been shown to enhance cellular responses to a subsequent stimulus) (Goldman et al., 1986; Norgauer et al., 1991; Yee and Chistou, 1993), by an increase in temperature (Tennenberg et al., 1988), and by receptor recycle (Zigmond et al., 1982). These long term changes in receptor number can be extensive, but can be quantified before the addition of a stimulus and accounted for in an initial value for R_s. Rapid, stimulus-induced receptor up-regulation (seconds to minutes) has been reported to give a 30-250% increase in surface receptors (Norgauer et al., 1991; Zigmond et al., 1982) but has not been fully characterized. Norgauer and co-workers have indicated that up-regulation is a saturable event occurring over several minutes (Norgauer et al., 1991). Recent studies by Sengelov and co-workers also demonstrate that receptor up-regulation is a rapid (t_1/2 = 100 s), stimulus-dependent event and suggest that secretory compartments, which contain a large pool of N-formyl peptide receptors, may fuse with the plasma membrane to supply surface receptors (Sengelov et al., 1993, 1994).

Another process omitted from binding models is the quenching of ligand as the ligand-receptor complex moves into acidic, intracellular vesicles. This component is an artifact of the experimental methodology in that the absorbance of the fluorescein moiety on the ligand is pH-sensitive. Thus movement of the ligand into acidic compartments results in an apparent quenching of the fluorescent signal. Instruments such as the flow cytometer measure total cell-associated fluorescence, and thus this quenched component is not observed. Quenching half-times observed after eliminating surface-bound fluorescence by dropping the extracellular pH have been reported to be in the range of t_1/2 = 180-240 s (Sklar et al., 1984b; Norgauer et al., 1989), and, for binding data that is collected for 3 min, the disappearance of fluorescence due to quenching must be included to correct for what might be incorrectly interpreted as the dissociation of ligand. Attempts to correct for this effect experimentally have involved addition of NH₄Cl to the buffer to neutralize acidic intracellular compartments (Sklar, 1987). However, this may not be the optimal solution to the problem, since NH₄Cl itself may alter other relevant functions.

To date, there have been no studies to address the integrated impact of N-formyl peptide binding kinetics, changes in receptor affinity, receptor up-regulation, complex internalization, and ligand quenching on the quantification of ligand-receptor dynamics at 37 °C for intact neutrophils. In this work, we have used an analysis of ligand binding data and knowledge of a variety of experimentally determined processing events (such as internalization, quenching, and desensitization) to extract information about the on and off rate constants for ligand binding to the N-formyl peptide receptor. We have determined that: 1) ligand-receptor binding rate constants, estimated from a new model that accounts for the processes described above, are significantly different from those estimated in intact cells using binding models reported in the literature; 2) receptor up-regulation can be extensive and is both temperature- and ligand-induced; 3) preservation of high time resolution data is essential for distinguishing improvements to the models by nonlinear statistical analysis of ligand binding data; 4) phenylarsine oxide (PhAsO), used in other cell systems to inhibit endocytosis (Lauffenburger and Linderman, 1993; Low et al., 1981; Tolley et al., 1987), differentially inhibits up-regulation and internalization in neutrophils and may be used with a reduced binding model to give estimates of 37 °C ligand-receptor binding rate constants in the absence of trafficking events; and 5) pertussis toxin inhibits both temperature- and stimulus-induced receptor up-regulation.

MATERIALS AND METHODS

Human neutrophils were isolated from citrated blood by the elutriation method of Tolley et al. (1987). Cells were held at 4 °C in buffer without added Ca²⁺ (HSB) containing 5 mM KCl, 147 mM NaCl, 1.9 mM KH₂PO₄, 0.22 mM Na₂HPO₄, 5.5 mM glucose, 0.3 mM MgSO₄, 1 mM MgCl₂, and 10 mM HEPES, at pH 7.4 until used in assays.

A 4 °C equilibrium ligand binding assay, described in Sklar and Finney (1982), was used to determine the number of N-formyl peptide receptors on the plasma membrane surface. N-formyl-norleucyl-leucyl-phenylalanyl-norleucyl-tyrosyl-lysine-fluorescein (FNLPNTL-FL) (Molecular Probes, Eugene, OR) stocks were made in dimethyl sulfoxide (Me₂SO) and were diluted to a final concentration of less than 0.01% Me₂SO for each assay. Samples were equilibrated for 1 h at 4 °C in the dark, then a flow cytometer (FACScan, Becton-Dickinson), calibrated with fluorescein isothiocyanate-labeled beads (Quantum 24, Flow Cytometry Standards, Research Triangle Park, NC), was used to quantify fluorescence binding per cell. Neutrophils were gated based on forward and side scatter parameters. Nonspecific binding was determined in the presence of 3 × 10⁵ M F-Met-Leu-Phe (FMLP) and subtracted from total binding to give specific binding. Two lots of calibration beads were utilized during the course of this study. When the second lot was received, it was checked against the first lot, and both sets gave the same slope for fluorescence mean channel number versus fluorescein equivalents listed by the manufacturer. Thus the standards were internally consistent and stable over the course of the experiments. In addition, one fluorescent bead standard from one lot was calibrated as described by Fay et al. (1991) by comparison with known concentrations of fluorescein and found to be within 6% of the value reported by the manufacturer. Sensitivity analysis showed that this small a difference in determination of R_s had no effect on calculation of the binding rate constants, and the nominal values for fluorescein equivalents per bead provided by the manufacturer were used for converting mean channel number to fluorescein equivalents per cell. Data for specific binding in fluorescein equivalents were converted to FNLPNTL-FL number per cell using a conversion factor of 1.22 FNLPNTL-FL equivalents/fluorescein equivalent as determined in Fay et al. (1991). Nonlinear regression of FNLPNTL-FL bound/cell versus free ligand using the equilibrium solution of Reaction I yielded the total number of receptors on the cell surface (R_s) and the equilibrium dissociation constant (K_d). We note that for a two-state interconverting receptor model, an equilibrium binding curve may yield a K_d that is intermediate to the K_d values of the individual species, but the maximum number of receptors will be unchanged (Lauffenburger and Linderman, 1993).

Surface receptor number, which has been reported to be sensitive to temperature (Tennenberg et al., 1988), was determined by warming cells (10⁶/ml) at 37 °C for 10 min in HSB and HSB plus Ca²⁺ (1.5 mM CaCl₂). After heating, cells were rapidly cooled to 4 °C in a 0 °C stirred bath, ligand (at concentrations described in the equilibrium binding assay) was added, and total surface receptor number (R_s) and K_d were determined.

To determine the stimulus-induced rate of receptor up-regulation, neutrophils at 10⁸/ml were prewarmed for 10 min in HSB plus Ca²⁺ and then exposed to 1 and 100 nM FNLPNTL-FL. At 15- second intervals, cells were diluted to 10⁶/ml with 4 °C HSB plus Ca²⁺ and R_s and K_d were determined by the 4 °C equilibrium binding assay. To assess the prestimulated R_s and temperature-dependent up-regulation, control cells were given vehicle without stimulus.

A kinetic binding protocol based on the methods described in (Sklar et al., 1984b) was used to collect data for determining FNLPNTL-FL association and dissociation rate constants. Cells at 10⁶/ml in HSB plus Ca²⁺ were prewarmed at 37 °C for 10 min and then placed on a flow cytometer (Lysis II software, FACScan, Becton Dickinson). The flow of cells was initiated to start the internal clock and obtain base-line values for forward scatter, side scatter, and cell autofluorescence. At 10 s, the tube of cells was taken from the instrument and FNLPNTL-FL was added with vortexing. The tube was immediately placed back onto the instrument. Data collection resumed in less than 3 s after the addition of ligand and was continued for a total of 3 min. Assay temperatures of 4 °C and 37 °C were maintained (<10% and <6% variation, respectively) during kinetic studies by submerging sample tubes in ice or in 37 °C water contained in insulated beakers. Nonspecific binding was determined in the presence of 3 × 10⁵ M FMLP and subtracted from total binding to give specific binding.

To analyze kinetic data, we developed a protocol to extract and convert data files from the Becton Dickinson FACScan Pascal data format to an ASCII format. Data was first converted to DOS-readable binary files using OSWEGO software (Oswego Software, Inc., Oswego, IL), uploaded to a UNIX platform, and then converted to ASCII. Neutrophils were gated with a rectangular mask based on forward and side scatter parameters. Fluorescence, forward, and side scatter data collected during each 200-ms time interval (typically 30-200 cells depending on cell concentration and flow rate) were averaged. Absolute fluorescence was converted to bound receptors using the calibration scheme described in the equilibrium binding assay. Binding data versus time were loaded into SimuSolv (Dow Chemical, Midland, MI), a simulation package that simultaneously solves differential equations and estimates unknown parameters by maximizing a least log likelihood function.

Utilizing residuals and a nested likelihood ratio that follows the chi-squared distribution (Miklavc et al., 1990), Reaction III (given below) was developed through statistically evaluated additions to Reaction II:

37 °C dissociation rate constants were determined by interrupting binding of FNLPNTL-FL at different time intervals to ``capture'' the dissociation kinetics from the high affinity receptor state. Based on the experimental protocol described by Sklar (1987) and the kinetic binding data collection described above, data were collected for two different FNLPNTL-FL concentrations (0.75 nM and 3.0 nM). After the addition of FNLPNTL-FL to cells at 10⁶/ml in HSB plus Ca²⁺ and the collection of ligand association data, the tube was again withdrawn from the sample port (at either 10 or 70 s after stimulus addition) and FMLP (final concentration 3 × 10⁵ M) was added to interrupt the binding of fluorescent peptide. After vortexing, the suspension was immediately placed back on the instrument. Data collection continued for 1 min after FMLP addition. Dissociation rate constants k_r and k_r2 were determined from a fit with two sets of Reaction III equations (see Appendix) to account for the binding of two competitive, stimulatory ligands. In equations that account for FNLPNTL-FL binding, k_f was fixed at the value determined by fitting the first 30 s of uncompeted FNLPNTL-FL (3 nM) association data with Reaction III. For FMLP binding, rate constants analogous to k_f, k_r, and k_r2 for FNLPNTL-FL binding were fixed at values 1 order of magnitude less than those of FNLPNTL-FL (unpublished competitive binding data). Other rate constants associated with up-regulation, receptor affinity conversion, ligand-receptor complex internalization, and fluorescence quenching were held at values indicated in Table I.

PhAsO treatment was performed following a protocol based on that established by Low et al. (1981) for adherent cells. Briefly, a stock of 0.05 M PhAsO (Sigma) was prepared in Me₂SO. Neutrophils at 10⁶/ml in HSB were incubated with gentle agitation at room temperature for 20 min with 1-100 µM PhAsO. Control cells were incubated with equivalent amounts of Me₂SO (0.2%). Following incubation, cells were washed and resuspended in HSB plus Ca²⁺. The extent of ligand-receptor complex internalization in control cells was determined 120 s after ligand addition, following methods outlined in (Fay et al., 1991), using dilute HCl to bring the pH to 2.0 in order to quench externally bound ligand. To test if PhAsO disrupted the ability of the cell membrane to maintain a pH gradient, the cytosol was labeled with the pH indicator 2,7-bis-(2-carboxyethyl)-5-(and-6)-carboxyfluorescein and the same acid quenching protocol employed. PhAsO concentrations up to 100 µM did not alter the ability of the cell membrane to maintain a pH gradient.

A stock of 50 µg/ml PT in 50 mM Tris, 10 mM glycine, 0.5 M NaCl, 50% glycerol, pH 7.5 was obtained from Sigma. Cells were resuspended at 10⁸/ml in a sterile, modified Krebs-Ringer buffer with 5.5 mM glucose, 25 mM HEPES, and 6.3 mg/ml cytochrome c. PT was added to cells at a final concentration of 2.5 µg/ml, and the sample was incubated at 37 °C with constant rocking for 2 h. Controls consisted of an equivalent amount of PT buffer without PT. Following incubation, cells were then washed in HSB, strained through nylon mesh to remove aggregates, and resuspended in HSB at 10⁸/ml. Trypan blue exclusion revealed a viability of >90% following the PT treatment. The efficiency of the PT treatment was monitored with a right angle light scatter assay as described by Sklar et al. (1985c). At this treatment level, no response to 100 nM FMLP stimulation was observed.

RESULTS

The time course of specific binding of FNLPNTL-FL to the N-formyl peptide receptor is shown in Fig. 1 for elutriated cells at two different assay temperatures, 4 °C and 37 °C. Specific binding of FNLPNTL-FL in 37 °C assays was between 1.5 and 2.5 times the quantity bound in 4 °C assays (n = 10 donors). The discrepancy in the number of available surface receptors suggests a rapid movement of receptors from an internal spare pool to the plasma membrane surface and/or a physical change in surface receptors that may expose a previously hidden binding pocket to the ligand. In the remainder of this paper, both of these will be referred to as receptor up-regulation.

Typical kinetic binding curves for the binding of FNLPNTL-FL to neutrophils at 4 °C () and 37 °C ().

The temperature effect on surface receptor number was determined using the standard 4 °C equilibrium binding protocol (as described under ``Materials and Methods'') on cells that had been preheated at 37 °C for 10 min. Results show that prestimulus levels of surface receptors are on average 45% higher for heated cells than for control cells held at 4 °C (n = 7 donors) and that the K_d values for the two treatments (means of 0.30 and 0.27 for warmed and 4 °C controls, respectively) are not statistically different (p < 0.05), indicating that up-regulated receptors have the same binding affinity as the pool initially on the cell surface. Representative 4 °C equilibrium curves for preheated and 4 °C control cells are given in Fig. 2A.

To determine the stimulus dependence of receptor up-regulation, neutrophils at 10⁸ cells/ml were prewarmed for 10 min at 37 °C, then exposed to FNLPNTL-FL at 37  °C, and the number of surface receptors as a function of time determined as described under ``Materials and Methods.'' The increase in surface receptors as a function of time after addition of FNLPNTL-FL is shown in Fig. 2B. Data in Fig. 2B were fit to the solution of d[R_upreg]/dt = k_up × [R_pool  R_upreg], where R_pool is the number of receptors in internal stores accessible to up-regulation and was allowed to vary because there was donor-to-donor variation in the extent of saturation by a given stimulus. In addition to donor variability, there was experimental variability in the preparation of the cells (the extent exposure to lipopolysaccharide or other priming factors), which may have changed the number of receptors in internal pools. The mean fit values for R_pool varied from 40 to 70% of the surface receptor number at time zero. For the particular donor shown in Fig. 2B, fits to the solution of the above equation yielded k_up = 0.007 s¹ for cells stimulated with 100 nM ligand and k_up = 0.003 s¹ for cells stimulated with 1 nM ligand. Up-regulation was independent of the external calcium concentration (data not shown).

Reaction I fits to 37 °C data were inadequate as judged by distinct patterns in residuals and by statistical analysis. Complexity was added until all the phenomena accounted for by Reaction III were included. The statistical improvement of each fit was determined by comparing the nested likelihood ratio for the full and reduced model to the ² distribution at the 0.05 significance level. The nested likelihood ratio is determined by the ratio of the log likelihood functions evaluated at the maximum likelihood estimates for the reduced model over that of the complete model (Miklavc et al., 1990; Painter et al., 1987). The best fit of the data was obtained with Reaction III. In this fit, k_f, k_r, and k_up were varied; k_r2 was held constant at 4.6 × 10³ s¹ (determined from dissociation experiments; see below); k_in was held constant at 3.3 × 10³ s¹ (Sklar, 1986); and k_q was held constant at 3.9 × 10³ s¹ (Sklar et al., 1984b). k_x was allowed to vary within the range reported in the literature (0.04-0.07 s¹; Sklar et al. (1989) and Sklar (1987)). R_pool was allowed to vary between 40 and 70% of the surface receptor number at time zero. The decision to allow R_pool and k_up to be fit parameters, rather than to fix them at the values reported above, was made because of lower resolution of the up-regulation data (see Fig. 2B) and the difficulty posed by doing up-regulation experiments on each donor.

Typical fits are shown in Figs. 3 and 7A for binding of 3 nM FNLPNTL-FL and Fig. 4 for 0.75 nM FNLPNTL-FL. Mean fit values for k_f, k_r, and k_up ± the standard error of the mean for 7 donors are given in Table I for binding of 3 nM ligand. Calculation of k_f and k_r from binding data with 0.75 nM ligand (n = 2) were not significantly different from those obtained with 3 nM ligand. Reaction III estimates for k_f and k_r were statistically different from literature values for intact neutrophils assayed at 37 °C (two-sided t test, p  0.05).

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3

1

Sensitivity of the model fits for k_f and k_r to variations in k_in and k_q (± 50%) was negligible. The fit value for k_up was sensitive to both the initial values for R_s (the number of surface receptors) and, to a lesser extent, k_q and k_in. Because of the sensitivity of k_up to R_s, it was necessary to accurately determine the number of surface receptors in preheated cells for every experiment. The mean estimate for k_up gives an increase of roughly 3,000 receptors/min and is consistent with the value observed in the time course studies using equilibrium binding (Fig. 2B). Fit values for k_r and k_r2 were sensitive to changes in k_x  20%. Fit values for k_x, however, varied less than 10% within a duplicate and only varied greater than 20% from donor to donor. Fit values of k_r and k_f were insensitive to a ±10% change in the initial value for R_s.

It is worth noting two other things that were tried in fitting the model. First, attempts were made to fit the data holding the value of k_r at the literature value for intact cells of 0.07 s¹ (Sklar et al., 1987). However, good data fits could not be obtained. The closest fits always significantly underpredicted the early time course of binding (0-30 s), and never gave as good a fit as those where k_r was allowed to vary. Second, attempts were made to add an additional receptor species, that of a precoupled receptor, allowing up to 10% of the receptors to be precoupled (as suggested by the work of Adams (1995)). The additional degrees of freedom did not yield an improved fit, as analyzed by the nested likelihood ratio.

The dissociation rate constant for the high affinity receptor, k_r2, was determined by fitting Reaction III to FNLPNTL-FL binding data interrupted with excess unlabeled ligand (FMLP) after 45-60 s of ligand binding. We found a mean fit value (± the standard error of the mean) for k_r2 of 4.6 ± 0.7 × 10³ s¹ (n = 3) that was consistent with values reported in the literature (two-sided t test, p  0.05). Results were insensitive to the binding rate constants assigned to FMLP (varied an order of magnitude) due to the excess (10,000:1 ratio) of FMLP:FNLPNTL-FL. Fig. 4 shows a typical fit to dissociation data interrupted with FMLP at 45 s. Dissociation data were also fit for 3 nM ligand disrupted after 15, 41, 60, and 75 s of binding and for 0.75 nM ligand disrupted after 17 s of binding. The Reaction III fits to the data gave values of k_r ranging from 3.0 × 10¹ to 4.8 × 10¹ s¹ (mean of 3.5 ± 0.3 × 10¹ s¹) and k_r2 ranging from 3.6 × 10³ to 7.5 × 10³ s¹ (mean of 5.2 ± 0.7 × 10³ s¹). Thus the calculation of k_r from association data and dissociation data were not significantly different. The value calculated for k_r in this work was significantly larger than that determined in previous reports with intact cells (Sklar et al., 1984b, 1987). In those studies, the half-time of dissociation was approximated from data collected by disrupting the binding of fluorescent ligand 10-12 s after ligand addition. It is likely that these estimates were biased by the rapid conversion of LR_s to the high affinity form. Our calculation takes into account the rapid conversion of receptors from the low to the high affinity form by fitting the dissociation data to a two-state model. The model predicts that after 12 s of binding, 50% of the receptors are already in the high affinity form. Our value is also higher than that determined by fitting binding and dissociation data to Reaction II (Sklar, 1987). Thus it appears that incorporation of receptor up-regulation and internalized receptor quenching, as well as utilization of high time resolution data, have a significant impact on the determination of the rate constants.

A 20-min treatment of 10 µM PhAsO at room temperature fully inhibited internalization of ligand-receptor complexes, while up-regulation of receptors required a 100 µM dose of PhAsO to reduce up-regulation to 6% of that observed in control cells. Control (Me₂SO-treated) and PhAsO-treated cells at 10⁶/ml were prewarmed for 10 min at 37 °C in HSB plus Ca²⁺ and then stimulated with 3 nM FNLPNTL-FL. After 95 s of binding, dilute HCl was added (final pH of 2.0) to quench externally bound ligand. Kinetic data for three different treatment levels of PhAsO (1, 10, and 100 µM) are shown in Fig. 5A. As the PhAsO treatment dose increased, the extent of both ligand bound and internalization decreased. With 4 °C equilibrium binding studies, we demonstrated that PhAsO affected neither the amount of bound ligand at equilibrium nor the K_d (see below). Treatment doses of 10 µM and 100 µM were equally effective in reducing internalization to the background fluorescence level of the 4 °C control (control data not shown). Dose-response curves for the PhAsO-induced inhibition of up-regulation and internalization are given in Fig. 5B. Extents are expressed as a fraction of the control and were determined for up-regulation and internalization by averaging the last 2 s of data before the addition of acid and by extrapolation of the quenched data to the time of acid addition (Fay et al., 1991), respectively. Binding of 3 nM FNLPNTL-FL at 37 °C to control cells (Me₂SO-treated) yielded binding curves similar to untreated cells (data not shown).

4 °C equilibrium binding studies with cells treated with 100 µM PhAsO yield saturable binding curves similar to those of the control (Me₂SO-treated) as well as cells maintained on ice for the duration of the experiment. For PhAsO-treated cells, the mean K_d and R_s were 0.46 nM (standard error of 0.05 nM) and 46,000, respectively. For Me₂SO-treated cells, the mean K_d and the value of R_s at time zero were 0.30 nM (standard error of 0.02 nM) and 47,000, respectively. Data reflect the mean of 3 donors on 5 occasions. Kinetic binding curves for control cells at 4 °C and PhAsO-treated cells at 37 °C also show the same extent of ligand binding over 3 min (Fig. 6).

PhAsO-treated cells at 37 °C () and control cells at 4 °C ().

Use of 37 °C binding data for neutrophils treated with 100 µM PhAsO afforded the determination of 37 °C rate constants for association and dissociation of ligand in isolation from events of receptor up-regulation, ligand-receptor internalization, and the subsequent fluorescence decay of internalized ligand. In the absence of these events, Reaction III simplifies to Reaction IIIa. FNLPNTL-FL binding data for 100 µMPhAsO-treated cells at 37 °C were fit with both the simplified model above and Reaction I. The surface number of receptors at time zero (determined by the 4 °C equilibrium binding assay) and k_xwere held constant at values determined for control cells from the same donor while k_f, k_r, and k_r2were varied. The least-log likelihood ratio for the nested models indicated that the simplified model above provided the best fit to the data. The two-site fit yielded means of k_f = 4.7 ± 0.6 × 10⁷M¹s¹, k_r = 3.0 ± 1.0 × 10¹s¹, and k_r2 = 0.07 ± 0.05 s¹(Table I). (Data are mean of four sets of duplicates from 3 donors ± the standard error of the mean). Standard ANOVA for k_fand k_rvalues obtained from Reaction III fits to control cells and simplified Reaction IIIa fits to PhAsO-treated cells showed no difference between treatments at the 5% confidence level.

A 2-h pertussis toxin treatment at 2.5 µg/ml completely inhibited G-protein mediated signal transduction as determined by the right angle light scatter assay (Sklar et al., 1985c) (data not shown). Kinetic binding to PT-treated cells (Fig. 7A) shows a binding extent of only 45% of that of the control, and a similar extent to that of 4 °C kinetic binding to cells from the same donor held on ice without PT during the PT treatment (Fig. 7B). A representative data fit to control cells (Fig. 7A) incubated for 2 h at 37 °C gave rate constants of k_f = 5.5 × 10⁷ M¹ s¹, k_r = 0.28 s¹, k_r2 = 1.0 × 10³ s¹, and k_x = 0.05 s¹. The best fit to kinetic data for PT-treated cells was obtained with k_up = 0, indicating that receptor up-regulation was inhibited; mean fit values for all other rate constants were otherwise similar to control cells assayed at 37 °C (k_f = 5.5 × 10⁷ M¹ s¹, k_r = 0.34 s¹, k_r2 = 3.6 × 10³ s¹, and k_x = 0.04 s¹). These data suggest that of the events shown in Reaction III, only receptor up-regulation is dependent on G_i-protein. That k_x, the conversion of low to high affinity receptor, is unaffected by pertussis toxin treatment is consistent with the observations of Sklar and co-workers, who found that FNLPNTL-FL dissociation from pertussis-toxin treated cells was equivalent to that of the high affinity receptor state (Sklar et al., 1987).

DISCUSSION

Neutrophils are highly sensitive to the binding of N-formyl peptide agonist to the N-formyl peptide receptor and are activated at receptor occupancy levels far below the equilibrium value. Because of the extreme sensitivity to ligand, quantification of bound receptors that correspond to neutrophil activation requires theoretical predictions. In this work, we have estimated that rate constants for binding at 37 °C are significantly larger than those cited previously in the literature for intact cells (see Table I) and that a model that accounts for affinity, trafficking, and fluorescence changes in the bound receptor pool not only provides better estimates of binding rate constants but also gives insight into the mechanism of receptor-mediated activation. We will demonstrate that the rate constants reported here translate into a statistically different number of ligand-receptor complexes (compared to predictions made with values from literature), a difference that affords different predictions for the rate and extent of actin polymerization.

One of the utilities of a mathematical model is to provide quantitative predictions of response behavior given a particular set of conditions. With Reaction III, we have simulated two types of experimental conditions that yield insight into the extreme sensitivity of the polymerization response to N-formyl peptide ligands. The first condition is that of ligand infusion. Omann and Sklar (1988) discovered that neutrophils are able to discriminate between and respond differently to ligand delivered either as a bolus injection or as an infusion, delivering the same total amount of ligand. Right angle light scatter response data (which correlates with actin polymerization; Sklar et al. (1985c)) generated under a bolus injection of 0.05 M FNLPNTL-FL and two ligand infusion rates of 0.58 and 0.30 pmol/s are given in Fig. 8, panel A. Results from a simulation of ligand infusion at the two infusion rates using both literature and our new estimates for binding rate constants are summarized in Table II. A representative profile of LR_s and LR_x formation for the 0.58 picomolar infusion is depicted in Fig. 8, panel B. The production of LR_s complexes increases exponentially (inset of panel B), and then climbs almost linearly until the point at which ligand infusion is terminated at 90 s. Comparing panel A (trace 2) and panel B, we note that the formation of LR_s is required not only to produce a response, but to sustain it. Upon termination of the infusion, the response rapidly decays, even though many LR_s complexes remain. This suggests that the amount of time during which a ligand-receptor complex is actively coupled to the polymerization response is even shorter lived than the LR_s form of the receptor. From looking at LR_s profiles and response kinetics we also deduce that the depolymerization mechanism is activated. First, we note that the response saturates submaximally (meaning that not all of the actin pool has been exhausted) for the two cases of infused ligand during the linear phase of the binding curve. If the depolymerization component exists in an active form at some constant, basal rate of activity, as suggested by Sklar et al. (1985b), then that rate could be determined from the steady-state condition in each response profile (the plateau of the response curves). Since there are different linear rates of LR_s production at the time of each polymerization plateau in panel A, we suggest that different rates of ``depolymerizing activity'' are necessary to achieve each plateau.

Table II. Actin polymerization and LRs production during ligand infusion Infusion rate Experimental data: actin polymerizationa Model predictions: linear rate of LRs production (s1) Extent Rate Our model Literature modela mol s1 % %/min 5.8  × 1013 10 15 6.5 4.0 3.0  × 1013 6 6 3.9 2.0 a  Taken from Omann and Sklar (1988).

From simulation results in Table II, it is clear that a 4-fold increase in the association rate constant (k_f = 8.4 × 10⁷ M¹ s¹ versus 1.2 × 10⁷ M¹ s¹, used for the calculation in Omann and Sklar (1988)) translates into a substantial quantitative difference in the prediction of the rate of LR_s formation. The same maximal rate of LR_s production is obtained for the combination of the lower infusion rate utilizing rate constants presented in this work and the higher infusion rate utilizing rate constants published in the literature. The resulting responses for these two infusion conditions, however, are significantly different.

In addition to providing estimates for rates of LR_s complex formation, experiments also indicate that the magnitude of ligand-receptor complex formation is also important for determining the shape of the polymerization response. A second experimental condition provides the same rate of stimulus (bolus injection of the same ligand concentration) but interrupts ligand binding after different amounts of LR_s are formed by the addition of either antagonist or antibody to fluorescein to prevent binding of free ligand (Sklar et al., 1985b). Using Reaction I and response data from such experiments, it was estimated that <0.1% of the receptors needed to be occupied to induce a half-maximal polymerization response. Simulation with Reaction III and our rate constants estimate that 0.6% receptor occupancy is required. Thus accurate knowledge of the binding rate constants is essential in order to understand quantitatively the relationship between ligand binding events and cell responses.

The collection of high time resolution data was critical to our statistical evaluation of the significance of each of the processes described in Reaction III. Reaction complexity was progressively added, starting with the base model (Reaction I) and assessing the improvement in fit to binding data by comparing likelihood ratios of nested models (Hoffman, 1995). Increases in the predicted rate constants of association, k_f, and dissociation from the low affinity receptor, k_r, over values reported for intact, untreated neutrophils at 37 °C (see Table I) were afforded by a 30-fold increase in the number of data points collected between 3 and 15 s. Association rate constants of this magnitude are plausible, based on theoretical calculations that place 8 × 10⁷ M¹ s¹ in the range of 1% (Lauffenburger and Linderman, 1993) to 10% (Koren and Hammes, 1976) of the diffusion limit. In experiments performed with and without on-line mixing (data not shown), we did not find any difference in binding kinetics, supporting theoretical calculations that ligand binding is not diffusion-limited. Adams (1995) has also found evidence for an N-formyl peptide association rate constant higher than those previously reported. They determined that a small pool of receptors (precoupled to guanine nucleotide binding proteins) had to bind ligand with a rate constant on the order of 10⁸ M¹ s¹ in order to model a substantial actin polymerization response at low ligand concentrations (0.1 nM FMLP).

To gain confidence in the rate constants predicted by a fit with the full model, we utilized phenylarsine-oxide to isolate 37 °C binding events from trafficking events. We discovered that phenylarsine oxide is not only a potent inhibitor of internalization, but also an inhibitor of receptor up-regulation. Treatment with up to 100 µM PhAsO did not alter the extent of N-formyl peptide binding, as determined by 4 °C equilibrium binding studies, but eliminated internalization and inhibited 94% of receptor up-regulation. Data for ligand binding at 37 °C to 100 µM PhAsO-treated cells were fit with both Reaction I and a simplified version of Reaction III (see Reaction IIIa under ``Results''). Statistical analysis showed that inclusion of a second receptor site in the simplified version of Reaction III afforded a superior fit to that of Reaction I. Values for association and dissociation rate constants, k_f and k_r, respectively, were not different from those found by fitting binding data from untreated cells with Reaction III, yielding confidence in the predicted values from the full fit. Mean values for k_r2, however, were an order of magnitude larger than the value for k_r2 determined by dissociation experiments, suggesting that either PhAsO alters the binding of ligand to the high affinity form of the receptor or inhibits the conversion from the low to high affinity receptor.

The inclusion of temperature- and stimulus-induced up-regulation of receptors was determined to be important for both the dynamic and equilibrium values for the total number of bound receptors (LR_app). We routinely determined R_s for cells held at 4 °C and cells preheated for 10 min at 37 °C and observed an average heat-induced increase in receptor number of 45% without a change in the K_d. We suggest that the discrepancy in the number of available surface receptors at 4 °C and 37 °C is due to a rapid movement of receptors from an internal spare pool to the plasma membrane surface and/or a physical change in surface receptors that may expose a previously hidden binding pocket to the ligand. Both experimental data and model fits yield an average rate of receptor up-regulation in elutriated cells of 3,000/min for stimulation by 3 nM FNLPNTL-FL. A plot of up-regulated receptor versus time (Fig. 2B) indicates almost a linear increase in the number of receptors over time, which differs from the saturable event described by Norgauer and co-workers (Norgauer et al., 1991). It is possible that the up-regulation that Norgauer observed included both the temperature- and stimulus-induced phenomena. Alternatively, the difference between the Norgauer work (Norgauer et al., 1991) and ours may be related to the difference in the extent of priming, although our observations with elutriated cells were that the temperature and ligand-induced receptor up-regulation were similar in cells treated with and without lipopolysaccharide.² Neither the receptor source nor the mechanism of up-regulation is known. Our data show that extensive treatments with both PhAsO and pertussis-toxin eliminate the up-regulation phenomenon, suggesting the possibility that tyrosine phosphatases (Deckert et al., 1994) and G-proteins may have roles in both temperature- and agonist-induced up-regulation of a receptor pool to the plasma membrane surface. Furthermore, utilizing data fits to determine rate constants for FNLPNTL-FL binding and conversion of receptor affinity states in control and pertussis-toxin-treated cells, we have determined that receptor up-regulation is the only process affected by pertussis toxin. Consistent with the data of Sklar et al. (1989), we observed no effect of pertussis toxin on k_x.

Recent efforts by other investigators to study N-formyl peptide receptor dynamics have focused on a permeabilized neutrophil system (Fay et al., 1991; Posner et al., 1994; Sklar et al., 1987; Neubig and Sklar, 1993). In this system, cells are permanently permeabilized by exposure to digitonin, and low and high affinity forms of the receptor are again observed, depending upon exposure of the cells to guanine nucleotide. A slowly dissociating form of the receptor is observed in the absence of guanine nucleotide, and appears to be a ligand-receptor-G-protein complex (without bound guanine nucleotide). This differs from the LR_x complex observed in intact cells in that the LRG complex is guanine nucleotide-sensitive (addition of guanine nucleotide to ligand-bound cells causes rapid dissociation) and it is not present in cells pretreated with pertussis toxin (Sklar et al., 1989). It would appear that the low affinity form of the receptor LR should be the same in both systems. However, it is unknown if the disruption of the membrane by the permeabilizing agents could alter the binding characteristics of LR. Evidence that the permeabilized cell system and intact cells may not be directly comparable is given by the observation that responses cannot be induced by N-formyl peptides in the permeabilized cells (Posner et al., 1994). We note, however, that a value of k_r for FNLPNTL-FL in permeabilized cells has been reported as 0.17 s¹ (in buffer containing Na⁺) (Sklar et al., 1987). This value is within the 95% confidence interval of our estimate, which can be calculated from the mean and standard error of the mean values (Mood et al., 1974) to be the interval 0.17-0.57 s¹. Comparisons of intact and permeabilized cells are further complicated by the fact that most of the recent data collected with permeabilized cells has been obtained for a different fluorescent ligand (Fay et al., 1991; Posner et al., 1994). For the fluorescently labeled pentapeptide N-formyl-Met-Leu-Phe-Phe-Lys-FL, k_f and k_r in permeabilized cells have been reported as 3 × 10⁷ M¹ s¹ and 0.1 s¹, respectively (Fay et al., 1991; Posner et al., 1994). These values are lower than those determined in our study for FNLPNTL-FL in intact cells. Thus in Table I we have restricted the comparison of our data to that obtained previously in intact cells.

The interpretation of the receptor species in intact cells that is consistent with Reaction III is essentially that of Sklar et al. (1989). The low affinity form of the receptor, LR_s, is not coupled to G-protein. We cannot determine from our data if this is receptor not yet coupled to G-protein or receptor that has been released from G-protein. The high affinity form of the receptor is LR_x, and LRG does not appear in Reaction III because it is such a transient species (Neubig and Sklar, 1993).

In addition, we suggest that agonist-induced receptor up-regulation, which has not previously been included in a model for N-formyl peptide binding, may provide a means by which the neutrophil can recognize and correctly orient itself in a picomolar chemotactic peptide gradient. With increasing evidence that the plasma membrane and its infrastructure is not a homogeneous pool of reactants, but instead comprises highly controlled and compartmentalized subunits, it is possible that stimulus-induced, localized receptor up-regulation in combination with rapid desensitization, afforded by interconverting receptor states, could provide for both the spatial and temporal sensitivity observed in chemotaxis. Although calculations based on Reaction III predict that stimulus-induced up-regulation over a period of 10 s accounts for less than 3% of the total amount of receptors bound, this quantity is sufficient to elicit actin polymerization, which requires <0.6% receptor occupancy. With sufficient quantity and placement of receptors, an asymmetric distribution of receptors could be generated and could potentially provide the cell with a mechanism by which to recognize a 1% gradient in peptide. Data from Johansson and co-workers (Johansson et al., 1993) support the hypothesis that receptors are ordered upon stimulation in that clusters of fluorescent agonist have been observed while fluorescent antagonist maintains a uniform distribution on the cell surface. It is not known, however, if the observed clusters represent active or desensitized receptors.

Because neutrophil responses are ultrasensitive to the binding of chemotactic peptides, we conclude that accurate quantitative predictions of the number of ligand-receptor complexes required to elicit and sustain responses require the use of models (such as Reaction III in this report) that account for subtle changes in receptor number and affinity, and that high resolution kinetic data must be collected in order to get meaningful results for the rate constants fit from such a model.