Correspondence to Jason M. Haugh: jason_haugh{at}ncsu.edu
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Introduction |
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Another example of chemotactic sensing is that of dermal fibroblasts in wound healing (Singer and Clark, 1999). PDGF, produced by platelets and macrophages, forms a gradient in the tissue and serves as a potent chemoattractant and mitogen, thus accelerating the rate of fibroblast invasion into the fibrin clot (Deuel et al., 1991; Heldin and Westermark, 1999). As with the aforementioned cell types, fibroblast motility and PDGF-stimulated chemotaxis rely on the activation of PI 3-kinase (Kundra et al., 1994; Wennström et al., 1994a,b; Wymann and Arcaro, 1994), and PDGF gradients elicit intracellular 3' PI gradients in the plasma membrane (Haugh et al., 2000). However, it is currently unknown whether or not there is a common signal transduction mechanism shared by all of these cell types in the regulation of 3' PImediated spatial gradient sensing. Indeed, there are indications that the PDGF-sensing mechanism differs. Migration of fibroblasts is far slower than that of amoeboid cells and is driven as much by differential adhesion as by membrane protrusion (Lauffenburger and Horwitz, 1996), suggesting distinct requirements for gradient sensing. PDGF signals through members of the receptor tyrosine kinase family, which activate different PI 3-kinase isoforms from those activated by GPCRs (Vanhaesebroeck et al., 2001). Most significantly, it is well established that PI 3-kinase signaling in response to uniform PDGF stimulation is not marked by rapid adaptation; although subject to receptor down-regulation on the time scale of hours, 3' PI levels achieve a quasisteady state after 510 min (Hawkins et al., 1992; Jackson et al., 1992; Haugh et al., 2000; Park et al., 2003).
In this paper, we present a quantitative analysis of PDGF gradient sensing in fibroblasts using a combination of mathematical modeling and live cell total internal reflection fluorescence (TIRF) imaging. Compared with the chemotactic responses of D. discoideum and neutrophils, we report that the PDGF gradientsensing mechanism in fibroblasts is less sensitive and strongly depends on both the relative PDGF gradient and its midpoint concentration. Optimal gradient sensing is observed in a narrow range of intermediate midpoint PDGF concentrations that yield near maximal PDGF receptormediated PI 3-kinase recruitment without saturating receptor occupancy. The model quantitatively matches the spatial pattern and kinetics of 3' PI signaling without including positive or negative feedback loops, and, accordingly, we show that Rho family GTPases are not required for PDGF-stimulated PI 3-kinase activation. These results indicate that although similar pathways are used across diverse cell/receptor systems, the regulatory mechanisms governing the sensitivity of PDGF gradient detection are fundamentally different from those characterized for classic GPCR-mediated chemotaxis.
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Results |
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From an analysis of the model equations, which relate the difference in PI 3-kinase enzyme recruitment between the front and back of the cell (e) to the corresponding difference in receptor dimerization/activation (
d) at quasisteady state, one predicts three distinct regimes of gradient sensitivity (Fig. 1, AC). At low midpoint concentrations of PDGF, most of the PI 3-kinase remains in the cytosol, and PI 3-kinase recruitment is simply proportional to the local density of activated receptors. In other words, gradient sensing is absolute:
![]() | (1) |
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As the midpoint PDGF concentration is increased, overall PI 3-kinase recruitment approaches saturation (e
1). In this regime, a specific location on the membrane binds its share of the limiting PI 3-kinase pool according to its local activated receptor density compared with the average. Here, gradient sensing is relative:
![]() | (2) |
At extremely high PDGF concentrations, however, all receptors are saturated with ligand, and the cell is unable to sense the gradient:
![]() | (3) |
A number of testable predictions emerge from this simple model (Fig. 1, AC), which we will show to be valid in fibroblasts responding to PDGF gradients: (1) The gradient in PI 3-kinase signaling, e, is sensitive to both the relative PDGF gradient (defined as
; equation 6) and its midpoint concentration, with the greatest sensitivity at intermediate midpoint concentrations. (2) Both the peak value of
e and the range of midpoint PDGF concentrations that yield robust intracellular 3' PI gradients (
e > 0.1, for example) are determined by the degree of PI 3-kinase saturation. With the parameter values constrained to approximately match the dose responses of receptor and PI 3-kinase activation measured in our cells (Park et al., 2003), the peak
e
, and the effective range of midpoint PDGF concentrations spans roughly two logs. (3) At intermediate concentrations of PDGF, where the gradient sensitivity is greatest, PI 3-kinase activation at the front of the cell exceeds the level observed under receptor-saturating conditions. Hence, if gradient stimulation is followed by a high uniform dose of PDGF, PI 3-kinase signaling at the front will be forced to decrease.
A more detailed kinetic model, accounting for PDGF receptor binding, dimerization, and internalization, was used to calculate 3' PI levels as a function of time in a typical cell stimulated with various gradients (assumed here to be established immediately at t = 0; Fig. 1 D). For now, tempering of the 3' PI gradient by lateral diffusion is neglected. After 20 min of gradient stimulation, the PDGF concentration is switched to a uniformly saturating value for a period of 10 min followed by rapid inhibition of PI 3-kinase and decay of the 3' PI level. These conditions reflect the protocol used in our experiments, and the calculated kinetics support the predictions of the quasisteady-state model.
Gradient sensing in fibroblasts is optimized in a relatively narrow range of PDGF concentrations, which is consistent with saturation of PI 3-kinase recruitment
The CFP-tagged pleckstrin homology domain of Akt (CFP-AktPH) was used as a specific biosensor for 3' PI production at the plasma membrane. Using a micropipette coloaded with PDGF and a fluorescent volume marker (Oregon green [OG] 514dextran), CFP-AktPHtransfected fibroblasts were presented with gradients of PDGF, and the local marker concentration and intracellular CFP-AktPH translocation were monitored using TIRF microscopy (Fig. 2). By varying the concentration of PDGF in the pipette across different experiments and observing cells at different distances from the source, we systematically analyzed responses to PDGF fields with varying midpoint concentration and gradient steepness. After 20 min of gradient stimulation, a high concentration of PDGF was added uniformly to normalize the response at each location. Subsequently, a high concentration of wortmannin was added to rapidly block PI 3-kinase and, thus, to assess the degradation of 3' PI lipids and the contribution of cytosolic CFP-AktPH to the overall TIRF fluorescence.
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PI 3-kinase signaling responses to PDGF gradients of varying midpoint concentration and steepness were consistent with model predictions (Fig. 3). Proper gradient sensing was apparent within a relatively narrow range of PDGF concentration, as PDGF gradients with low midpoint concentrations elicited little change in the TIRF profile, whereas cells exposed to gradients with very high midpoint concentrations showed little change after the uniform stimulus; optimal gradient sensing was often accompanied by a decrease in fluorescence at the front and a corresponding increase at the back after the uniformly saturating dose (Fig. 3 A). In all cases, the observed kinetics were consistent with those calculated in Fig. 1 D. It should be noted that these experiments were performed at room temperature to inhibit cell motility (Haugh et al., 2000) so that the regions would remain stationary during the experiment. The qualitative predictions of the model were also validated in experiments conducted at 37°C, in which spatially biased membrane-spreading events were also observed (Fig. S1, available at http://www.jcb.org/cgi/content/full/jcb.200509028/DC1).
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The quality of the gradient-sensing response was assessed in terms of the difference in between the front and back (
). In contrast with the whole cellaveraged response, robust front-to-back asymmetry (
> 0.3) was only predominant in cells exposed to fairly steep PDGF gradients, with intermediate midpoint concentrations spanning a range of roughly two logs (Fig. 3 C). In accord with the models, this intermediate range is shifted slightly toward higher PDGF concentrations compared with the dynamic range for the average response; an overlay of the curves from Fig. 1 C underscores the good correspondence with model predictions. At midpoint PDGF concentrations <0.1 nM, only 1/31 cells (3%) exhibited a robust gradient-sensing response, and PDGF gradients with midpoint concentrations >2 nM also yielded a low percentage (3/24 cells or 13%). Gradients with intermediate midpoint concentrations (0.12 nM) are further subdivided into low and high steepness (cut-off of
= 0.3), eliciting robust gradient-sensing responses 14% (3/21) and 57% (13/23) of the time, respectively. The superiority of the latter population, which included 8 of the top 10
values, is further supported by pair-wise comparisons of its
mean with those of the three other populations, which were all significant at the 0.05 level by the Tukey-Kramer test.
Another way to assess the gradient responses is by plotting the value of the front versus that of the back for each cell; cells were grouped according to the four subpopulations outlined in the previous paragraph (Fig. 3 D). Cells exposed to gradients with intermediate concentrations and high steepness were much more likely to lie above the y = x line (
> 0) on this plot, which is indicative of proper gradient sensing. Consistent with another model prediction, several of these cells populated the upper left quadrant (
f > 1 and
b < 1), meaning that the TIRF intensity at the front decreased and the intensity at the back increased after the uniform stimulation.
Spatial modeling of gradient responses and comparison with intracellular TIRF profiles
To refine our quasisteady-state model of PDGF gradient sensing, finite element calculations were performed that allowed us to directly compare the predicted fluorescence profile, f (equation 4), with the acquired TIRF images at each point in the contact area (Fig. 4). The actual PDGF concentration field and irregular cell geometry are inputs to the model, which accounts for pseudo-steady receptor and PI 3-kinase activation as well as lateral diffusion of 3' PI lipids and recruitment of the CFP-AktPH probe from the cytosol. Order of magnitude estimates of the model parameter values were assigned based on our previous experimental and modeling studies of fibroblast responses to uniform PDGF stimulation (Haugh et al., 2000; Park et al., 2003; Haugh and Schneider, 2004; Schneider and Haugh, 2004; Schneider et al., 2005) and to approximately match the overall fluorescence intensities observed before stimulation and after uniform saturation. No parameters were fitted to the gradient response.
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Kinetic analysis of responses to transient PDGF pulses
Another test of a mathematical model is its ability to reproduce the cellular response to a transient or pulsed stimulus, an approach that can indicate the presence of feedback interactions (Bhalla et al., 2002). To determine whether our model could explain the 3' PI responses to transient PDGF stimulation, PDGF was pulsed from the micropipette for a certain period, and CFP-AktPH translocation during and after the pulse was recorded using TIRF microscopy (Fig. 5). By adjusting the flow rate, the PDGF gradient during the pulse could be tuned to be steep (Fig. 5 A and Video 1, available at http://www.jcb.org/cgi/content/full/jcb.200509028/DC1) or essentially uniform across cellular dimensions (Fig. 5, B and C). In both situations, PI 3-kinase signaling tends to persist for several minutes after decay of the stimulus; in fact, the peak response was typically observed minutes after the PDGF concentration began to drop. Our kinetic model captures this behavior. It predicts that the 3' PI decay will lag whenever the duration of the pulse is insufficient for establishing a quasisteady state (510 min), with the time interval of the lag and rate of decay after the peak depending on the degree of PI 3-kinase saturation. Persistence of 3' PI levels after PDGF withdrawal is not attributed to positive feedback but rather to the fairly slow kinetics of PI 3-kinase redistribution to the cytosol and 3' PI turnover, and the model and experiment are in quantitative agreement when one allows for modest cell-to-cell variation in receptor and PI 3-kinase expression levels (Fig. 5 C).
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When toxin-treated fibroblasts were exposed to PDGF gradients, CFP-AktPH translocation was readily observed, and asymmetric TIRF profiles consistent with proper gradient sensing were seen in some cells (Fig. 6 C). This outcome was not as robust as in our other gradient experiments, however, which was to be expected given the much smaller distance across the cells (15 µm). This yields both smaller relative PDGF gradients and significant tempering of the intracellular 3' PI gradient through lateral diffusion of the lipid.
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Discussion |
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Another wrinkle in the PDGF-sensing mechanism is the influence of 3' PI hot spots, which we recently characterized in the context of uniform PDGF stimulation (Schneider et al., 2005). Regions of locally enhanced 3' PI levels have also been observed in chemoattractant-stimulated D. discoideum (Postma et al., 2004) and primary dendritic cells (Arrieumerlou and Meyer, 2005), although there are differences in the kinetics across cell types. In PDGF-stimulated fibroblasts, hot spots exhibit characteristics that are consistent with locally enhanced PI 3-kinase activation and reduced 3' PI turnover, and it is conceivable that feedback loops upstream of PI 3-kinase are spatially focused in these regions. Their localization in apparent membrane protrusion structures at the leading edges suggests involvement of the cytoskeleton and/or Rho family GTPases and an importance in cell motility. Thus, as illustrated in Fig. 4, the overall asymmetry in PI 3-kinase signaling depends on the morphological polarity of the cell relative to the gradient. A conceptual model emerges in which cells integrate both intrinsic and external spatial biases in order to migrate persistently toward PDGF gradients (Fig. 7).
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This is not to say that PDGF receptormediated signaling through PI 3-kinase and other pathways is unregulated. Activated PDGF receptors are rapidly internalized, mediating receptor down-regulation and establishment of a true steady state after 1 h of constant stimulation. This mode of regulation may provide the answer to the next, most important question with regard to fibroblast invasion of wounds: if chemotaxis is sensitive to the gradient steepness and absolute concentration of PDGF, how can this sensitivity be maintained as the fibroblast front (granulation tissue) progresses deeper into the clot? In solid tissue, it is likely that endocytosis of active PDGFPDGF receptor complexes contributes significantly to the clearance of PDGF from the extracellular milieu, which is an effect that would be fibroblast density dependent. The invading granulation tissue could thus shape and maintain a relatively constant and sharp PDGF gradient, spanning the optimal midpoint concentration at its leading front.
Given the complexity of cell polarity, cytoskeletal dynamics, and overall migration processes as well as the issues raised above concerning the integrated physiological system, it is reasonable to expect that mathematical modeling and other quantitative approaches will be increasingly valuable in their analysis. Especially when designed in tandem with experiments, as applied here to PDGF gradient sensing, such approaches can reveal and aid in characterizing the key underlying mechanisms.
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Materials and methods |
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TIRF microscopy
TIRF microscopy is a mode of live cell imaging whereby fluorophores within 100 nm of the membrane contact area are selectively excited (Axelrod, 2001; Steyer and Almers, 2001; Toomre and Manstein, 2001). Our prism-based TIRF microscope was described previously (Schneider and Haugh, 2004). In brief, this system was built around a microscope (Axioskop 2 FS; Carl Zeiss MicroImaging, Inc.) with 20x NA 0.5 or 40x NA 0.8 water immersion objectives (Achroplan; Carl Zeiss MicroImaging, Inc.) and a 0.63x camera mount. TIRF excitation was from two laser heads (Melles Griot): a tunable wavelength Ar ion laser head emitting lines of 488 (GFP at 60 mW) or 514 nm (YFP/OG 514 at 60 mW) and a HeCd laser head emitting a 442-nm line (CFP at 120 mW). Band-pass emission filters (Chroma Technology Corp.) were 480/30 nm (CFP), 515/30 nm (GFP), and 535/30 nm (YFP and OG 514). Digital images were acquired using a cooled CCD camera (ORCA ER; Hamamatsu) and Metamorph software (Universal Imaging Corp.), with 2 x 2 binning and a fixed exposure time x gain setting of
400 ms for GFP, YFP, and OG 514dextran and
2,400 ms for CFP.
PDGF gradients were produced and imaged as follows: a micropipette, pulled to a diameter of 50 µm and backfilled with a solution of 030 nM PDGF and 5 µM OG 514dextran in imaging buffer, was controlled using a syringe pump (World Precision Instruments) and micromanipulator (Applied Scientific Instrumentation). Once a suitable field of cells had been chosen, the pump was set to a flow rate of 3080 nl/min, and sequential TIRF images of CFP-AktPH and the OG 514dextran gradient were acquired every 20 s. Except where noted otherwise, all experiments were performed at room temperature (2629°C). Controls with no PDGF in the tip verified that cells were not stimulated by either the small flow or volume marker.
Gradient association/dissociation experiments and analysis of fluorescence profiles
In the gradient association/dissociation protocol, cells are stimulated with a PDGF gradient for 20 min, followed by a uniformly saturating PDGF dose (10 nM) for 10 min, after which a high dose of wortmannin (5 µM) is added to rapidly block PI 3-kinase activity. Extensive controls have been described previously (Schneider and Haugh, 2004; Schneider et al., 2005). The intracellular TIRF above background, F, was normalized by its value at the end of the fluorescence decay, Fcyt, to yield the normalized fluorescence, f, as a function of position and time (Schneider and Haugh, 2004):
![]() | (4) |
The fractional gradient response, , relates the fluorescence observed after gradient stimulation to the initial prestimulus value and the peak value observed after uniform stimulation (all averaged over 1-min intervals):
![]() | (5) |
Thus, a value of zero indicates that gradient stimulation elicited no change from the initial fluorescence, whereas a value of one indicates that the fluorescence did not change after the addition of 10 nM PDGF. The average response,
, is defined using whole cellaveraged f values, whereas the ability to sense the gradient is quantified as the difference in
values between front and back regions (
25 pixels) relative to the gradient (
=
f
b).
The PDGF (ligand) concentration, [L], as a function of position was estimated by assuming that the highest OG 514dextran TIRF intensity above background, at the point nearest the pipette, corresponds to the concentration of PDGF loaded in the pipette; accordingly, this fluorescence value does not change when the flow rate is increased. At steady state, the relative gradient is insensitive to any (small) difference in diffusion coefficient between PDGF and OG 514dextran, and so the proportionality of the two concentrations was assumed at all locations. TIRF excitation of the volume marker is partially occluded by cells; hence, PDGF concentrations at the front and back regions of the cell, [L]f and [L]b, were estimated as follows: a line scan was drawn through the two regions and extending outside of the cell contact area boundaries. The fluorescence values across this line scan were averaged over the same time interval used to calculate fgradient, and PDGF concentrations were estimated by fitting the portions of the line scan outside the contact area to a polynomial (Fig. 2 B). The relative PDGF gradient, , is defined as
![]() | (6) |
Cells were chosen for analysis based on the following criteria. At all times, the whole cell value of F must be at least 250 fluorescence units above background, and the average OG 514dextran fluorescence around the cell during gradient stimulation must be at least 100 fluorescence units above background. Finally, the cell must show a significant whole cell response to the uniform stimulation (funiform finitial > 0.3).
Mathematical model formulation
Here, we outline the basic modeling assumptions and methods, which build upon previous studies (Haugh et al., 2000; Park et al., 2003; Haugh and Schneider, 2004; Schneider and Haugh, 2004; Schneider et al., 2005); a more complete description of the model equations and their derivation is provided in the supplemental Modeling details.
We used two different models to describe the activation of PDGF receptors. An experimentally validated kinetic model of PDGF receptor binding, dimerization, and endocytosis as a function of time was described previously (Park et al., 2003), to which we have added receptor synthesis and basal turnover. The output of the model is the dimer fraction, d, calculated as a function of time using standard numerical integration. After 510 min of PDGF stimulation, PI 3-kinase activation reaches a plateau, for which a simplified, quasisteady-state model is adequate, with
![]() | (7) |
The dimensionless PDGF concentration u is related to the actual PDGF concentration through the scaling constant L*, which is the concentration of PDGF that yields one-third maximum receptor phosphorylation. Together, these models accurately and quantitatively describe the kinetics and cooperative doseresponse behavior of PDGF receptor phosphorylation in our cells (Park et al., 2003).
Receptor-mediated recruitment of PI 3-kinase activity to the plasma membrane depends on both the local and average density of activated receptors because receptors draw upon a common cytosolic PI 3-kinase pool. Our model is simplified by assuming fast diffusion of PI 3-kinase in the cytosol and pseudo-equilibrium binding with activated receptors. The dimensionless PI 3-kinase (enzyme) recruitment as a function of position, e(), is thus given by
![]() | (8) |
The relationship between e and d is defined by the relative receptor/PI 3-kinase expression ratio and the dimensionless receptor/PI 3-kinase dissociation constant
E; variables in elbow brackets signify spatial averages.
Membrane 3' PI is produced locally by the receptor-bound enzyme, and there is also a contribution from cytosolic PI 3-kinase, which defines the basal 3' PI level. 3' PI lipids are degraded by a constitutive first-order mechanism as described previously (Schneider and Haugh, 2004).
Spatial modeling, in which the contact area geometry and lateral diffusion of 3' PIs are explicitly considered, was implemented using FEMLAB finite element modeling software (Comsol). The pseudosteady-state receptor activation model (equation 7) was used in these calculations. The geometry of the cell was constructed as described previously (Schneider et al., 2005), with PI 3-kinase activation in the nonadherent membrane only (Haugh et al., 2000; Schneider and Haugh, 2004). Normalized fluorescence is calculated by assuming pseudo-equilibrium binding of the GFP-AktPH probe (Haugh and Schneider, 2004).
Online supplemental material
The Modeling details supplement provides a more complete description of the model equations and their derivation. Fig. S1 shows representative responses to the gradient association/dissociation protocol at 37°C. Fig. S2 presents a spatial modeling analysis of another cell as performed in Fig. 4. Video 1 shows side-by-side time courses of the moving PDGF gradient and PI 3-kinase signaling response for the experiment depicted in Fig. 5 A (7.5 frames/s and 150x speed up). Online supplemental material is available at http://www.jcb.org/cgi/content/full/jcb.200509028/DC1.
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Acknowledgments |
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This work was supported by grants from the Office of Naval Research (N00014-03-1-0594), the Whitaker Foundation (RG-01-0150), and the Cell Migration Consortium Modeling Initiative. Microscopy equipment was purchased using funds from a New Faculty Award to J.M. Haugh from the Henry and Camille Dreyfus Foundation.
Submitted: 6 September 2005
Accepted: 27 October 2005
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References |
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