TIRF imaging of extracellular and intracellular gradients. (A) A micropipette was coloaded with Oregon green (OG) 514–dextran and a prescribed concentration of PDGF, and PDGF gradients were presented to NIH 3T3 fibroblasts transfected with CFP-AktPH. Bar, 100 μm. (B) Although the TIRF excitation of the volume marker is partially occluded by the cells (Lanni et al., 1985), the surrounding regions allow the estimation of the PDGF concentration profile across the cell, as described in Materials and methods. The solid curve in the plot is the best polynomial fit to the fluorescence profiles on either side of the cell, along the line scan depicted in the TIRF image. Bar, 30 μm.

Spatial modeling of intracellular TIRF profiles. (A) TIRF images showing the extracellular OG 514–dextran profile (PDGF) and intracellular CFP-AktPH profiles as in Fig. 3 A (the cell is the same as in Fig. 3 A, with midpoint [PDGF] = 0.61 nM and δ = 0.75). All CFP-AktPH images use the same absolute pseudocolor scale, and the OG 514–dextran image is scaled such that black is the background and white is the TIRF intensity at the pipette tip. Bar, 30 μm. (B) Virtual images obtained from finite element calculations (see supplemental Modeling details for specifics and parameter definitions, available at http://www.jcb.org/cgi/content/full/jcb.200509028/DC1). Dimensionless parameter values describing 3′ PI diffusion and the AktPH interaction are the same as those used previously (Haugh and Schneider, 2004; Schneider and Haugh, 2004; Schneider et al., 2005: Da = 3; μ = 5; κ_P = 2; υ_t = e + x₀(1 − 〈e〉); and υ_b = x₀(1 − 〈e〉). Parameters describing the PDGF dose response have the same values used in Figs. 1 and 3: αd_max = 10; κ_E = 0.1; and L* = 1 nM. The two remaining parameter values (σ = 15.0 and x₀ = 0.016) were specified to match the overall fluorescence intensities observed before stimulation and after uniform PDGF stimulation. (C) Finite element calculations accounting for enhanced 3′ PI levels in leading edge hot spots. Hot spots were modeled as regions with locally enhanced PI 3-kinase activity (υ_b = υ_t = e + x₀[1 − 〈e〉]) and slower 3′ PI diffusion coefficient (reduced by half). Other parameters are as in B except σ = 16.3 and x₀ = 0.015. (D) Comparison of observed (dots) and calculated (solid lines; the model with hot spots is in red) TIRF profiles along the line scan indicated.

PDGF-stimulated PI 3-kinase activation is not dependent on Rho family GTPases. (A) Bright field, TIRF, and epifluorescence images of GFP-AktPH–transfected fibroblasts that were pretreated with C. difficile toxin B responding to successive additions of 10 nM PDGF and wortmannin (wort). Inactivation of Rho family GTPases dramatically alters cell morphology but not PDGF-stimulated PI 3-kinase activation. Bar, 30 μm. (B) TIRF images of a fibroblast cotransfected with YFP-AktPH and the membrane marker Lyn-CFP treated as in A. Ratio images are YFP/CFP. The average normalized TIRF intensity is plotted as a function of time for the YFP-AktPH (closed circles) and Lyn-CFP (open circles) channels; the dotted lines indicate the additions of uniform PDGF and wortmannin. (C) PDGF gradient sensing after inactivation of Rho family GTPases. Toxin-treated cells typically showed AktPH translocation in TIRF but not a definite gradient-sensing response, which was expected given the relatively small cell dimensions. The cell shown is one of those in which a noticeable gradient response was seen. The arrow indicates the PDGF gradient orientation from high to low. (B and C) Bars, 15 μm.

Sensitivity of the PDGF gradient–sensing mechanism: mathematical modeling predictions. (A–C) Predictions based on the quasi–steady-state model of receptor activation (equation 7) and pseudo-equilibrium binding of PI 3-kinase (equation 8). (A) Dimensionless PI 3-kinase recruitment, e, as a function of midpoint PDGF concentration, with a 50% gradient across the cell, at the front (closed circle) and back (open circle) relative to the gradient and averaged over the cell membrane (solid line); the receptor activation level, 〈d〉, is also shown (dotted line). The adjustable parameters are the maximum activated receptor/PI 3-kinase ratio (αd_max = 10) and dimensionless dissociation constant of the receptor/PI 3-kinase interaction (κ_E = 0.1). These values yield saturable PI 3-kinase activation, matching the population dose responses reported in Park et al. (2003). (B) Difference in e between the front and back, Δe, for the parameter values in A (solid curve). Also shown are results assuming stoichiometric binding (κ_E = 0) with αd_max values of 1 and 10 (dashed line) and in the limit of infinite αd_max (dotted line); the latter is equivalent to the relative receptor activation gradient, Δd/〈d〉. (C) Values of the relative gradient δ and midpoint PDGF concentration that yield a given Δe; αd_max = 10 and κ_E = 0.1. (D) Front (closed circle), back (open circle), and average (solid line) 3′ PI levels were calculated as a function of time using a kinetic receptor activation model (see supplemental Modeling details, available at http://www.jcb.org/cgi/content/full/jcb.200509028/DC1) under conditions that mimic our experimental protocol. A 50% gradient of varying midpoint PDGF concentration, as indicated, was administered for 20 min followed by a uniformly saturating dose (10 nM) for another 10 min. Thereafter, PI 3-kinase activity was turned off as if inhibited by wortmannin (wort).

Sensitivity of the PDGF gradient–sensing mechanism: experimental validation. (A) Representative cell responses to steep PDGF gradients with different midpoint concentrations. The montages shows TIRF images acquired prestimulus (initial), at the peak of the gradient response, after bolus addition of 10 nM PDGF (uniform), and after PI 3-kinase inhibition with wortmannin (wort). The arrows indicate PDGF gradient orientation from high to low, and the relative gradients δ across these four cells were 0.75, 0.63, 0.75, and 0.59 (from top to bottom). Bars, 30 μm. The normalized TIRF intensities at the front (closed circles) and back (open circles) of each cell with respect to the gradient are shown as a function of time, with dotted lines indicating the additions of uniform PDGF and wortmannin. (B–D) The local normalized response to the gradient stimulation is defined as Γ (equation 5). (B) Whole cell average responses, 〈Γ〉, of individual cells to various gradients tend to increase with midpoint PDGF concentration and are not affected by gradient steepness. Values of 〈Γ〉 were classified as low (<0.3; blue triangles), intermediate (0.3–0.7; green squares), or high (>0.7; red circles). PDGF concentration cut-offs of 0.05 and 1 nM (vertical dotted lines) demarcate cell populations that tend to exhibit low or high average responses. (C) The difference in response between the front and back is optimized at intermediate PDGF concentrations and depends on the gradient steepness. Values of ΔΓ were classified as low (<0.1; blue triangles), intermediate (0.1–0.3; green squares), or high (>0.3; red circles). The quasi–steady-state model results from Fig. 1 C, with L* = 1 nM, are overlaid for comparison. (D) Fractional responses at the front and back are plotted for the cells depicted in B and C and are grouped according to the midpoint concentration and steepness of the PDGF gradient: black diamonds, <0.1 nM PDGF; blue triangles, 0.1–2 nM PDGF and δ < 0.3; red circles, 0.1–2 nM PDGF and δ > 0.3; green squares, >2 nM PDGF.

PI 3-kinase signaling kinetics in response to transient PDGF stimulation. (A) A CFP-AktPH–transfected fibroblast was stimulated with a moving PDGF gradient for 21 min, after which 10 nM PDGF (uniform) and wortmannin (wort.) were added as in Fig. 3. The time course montage shows TIRF images of the CFP-AktPH translocation (top) and OG 514–dextran gradient (bottom). Bar, 30 μm. Video 1 shows this time course (available at http://www.jcb.org/cgi/content/full/jcb.200509028/DC1). (B) TIRF images of CFP-AktPH–transfected fibroblasts treated with a brief pulse of PDGF at 2 min, 10 nM PDGF (uniform) at 20 min, and wortmannin (wort.) at 30 min. Bar, 60 μm. (C) The left panels plot average normalized TIRF intensity in the CFP-AktPH (closed circles) and OG 514–dextran (open circles) channels as a function of time for the two cells indicated in B. The right panels are the corresponding kinetic model calculations (see supplemental Modeling details). The dashed curves show the PDGF concentration time courses assumed for each cell before the addition of the 10-nM PDGF bolus.

Integration of external and intrinsic biases in PDGF gradient sensing. Cells are depicted at three positions in a PDGF gradient corresponding to low, intermediate, and high midpoint concentrations. Optimal sensing of the external gradient is seen in a narrow range of intermediate concentrations that is sufficient for maximal PI 3-kinase activation at the plasma membrane. Higher concentrations that saturate receptor occupancy have a leveling effect on PI 3-kinase recruitment across the cell. Hot spots of PI 3-kinase signaling are located at the leading edge and other regions of membrane protrusion, imposing an intrinsic, localized bias that depends on the cell's direction of movement. Thus, when a cell is oriented toward the PDGF source (top), signaling in hot spots tends to synergize with the external gradient, whereas the two spatial biases are in conflict when the cell is oriented away from the source (bottom). This suggests a mechanism by which a fibroblast would migrate with even greater speed and/or persistence when its trajectory is properly aligned with the gradient.