An integrated stochastic model of "inside-out" integrin activation and selective T-lymphocyte recruitment

Abstract

The pattern of T-lymphocyte homing is hypothesized to be controlled by combinations of chemokine receptors and complementary chemokines. Here, we use numerical simulation to explore the relationship among chemokine potency and concentration, signal transduction, and adhesion. We have developed a form of adhesive dynamics-a mechanically accurate stochastic simulation of adhesion-that incorporates stochastic signal transduction using the next subvolume method. We show that using measurable parameter estimates derived from a variety of sources, including signaling measurements that allow us to test parameter values, we can readily simulate approximate time scales for T-lymphocyte arrest. We find that adhesion correlates with total chemokine receptor occupancy, not the frequency of occupation, when multiple chemokine receptors feed through a single G-protein. A general strategy for selective T-lymphocyte recruitment appears to require low affinity chemokine receptors. For a single chemokine receptor, increases in multiple cross-reactive chemokines can lead to an overwhelming increase in adhesion. Overall, the methods presented here provide a predictive framework for understanding chemokine control of T-lymphocyte recruitment.

Figure 1

In vitro Dynamics of T Lymphocyte Recruitment (A) Video micrograph of Jurkat T cells interacting with immobilized CXCL12/ICAM-1 in shear flow. Cells were perfused into parallel plate flow chambers at a shear rate of 100 s⁻¹ (right to left). Trajectories for eight individual cells that ultimately arrested were reconstructed from video analysis. (B) Three characteristic velocity-distance profiles for cells that tethered, rolled, and arrested within the frame of view (red). The trajectory of a non-adherent cell is shown for comparison (gray). (C) Instantaneous velocity distribution for one individual cell prior to arrest. The macroscopic rolling velocity, v_roll, is given by the mean of the distribution. (D) Population-level distribution of mean rolling velocities indicated significant heterogeneity among cells. In both (C) and (D), velocities varied according a gamma distribution (blue line), consistent with theory [18]. (E) Velocity-distance profiles from all cell trajectories were synchronized to the moment of tether formation to identify the range of arrest distances. The population average velocity as a function of distance is indicated (red).

Figure 2

Kinetic Model for Chemokine-Triggered Inside-Out Integrin Activation. (A) Inside-out reaction network linking chemokine recognition to integrin activation. Arrows indicate molecular association/dissociation (black) or catalytic phosphorylation/nucleotide transfer (red). (B) Experimental and simulated inside-out dynamics. The kinetic model (lines) was trained against a collection of experimental data (symbols) describing inside-out activation of α_Lβ₂ integrins in human neutrophils responding to soluble CXCL8. (C) Model geometry for simulating T lymphocyte adhesion under flow. Membrane and cytosolic compartments were discretized into subvolumes based on a spherical lattice. (D). Projected cell surface from the reference frame of the cell. In (C) and (D), the extent of the cell-substrate contact zone is indicated by the subvolumes highlighted in red.

Figure 3

Integrated Simulation of T Lymphocyte Recruitment. Time course and statistics of signaling events during T cell rolling and arrest were compiled from five-hundred simulations. (A) Accumulation of the indicated species is shown for individual cells (gray); color trajectories denote population averages. All simulations were synchronized to the moment of initial tether formation (t = 0 s). (B) Spatio-temporal snapshots of select membrane-associated species from the cell reference frame. In each column, the membrane concentration of the indicated species was projected to a plane centered on the cell-substrate contact zone (encircled, cf. Fig. 1D). Cell rolling results in the convection of molecules activated in the contact zone from right to left through the reference frame, as seen in the early stages of CCR binding and Rap1^GTP activation. Frames correspond to 1 s intervals (C–E) Predicted distributions of instantaneous cell velocities, (C), arrest times, Δt_arrest, (D), and arrest distances, Δx_arrest (E).

Figure 4

Chemokine Regulation of T Cell Arrest. (A) Effect of increasing chemokine substrate concentration on time (Δt_arrest) and distance (Δx_arrest) to cell arrest. 500 trajectories synchronized to the moment of arrest and distance of tether formation are shown. The population mean is indicated in red. (B) Cell arrest metrics over four decades of chemokine concentration. Dashed lines indicate the minimum time and distance required to integrate inside-out stimuli. (C) Standard deviations of Δt_arrest and Δx_arrest distributions increase linearly with population mean. For both metrics, the coefficient of variation (CV) equals 0.60.

Figure 5

Impact of Surface Receptor Expression on T Cell Recruitment. Arrest statistics were compiled for cells expressing variable levels of (A) L-selectin, (B) chemokine receptor, and (C) integrin α_Lβ₂. Receptor expression was varied one-at-a-time and normalized to those levels that yielded arrest metrics similar to those observed in adhesion assays (1.25×10⁴ L-selectin/cell, 5×10⁴ CCR/cell, and 10⁴ α_Lβ₂/cell). Shaded regions indicate the range of cell behaviors observed in vitro (cf. Table 1). The concentration of surface ligands were 10² sLe^x/μm², 10³ CC/μm², and 10³ ICAM-1/μm². Data reflect the mean ± s.d. of twenty simulations. In (A), cells cease to roll at ~3× above normalized L-selectin levels.

Figure 6

Additive Integration of Multiple Chemokine Stimuli. (A–B) Receptor signaling motifs for two chemokines. Predicted T cell arrest distances for the corresponding motifs under additive conditions (left) or synergistic conditions (right) are shown. (C) Predicted arrest distances for increasing substrate concentrations of two chemokines at physiological affinities: K_D.1 = K_D.2 = 5×10⁵ μm⁻². For either motif, the net effect of multiple chemokines on T cell arrest is identical to an equivalent concentration of one chemokine. In all simulations, CCR = CCR₁ = CCR₂ = 5×10⁴ #/cell.

Figure 7

Recruitment Sensitivity to Chemokine-Receptor Kinetics. (A) Fractional receptor occupancy as predicted by Eq. 6.1 and (B) frequency of receptor occupancy as predicted by Eq. 6.2. The enclosed regions in (A) and (B) indicate physiological parameter space. (C) Predicted arrest distance as a function chemokine-receptor kinetics. (D) Mean arrest distance as a function of chemokine affinity and chemokine receptor expression. In all simulations [CC] = 10³ μm⁻².

Figure 8

Three Modes of Selective T Lymphocyte Recruitment. The predicted range of T cell populations expressing one or two chemokine receptors that arrested within 100 μm of tethering are indicated. Regulated expression of one (A) or (B) two chemokines or chemokine affinity (C) resulted in population specific recruitment patterns.