Fig 1.
(a) Sketch of the interaction between a T-lymphocyte cell (T-cell) and a supported antigen-seeded bilayer.
The two membranes are separated by transmembrane receptors bound to ligands in the bilayer. (b) Close-up schematic view of the synaptic cleft formed between the T-cell membrane and the glass supported bilayer. The cell membrane has a thickness b ≈ 8 nm and the membrane gap height is given by h = h(x, y, t). The trans-membrane receptors form bonds with the ligands in the bilayer with lengths and concentrations, TCR − pMHC ≈ 15 nm, C1(x, y, t), and LFA − ICAM ≈ 45 nm, C2(x, y, t). During protein bond formation and depletion, the cell membrane deforms generating a viscous flow u(x, y, z) in the membrane gap. The flow generates a viscous frictional force Fμ parallel with the glass supported bilayer that acts on the cell membrane and the transmembrane proteins and thus affects their motion. Any deformation of the membrane generates a restoring elastic bending force FB, while the deformation of the TCR-pMHC and LFA-ICAM bonds generates a spring force Fκ.
Table 1.
Description of the material parameters that appear in Eqs 1–4.
Table 2.
By substituting the scaled variables in Eqs 1–4; p(x, y, t) = p*(x, y, t)p0 = p*(x, y, t)C0 κl2, h(x, y, t) = h(x, y, t)*l2, x = x*L, y = y*L, t = t*τμ, Ci(x, y, t) = Ci(x, y, t)*C0 gives the non-dimensional numbers above.
These non-dimensional numbers characterize the relative influence of membrane mechanics, protein kinetics, geometry and hydrodynamics.
Fig 2.
Comparison between an experimental (left) and numerical (right) realization of the TCR-pMHC and LFA-ICAM protein patterning dynamics in the IS.
The simulations are based on Eqs 1–4 allowing fluid flux at the edge of the IS, where the height and number of proteins per membrane area is fixed. In the experiment a T-cell interacts with an antigen seeded lipid bilayer [20]. The upper row shows the density of bonded TCR-pMHC, the middle row the bonded LFA-ICAM proteins and the last row their union. The right panel shows the numerical simulation with B = 2 × 10−9 and τ = 15 with non-dimensional times . All other non-dimensional numbers are reported in Table 2. At short-times, protein clusters nucleate on the membrane, with a dynamics given by the interplay between membrane mechanics, protein kinetics and fluid flow. At late times protein clusters interact and coalesce into large spatial patterns that mimic pSMAC and cSMAC structures. A “donut shaped” LFA ring surrounds a dense TCR region at the center of the synapse at late times.
Fig 3.
(a)-(c) Simulation of Eqs 1–4 with B = 2 × 10−9 and τ = 15 and the other dimensionless numbers are reported in Table 2.
(a) Contour plots of the time history of the pressure (p), along with the velocity (−h2∇p). The second row shows the corresponding protein pattern of TCR-pMHC and LFA-ICAM, see Fig 3 for color scale. At short times (t < 4 min) the nucleation and coalescence of protein domains generates a local flow field. At late times (t ≥ 12min) a global centripetal flow is generated that “compress” the TCR cluster radially generating a “bulls-eye”-like protein pattern, which becomes unstable at t ≈ 60min. (b-c)The total number of attached receptors of (b) TCR-pMHC and (c) LFA-ICAM. (b-c) Direct comparison between the total number of attached TCR in the IS in simulation and in experiment [3] shows that the results are in good agreement for t < 20 min. This suggests that passive dynamics suffices to describe the short-time formation and organization of protein domains while the long-time IS dynamics and its stability is likely controlled by active processes.
Fig 4.
Phase space that characterizes the different regimes of membrane protein patterns as a function of and
(see Table 2).
The simulations are based on Eqs 1–4 and the patterning is measured at t = 40 min where a synaptic pattern is typically formed in experiments [2, 3, 20, 21], i.e. in dimensionless units (L/l2)2 t = 16. Two different protein patterns are identified; large diffuse patches and dispersed kinetic clusters, which are categorized into three regimes. In the diffusional dominated limit (τ < 0.3) large diffusive patches are predicted that translocate on the membrane. A transition to a dispersed protein pattern is observed for τ > 0.3. In the intermediate regime (0.3 ≤ τ ≤ 3), long-lived LFA clusters form on the membrane. When the protein dynamics is an active process (τ > 3) micro-scale TCR clusters nucleate and coalesce as they are transported radially forming a central dense pattern. In the kinetic regime we see that the cluster size varies as a function of B, similar to our scaling prediction . At equilibrium, all simulations predict a flat membrane with a single protein phase for the case where fluid flux at the edge of the IS is free and the membrane height and number of proteins per membrane area is fixed.