Real leukocytes exiting the bloodstream at a site of inflammation follow Springer's multistep adhesion cascade: fast axial flow → selectin-mediated tethering/rolling → chemokine-triggered integrin activation → firm arrest → transmigration (diapedesis). This 2D view is a lengthwise cross-section through the vessel axis, so both walls (top and bottom) are visible at once.
Poiseuille flow across the section:
v(d) = v_max (1 − (d/R)²)
d = distance from centreline, R = half-height
wall shear rate: γ = 2·v_max / R
wall shear stress: τ = μ·γ (μ = plasma viscosity)
Selectin–ligand bonds are catch-slip bonds: unlike ordinary bonds, moderate tensile force initially strengthens them (catch) before very high force breaks them faster (slip) — the reason rolling is most stable at an intermediate wall shear stress, not at zero shear (Marshall et al. 2003; Sokurenko et al.):
bond off-rate: k_off(F) = k_c·exp(−F/F_c) + k_s·exp(F/F_s)
tether force: F = 2τ (illustrative, pN)
- Wall shear stress τ — sets both flow speed and bond force F. Too low: too few tethers form. Too high: catch-slip bonds shift into the slip regime and strip off. Rolling is smoothest at an intermediate τ.
- Selectin density — the per-frame probability that a marginated (near-wall) free cell tethers and starts rolling.
- Chemokine / integrin activation — the rate at which a rolling cell's LFA-1/VLA-4 integrins switch to high-affinity and lock the cell into firm arrest inside the highlighted chemokine zone (toggle it off to watch cells roll straight through instead).
- Circulating leukocyte pool — how many cells are in the vessel segment at once, analogous to circulating white-cell count (e.g. leukocytosis during infection).
The strip chart under the vessel plots the live velocity of the currently tracked (ringed) cell — the rolling-then-arrest kinematic signature: fast free flow, a stochastic slow saw-tooth while rolling, then a hard drop to zero at firm arrest. After firm arrest a cell holds position briefly (integrin-mediated crawling to a junction, simplified here) before transmigrating radially through the endothelium and re-entering circulation upstream, keeping the simulated pool constant.