Leukocyte Rolling & Adhesion Cascade

Vessel & Blood Flow

Wall shear stress τ 4.0 dyn/cm²

Selectin density 50%

Chemokine / integrin activation 50%

Circulating leukocyte pool 70 cells

Live State

Rolling

Firmly adherent

Transmigrated (total)

Avg rolling velocity

0 µm/s

Free-flowing (core & margination) Rolling (selectin bonds) Firmly adherent (integrin) Transmigrating through wall

How it works

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).

Poiseuille flow in the venule:
  v(r) = v_max (1 − (r/R)²)
  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; also the step most sensitive to inflammatory signalling (e.g. IL-8, fMLP).
Circulating leukocyte pool — how many cells are in the vessel segment at once, analogous to circulating white-cell count (e.g. leukocytosis during infection).

After firm arrest a cell holds position for a few seconds (integrin-mediated crawling to a junction, simplified here) before transmigrating radially through the endothelium and re-entering circulation upstream, keeping the simulated pool constant.

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