A transplanted organ or implant surface is instantly coated by blood plasma proteins (the protein corona). If opsonins such as IgG and complement fragment C3b accumulate past a threshold coverage, macrophages and complement receptors recognize the surface as foreign and trigger rejection. Grafting a dense layer of PEG (polyethylene glycol) or a zwitterionic polymer onto the surface suppresses this via steric brush repulsion: an approaching protein must compress the polymer brush, costing free energy that falls exponentially with grafting density.
p_ads(σ) = p₀ · exp(−k·σ) (effective adsorption probability per contact)
dC/dt = k_on·(1−θ)·p_ads·[protein] − k_off·C (Langmuir-type coverage kinetics)
θ = C / C_max (fractional surface coverage)
D(T) ∝ T / η(T) (Stokes–Einstein: diffusion rises with T)
- PEG graft density σ — steric shielding strength; higher σ exponentially suppresses adsorption probability per collision (Jeon–Andrade brush theory).
- Plasma protein concentration — sets how many opsonin particles are spawned per second, i.e. the collision frequency with the surface.
- Temperature — raises the Brownian diffusion coefficient (Stokes–Einstein), so proteins reach the surface faster at higher T.
- When cumulative coverage θ crosses ~65%, a macrophage-like sentinel docks onto the surface — the visual analogue of immune recognition and the start of a rejection cascade.
Real-world relevance: PEGylation and zwitterionic "stealth" coatings are used on vascular grafts, islet-cell encapsulation devices and drug-eluting stents specifically to delay this opsonization window long enough for the graft to integrate before the immune system mounts a response.