Targeted Nanoparticle Drug Delivery: Receptor Binding Under Flow

Vessel Flow & Targeting

Wall shear rate γ 600 s⁻¹

Antibody (ligand) density 0.50

Receptor expression 0.50

Bond affinity (1/k_off0) 0.50

Nanoparticle diameter 100 nm

Live Readouts

Bound fraction

Capture rate

0 / s

Shear force / bond

0 pN

Mean off-rate k_off

0 s⁻¹

Free nanoparticle (flowing)
Bound to receptor
Diseased-cell wall (receptors)

How it works

Nanoparticles are advected down a cylindrical vessel by Poiseuille flow, v(r) = v_max(1 − r²/R²), and diffuse radially toward the wall. Near the wall a particle can form an antibody–receptor bond; whether it does, and how long it survives, is governed by two coupled rate laws used throughout the nanomedicine adhesion literature (Hammer & Lauffenburger; Decuzzi & Ferrari):

Bond formation:  P(on)  = 1 − exp(−k_on · ρ_L · ρ_R · dt)
Bell model:      k_off  = k_off0 · exp(F·x_β / k_B T)
Shear force:     F      = 6π · η · a² · γ

ρ_L and ρ_R are the normalized antibody and receptor surface densities, γ is the local wall shear rate, a is the particle radius, η is blood plasma viscosity (≈ 3.5 mPa·s), x_β is the bond's reactive compliance (0.5 nm), and k_BT is thermal energy at 310 K. A bound particle is a green dot; the hydrodynamic drag tries to tear it free at rate k_off, so it detaches back into the flow when a random draw beats that rate.

Shear rate — faster flow raises the tensile force on every bond, shortening dwell time (higher k_off).
Antibody / receptor density — both must be present for a bond to nucleate; either at zero gives zero capture, exactly as in real ligand–receptor targeting.
Bond affinity — a stronger antibody–receptor pair lowers the unstressed off-rate k_off0, letting bonds survive higher shear.
Particle size — bigger particles feel quadratically more drag (F ∝ a²) but also intercept more receptors, so real formulations trade size against shear resistance.

This is the same physics behind why larger, floppier liposomes shed off in fast-flowing arteries while small, densely-antibody-coated nanoparticles marginate and stick in the slower, leaky microvasculature around a tumor.

0 particles · 0 bound

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Targeted Nanoparticle Drug Delivery: Receptor Binding Under Blood Flow