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Research Papers

Nanocarrier–Cell Surface Adhesive and Hydrodynamic Interactions: Ligand–Receptor Bond Sensitivity Study

[+] Author and Article Information
B. Uma

Department of Anesthesiology and Critical Care,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: umab@seas.upenn.edu

R. Radhakrishnan

Department of Bioengineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: rradhak@seas.upenn.edu

D. M. Eckmann

Department of Anesthesiology and Critical Care,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: David.Eckmann@uphs.upenn.edu

P. S. Ayyaswamy

Department of Mechanical Engineering
and Applied Mechanics,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: ayya@seas.upenn.edu

1Corresponding author.

Manuscript received April 27, 2012; final manuscript received August 21, 2012; published online January 18, 2013. Assoc. Editor: Debjyoti Banerjee.

J. Nanotechnol. Eng. Med 3(3), 031010 (Jan 18, 2013) (8 pages) doi:10.1115/1.4007522 History: Received April 27, 2012; Revised August 21, 2012

A hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics is employed to study the motion of a neutrally buoyant nanocarrier in an incompressible Newtonian stationary fluid medium. Both hydrodynamic interactions and adhesive interactions are included, as are different receptor–ligand bond constants relevant to medical applications. A direct numerical simulation adopting an arbitrary Lagrangian–Eulerian based finite element method is employed for the simulation. The flow around the particle and its motion are fully resolved. The temperatures of the particle associated with the various degrees of freedom satisfy the equipartition theorem. The potential of mean force (or free energy density) along a specified reaction coordinate for the harmonic (spring) interactions between the antibody and antigen is evaluated for two different bond constants. The numerical evaluations show excellent comparison with analytical results. This temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion has important implications for designing nanocarriers for vascular targeted drug delivery.

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Figures

Grahic Jump Location
Fig. 1

Schematic representation of a nanoparticle in a cylindrical vessel (tube) (not to scale). Diameter of the tube: D=5μm; length of the tube: L=10 μm; diameter of the nanoparticle: d=500 nm; viscosity of the fluid: μ=10-3 kg/ms; density of the fluid and the nanoparticle: ρ(f)=ρ(p)=103 kg/m3; and spring constant: 0.01 N/m≤k≤10 N/m.

Grahic Jump Location
Fig. 2

Representation of a ten-node tetrahedron

Grahic Jump Location
Fig. 3

Finite element surface mesh of a cylindrical tube with one spherical nanoparticle

Grahic Jump Location
Fig. 4

Translational and rotational temperatures of the neutrally buoyant Brownian particle trapped in a harmonic potential in a stationary fluid medium as a function of the bond constant k. The nondimensionalized characteristic memory times are τ1/τν=0.12 and τ2/τν=0.088. The error bars have been plotted from standard deviations of the temperatures obtained with 15 different realizations, consisting of 100,000 time steps per realization.

Grahic Jump Location
Fig. 5

Equilibrium probability density of the (a) and (c) translational and (b) and (d) rotational velocities of the neutrally buoyant nanocarrier (a = 250 nm) trapped in a harmonic potential in a Newtonian fluid for bond constant k = 0.1 N/m (a) and (b) and k = 1.0 N/m (c) and (d). The nondimensionalized characteristic memory times are τ1/τν=0.12 and τ2/τν=0.088. The distributions agree within 6% error (see dotted line) with that of the analytical Maxwell–Boltzmann distribution.

Grahic Jump Location
Fig. 6

Equilibrium probability density of the displacement of spring length using hybrid scheme for bond constant (a) k = 0.1 N/m and (b) k = 1.0 N/m, where the standard deviation σ=kBT/k. The nondimensionalized characteristic memory times are τ1/τν=0.12 and τ2/τν=0.088. The distributions agree within 6% error (see dotted line) with the analytical Maxwell–Boltzmann distribution.

Grahic Jump Location
Fig. 7

Translational ((a) and (b)) and rotational ((c) and (d)) VACFs of the harmonically trapped Brownian particle of radius a = 250 nm through a circular vessel of radius R=2.5 μm obtained using hybrid scheme. The nondimensionalized characteristic memory times are τ1/τν=0.12 and τ2/τν=0.088.

Grahic Jump Location
Fig. 8

The calculated PMF W(y) at a temperature of 310 K for different values of the bond constant, k

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