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Research Papers

On Stability of Specific Adhesion of Particles to Membranes in Simple Shear Flow

[+] Author and Article Information
Mohammad Hossein Moshaei, Mohammad Tehrani

Department of Mechanical Engineering,
Ohio University,
Athens, OH 45701

Alireza Sarvestani

Department of Mechanical Engineering,
Ohio University,
Athens, OH 45701;
Department of Mechanical Engineering,
Mercer University,
Macon, GA 31207
e-mail: sarvesta@ohio.edu

1Corresponding author.

Manuscript received November 23, 2017; final manuscript received July 25, 2018; published online October 17, 2018. Assoc. Editor: Sarah Kieweg.

J Biomech Eng 141(1), 011005 (Oct 17, 2018) (10 pages) Paper No: BIO-17-1546; doi: 10.1115/1.4041046 History: Received November 23, 2017; Revised July 25, 2018

Adhesion of carrier particles to the luminal surface of endothelium under hemodynamic flow conditions is critical for successful vascular drug delivery. Endothelial cells (ECs) line the inner surface of blood vessels. The effect of mechanical behavior of this compliant surface on the adhesion of blood-borne particles is unknown. In this contribution, we use a phase-plane method, first developed by Hammer and Lauffenburger (1987, “A Dynamical Model for Receptor-Mediated Cell Adhesion to Surfaces,” Biophys. J., 52(3), p. 475), to analyze the stability of specific adhesion of a spherical particle to a compliant interface layer. The model constructs a phase diagram and predicts the state of particle adhesion, subjected to an incident simple shear flow, in terms of interfacial elasticity, shear rate, binding affinity of cell adhesive molecules, and their surface density. The main conclusion is that the local deformation of the flexible interface inhibits the stable adhesion of the particle. In comparison with adhesion to a rigid substrate, a greater ligand density is required to establish a stable adhesion between a particle and a compliant interface.

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Figures

Grahic Jump Location
Fig. 1

(a) The distance z between free ligands and receptors increases by application of tension on the specific bonds formed between a particle and a deformable interface [28]. (b) The bond and deformable substrate are modeled as linear springs with spring constants sb and si, assembled in series.

Grahic Jump Location
Fig. 2

Schematic presentation of a particle adhered to an interfacial membrane separating two Newtonian fluids with the viscosity of μ1 and μ2, subjected to a simple shear flow. The flow-induced dislodging force and torque are shown by Fh and Th, respectively.

Grahic Jump Location
Fig. 3

The force dependency of potential energy as presented by the two-pathway model [40]. Solid line shows the potential energy of the bond in state of equilibrium xe. Dissociation of ligand and receptor may happen via two pathways with different energy barriers at xc and xs, corresponding to the catch and slip states, respectively. Initially, the energy barrier toward the catch pathway (solid line) is lower. The pulling force fb alters the energy barriers and facilitates taking the slip pathway (dashed line).

Grahic Jump Location
Fig. 4

The algorithm of the computational process

Grahic Jump Location
Fig. 5

A typical φf − φb phase-plane. The cross section of φf = 1 and φb˙=0 show the steady-state solutions. The separatrix divides the phase-plane into the stable and unstable domains. The lower boundary is shown by τ = 1, below which no established bond is fully strained (φl = 677, σ = 20, α = 30, θ = 0.1, δ = 0.001, and bonds are slip bonds with κs = 0.94).

Grahic Jump Location
Fig. 6

Variation of admissible ligand density with the dissociation rate κs of slip bonds considering different values for interfacial compliance (θ = 1, and δ = 0.001)

Grahic Jump Location
Fig. 7

Variation of the total dislodging drag force exerted on a stationary particle with the shear rate of the host fluid. The comparison is made between adhesion to a rigid substrate and an interfacial membrane (λ = 1, m = 0.996).

Grahic Jump Location
Fig. 8

Variation of admissible ligand density with the dissociation rate (a) κs and (b) κc of catch-slip bonds considering different values for interfacial compliance. (c) Dependency of admissible φl on the dissociation rates κs and κc of catch-slip bonds at σ = 10 (α = 22, θ = 0.1, and δ = 0.001).

Grahic Jump Location
Fig. 9

Variation of admissible ligand density with the compliance of membrane considering different values for hydrodynamic dislodging force (κs=3×10−5, κc=3×10−4, θ=0.1, and δ = 0.001)

Grahic Jump Location
Fig. 10

(a) Lifetime versus unbinding force for single bonds formed between PSGL-1 and P-selectin [38]. Solid line shows the prediction of two-pathway model fitted to the experimental data. The unbinding rates ks0 and kc0 are found to be 0.14 s−1 and 23 s−1, respectively. (b) Comparison between the experimental data of Patil et al. [49] and model predictions for rigid and compliant substrates (Nl/4πRc2≈1000 μm−2, θ = 1, δ = 0.001 and k0+cr=84 s−1 [18]).

Grahic Jump Location
Fig. 11

A phase-plane representing the variation of admissible ligand density on the particle with unbinding rate (κc). The unbinding rates of P-selectin-PSGL bonds are extracted from the experimental data, shown by Fig. 10(a). A significant decrease in binding affinity (top arrow) undermines the stability of adhesion at a given ligand density. The presented results are obtained assuming k0+cr=84 s−1 [18]. Other parameters include θ = 1 and δ = 0.001.

Grahic Jump Location
Fig. 12

A schematic depiction of membrane profile around a bond, subjected to the tensile force fb. The bond is assumed to be a large macromolecule with cylindrical symmetry and a characteristic size of lb.

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