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Research Papers

Modeling the Adhesive Contact Between Cells and a Wavy Extracellular Matrix Mediated by Receptor–Ligand Interactions

[+] Author and Article Information
B. Chong, Z. Gong

Department of Mechanical Engineering,
The University of Hong Kong,
Hong Kong, China

Y. Lin

Department of Mechanical Engineering,
The University of Hong Kong,
Hong Kong, China
e-mail: ylin@hku.hk

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 9, 2016; final manuscript received October 3, 2016; published online October 26, 2016. Editor: Yonggang Huang.

J. Appl. Mech 84(1), 011010 (Oct 26, 2016) (7 pages) Paper No: JAM-16-1397; doi: 10.1115/1.4034931 History: Received August 09, 2016; Revised October 03, 2016

In this study, we examine the outstanding issue of how surface topology affects the adhesion between cells and the extracellular matrix (ECM). Specifically, we showed that the adhesive contact can be well described by treating the attraction as continuous along the interface if the wavelength of surface undulations is larger than a few microns. On the other hand, the discrete nature of cell–ECM interactions, i.e., adhesion is achieved through the formation of individual receptor–ligand bonds, must be taken into account for wavy surfaces with a much smaller characteristic length. Interestingly, it was found that, due to the interplay between substrate elasticity and stochastic breakage/reformation of molecular bonds, the strength of cell–ECM adhesion will reach its maximum when the surface roughness is of the order of 20–40 nm, in quantitative agreement with recent experiments. In addition, because of the bonding kinetics involved, the apparent adhesion energy was predicted to be strongly rate-dependent with increasing detaching speed between surfaces leading to a rapidly elevated work of separation, a phenomenon that has been widely observed in bio-adhesion.

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Figures

Grahic Jump Location
Fig. 1

Schematic plot of a cell in adhesive contact with a wavy substrate where attachment is achieved at discrete bonding sites

Grahic Jump Location
Fig. 2

The average contact pressure (p¯) versus normalized adhesion size (Ψ=πL/λ) relationship. Dashed lines represent results from our discrete model, while the solid line corresponds to the continuum prediction by Eq. (8). Parameters values chosen here are E=10 kPa, ν=0.5, γ=2.22 μN/m,  α=0.2, k=1 pN/nm, and 2b=30 nm. The value of Δ is adjusted from 21.6 to 61.1 nm as the number of bonds in one period increases from 21 to 151 to ensure that the same  α (=0.2) is maintained.

Grahic Jump Location
Fig. 3

Dependence of the flatten pressure (normalized by the continuous prediction) on the density and stiffness of bonds. Here, Δ=50 nm  is fixed, while the value of dcr (and hence γ) is varied to maintain a constant α (=0.2) when the number of bonds in each period increases.

Grahic Jump Location
Fig. 4

Influence of surface roughness on the strength of cell–substrate adhesion, where 2b and Δ/λ are fixed as 30 nm and 0.4, respectively. The normalization is conducted by setting Ip=p−pcr_min/pcr_max−pcr_min, with pcr_max and pcr_min being the maximum and minimum critical pulloff pressure obtained in our simulation.

Grahic Jump Location
Fig. 5

The adhesion strength σ as a function of the surface roughness. Results shown here are based on 10,000 independent Monte Carlo simulations, where undulation amplitude Δ was varied to achieve different surface roughness. The normalization is conducted by setting Iσ=σ−σmin/σmax−σmin, with σmax and σmin being the maximum and minimum strength obtained in our simulation. In comparison, the normalized areal density  IA of human HeLa (or A549 lung carcinoma) cells adhered on a rough silicon-based substrate measured by Gentile et al. [12] is also shown by the square (or circular) symbol.

Grahic Jump Location
Fig. 6

Influence of bond stiffness and cell modulus on the optimum roughness for achieving maximum cell–substrate adhesion. The values of 2b and Δ/λ are fixed as 30 nm and 0.4, respectively.

Grahic Jump Location
Fig. 7

Effect of the threshold lifetime value on the adhesion strength

Grahic Jump Location
Fig. 8

(a) The load–displacement curve during the detaching process predicted by the deterministic formulation. (b)–(d) Typical trajectories from stochastic Monte Carlo simulations under different separation speed. The area of the shaded region in (b) represents the work of separation. Parameters adopted here are 2b=30 nm, 2N+1=21, and Δ/λ=0.4.

Grahic Jump Location
Fig. 9

Simulated work of separation (normalized by its value at the detaching rate of 5 nm/s) as a function of the normalized separation speed. In comparison, the measured fracture strength (and work of separation) of the peptide/membrane [40] (and film-terminated fibrillary [41]) interface is also shown by the square (and diamond) symbols.

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