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Research Papers

Probing the Instability of a Cluster of Slip Bonds Upon Cyclic Loads With a Coupled Finite Element Analysis and Monte Carlo Method

[+] Author and Article Information
Xiaofeng Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China

Bin Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China
e-mail: chenb6@zju.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 17, 2014; final manuscript received August 20, 2014; accepted manuscript posted August 28, 2014; published online September 17, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(11), 111002 (Sep 17, 2014) (7 pages) Paper No: JAM-14-1261; doi: 10.1115/1.4028437 History: Received June 17, 2014; Revised August 20, 2014; Accepted August 28, 2014

Cells are subjected to cyclic loads under physiological conditions, which regulate cellular structures and functions. Recently, it was demonstrated that cells on substrates reoriented nearly perpendicular to the stretch direction in response to uni-axial cyclic stretches. Though various theories were proposed to explain this observation, the underlying mechanism, especially at the molecular level, is still elusive. To provide insights into this intriguing observation, we employ a coupled finite element analysis (FEA) and Monte Carlo method to investigate the stability of a cluster of slip bonds upon cyclic loads. Our simulation results indicate that the cluster can become unstable upon cyclic loads and there exist two characteristic failure modes: gradual sliding with a relatively long lifetime versus catastrophic failure with a relatively short lifetime. We also find that the lifetime of the bond cluster, in many cases, decreases with increasing stretch amplitude and also decreases with increasing cyclic frequency, which appears to saturate at high cyclic frequencies. These results are consistent with the experimental reports. This work suggests the possible role of slip bonds in cellular reorientation upon cyclic stretch.

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Figures

Grahic Jump Location
Fig. 1

An elastic fiber is adhered to a rigid substrate through a cluster of slip bonds. The fiber is subjected to a periodic force, F(t), on its right end. The bonds are formed between receptors and ligands, which are uniformly distributed along the fiber or on a portion of substrate surface with neighboring distance, l0. The total number of receptors is n and the total number of ligands is N. In the model, the fiber is considered as 1D elastic rod and the bonds as elastic springs.

Grahic Jump Location
Fig. 2

The flow chart of the coupled FEA and Monte Carlo method to determine the lifetime of the bond cluster upon a cyclic load

Grahic Jump Location
Fig. 3

Variation of the lifetime of a single slip bond with stretch amplitude (a) and with cyclic frequency (b) and (c). In the calculation, A = 5 pN and k0 = 0.01s-1 for (a) and (b), and, A = 5 pN and α = 0.8 for (c).

Grahic Jump Location
Fig. 4

Variation of the lifetime of a cluster of slip bonds without rebinding with stretch amplitude (a) and with cyclic frequency (b) and (c). In the simulation, A = 200 pN and k0 = 0.01s-1 for (a) and (b) while A = 200 pN and α = 0.8 for (c).

Grahic Jump Location
Fig. 5

Two characteristic failure modes: (1) sliding mode, where a significant number of bonds rebind to the substrate after broken as shown in (a) and the fiber gradually slides forward for a relatively long time as shown in (b); (2) catastrophic failure, where only a few bonds rebind to the substrate after broken as shown in (c) and the fiber quickly detaches from the substrate as shown in (d). Each minicircle in (a) or (c) represents a bond breaking event at a specific time at a specific site on substrate surface. The vertical coordinate in (a) and (c) is the sequential number of ligands on the surface of substrate and that in (b) and (d) is the displacement of the right end of the fiber. In the simulation, A = 60 pN, α = 0.5, and f = 0.3 Hz for (a) and (b), while A = 60 pN, α = 0.5, and f = 10 Hz for (c) and (d).

Grahic Jump Location
Fig. 6

Variation of the lifetime of a cluster of slip bonds with rebinding with stretch amplitude (a) and cyclic frequency (b) and (c). In the simulation, A = 60 pN for (a) and (b), and A = 60 pN and α = 0.5 for (c).

Grahic Jump Location
Fig. 7

(a) Variation of the lifetime of a cluster of slip bonds with rebinding with stretch amplitude. (b) Bond breaking sequence versus time. Each point represents a bond breaking event on substrate surface. (c) The displacement of the right end of stress fiber versus time. In the simulation, A = 60 pN, β in Eq. (1) is set to be 1, α = 0.8, and f = 0.3Hz.

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