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Research Papers

Simplified Analysis for the Association of a Constrained Receptor to an Oscillating Ligand

[+] 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 May 2, 2016; final manuscript received June 13, 2016; published online July 1, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(9), 091006 (Jul 01, 2016) (5 pages) Paper No: JAM-16-1223; doi: 10.1115/1.4033891 History: Received May 02, 2016; Revised June 13, 2016

The stability of a bond cluster upon oscillated loads under physiological conditions is strongly regulated by the kinetics of association and dissociation of a single bond, which can play critical roles in cell–matrix adhesion, cell–cell adhesion, etc. Here, we obtain a simplified analysis for the bond association process of a constrained receptor to an oscillating ligand due to its diffusion-independence, which can facilitate the potential multiscale studies in the future. Based on the analysis, our results indicate that the mean passage time for bond association intriguingly saturates at high oscillating frequencies, and there can also surprisingly exist optimal bond elasticity for bond association. This work can bring important insights into understanding of the behaviors of bond cluster under cyclic loads at the level of a single bond.

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Figures

Grahic Jump Location
Fig. 1

(a) Schematics of the model. A receptor, represented as a linear spring with a spring constant, k, and constrained at x = 0, can bind to a ligand (left), which oscillates periodically around x0 with an amplitude A and a frequency f (right). ((b) and (c)) For a static ligand, U evolves with time for different x0 and Tpkon0 varies with x0 when A = 0.

Grahic Jump Location
Fig. 2

Variation of Tp with D for a receptor binding to an oscillating ligand, when k = 0.01 pN/nm (a), 0.05 pN/nm (b), 0.1 pN/nm (c), and 0.5 pN/nm (d). In the figures, squares, triangles, circles, and diamonds represent the results for kon0  = 10/s, 100/s, 1000/s, and 10,000/s, respectively.

Grahic Jump Location
Fig. 3

((a)–(c)) Variation of Tp  with f for different A, k, and kon0, respectively, (d) variation of Tp  with A, (e) variation of Tp  with x0, and (f) variation of Tp  with kon0. In this figure, symbols are results obtained from the full analysis and curves are those obtained from the simplified analysis.

Grahic Jump Location
Fig. 4

((a)–(c)) Variation of Tp  with k for different A, f, and kon0, respectively. (d) Evolution of U with time for a receptor and a moving ligand at a constant velocity, v. From the bottom to the top, the curves are the results for v = 1, 5, 10, 20, 30, 50, 100, and 200 nm/s, respectively. In this figure, symbols are results obtained from the full analysis and curves are those obtained from the simplified analysis.

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