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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Erdmann, T. , and Schwarz, U. S. , 2004, “ Stochastic Dynamics of Adhesion Clusters Under Shared Constant Force and With Rebinding,” J. Chem. Phys., 121(18), pp. 8997–9017. [CrossRef] [PubMed]
Erdmann, T. , and Schwarz, U. S. , 2004, “ Stability of Adhesion Clusters Under Constant Force,” Phys. Rev. Lett., 92(10), p. 108102. [CrossRef] [PubMed]
Kramers, H. A. , 1940, “ Brownian Motion in a Field of Force and the Diffusion Model of Chemical Reactions,” Physica, 7(4), pp. 284–304. [CrossRef]
Bell, G. I. , 1978, “ Models for the Specific Adhesion of Cells to Cells,” Science, 200(4342), pp. 618–627. [CrossRef] [PubMed]
Evans, E. , and Ritchie, K. , 1997, “ Dynamic Strength of Molecular Adhesion Bonds,” Biophys. J., 72(4), pp. 1541–1555. [CrossRef] [PubMed]
Erdmann, T. , and Schwarz, U. S. , 2006, “ Bistability of Cell–Matrix Adhesions Resulting From Nonlinear Receptor-Ligand Dynamics,” Biophys. J., 91(6), pp. L60–62. [CrossRef] [PubMed]
Filippov, A. , Klafter, J. , and Urbakh, M. , 2004, “ Friction Through Dynamical Formation and Rupture of Molecular Bonds,” Phys. Rev. Lett., 92(13), p. 135503. [CrossRef] [PubMed]
Kong, D. , Ji, B. , and Dai, L. , 2008, “ Stability of Adhesion Clusters and Cell Reorientation Under Lateral Cyclic Tension,” Biophys. J., 95(8), pp. 4034–4044. [CrossRef] [PubMed]
Mao, Z. , Chen, X. , and Chen, B. , 2015, “ Stability of Focal Adhesion Enhanced by Its Inner Force Fluctuation,” Chin. Phys. B, 24(8), p. 088702. [CrossRef]
Dartsch, P. , Hämmerle, H. , and Betz, E. , 1986, “ Orientation of Cultured Arterial Smooth Muscle Cells Growing on Cyclically Stretched Substrates,” Cells Tissues Organs, 125(2), pp. 108–113. [CrossRef]
Kemkemer, R. , Neidlinger-Wilke, C. , Claes, L. , and Gruler, H. , 1999, “ Cell Orientation Induced by Extracellular Signals,” Cell Biochem. Biophys., 30(2), pp. 167–192. [CrossRef] [PubMed]
Buck, R. C. , 1980, “ Reorientation Response of Cells to Repeated Stretch and Recoil of the Substratum,” Exp. Cell Res., 127(2), pp. 470–474. [CrossRef] [PubMed]
Greiner, A. M. , Chen, H. , Spatz, J. P. , and Kemkemer, R. , 2013, “ Cyclic Tensile Strain Controls Cell Shape and Directs Actin Stress Fiber Formation and Focal Adhesion Alignment in Spreading Cells,” PLoS One, 8(10), p. e77328. [CrossRef] [PubMed]
Jungbauer, S. , Gao, H. , Spatz, J. P. , and Kemkemer, R. , 2008, “ Two Characteristic Regimes in Frequency-Dependent Dynamic Reorientation of Fibroblasts on Cyclically Stretched Substrates,” Biophys. J., 95(7), pp. 3470–3478. [CrossRef] [PubMed]
Freund, L. , 2009, “ Characterizing the Resistance Generated by a Molecular Bond as It is Forcibly Separated,” Proc. Natl. Acad. Sci. U.S.A., 106(22), pp. 8818–8823. [CrossRef] [PubMed]
Freund, L. , 2014, “ Brittle Crack Growth Modeled as the Forced Separation of Chemical Bonds Within a K-Field,” J. Mech. Phys. Solids, 64, pp. 212–222. [CrossRef]
Saunders, T. E. , 2015, “ Aggregation-Fragmentation Model of Robust Concentration Gradient Formation,” Phys. Rev. E, 91(2), p. 022704. [CrossRef]
Gambin, Y. , Lopez-Esparza, R. , Reffay, M. , Sierecki, E. , Gov, N. , Genest, M. , Hodges, R. , and Urbach, W. , 2006, “ Lateral Mobility of Proteins in Liquid Membranes Revisited,” Proc. Natl. Acad. Sci. U.S.A., 103(7), pp. 2098–2102. [CrossRef] [PubMed]
Rinko, L. J. , Lawrence, M. B. , and Guilford, W. H. , 2004, “ The Molecular Mechanics of P-and L-Selectin Lectin Domains Binding to PSGL-1,” Biophys. J., 86(1), pp. 544–554. [CrossRef] [PubMed]
Chen, X. , Li, D. , Ji, B. , and Chen, B. , 2015, “ Reconciling Bond Strength of a Slip Bond at Low Loading Rates With Rebinding,” Europhys. Lett., 109(6), p. 68002. [CrossRef]
Gao, H. , Qian, J. , and Chen, B. , 2011, “ Probing Mechanical Principles of Focal Contacts in Cell–Matrix Adhesion With a Coupled Stochastic-Elastic Modelling Framework,” J. R. Soc., Interface, 8(62), pp. 1217–1232. [CrossRef]
Chen, B. , Kemkemer, R. , Deibler, M. , Spatz, J. , and Gao, H. , 2012, “ Cyclic Stretch Induces Cell Reorientation on Substrates by Destabilizing Catch Bonds in Focal Adhesions,” PLoS One, 7(11), p. e48346. [CrossRef] [PubMed]
Chen, X. , and Chen, B. , 2014, “ Probing the Instability of a Cluster of Slip Bonds Upon Cyclic Loads With a Coupled Finite Element Analysis and Monte Carlo Method,” ASME J. Appl. Mech., 81(11), p. 111002. [CrossRef]
Chen, B. , 2014, “ Probing the Effect of Random Adhesion Energy on Receptor-Mediated Endocytosis With a Semistochastic Model,” ASME J. Appl. Mech., 81(8), p. 081013. [CrossRef]
Li, L. , Yao, H. , and Wang, J. , 2015, “ Dynamic Strength of Molecular Bond Clusters Under Displacement- and Force-Controlled Loading Conditions,” ASME J. Appl. Mech., 83(2), p. 021004. [CrossRef]
Jonsdottir, F. , and Freund, L. B. , 2014, “ Large Amplitude Thermal Fluctuations of Confined Semiflexible Biopolymer Filaments,” ASME J. Appl. Mech., 81(11), p. 111006. [CrossRef]
Seifert, U. , 2002, “ Dynamic Strength of Adhesion Molecules: Role of Rebinding and Self-Consistent Rates,” Europhys. Lett., 58(5), p. 792. [CrossRef]
Friddle, R. W. , Podsiadlo, P. , Artyukhin, A. B. , and Noy, A. , 2008, “ Near-Equilibrium Chemical Force Microscopy,” J. Phys. Chem. C, 112(13), pp. 4986–4990. [CrossRef]
Friddle, R. W. , Noy, A. , and De Yoreo, J. J. , 2012, “ Interpreting the Widespread Nonlinear Force Spectra of Intermolecular Bonds,” Proc. Natl. Acad. Sci. U.S.A., 109(34), pp. 13573–13578. [CrossRef] [PubMed]
Li, D. , and Ji, B. , 2014, “ Predicted Rupture Force of a Single Molecular Bond Becomes Rate Independent at Ultralow Loading Rates,” Phys. Rev. Lett., 112(7), p. 078302. [CrossRef] [PubMed]
Li, D. , and Ji, B. , 2015, “ Crucial Roles of Bond Rebinding in Rupture Behaviors of Single Molecular Bond at Ultralow Loading Rates,” Int. J. Appl. Mech., 7(01), p. 1550015. [CrossRef]
Alsteens, D. , Pfreundschuh, M. , Zhang, C. , Spoerri, P. M. , Coughlin, S. R. , Kobilka, B. K. , and Müller, D. J. , 2015, “ Imaging G Protein-Coupled Receptors While Quantifying Their Ligand-Binding Free-Energy Landscape,” Nat. Methods, 12(9), pp. 845–851. [CrossRef] [PubMed]


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. 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. 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.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In