Research Papers

Dynamic Strength of Molecular Bond Clusters Under Displacement- and Force-Controlled Loading Conditions

[+] Author and Article Information
Long Li

Key Laboratory of Mechanics on Disaster and
Environment in Western China,
Ministry of Education,
College of Civil Engineering and Mechanics,
Lanzhou University,
Lanzhou, Gansu 730000, China;
Department of Mechanical Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon 999077, Hong Kong SAR, China

Haimin Yao

Department of Mechanical Engineering,
The Hong Kong Polytechnic University,
Hung Hom,
Kowloon 999077, Hong Kong SAR, China

Jizeng Wang

Key Laboratory of Mechanics on Disaster and
Environment in Western China,
Ministry of Education,
College of Civil Engineering and Mechanics,
Lanzhou University,
Lanzhou, Gansu 730000, China
e-mail: jzwang@lzu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 1, 2015; final manuscript received October 13, 2015; published online November 11, 2015. Editor: Yonggang Huang.

J. Appl. Mech 83(2), 021004 (Nov 11, 2015) (6 pages) Paper No: JAM-15-1530; doi: 10.1115/1.4031802 History: Received October 01, 2015; Revised October 13, 2015

Existing experimental and theoretical studies on the adhesion of molecular bond clusters are usually based on either displacement- or force-controlled loading conditions. Very few studies have addressed whether or not and how the loading conditions affect the stochastic behavior of clusters. By considering the reversible breaking and rebinding process of ligand–receptor bonds, we directly solve the master equation about reactions between receptor–ligand bonds and conduct the corresponding Monte Carlo simulation to investigate the rupture forces of adhesion molecular clusters under linearly incremented displacement and force loading, respectively. We find that the rupture force of clusters strongly depends on loading conditions. Bond breaking and rebinding are independent of each other under displacement-controlled loading, whereas the rupture force highly depends on the state of each single bond under force-controlled loading. The physical mechanism of the dependence of rupture force on loading rate is also analyzed. We identify three reaction regimes in terms of loading rate: the regimes of equilibrium breaking/rebinding reactions, near-equilibrium reaction, and far from equilibrium with only bond breaking. These findings can help improve the current understanding of the stochastic behaviors of the adhesion clusters of molecular bonds under dynamic loading conditions.

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Discher, D. E. , Janmey, P. , and Wang, Y. I. , 2005, “ Tissue Cells Feel and Respond to the Stiffness of Their Substrate,” Science, 310(5751), pp. 1139–1143. [CrossRef] [PubMed]
Engler, A. J. , Sen, S. , Sweeney, H. L. , and Discher, D. E. , 2006, “ Matrix Elasticity Directs Stem Cell Lineage Specification,” Cell, 126(4), pp. 667–689. [CrossRef]
He, S. , Su, Y. , Ji, B. , and Gao, H. , 2014, “ Some Basic Questions on Mechanosensing in Cell–Substrate Interaction,” J. Mech. Phys. Solids, 70, pp. 116–135. [CrossRef]
Zhu, C. , Long, M. , Chesla, S. E. , and Bongrand, P. , 2002, “ Measuring Receptor/Ligand Interaction at the Single-Bond Level: Experimental and Interpretative Issues,” Ann. Biomed. Eng., 30(3), pp. 305–314. [CrossRef] [PubMed]
Lo, Y. S. , Zhu, Y. J. , and Beebe, T. P. , 2001, “ Loading-Rate Dependence of Individual Ligand–Receptor Bond-Rupture Forces Studied by Atomic Force Microscopy,” Langmuir, 17(2), pp. 3741–3748. [CrossRef]
Merkel, R. , Nassoy, P. , Leung, A. , Ritchie, K. , and Evans, E. , 1999, “ Energy Landscapes of Receptor–Ligand Bonds Explored With Dynamic Force Spectroscopy,” Nature, 397(6714), pp. 50–53. [CrossRef] [PubMed]
Evans, E. , and Ritchie, K. , 1997, “ Dynamic Strength of Molecular Adhesion Bonds,” Biophys. J., 72(4), pp. 1541–1555. [CrossRef] [PubMed]
Keten, S. , and Buehler, M. J. , 2008, “ Asymptotic Strength Limit of Hydrogen Bond Assemblies in Proteins at Vanishing Pulling Rates,” Phys. Rev. Lett., 100(19), p. 198301. [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]
Raible, M. , Evstigneev, M. , Reimann, P. , Bartels, F. W. , and Ros, R. , 2004, “ Theoretical Analysis of Dynamic Force Spectroscopy Experiments on Ligand–Receptor Complexes,” J. Biotechnol., 112(1–2), pp. 13–23. [CrossRef] [PubMed]
Bullerjahn, J. T. , Sturm, S. , and Kroy, K. , 2014, “ Theory of Rapid Force Spectroscopy,” Nat. Commun., 8, p. 4463.
Hummer, G. , and Szabo, A. , 2003, “ Kinetics From Nonequilibrium Single-Molecule Pulling Experiments,” Biophys. J., 85(1), pp. 5–15. [CrossRef] [PubMed]
Dudko, O. K. , Hummer, G. , and Szabo, A. , 2006, “ Intrinsic Rates and Activation Free Energies From Single-Molecule Pulling Experiments,” Phys. Rev. Lett., 96(10), p. 108101. [CrossRef] [PubMed]
Maitra, A. , and Arya, G. , 2010, “ Model Accounting for the Effects of Pulling-Device Stiffness in the Analyses of Single-Molecule Force Measurements,” Phys. Rev. Lett., 105(25), p. 259902. [CrossRef]
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,” ASME Int. J. Appl. Mech., 7(1), p. 1550015. [CrossRef]
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]
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]
Chen, A. , and Moy, V. T. , 2000, “ Cross-Linking of Cell Surface Receptors Enhances Cooperativity of Molecular Adhesion,” Biophys. J., 78(6), pp. 2814–2820. [CrossRef] [PubMed]
Sulchek, T. , Friddle, R. W. , and Noy, A. , 2006, “ Strength of Multiple Parallel Biological Bonds,” Biophys. J., 90(12), pp. 4686–4691. [CrossRef] [PubMed]
Friddle, R. W. , Noy, A. , and Yoreo, J. J. D. , 2012, “ Interpreting the Widespread Nonlinear Force Spectra of Intermolecular Bonds,” Proc. Natl. Acad. Sci. USA, 109(34), pp. 13573–13578. [CrossRef]
Seifert, U. , 2000, “ Rupture of Multiple Parallel Molecular Bonds Under Dynamic Loading,” Phys. Rev. Lett., 84(12), pp. 2750–2753. [CrossRef] [PubMed]
Seifert, U. , 2002, “ Dynamic Strength of Adhesion Molecules: Role of Rebinding and Self-Consistent Rates,” Europhys. Lett., 58(5), pp. 792–798. [CrossRef]
Li, F. , and Leckband, D. , 2006, “ Dynamic Strength of Molecularly Bonded Surfaces,” J. Chem. Phys., 125, p. 194702.
Erdmann, T. , Pierrat, S. , Nassoy, P. , and Schwarz, U. S. , 2008, “ Dynamic Force Spectroscopy on Multiple Bonds: Experiments and Model,” Europhys. Lett., 81(4), p. 48001. [CrossRef]
Zhang, W. L. , Lin, Y. , Qian, J. , Chen, W. Q. , and Gao, H. J. , 2013, “ Tuning Molecular Adhesion Via Material Anisotropy,” Adv. Funct. Mater., 23(37), pp. 4729–4738.
Willemsen, O. H. , Snel, M. M. E. , Cambi, A. , Greve, J. , Grooth, B. G. , and Figdor, C. G. , 2000, “ Biomolecular Interactions Measured by Atomic Force Microscopy,” Biophys. J., 79(6), pp. 3267–3281. [CrossRef] [PubMed]
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. 8897–9017. [CrossRef] [PubMed]
Evans, E. A. , and Calderwood, D. A. , 2007, “ Forces and Bond Dynamics in Cell Adhesion,” Science, 316(5828), pp. 1148–1153. [CrossRef] [PubMed]
Erdmann, T. , and Schwarz, U. S. , 2007, “ Impact of Receptor–Ligand Distance on Adhesion Cluster Stability,” Eur. Phys. J. E, 22(2), pp. 123–137. [CrossRef]
Erdmann, T. , and Schwarz, U. S. , 2006, “ Bistability of Cell–Matrix Adhesions Resulting From Nonlinear Receptor–Ligand Dynamics,” Biophys. J., 91(6), pp. L60–L62. [CrossRef] [PubMed]
Qian, J. , Wang, J. Z. , and Gao, H. J. , 2008, “ Lifetime and Strength of Adhesive Molecular Bond Clusters Between Elastic Media,” Langmuir, 24(4), pp. 1262–1270. [CrossRef] [PubMed]
Gillespie, D. T. , 1976, “ A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions,” J. Comput. Phys., 22(4), pp. 403–434. [CrossRef]
Gillespie, D. T. , 1977, “ Exact Stochastic Simulation of Coupled Chemical Reactions,” J. Phys. Chem., 81(25), pp. 2340–2361. [CrossRef]
Kong, F. , Garcia, A. J. , Mould, A. P. , Humphries, M. J. , and Zhu, C. , 2009, “ Demonstration of Catch Bonds Between an Integrin and its Ligand,” J. Cell Biol., 185(7), pp. 1275–1284. [CrossRef] [PubMed]
Bhatia, S. K. , King, M. R. , and Hammer, D. A. , 2003, “ The State Diagram for Cell Adhesion Mediated by Two Receptors,” Biophys. J., 84(4), pp. 2671–2690. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Schematic diagram of the separation of molecularly bonded surfaces under linear displacement loading with velocity μ or linear force loading with velocity m. lb and lbind are the rest length of the receptor and the reacting radius of the binding site, respectively. δ denotes the separation between two surfaces, and Δδ is the distance between the free receptor and ligand molecule for the opened state and the deformation length of the bond for the closed state.

Grahic Jump Location
Fig. 2

Normalized number of closed bonds Nc/Nt versus time for different loading rates with a total number of bonds Nt = 100: (a) linear displacement loading and (b) linear force loading. The theoretical results (solid lines) show excellent agreement with the Monte Carlo simulations (symbols).

Grahic Jump Location
Fig. 3

Force acting on surfaces as a function of time for a total number of bonds Nt = 100 (lines: theoretical results; symbols: Monte Carlo simulations): (a) linear displacement loading and (b) linear force loading

Grahic Jump Location
Fig. 4

Rupture force of the adhesion cluster as a function of loading rate under linear displacement- and force-controlled loadings (lines: theoretical results; symbols: Monte Carlo simulations). μkLR represents the loading rate under displacement loading. In the only bond breaking regime, the rupture forces are plotted as dashed-dotted lines for displacement loading and dashed curves for force loading. Fc is a critical rupture force. For any loading rate, the rupture force never decreases below the critical value.

Grahic Jump Location
Fig. 5

At the equilibrium state of the receptor–ligand reactions, the surface force acts as a function of the stretched length of the receptor–ligand bond (lines: theoretical results; symbols: Monte Carlo simulations)

Grahic Jump Location
Fig. 6

Different regimes of the rupture force of the adhesion cluster in terms of loading rate under linear force loading (lines: theoretical results; symbols: Monte Carlo simulations). The dashed curve denotes the theoretical results based on the bond breaking model. The solid line denotes the theoretical results from the current reversible breaking/rebinding model.



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