Research Papers

Concurrent Rupture of Two Molecular Bonds in Series: Implications for Dynamic Force Spectroscopy

[+] Author and Article Information
Ji Lin

Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, Zhejiang, China

Yuan Lin

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

Jin Qian

Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, Zhejiang, China
e-mail: jqian@zju.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 17, 2017; final manuscript received September 3, 2017; published online September 21, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(11), 111007 (Sep 21, 2017) (7 pages) Paper No: JAM-17-1445; doi: 10.1115/1.4037884 History: Received August 17, 2017; Revised September 03, 2017

The immobilization of receptor–ligand molecules in dynamic force spectroscopy (DFS) often relies on an extra noncovalent linkage to solid surfaces, resulting in two barrier-crossing diffusion processes in series and concurrent bond dissociations. One outstanding theoretical issue is whether the linkage between the immobilizer and biomolecule is sufficiently strong during repeated force ramping in the measurements and how it might influence the interpretation on receptor–ligand kinetics. Following the classical framework by Kramers, we regard each dissociation process as a flux of probabilistic bond configuration outward over an energy barrier in the coordinated energy landscape, and solve the two coupled boundary value problems in the form of Smoluchowski equation. Strong kinetic and mechanical coupling is observed between the two molecular bonds in series, with the results showing that involving a noncovalent linkage in DFS can obscure the unbinding characteristics of the receptor–ligand bond. Our approach provides a quantitative assessment to the hidden effects of having a fragile molecular anchorage in DFS and allows the corrected interpretation on receptor–ligand dissociation kinetics in the case.

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Grahic Jump Location
Fig. 1

Problem description. (a) Schematic of DFS experiments characterizing of a receptor–ligand bond, where a noncovalent linkage is involved to immobilize the protein complex under pulling. Schematic is not drawn to scale. (b) Energy landscapes of the two molecular interactions in series along the corresponding reaction coordinates of bond dissociation. The rates of two simultaneous dissociation processes can be calculated from the native profile of noncovalent interactions in addition to the extra energy stored in the harmonic transducers induced by the pulling velocity v.

Grahic Jump Location
Fig. 3

Survival probability versus time for the two molecular bonds in series with different values of c1/c2, i.e., the ratios in depth of the bond energy wells

Grahic Jump Location
Fig. 2

Evolving probability distributions for the bonding status of bond 1 and 2 when (a) c1/c2=1 and (b) c1/c2=1.2

Grahic Jump Location
Fig. 4

The actual separation of individual bonds during the ramping process at different ratios of bond strength

Grahic Jump Location
Fig. 5

(a) Nominal survival probability combining the contributions from both bonds versus time and (b) probability distribution of rupture forces of the two bonds in series. The value of c1/c2 varies from 0.8 to 1.2, in comparison with the case with permanent immobilizer.

Grahic Jump Location
Fig. 6

Force-dependent dissociation rate converted from the rupture force histograms for various combinations of bond characteristics: (a) the depth ratio c1/c2 and (b) half-width ratio a1/a2 of the bond energy wells, indicating the significant effects of additional molecular linkage on the interpretation of receptor–ligand dissociation rate



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