Research Papers

Adhesive Dynamics

[+] Author and Article Information
Daniel A. Hammer

Departments of Bioengineering and
Chemical and Biomolecular Engineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: hammer@seas.upenn.edu

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received October 8, 2013; final manuscript received December 30, 2013; accepted manuscript posted January 2, 2014; published online February 5, 2014. Editor: Victor H. Barocas.

J Biomech Eng 136(2), 021006 (Feb 05, 2014) (10 pages) Paper No: BIO-13-1472; doi: 10.1115/1.4026402 History: Received October 08, 2013; Revised December 30, 2013; Accepted January 02, 2014

Adhesive dynamics (AD) is a method for simulating the dynamic response of biological systems in response to force. Biological bonds are mechanical entities that exert force under strain, and applying forces to biological bonds modulates their rate of dissociation. Since small numbers of events usually control biological interactions, we developed a simple method for sampling probability distributions for the formation or failure of individual bonds. This method allows a simple coupling between force and strain and kinetics, while capturing the stochastic response of biological systems. Biological bonds are dynamically reconfigured in response to applied mechanical stresses, and a detailed spatio-temporal map of molecules and the forces they exert emerges from AD. The shape or motion of materials bearing the molecules is easily calculated from a mechanical energy balance provided the rheology of the material is known. AD was originally used to simulate the dynamics of adhesion of leukocytes under flow, but new advances have allowed the method to be extended to many other applications, including but not limited to the binding of viruses to surface, the clustering of adhesion molecules driven by stiff substrates, and the effect of cell-cell interaction on cell capture and rolling dynamics. The technique has also been applied to applications outside of biology. A particular exciting recent development is the combination of signaling with AD (so-called integrated signaling adhesive dynamics, or ISAD), which allows facile integration of signaling networks with mechanical models of cell adhesion and motility. Potential opportunities in applying AD are summarized.

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Fig. 1

Idealized rendering of a leukocyte in the original version of adhesive dynamics, where the leukocyte was modeled as a hard sphere with adhesive springs. The net motion of the cell comes from a balance of forces, easily derived from tracking the endpoints of each adhesion molecule. Figure reproduced from Ref. [1] with permission from Elsevier.

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Fig. 2

The state diagram for leukocyte adhesion, reprinted from Ref. [13] with permission from the National Academy of Sciences. The dynamic states of leukocyte adhesion are calculated as a function of the unstressed off rate (kro) and reactive compliance (γ). Different dynamic states of adhesion are realized, including firm adhesion, transient or rolling adhesion, and no adhesion. Symbols represent independent measurements of kro- γ for molecules known to support rolling, consistent with the model predictions.

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Fig. 3

A simulation of a single particle rolling in Couette flow on a P-selectin surface, reproduced from Ref. [15] with permission of Elsevier. Panel (a) shows the distribution of bonds in the reference frame of the cell, which is moving from left to right. Bonds are line segments that are color coded, where red indicates bonds that are under strain. Bond are convected from the back to the front of the contact zone. Panel (c) shows the total number of bonds as a function of time, which fluctuates. The number of bonds needed to support rolling is very small. Panel (b) shows the rolling velocity, which fluctuates and is anti-correlated with the bond number.

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Fig. 4

The leukocyte activation diagram, calculated in Bhatia and Hammer [26]. This diagram calculates the state of adhesion as a function of the properties of integrin receptors, including the on rate, the density, and the strength of integrins that are necessary to stop a leukocyte. Any combination of these parameters to the right of the dotted line indicates a cell will adhere firmly if the reactive compliance is below the number indicated on the line, or above the integrin density or greater than the on rate associated with the line. Integrin activation is tantamount to increasing integrin density (such as increased expression of Mac-1), increasing the integrin on-rate (moving up on this diagram) or moving the dotted line to the left, which captures a larger region of the diagram in firm adhesion. Reprinted from [26] with permission of the National Academy of Sciences.

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Fig. 5

Integrated adhesive dynamics (ISAD) for the simulation of T-cell adhesion under flow. Panel (a) shows the reaction pathways that are simulated as a part of ISAD, starting with the chemokine and ending at the activation of the integrin into a high strength state. Panel (b) shows the progressive accumulation of each important molecule, starting from the chemokine and culminating in the ligation of Rap1 at the integrin. Panel (c) shows the spatio-temporal dynamics of molecular engagement from adhesion molecules to signaling molecules in the vicinity of the contact zone (the circle) during the progressive activation of the cell. Image taken from Ref. [32] with permission of the American Chemical Society.

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Fig. 6

Simulation by Jadhav and coworkers [35] on the effect of macroscopic deformation on the progressive rolling and firm adhesion of a cell, modeled with an elastic shell of varying stiffness. The calculations account for the deformation, spreading, increased contact zone and decreased rolling velocity for more deformable cells in higher shear fields. Reprinted from [35] with the permission of the authors and Elsevier.

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Fig. 7

A simulation of the organization of TCR-gp120 bonds during the docking of HIV to the cell surface. Color coding indicates TCR that are bound to the same virus triskelion. The simulations indicate that after 12 s, the disorganized binding has minimized energy to lead to the formation of several well organized trimers. Figure reproduced from Ref. [57] with the permission of Elsevier.

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Fig. 8

AD simulation of the clustering of integrin receptors against elastic substrate with a glycocalyx. Panel (a) shows a schematic of the simulation, and panel (b) shows the progressive accumulation of receptor clusters on the adhesive interface, driven by resistance from both the glycocalyx and the stiffness of the substrate. Image taken from Ref. [53].




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