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Noncovalent bonds dictate cell rheology

Ning Wang's picture

Over the last ten years, a peculiar behavior of living cells is revealed: their modulus increases weakly with loading frequency (the so-called weak power law behavior) (for a pure elastic solid, the slope is 0; for a viscous fluid, the slope is 1).  The underlying mechanism is not clear at all; although a phenomenological soft glass rheology model (a model based on a disordered structure system) has been proposed, it cannot explain the multi-power laws at different loading frequencies (see Stamenovic et al, Biophys J Letter, 2007). 

In the recent Biophys J paper, we have revealed the molecular mechanism of cell rheology.  Basically, when the loading frequency is much higher than the intrinsic protein-protein noncovalent bond characteristic dissociation rate, it is in the nonequilibrium regime; more and more bonds are trapped at the bond state, resulting higher stiffness or modulus.  when the loading frequency is much lower than the intrinsic rate, the behavior switches toward the "equlibrium" state, resulting a different and higher power law slope.  Living cells data on embryonic stem cells and their differentiated counterparts are consistent with the model prediction.   The model is also consistent with published papers from different labs over the last several years.  For details, see http://www.biophysj.org/cgi/rapidpdf/biophysj.108.139832v1

Comments

Dear Prof. Wang,

The simple adheson cluster model and its result is very interesting, and explains multi power law at the nonconvalent bonds. There also exists multi power law in the response of adhered cells to external strain, characterized by characteristic time of cell reorientation, as shown in Jungbauer et al. 2008. What's the difference in their mechanism in the case of cell subject to dynamic strain, even these are different problems. This problem is so attractive, I think there's something similar underneath, but it's not clear in my brain now. The frequency of exteranl stimulus or loading velocity plays strong role on the cells, and we use a similar adhesion cluster model to study focal adhesion subject to external strain on the substrate, pulished as Kong et al. 2008. In our work, the external time sclae (frequency) is related to internal time scale (i.e., forward reaction of integrin-ligand bonds), and then dertermines rebinding process of integrin and ligand molecules.

Best wishes,

Dong 

 

Jungbauer et al. 2008.

http://www.biophysj.org/cgi/content/abstract/95/7/3470

Kong et al. 2008

http://www.biophysj.org/cgi/reprint/95/8/4034

 

Ning Wang's picture

Dong, Thank you for your comments.  Certainly your paper and ours are consistent with each other.  To help understand the history of the problem, I would like to point out a few issues:

1.  All published work so far (see J Crocker et al, PNAS, 2006; F. Gallet et al, 2006; D Navajas et al, 2003; Fredberg group, 01-07) suggests that it does not matter how one probes the cell: either from cell surface or from inside the cytoplasm, the cells still exhibit weak power laws, although the magnitudes of the stiffnesses vary greatly.  All these data suggest that this behavior is not limited to cell adhesion molecules, but maybe applicable to all non-covalent interactions.

 2.  Our work shows that one needs not to invoke the disordered and metastable structure of the soft glass rheology (SGR) proposed by Sollich (98), nor one needs to invoke a large number of time constants (see B. Fabry et al, 01) to achieve the power law behavior.

 3.  Our data essentially excluded the possibility of these proposed models for the power laws: polymer entanglement, jamming, crowding, caging, co-valent bonds.  Some of these may be associated with the power law, but they are not essential for the power law behavior.

4.  A recent paper by D Mooney lab that shows crosslinking the cell aggregates with alginate via integrins also show two power laws; the behavior that transits from a more fluid-like (the cells and alginate not crosslinked) to a more solid-like after crosslinking is consistent with the more ordered structure exhibiting power laws, a major departure from Sollich's disordered structure model.

5.  Intrinsic characteristic time constants of the crosslinking proteins are the key to set the transition frequency in living cells.  See our discussion. 

 

Thank you very much, your comments are very useful for my understanding

Dong  

 

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