How mechanical stresses shape the cytoskeleton of living cells

Modelling apsects of the living cell has always been complex. Here Karin John, Thomas Stöter and Chaouqi Misbah explain their recent work on how mechanical stresses can affect the actin network growth of the cytoskelton. You can read the full paper here.

Living cells have an outstanding property: depending on their environment they can polarize and migrate in a certain direction to perform specific tasks, for example fighting pathogens in the case of immune cells. Polarity and migration depend on the self-assembly of actin molecules (cytoplasmic proteins) into a complex interconnected network. The self-assembly of actin molecules creates naturally mechanical stresses in the network, which we show strongly influence the growth dynamics of the network. It is a major challenge to build a model that combines the actin network growth kinetics and the mechanical stresses in a consistent manner, and to analyze its far reaching consequences.

Left: Sketch of a filament network shell grown form the surface of a biomimetic bead. Residual stresses arise from the spherical growth geometry. Right: Schematic view of a growing dendritic actin network in contact with a nucleating surface, which contains activators of the cross-linker protein. Filament elongate at the barbed ends and shorten at their pointed ends. Cross-linking occurs via nucleation of new filaments from existing branches. Barbed ends further away from the surface are prevented from elongation by capping proteins. © 2016 IOP Publishing Ltd. Allr ights reserved.

Left: Sketch of a filament network shell grown form the surface of a biomimetic
bead. Residual stresses arise from the spherical growth geometry. Right: Schematic view of a
growing dendritic actin network in contact with a nucleating surface, which contains activators
of the cross-linker protein. Filament elongate at the barbed ends and shorten at their pointed
ends. Cross-linking occurs via nucleation of new filaments from existing branches. Barbed
ends further away from the surface are prevented from elongation by capping proteins. © 2016 IOP Publishing Ltd. Allr ights reserved.

In our paper published in JPCM, we develop such a model and exploit it in a simplified configuration, which has been studied experimentally: the self-assembly of actin networks on biomimetic beads. In this system the bead surface initiates growth of actin molecules suspended in solution into a network. Initially, the network grows in a symmetric manner around the bead before it develops spontaneously a polarity. This natural, spontaneous symmetry-breaking highlights the fact that polarity, besides complex biochemical actors within living cells, can be triggered solely by the coupling between growth kinetics and mechanical stresses.

Two fundamental problems arise in the theoretical description of this system. First, how can we evaluate the stresses built within the network (pre-stress), which depend on the growth history of the network and which should be consistent with a constitutive law? Second, what is the proper way to include these pre-stresses into the growth dynamics at the interfaces, without making ad hoc assumptions? Our understanding of symmetry-breaking phenomena relies on the thermodynamic consistent coupling between all physical effects involved. Therefore, we felt that the central question of a mechano-chemical coupling, which unifies material description and first principles of non-equilibrium linear thermodynamics, had not been addressed in a satisfying manner.

The model is developed in three steps. We first define the network geometry and introduce local linear interactions between the nodes of the network. Second, we derive a macroscopic constitutive law in the continuum limit (by using the so-called homogenization technique) that relates the stress to the strain. The resulting law is nonlinear, even though the network interfaces derive the growth kinetics and its relation to the actual mechanical stresses within the network. We show that (i) our approach automatically preserves thermodynamic symmetry-properties, which is not the case for the often cited rubber-band model and (ii) leads to a robust morphological instability of the network interfaces, causing an asymmetric evolution of the network shell. This study opens new and interesting perspectives for the basic understanding of polarity and migration of cells. In order to study motility, we plan to extend our approach to active gels following the same spirit.

Schematic representation of possible network shapes upon symmetry-breaking of the actin network shell. While the left most “comet”’-like shape is dominating, the dissipation relation suggest that dierent shapes might be observed under the same conditions, which has been shown experimentally. © 2016 IOP Publishing Ltd. All rights reserved.

Schematic representation of possible network shapes upon symmetry-breaking of
the actin network shell. While the left most “comet”’-like shape is dominating, the dissipation
relation suggest that different shapes might be observed under the same conditions, which has been shown experimentally. © 2016 IOP Publishing Ltd. All rights reserved.


About the authors

Karin John is a research associate at the CNRS in France and her research interests are Soft Matter systems at the interface of Biology, Physics, Chemistry and the Engineering Sciences. Examples of recently studied systems include the dynamics of droplets on vibrated substrates, the nonlinear rheology of semiflexible filament networks and complex patterns formed by chemical reactions in micro-emulsions. Thomas Stoeter is currently pursuing a Ph.D. thesis at the Technical University Dresden in Germany. Chaouqi Misbah is a research director at the CNRS in France.


CC-BY logoThis work is licensed under a Creative Commons Attribution 3.0 Unported License. Figures taken from Karin John et al 2016 J. Phys.: Condens. Matter 28 375101. © 2016 IOP Publishing Ltd. All rights reserved.



Categories: Journal of Physics: Condensed Matter

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