Epithelial Tissues as Active Solids: From Nonlinear Contraction Pulses to Rupture Resistance

Shahaf Armon, Matthew S. Bull, Avraham Moriel, Hillel Aharoni, Manu Prakash

Posted on: 11 July 2020

Preprint posted on 16 June 2020

Understanding epithelial tissue mechanics.

Selected by Mariana De Niz

Categories: biophysics, cell biology


Epithelial cells form confluent layers and are thus inherently mechanically coupled. Epithelial tissues in many contexts can be viewed as soft active solids. Their active nature is manifested in the ability of individual cells within the tissue to contract and/or remodel their mechanical properties in response to various conditions. Little is known about the emergent properties of such materials. Specifically, how an individual cellular activity gives rise to collective spatiotemporal patterns is not fully understood.Theoretical works suggest models to explain the contractile patterns, models that include mechanical alongside chemical fields, diffusion, or active transport. Recently, Armon et al (1) reported the observation of ultrafast contraction dynamics in the dorsal epithelium of T. adhaerens while the animal is freely moving, including traveling pulses that propagate across the entire animal. They speculated these propagate via mechanical fields. This early-divergent animal has no reported muscles, neurons or synapses, and its epithelium has no gap junctions that can support cell-cell transport. Moreover, since propagation speeds are extremely fast, it excludes slower processes (such as transcription) from being involved. This raises the speculation that mechanics governs the contraction propagation. T. adherens is an ideal system to investigate epithelium dynamics. Due to the animal’s erratic, locally-driven ciliary locomotion, the tissue is found constantly under alternating tensile/compression stresses. The main candidate thought to be involved in such fast contraction dynamics is calcium, however, it is unclear how one contraction triggers the other during a contraction pulse in an early animal that lacks synapses or gap junctions. In their present work, Amon et al (2) propose a mechanical model for inter-cellular transmission of contraction in epithelia.

Figure 1. Modeling epithelium with cellular EIC (extension-induced-contraction). 1D and 2D settings of simulations. (From Ref 2).

Key findings and developments

The authors begin by looking at the recently-measured contraction profile in T. adherens (1), which shows the strain evolution of a single cell during a single contraction event. On average, during this contraction event, the cell area increases gradually to a critical point, then abruptly decreases to about half its initial value, and then relaxes towards its initial area. Activation of contraction in response to stretch – is sufficient to give rise to nonlinear propagating contraction pulses. The contraction’s reach suggests that it includes a force and time scale different from the viscoelastic ones. As the contraction seems to happen at a critical cell size, an additional scale is required to describe the extension need for activation. Together, these are the three minimal requirements for the minimal numerical model proposed.

Theoretical considerations include a mechanical circuit that can be found in one of two modes: an excitable mode (whereby cells contract only in response to external stretch); or an oscillatory mode (whereby contraction events oscillate spontaneously without any extra stimulation).

The authors modelled a single cell as an overdamped elastic entity connected in parallel to an active contractile unit. Using a set of 3 non-dimensional parameters: normalized time, normalized force and normalized strain – the authors show that when the system satisfies these criteria, a pulse propagates indefinitely in the tissue with fixed speed, while in the absence of these requirements, the initial stretch decays, and bulk cells stay at their rest lengths indefinitely. The model explains observed phenomena in T. adhaerens (e.g. excitable or spontaneous pulses, pulse interaction) and predicts other phenomena (e.g. symmetric strain profile, “spike trains”).

The authors then explore differences between 1D and 2D settings, and show that a unique feature of the 2D case is the fact that the system is prone to mechanical frustration. In 2D, the rim cells can only release stresses in the radial axis, but not in the azimuthal one. As a result, rim-cells are not beating like isolated cells. Although rim cells relax faster than bulk cells, they still need to ‘wait’ for the entire system to relax before they can do so too. Moreover, bulk cells relax slowly due to viscosity and due to the energy wells they reach at concave shapes. This results in long intervals of quiescence.

An active two-dimensional sheet dynamically distributes external loads across its surface, facilitating tissue resistance to rupture due to cellular strain. Adding a cellular softening-threshold further enhances the tissue resistance to rupture at cell-cell junctions. As cohesion is key for epithelial physiology, the authors discuss that the model hereby presented, may be relevant to many other epithelial systems, even if manifested at different time/length scales.


What I like about this preprint

I like that the work explores dynamic phenomena in epithelial tissues from a mechanical point of view. I think having an interdisciplinary approach to study phenomena in living organisms/tissues is necessary for gaining a deep understanding of such phenomena.


Open questions 

  1. How do single cell extension-induced-contraction vary across cell types and tissues? How is this relevant to rupture resistance?
  2. How does your model predict interactions between different cell populations within the same tissue?
  3. You mention your model might be relevant to understanding epithelial tissue function under challenging conditions such as lung, gut and vasculature. Two questions regarding this topic are a) whether it is possible to predict how tissues/cells will be altered in transient disease conditions such as infection- and therefore how this affects rupture resistance; and b) since you mention vasculature, can you model also how rupture resistance varies with age, and how vessel aging/stiffening can be better understood in terms of biophysics, and whether vascular accidents can be predicted using your model?



  1. Amon, S. Ultrafast epithelial contractions provide insights into contraction speed limits and tissue integrity, PNAS, 2018
  2. Amon, S. Epithelial tissues as active solids: from nonlinear contraction pulses to rupture resistance, bioRxiv, 2020




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