Entanglement metric and percolation threshold in cellularized tangles under stretch*

Intermediate filaments (IFs) are a major class of cytoskeletal biopolymers, along with actin filaments (AFs) and microtubules (MTs). While AFs are widely recognized to largely control cell mechanics, it has been shown that IFs crucially contribute to the resilience of cell monolayers under severe stretch [Latorre et al, Nature, 2018]. AFs and MTs turnover quickly and form mechanically stable networks through crosslinking, whereas IFs are weakly crosslinked and turnover very slowly. Based on these features, we hypothesize that IFs can form stable tissue-wide networks thanks to physical entanglement. To examine this, we seek for a link between the degree of entanglement of a cellularized tangle, i.e. a set of open chains with the ends constrained to the enclosing cell boundaries, and the emergent mechanical response of the network under stretch.

 

Combining theoretical and computational modeling, we propose a topological measure of entanglement that defines a percolation threshold for the mechanical response of a cellularized tangle of extensible filaments [Pensalfini et al, arXiv:2206.04043]. Above such threshold, cell stretching leads to stiffening thanks to IF self-organization into a mechanically optimal 'star-shaped' arrangement, where thick bundles radiate from a central tight tangle, in close agreement with experimental observations in superstretched epithelial sheets.