Active T1 transitions in cellular networks

Abstract

In amorphous solids as in tissues, neighbor exchanges can relax local stresses and allow the material to flow. In this paper, we use an anisotropic vertex model to study T1 rearrangements in polygonal cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic bond tension and (ii) anisotropic cell stress. Interestingly, the two types of active stress lead to patterns of relative orientation of T1 transitions and cell elongation that are different. Our work suggests that these two realizations of anisotropic active stresses can be observed in vivo. We describe and explain these results through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the dynamic tissue and express the energy balance in terms of internal elastic energy, mechanical work, chemical work and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy. Graphic abstract

The role of non-affine deformations in the elastic behavior of the cellular vertex model

“…1b). This rigidity transition occurs at constant cell density and is driven by both active processes, such as fluctuations in cell-edge tension and cell motility [21][22][23][26][27][28][29][30] , as well as by geometric constraints 25,31 < l a t e x i t s h a 1 _ b a s e 6 4 = " e a u G s T r z F a 9 Z K P J 5 Y 5 c Q A p b K M r g = " > A A A B 7 H i c b V B N S 8 N A E J 3 U r 1 q / q h 6 9 L B a h p 5 K I q A c P B S 8 e K 5 i 2 0 I a y 2 W 7 a p Z t N 2 J 0 I J f Q 3 e P G g i F d / k D f / j d s 2 B 6 0 + G H i 8 N 8 P M v D C V w q D r f j m l t f W N z a x P k i 2 N n 5 M w q Q x I l 2 p Z C s l B / T u Q 0 N m Y a h 7 Y z p j g 2 q 9 5 c / M / r Z R h d B 7 l Q a Y Z c s e W i K J M E E z L / n A y F 5 g z l 1 B L K t L C 3 E j a m m j K 0 + V R s C N 7 q y 3 9 J + 7 z h X T a 8 + 4 t a s 1 7 E U Y Y T O I U 6 e H A F T b i D F v j A Q M A T v M C r o 5 x n 5 8 1 5 X 7 a W n G L m G H 7 B + f g G W e + N p g = = < / l a t e x i t > a = 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " r f a Y 0 q i O V M N J j H j c A V + U m 3 M 0 w 5 w = " > A A A B 7 n i c b V D L S g N B E O y N r x h f U Y 9 e B o O Q U 9 g V U U 8 S 8 O I x g n l A s o T Z y W w y Z H Z 2 m O k V Q s h H e P G g i F e / x 5 t / 4 y T Z g 0 Y L G o q q b r q 7 I i 2 F R d / / 8 g p r 6 x u b W 8 X t 0 s 7 u 3 v 5 B + f C o Z d P M M N 5 k q U x N J 6 K W S 6 F 4 E w…”

“…1b). This rigidity transition occurs at constant cell density and is driven by both active processes, such as fluctuations in cell-edge tension and cell motility, [21][22][23][26][27][28][29][30] as well as by geometric constraints. 25,31 Recent work by us and others has shown that even in the absence of fluctuations and topological rearrangements, vertex models exhibit a rigidity transition associated with geometrical frustration.…”

Remodeling of lipid-foam prototissues by network-wide tension fluctuations induced by active particles

“…Tissue remodeling and fluidization of biological tissue is enabled by exchange of neighboring cells by so-called T1 transitions. 28 A T1 transition is a topological rearrangement event, where one cell edge shrinks to a point and then expands in a perpendicular direction, resulting in the swap of neighboring cells. We observed a similar remodeling upon mechanically loading our structure (Movie M1, Fig.…”

On the origins of order

“…8,21 As addressed below, energy barriers that typify the jammed system-which by definition is solid-like, elastic, and static--are not to be confused with frictional energy dissipation, and associated metabolic demands as would be required to propel a migrating unjammed system. 22,23…”