Figures and data in Generating active T1 transitions through mechanochemical feedback

Version of Record: May 4, 2023
Version of Record: May 3, 2023
Accepted Manuscript: April 24, 2023
Accepted Manuscript: April 11, 2023

Download
A two-part list of links to download the article, or parts of the article, in various formats.
Downloads (link to download the article as PDF)
- Article PDF
- Figures PDF
Open citations (links to open the citations from this article in various online reference manager services)
- Mendeley
Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)
Rastko Sknepnek

Ilyas Djafer-Cherif

Manli Chuai

Cornelis Weijer

Silke Henkes

(2023)
Generating active T1 transitions through mechanochemical feedback

eLife 12:e79862.

https://doi.org/10.7554/eLife.79862
- Download BibTeX
- Download .RIS
Cite
Share
CommentOpen annotations (there are currently 0 annotations on this page).

Figures
Tables
Additional files

8 figures, 2 tables and 1 additional file

Figures

Figure 1 with 2 supplements

Download asset Open asset

An active junction.

(A) An external pulling force of magnitude $T_{ext}$ induces tension $T$ in a cell–cell junction of length $l$ , which consists of passive viscoelastic and active components. The passive component consists of …

Figure 1—figure supplement 1

Download asset Open asset

Key ingredients of the single active junction model.

(A) The junction is modelled as a Maxwell element with stiffness $k$ and viscosity $η$ (and the relaxation timescale $τ_{v} = η / k$ ) connected in parallel with the active forcing, and an elastic barrier with …

Figure 1—figure supplement 2

Download asset Open asset

A linear chain of active junctions.

(A) Schematic of a linear chain for viscoelastic junctions with active tension feedback. The chain is formed by connecting in series the active viscoelastic elements shown in Figure 1—figure …

Figure 2 with 14 supplements

Download asset Open asset

An active T1 transition event.

(A) Top panel: the mechanical anisotropy in the initial state is produced by applying pulling forces (green arrows) in the horizontal direction to the left and right boundaries. Bottom panel: the …

Figure 2—figure supplement 1

Download asset Open asset

Schematic representation of the key ingredients in the vertex model with active junctions.

(A) The total force on vertex i can be expressed as a sum of forces due to junctions. For the junction $e$ , $C_{e, l}$ and $C_{e, r}$ are the cells to the left and the right, respectively, when looking in the …

Figure 2—video 1

Download asset

posterframe for video — Simulation of a passive system with applied horizontal pulling for $f_{pull} = 0.15 f^{*}$ .

Left panel - junction and cell myosin; right panel - junction tension, cells are coloured by type, active (dark grey), buffer (intermediate grey), passive (light grey). In this video activity is …

Figure 2—video 2

Download asset

Figure 2—video 3

Download asset

Figure 2—video 4

Download asset

Figure 2—video 5

Download asset

Figure 2—video 6

Download asset

Figure 2—video 7

Download asset

Figure 2—video 8

Download asset

Figure 2—video 9

Download asset

Figure 2—video 10

Download asset

Figure 2—video 11

Download asset

Figure 2—video 12

Download asset

Figure 2—video 13

Download asset

Figure 3 with 1 supplement

Download asset Open asset

Junction dynamics during the active T1 transition shown in Figure 2.

(A) Definition of central (red/blue – junction that disappears/appears), inner (orange), and outer (blue-green) shoulder junctions through the T1 transition. (B) Central junction: myosin, $m$ (green; …

Figure 3—figure supplement 1

Download asset Open asset

Continuous strain tensors through the active T1 transition, for $β = 0.8 f^{*}$ , $f_{pull} = 0.15 f^{*}$ , and the other parameters corresponding to Figure 2 and Figure 3.

(A) Statistical strain tensor $\hat{U}$ defined in Equation 20, with the initial undeformed state used as reference configuration. (B) Total strain, that is, integrated $\hat{V}$ tensor defined in Equation 24. (C)…

Figure 4

Download asset Open asset

Existence and timescales of T1 transitions in the vertex model with active junctions as a function of $f_{pull}$ and $β$ , averaged over $n = 32$ simulations with different realisations of the myosin noise.

(A) Probability of a central T1 transition. The red line is the 50% probability contour of any T1 occurring in the simulation. (B) Typical timescale for the T1 transition to occur, measured as the …

Figure 5

Download asset Open asset

Robustness of the T1 mechanism as a function of $τ_{v}$ and $τ_{m}$ for $β = 1.0 f^{*}$ and $f_{pull} = 0.15 f^{*}$ .

(A) Probability of a central T1 event, averaged over $n = 32$ simulations with different realisations of the myosin noise. The probability of any T1 event is 1 throughout. (B) Contraction time to collapse …

Figure 6 with 2 supplements

Download asset Open asset

Disordered active tissue at time $t \approx 700 t^{*}$ as a function of the magnitude of the pulling force $f_{pull}$ and activity $β$ .

The region of convergence–extension is at the centre of the diagram, around $β \approx 0.4 - 0.6 f^{*}$ and $f_{pull} \approx 0.1 - 0.3 f^{*}$ . The remaining parameters are the same as in Figure 2.

Figure 6—video 1

Download asset

Figure 6—video 2

Download asset

Figure 7 with 3 supplements

Download asset Open asset

Characterisation of convergence-extension in a random tissue patch.

(A) Snapshot of a random tissue patch for $β = 0.5 f^{*}$ and $f_{pull} = 0.2 f^{*}$ at $t \approx 700 t^{*}$ ,that is during the convergence–extension flow. Red arrow indicates that a constant pulling force is applied throughout the entire …

Figure 7—figure supplement 1

Download asset Open asset

Continuous strain tensors for the fully active tissue at $β = 0.5 f^{*}$ , $f_{pull} = 0.2 f^{*}$ , and the other parameters corresponding to Figure 2 and Figure 3.

(A) Statistical strain tensor $\hat{U}$ defined in Equation 20, with the initial undeformed state used as reference configuration. (B) Total strain, that is, integrated $\hat{V}$ tensor defined in Equation 24. (C)…

Figure 7—figure supplement 2

Download asset Open asset

Measuring T1 transitions in the fully active random patch.

A representative example taken from a sample of $n = 5$ simulations for $β = 0.5 f^{*}$ , $f_{pull} = 0.2 f^{*}$ . (A) Appearing and disappearing junctions as a function of simulation frame number and angle, before filtering. Inset: raw …

Figure 7—figure supplement 3

Download asset Open asset

T1 histograms in the parameter range where no convergence–extension occurs.

(A) Passive tissue at $β = 0$ pulled with $f_{pull} = 0.2 f^{*}$ , T1s are passive and aligned along pulling direction. (B) Active tissue at $β = 0.5 f^{*}$ with no applied force $f_{pull} = 0.0 f^{*}$ , here T1s are distributed isotropically. (C) …

Figure 8 with 3 supplements

Download asset Open asset

Analysis of the tissue flows in the early-stage chick embryo.

(A) Image of a typical early-stage chick embryo prior to the gastrulation (i.e. primitive streak formation). The primitive streak will form along the yellow dashed line. The direction of myosin …

Figure 8—figure supplement 1

Download asset Open asset

Region of interest in the anterior of the embryo.

(A) Integrated total strain ${\hat{ε}}^{tot} (t)$ and (B) elastic strain $\hat{U} (t)$ .

Figure 8—video 1

Download asset

Figure 8—video 2

Download asset

Tables

Table 1

Values of the parameters in the single-junction model.

Units: length ( $a$ ), time ( $t^{*} = ζ / k$ ), force ( $k a$ ).

Base
Parameter	Description
$k$	Spring constant
$a$	Barrier rest length
$ζ$	Friction with substrate
Model
Parameter	Description	Value range
$B$	Barrier spring constant	$0 - 0.2 k$
$T_{ext}$	Applied external tension	$0 - 1 k a$
$β$	Myosin activity	$0 - 3 k a$
$τ_{v}$	Viscoelastic time	$10 t^{*}$
$τ_{m}$	Myosin time	$10 t^{*}$
$m_{0}$	Myosin reference level	0.5
$T^{*}$	Threshold tension	$0.3 k a$
$k_{0}$	Slope of $m$ vs. $T$ at $T^{*}$	$2 / T^{*}$
$α$	Tension-independent myosin dissociation	1

Table 2

Values of the parameters used in the vertex model with active junctions.

Units: length ( $a$ ), time ( $t^{*} = ζ / (Γ + k)$ ), force ( $f^{*} = (Γ + k) a$ ).

Base
Parameter	Description
$a$	Hexagonal cell edge length
$Γ$	Perimeter modulus
$k$	Spring constant
$ζ$	Friction with substrate
Model
Parameter	Description	Value range
$κ$	Area modulus	$1 f^{*} / a^{3}$
$A_{0}$	Target cell area	$3 \sqrt{3} a^{2} / 2$
$P_{0}$	Target cell perimeter	$6 a$
$f_{pull}$	Pulling force	$0.0 - 0.3 f^{*}$
$β$	Myosin activity	$0.0 - 1.4 f^{*}$
$τ_{v}$	Viscoelastic time	$10^{0} - 10^{3} t^{*}$
$τ_{m}$	Myosin time	$10^{1} - 10^{3} t^{*}$
$T^{*}$	Threshold tension	$0.3 f^{*}$
$K_{0}$	Slope of $m$ vs. $T$ at $T^{*}$	$2 / T^{*}$
$m_{0}$	Myosin reference level	0.5
$M$	Total cell myosin	6
$f$	Variance of myosin fluctuations	1
$α$	Tension-independent myosin dissociation	0.1