[Paper Review] Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Indrajit Tah, Daniel Haertter+4 more|arXiv (Cornell University)|Dec 20, 2023

Cellular Mechanics and Interactions7 citations

TL;DR

This paper extends the standard vertex model with time-varying preferred perimeters and perimeter polydispersity to explain why the amnioserosa remains solid (no neighbor exchanges) during Drosophila dorsal closure despite high cell shape anisotropy. The model quantitatively matches experiments and predicts non-monotonic junction tension verified by laser ablation.

ABSTRACT

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster. During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, the aspect ratio of amnioserosa cells increases markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrinkage of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Motivation & Objective

• Explain why amnioserosa (AS) remains solid during dorsal closure despite high mean cell shape index.
• Develop a minimal vertex-model extension that incorporates time-varying preferred perimeters and perimeter polydispersity.
• Validate model predictions against experimental measurements of cell shape, orientation, and junction tension.

Proposed method

• Use a 2D vertex model for the AS as a rectangular sheet with periodic boundaries.
• Introduce a linearly decreasing preferred cell perimeter p0,i with closure progress ΔA(t).
• Incorporate initial polydispersity in preferred perimeters to reflect variability in q_i at onset.
• Simulate tissue deformation by quasi-static uniaxial changes and minimize energy after each step.
• Estimate junction tension τJ from the model and compare with laser ablation recoil data.
• Compare model outputs to experimental measurements of q, σq, Q, and junction recoil velocities.

Experimental results

Research questions

• RQ1 Can time-varying preferred perimeters and perimeter polydispersity explain the solid-like behavior of the AS during dorsal closure?
• RQ2 How do changes in p0,i and tissue anisotropy affect rigidity and neighboring rearrangements in the model?
• RQ3 Do model predictions of junction tension and cell shape distributions match laser ablation and imaging data?

Key findings

• The AS remains in a solid phase throughout closure, despite q > 3.81 (the standard model solid-fluid threshold).
• A linear decrease of the preferred perimeter p0,i coupled with perimeter polydispersity reproduces observed cell shapes and reduces neighbor exchanges.
• Junction tension τJ in the model increases up to ΔA ≈ 0.55 and then decreases, matching non-monotonic recoil velocities seen in laser cuts.
• Junction straightness S correlates with recoil velocity v_r, showing a similar non-monotonic trend as ΔA progresses.
• Phase diagram shows solid vs. fluid states with f_r ≈ f_c ≈ 0.66; the AS stays solid because f_r remains above f_c during closure.
• Percolation of nonzero-tension junctions (f_r > f_c) is maintained; removing the decreasing p0,i would lead to fluidization.