Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

Reviewer #1 (Public Review):

The authors consider data by the Heisenberg group on rheological properties of non-confluent tissue in zebrafish embryos. These data had shown a steep increase and subsequent saturation in viscosity with cell density. The authors introduce a physical agent-based model of such tissues that accounts for the dispersion in cell size and the softness of the cells. The model is inspired by previous models to study glassy dynamics and reveals essential physical features that can explain the observed behavior. It goes beyond previous studies that had analysed the observations in terms of a percolation problem. The numerics are thoroughly done and could have a deep impact on how we describe non-confluent tissues.

A major weakness of the manuscript is the way it is written, which gives the impression to have been done rather carelessly. Several quantities are not properly introduced and at places physical jargon is used that makes the work difficult to access for readers without a background in soft matter.

Reviewer #2 (Public Review):

This paper explores how minimal active matter simulations can model tissue rheology, with applications to the in vivo situation of zebrafish morphogenesis. The authors explore the idea of active noise, particle softness and size heterogeneity cooperating to give rise to surprising features of experimental tissue rheologies (in particular an increase and then a plateau in viscosity with fluid fraction). In general, the paper is interesting from a theoretical standpoint, by providing a bridge between concepts from jamming of particulate systems and experiments in developmental biology. The idea of exploring a free space picture in this context is also interesting.

However, I'm still unsure right now though of how much it can be applied to the specific system that the authors refer to - which could be fixed either by considering other experimental systems/models reported in the recent literature or by doing the following theoretical checks:

- Take your current simulations and smoothly change the ratio of polydispersity from 8 to 0 to see exactly how much dispersity is needed to explain viscosity plateauing, and at which point the transition occurs.

- Cellular self-propulsion does not seem to play a role in zebrafish blastoderm, see Ref. [14]. Active noise has been proposed to play key roles in other systems and you could check whether such active noise could replace self-propulsion in your model, see for example Kim & Campas, Nat Phys, 2021.

- Could you simulate realistic rheological deformations to see how much they match both your expectation and the data?

Reviewer #3 (Public Review):

The authors successfully explain the sharp rise and subsequent saturation of the viscosity in dependence of cell packing fraction in zebrafish blastoderm with the help of a 2d model of soft deformable, polydisperse and self-propelled (active) disks. The main experimental observations can be reproduced and the unusual dependence of the viscosity on packing fraction can be explained by the available free area and the emergent motility of small sized cells facilitating multi-cell rearrangement in a highly jammed environment.

The paper is very well written, the results (experimental as well theoretical) are original and scientifically valid. This is an important contribution to understand rheological properties of non-confluent tissues linking equilibrium and transport properties.