Cell monolayers behave as active, orientationally ordered materials whose mechanical behavior can depart significantly from near-equilibrium assumptions. Conventional continuum descriptions often adapt equilibrium liquid-crystal frameworks, which can obscure explicitly nonequilibrium effects. To address this, the authors develop a minimal continuum formulation that explicitly encodes nonequilibrium symmetry breaking through the language of odd mechanics.
The work presents a two-dimensional continuum model constructed to capture the essential mechanical response of monolayer tissues while respecting broken symmetries characteristic of active systems. The model departs from equilibrium-based liquid-crystal constitutive assumptions and instead allows for antisymmetric, non-dissipative contributions to the viscous response that are permitted when time-reversal symmetry and certain spatial symmetries are broken. The paper frames the model as minimal: it includes the fewest ingredients necessary to generate experimentally observed nonequilibrium mechanical signatures in cell monolayers.
A central theoretical result is that nematic order in the monolayer can support an odd viscous modulus generated by broken time-reversal symmetry together with spatial anisotropy. Crucially, the authors emphasize that this odd viscous response does not require chirality. In other words, achiral systems with orientational order and nonequilibrium driving can exhibit viscous couplings that are antisymmetric in nature; these couplings produce stresses and flows distinct from those predicted by conventional viscous tensors inherited from equilibrium liquid-crystal theory.
The model is tested against experimental observables in Madin–Darby canine kidney (MDCK) monolayers. It reproduces the motion of half-integer topological defects and the spatial profiles of stress measured in these epithelial monolayers. By matching the sign and qualitative features of defect trajectories and surrounding stress fields, the model provides a parsimonious explanation for how antisymmetric viscous terms alter defect dynamics in real tissues.
Beyond MDCK data, the authors show that the model captures defect-associated patterns of cell density change reported in other systems. Specifically, the framework reproduces observations of cell accumulation and depletion near defects in neural progenitor cultures and in ovarian mesothelium. These phenomena, which couple orientational order, flow, and local cell rearrangement, are consistent with stresses and fluxes that arise from the model’s odd-viscous contributions.
To connect theory and data, the authors estimate components of the viscous-moduli tensor using measured stress, velocity, and orientation fields in MDCK monolayers. From these empirical fields they infer a nonzero odd modulus, providing direct evidence in the sampled data that an antisymmetric viscous coupling is present. The source reports these estimates and interprets them as support for the model assertion that achiral odd viscosity can exist in nematic cell monolayers under nonequilibrium conditions.
The study positions odd mechanics as a minimal theoretical framework that complements conventional active-nematic approaches. Because it explicitly incorporates nonequilibrium antisymmetric viscous responses, the odd-mechanics formulation can account for stress and flow signatures—such as defect motion and localized density changes—that may be difficult to capture within equilibrium-inspired constitutive choices. The authors suggest that odd mechanics provides a compact alternative for describing nonequilibrium phenomena in cell monolayers.
This work is presented as a bioRxiv preprint and has not been peer reviewed. The authors declare no competing interests. Funding sources reported include the U.S. National Science Foundation, the NIH Common Fund, and the International Human Frontier Science Program Organization. The preprint contains the detailed mathematical formulation, parameter choices, and quantitative fits; readers should consult the full manuscript for those specifics.
Notes on scope and limits of this summary: All statements above are drawn from the source preprint abstract and front matter. Specific equations, numerical parameter values, full datasets, and detailed estimation procedures are described in the full preprint but are not reproduced here verbatim.