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During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single-cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate, in particular, the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming or unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening, and discontinuous shear thickening. These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.
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Continuum theory for confluent cell monolayers: Interplay between cell growth, division, and intercalation
Mechanical forces generated by dynamic cellular activities play a crucial role in the morphogenesis and growth of biological tissues. While the influence of mechanics is clear, many questions arise regarding the way by which mechanical forces communicate with biological processes at the level of a confluent cell population. Some answers may be found in the development of mathematical models that are capable of describing the emerging behavior of a large population of active agents based on individualistic rules (single-cell response). In this perspective, the present work presents a continuum-scale model that can capture, in an average sense, the active mechanics and evolution of a confluent tissue with or without external mechanical constraints. For this, we conceptualize a confluent cell population (in a monolayer) as a deformable dynamic network, where a single cell can modify the topology of its neighborhood by swapping neighbors or dividing. With this description, we use concepts from statistical mechanics and the transient network theory to derive an equivalent active visco-elastic continuum model, which can recapitulate some of the salient features of the underlying network at the macroscale. Without loss of generality, the cell network is here assumed to follow well-known rules used in vertex model simulations, which are: (a) cell elasticity based on its bulk and cortical elasticity, (b) cell intercalation (or T1 transition), and (c) cell proliferation (expansion and division). We show, through examples and illustrations, that the model is able to characterize complex cross-talk between mechanical forces and biological processes, which are likely to drive the emergent growth and deformation of cell aggregates.
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- Award ID(s):
- 2135057
- PAR ID:
- 10477410
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of the Mechanics and Physics of Solids
- Volume:
- 181
- ISSN:
- 0022-5096
- Page Range / eLocation ID:
- 105443
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jmps.2023.105443
