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Mechanical stress inference for two dimensional cell arrays.

ABSTRACT: Many morphogenetic processes involve mechanical rearrangements of epithelial tissues that are driven by precisely regulated cytoskeletal forces and cell adhesion. The mechanical state of the cell and intercellular adhesion are not only the targets of regulation, but are themselves the likely signals that coordinate developmental process. Yet, because it is difficult to directly measure mechanical stress in vivo on sub-cellular scale, little is understood about the role of mechanics in development. Here we present an alternative approach which takes advantage of the recent progress in live imaging of morphogenetic processes and uses computational analysis of high resolution images of epithelial tissues to infer relative magnitude of forces acting within and between cells. We model intracellular stress in terms of bulk pressure and interfacial tension, allowing these parameters to vary from cell to cell and from interface to interface. Assuming that epithelial cell layers are close to mechanical equilibrium, we use the observed geometry of the two dimensional cell array to infer interfacial tensions and intracellular pressures. Here we present the mathematical formulation of the proposed Mechanical Inverse method and apply it to the analysis of epithelial cell layers observed at the onset of ventral furrow formation in the Drosophila embryo and in the process of hair-cell determination in the avian cochlea. The analysis reveals mechanical anisotropy in the former process and mechanical heterogeneity, correlated with cell differentiation, in the latter process. The proposed method opens a way for quantitative and detailed experimental tests of models of cell and tissue mechanics.

SUBMITTER: Chiou KK

PROVIDER: S-EPMC3355066 | biostudies-literature | 2012

REPOSITORIES: biostudies-literature

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Mechanical stress inference for two dimensional cell arrays.

Chiou Kevin K KK Hufnagel Lars L Shraiman Boris I BI

PLoS computational biology 20120517 5

Many morphogenetic processes involve mechanical rearrangements of epithelial tissues that are driven by precisely regulated cytoskeletal forces and cell adhesion. The mechanical state of the cell and intercellular adhesion are not only the targets of regulation, but are themselves the likely signals that coordinate developmental process. Yet, because it is difficult to directly measure mechanical stress in vivo on sub-cellular scale, little is understood about the role of mechanics in developmen ...[more]

PMID: 22615550

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Project description:Metamaterials, rationally designed multiscale composite systems, have attracted extensive interest because of their potential for a broad range of applications due to their unique properties such as negative Poisson's ratio, exceptional mechanical performance, tunable photonic and phononic properties, structural reconfiguration, etc. Though they are dominated by an auxetic structure, the constituents of metamaterials also play an indispensable role in determining their unprecedented properties. In this vein, 2D materials such as graphene, silicene, and phosphorene with superior structural tunability are ideal candidates for constituents of metamaterials. However, the nanostructure-property relationship and composition-property relationship of these 2D material-based metamaterials remain largely unexplored. Mechanical anisotropy inherited from the 2D material constituents, for example, may substantially impact the physical stability and robustness of the corresponding metamaterial systems. Herein, classical molecular dynamics simulations are performed using a generic coarse-grained model to explore the deformation mechanism of these 2D material-based metamaterials with sinusoidally curved ligaments and the effect of mechanical anisotropy on mechanical properties, especially the negative Poisson's ratio. The results indicate that deformation under axial tensile load can be divided into two stages: bending-dominated and stretching-dominated, in which the rotation of junctions in the former stage results in auxetic behavior of the proposed metamaterials. In addition, the auxetic behavior depends heavily on both the amplitude/wavelength ratio of the sinusoidal ligament and the stiffness ratio between axial and transverse directions. The magnitude of negative Poisson's ratio increases from 0 to 0.625, with an associated increase of the amplitude/wavelength ratio from 0 to 0.225, and fluctuates at around 0.625, in good agreement with the literature, with amplitude/wavelength ratios greater than 0.225. More interestingly, the magnitude of negative Poisson's ratio increases from 0.47 to 0.87 with the increase of the stiffness ratio from 0.125 to 8, in good agreement with additional all-atom molecular dynamics simulations for phosphorene and molybdenum disulfide. Overall, these research findings shed light on the deformation mechanism of auxetic metamaterials, providing useful guidelines for designing auxetic 2D lattice structures made of 2D materials that can display a tunable negative Poisson's ratio.

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Mechanical stress inference for two dimensional cell arrays.

Publications

Mechanical stress inference for two dimensional cell arrays.

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