Temporal Variation in Single-Cell Power-Law Rheology Spans the Ensemble Variation of Cell Population

Abstract

Changes in the cytoskeletal organization within cells can be characterized by large spatial and temporal variations in rheological properties of the cell (e.g., the complex shear modulus G). Although the ensemble variation in G of single cells has been elucidated, the detailed temporal variation of G remains unknown. In this study, we investigated how the rheological properties of individual fibroblast cells change under a spatially confined environment in which the cell translational motion is highly restricted and the whole cell shape remains unchanged. The temporal evolution of single-cell rheology was probed at the same measurement location within the cell, using atomic force microscopy-based oscillatory deformation. The measurements reveal that the temporal variation in the power-law rheology of cells is quantitatively consistent with the ensemble variation, indicating that the cell system satisfies an ergodic hypothesis in which the temporal statistics are identical to the ensemble statistics. The autocorrelation of G implies that the cell mechanical state evolves in the ensemble of possible states with a characteristic timescale.

Spatiotemporal dynamics of single cell stiffness in the early developing ascidian chordate embryo

“…Previous studies have reported that the number distribution of cell mechanical properties exhibits a large variation in single cells 41 , 42 and the cell stiffness and tension are very broadly varied over a long intercellular distance in a cell monolayer 43 – 46 . In contrast, the embryonic cells in the vegetal hemisphere exhibited broad spatiotemporal heterogeneity occurring at the single-cell level.…”

Fractional viscoelastic models for power-law materials

“…with an empirically derived model known as the structural damping (or hysteretic damping) model 33,[137][138][139][140][141][142] whose complex modulus is given by:…”

Spontaneous Spatial Correlation of Elastic Modulus in Jammed Epithelial Monolayers Observed by AFM

“…where F is the loading force, d is the indentation depth, and n is the Poisson's ratio of the cell, assumed here to be 0.5 (16,(18)(19)(20)34), which corresponds to a perfectly incompressible material (33). We estimated E from the force-indentation curve in the region of d < 0.6 mm (see Fig.…”

“…The intracellular stiffness is a fundamental cell mechanical property. Previous studies of isolated single cells adhered to a substrate revealed that the intracellular stiffness-that is, the Young's modulus, E-measured by atomic force microscopy (AFM) is mainly dominated by actin cytoskeletal structures (16)(17)(18)(19) and can change in response to the rigidity of the substrate to which the cells adhere (20,21); specifically, the intracellular stiffness increases with increasing substrate rigidity. However, little is known about how the intracellular stiffness changes in response to neighboring cells in a cell monolayer system.…”

“…However, little is known about how the intracellular stiffness changes in response to neighboring cells in a cell monolayer system. Furthermore, although single cells are known to exhibit large cell-tocell variations in the cell stiffness (18,19), the cell-to-cell variation in the intracellular stiffness in a cell monolayer system is not well understood.…”