mechanical stress
a fundamental quantity for understanding how a cell senses, generates, and responds to forces.
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| Term | Definition |
|---|---|
| mechanical stress | a fundamental quantity for understanding how a cell senses, generates, and responds to forces. |
| mechanical stresses are NOT | point forces |
| mechanical stresses ARE | forces distributed over surfaces or within volumes |
| examples of mechanical stresses in a cell | — An adherent cell exerts forces on its substrate in order to migrate. — The nucleus undergoes stresses when passing through narrow pores. — The mechanical environment influences cell differentiation (mechanotransduction). — The cytoskeleton continuously adapts to balance internal and external forces. |
| traction force microscopy | measurement of forces exerted by the cell on the substrate. |
| mechanical stresses of nuclear rupture during migration | compression and shear of the nucleus |
| mechanical stresses of actin network under tension | transmission of forces along the cytoskeleton |
| mechanical stresses of confined or rigid environments | adaptation of cellular behavior to mechanical stress |
| continuous medium | a body assumed to be made of matter distributed homogeneously and without discontinuities, even at very small scales. |
| hypothesis of continuous medium | It is assumed that at every point in space, physical quantities (such as force, density, or stress) can be defined and vary continuously in space. |
| continuous medium can be used to describe ______ _______ with use of differential calculus tools | — Spatial variations of stresses or velocities within a cell. — Local deformations induced by internal forces. — Matter fluxes, as in actin gels. |
| how is a cell described as a continuous medium? | the overall behavior (mechanical, diffusive, or flow-related) is described continuously |
| example of a cell as a continuous medium | the cell cortex can be modeled as a thin continuous layer with an active distributed tension |
| limits of continuous approach | — At the molecular scale (nm), this assumption is no longer valid : a discrete (microscopic) description is required. — In highly heterogeneous regions (e.g., filament networks), a continuous average may not accurately represent the physics. |
| stress | the force exerted by one part of a material on another, across an imaginary surface. it is defined as force per unit area. |
| internal mechanical interactions are described by what in a continuous medium? | by forces distributed across imaginary internal surfaces |
| variables of stress | depends on the orientation of the surface may vary from one point to another within the material |
| biological example of stress - actin cortex of a cell | each portion exerts internal forces on its neighbors. these forces can be compressive (pressure) or shear (contractility) |
| stress vector | denoted as T⃗ (⃗n), where ∆F⃗ is the force exerted across a small surface ∆S. measured in N/m2 (pascal, Pa) |
| stress decomposition | T⃗(⃗n) = Tn⃗n + T⃗t |
| normal stress | Tn = T⃗ · ⃗n (tension if Tn > 0, compression if Tn < 0) |
| tangential stress | shear T⃗ |
| biological example of tangential stress | lamellipodia of migrating cells generating this stress on their substrate. measured via traction force microscopy |
| stress tensor in 3D | on a 3D cartesian basis, a tensor is writting in matrix form σij each component: force per unit area in direction >> i which is exerted on a surface whose normal is oriented along >> j |
| normal stress components | σxx, σyy, σzz |
| tangential stress (shear) components | σxy, σyz |
| biological example of shear stress | the actin cytoskeleton of an epithelial cell experiences shear stresses during tissue stretching >> leading to fiber reorganization and polarization of the network along the main stress directions |
| stress tensors are symmetric, true or false? | true |
| principal stresses | σi a basis found in which the tensor is diagonal |
| tensor σ groups all ___ ? | stress components at a point |
| the stress applied on a surface oriented by n is given by? | T⃗(⃗n) = σ · ⃗n |
| uniaxial stress | tension/compression in a single direction ex: a cell suspended between two micropillars |
| plane/biaxial stress | ex: a flat cell migrating on a 2D substrate |
| hydrostatic stress | isotropic compression σ = −p · I p = internal pressure, all axes experience the same compression ex: osmotic pressure in a vesicle or spherical cell |
| pure shear | involves only tangential components ex: cytoplasmic fluid under shear or a cell in viscous flow |