II: Mechanical Stresses in the Cell

Created by Gabrielle Steppic

mechanical stress
a fundamental quantity for understanding how a cell senses, generates, and responds to forces.

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TermDefinition
mechanical stressa fundamental quantity for understanding how a cell senses, generates, and responds to forces.
mechanical stresses are NOTpoint 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 microscopymeasurement of forces exerted by the cell on the substrate.
mechanical stresses of nuclear rupture during migrationcompression and shear of the nucleus
mechanical stresses of actin network under tensiontransmission of forces along the cytoskeleton
mechanical stresses of confined or rigid environmentsadaptation of cellular behavior to mechanical stress
continuous mediuma body assumed to be made of matter distributed homogeneously and without discontinuities, even at very small scales.
hypothesis of continuous mediumIt 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limits of continuous approach— At the molecular scale (nm), this assumption is no longer valid : a discrete (microscopic) description is required.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.
stressthe 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 stressdepends on the orientation of the surface may vary from one point to another within the material
biological example of stress - actin cortex of a celleach portion exerts internal forces on its neighbors. these forces can be compressive (pressure) or shear (contractility)
stress vectordenoted as T⃗ (⃗n), where ∆F⃗ is the force exerted across a small surface ∆S. measured in N/m2 (pascal, Pa)
stress decompositionT⃗(⃗n) = Tn⃗n + T⃗t
normal stressTn = T⃗ · ⃗n (tension if Tn > 0, compression if Tn < 0)
tangential stressshear T⃗
biological example of tangential stresslamellipodia of migrating cells generating this stress on their substrate. measured via traction force microscopy
stress tensor in 3Don 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 componentsσxx, σyy, σzz
tangential stress (shear) componentsσxy, σyz
biological example of shear stressthe 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 stressesσi 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 stresstension/compression in a single direction ex: a cell suspended between two micropillars
plane/biaxial stressex: a flat cell migrating on a 2D substrate
hydrostatic stressisotropic compression σ = −p · I p = internal pressure, all axes experience the same compression ex: osmotic pressure in a vesicle or spherical cell
pure shearinvolves only tangential components ex: cytoplasmic fluid under shear or a cell in viscous flow