examples of confined migration

tumorogenesis sub-cellular and sub-nuclear pores tunnel-like trucks

tumorogenesis

from primary to secondary tumor metastatis development

sub-cellular and sub-nuclear pores

from 1 μm to 10 μm

tunnel-like trucks

3 μm to 30 μm in width and from 100 μm to 600 μm in length

confined migration in tumors

exhibits aligned, bundled collagen fibers fibrillar collagen along or within blood vessels has epithelial or endothelial surfaces encased in muscle fibre

experimental approaches

- biomimetic hydrogels - micro-channels - grooved substrates - microcontact-printed and micro-patterned lines - vertical confinement devices - micropost arrays

biomimetic hydrogels

3D gels formed of extracellular matrix proteins or chemically produced polymers

micro-channels devices

rectangular cross-sections with widths and heights between 3 μm and 50 μm

grooved substrates

substrates with parallel, rectangular or trapezoidal troughs that run unidirectionally for lengths much greater than the cell diameter

microcontact-printed and micro-patterned lines

thin stripes or patterns of a polymer are deposited on a 2D surface that is otherwise non-adhesive to cells

vertical confinement devices

- cells plated on a 2D substrate are sandwiched beneath a PDMS roof - free to migrate laterally but confined at their basal and apical surfaces

micropost arrays

defined but discontinuous barriers to cell migration in the form of vertical posts

nucleus role in confined migration

- most voluminous - stiffest - nucleoplasm (≅ 25 Pa) + lamina (≅ 3000 Pa) - critical treshold: 7 μm in collagen gels - modulation of stiffness - knockdown of lamin A

determinants of confined migration

confined cells high cellular adhesion high degree of cellular contractility linear elastic matrix fibroblasts present actin polymerization inhibited

nucleus mechanics

o mechanical stress and strain o localized ruptures of the lamina - DNA damage o apoptosis without repair

mechanicall model of confined migration has

o 2D geometry o cell modeled as a hybrid continuum - organelles represented by characteristic functions o deformation gradient decomposition o generalized Maxwell model o micro-channel with rigid walls

constitutive law of confined migration

o generalized Maxwell model o nucleus - nucleoplasm (fluid phase) - lamina (solid phase) o cytoplasm - cytosol (fluid phase) - membrane (solid phase) o polymerization and depolymerization in the cytosol

some mathematical equations that can be used to model confined migration

- global equilibrium - active strains - adhesion forces - micro-channels contact force

micropillared substrate

o quantify nuclear forces and self strain o is gravity driving nucleus movement ? o is the nucleus pushed or pulled ? -> contractile fibers - above the nucleus: perinuclear actin cap (PAC) - around the pillar beneath the nucleus

spreading of a micropillared substrate

o passive phase - cell settles under gravity action - deforms depending on its stiffness o active phase - protrusion and contraction

constitutive law of micropillared substrate is measured with

o generalized Maxwell model - solid and fluid phases - active strains in the cytosol

some forces that can be measured to mathematically model migration on a micropillared substrate are

gravity contact force adhesive-spreading force

active strains of confined migration

- two cellular regions results: nucleus displacement and inverted gravity has negligible effect