migration steps
1. protrusion at the frontal edge
2. focal adhesions at the frontal edge
3. contraction at the rear edge
4. focal adhesions at the rear edge
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| Term | Definition |
|---|---|
| migration steps | 1. protrusion at the frontal edge 2. focal adhesions at the frontal edge 3. contraction at the rear edge 4. focal adhesions at the rear edge |
| active strains | - decomposition of the deformation gradient - intensity of the strain - cyclic manner - chemotaxis - pulsatile movement |
| active strains = | protrusions |
| decomposition of the deformation gradient is measured by | F = Fse * Fsa |
| intensity of the strain is measured by | Fsa = e0 |
| cyclic manner is measured by | Fsa = e0sin(2π * t/T) |
| chemotaxis is measured by | Fsa= e0sin(2π * t/T) * i(θ)*i(θ) iθ = cosθ(t)ix+sinθ (t)iy |
| ∂|Fsa|/∂t > 0 | protrusion |
| ∂|Fsa|/∂t < 0 | contraction |
| frontal and rear edge adhesion forces are measured by | regularized Heaviside functions |
| generalized Maxwell model | Fsa = polymerization/depoly. Os/Fse = actin filaments Ofe, Ffe = organelles Ofv, Ffv = cytosol |
| output of maxwell model | O = Os + Of F = Fs + Ff |
| numerics generalized maxwell model | 2 eqns ρa = Divx(JσF^-T) θ̇ + θ − θinfinity/τinfinity |
| obstacles | - regularized heaviside function - additional adhesion forces |
| 2 strategies to avoid obstacles | - velocity sensor / "run-and-tumble" - distance sensor / "look-and-run" |
| velocity sensor equation | Vc = 1/|Ωc|[differential]Ωc vdV |
| filtering the velocity helps to | avoid oscillations d^2Vcf/dt^2 + 2fωf * dVcf/dt + ωfVcf = Vc |
| in the "run-and-tumble" model | - if there is no obstacle: cell migrates towards θinfinity - if there is an obstacle: some rendition of regularized heaviside functions |
| pseudopods | - membrane protrusions - perpendicular to the membrane |
| splitting of existing pseudopods | zig-zag trajectory |
| new pseudopods at not active regions | any direction |
| measuring the active strain within migration with pseudopods | - sum of the strain in each pseudopod - gradient along the pseudopod axis - uniform inside the pseudopod - gradient + uniform |
| static pseudopods | |
| temporal sensing model | - protrusion - multiple simultaneous pseudopods - minimal distance between pseudopods (5 degrees) - contraction - pseudopod best oriented towards the source - same frame as the source |
| spatial sensing model | - protrusion; only one pseudopod at the time |
| durotaxis and polarity | isotropy-anisotropy of the cell |
| durotaxis - functions to analyze substrates | functions for stiff, soft, and viscous forces stiff: x < x0 soft: x > x0 |
| eqns to analyze equilibrium and constitutive law of the cell | |
| durotaxis - analyzing the solid phase of a cell | σse=1/Jse * FseSseF^Tse anisotropic hyperelastic saint-venant material |
| durotaxis - anisotropic hyperelastic saint-venant material | Sse = RCloc(R^TEseR)R^T R: found via rotation matrix; ploc = Rp Cloc: found via local elastic tensor Ese: found via green-lagrange tensor |
| durotaxis - in the local elastic tensor A and B come from their own fcns... | soft substrate: E0 = Ea stiff substrate: Ea = 0.1E0 |
| durotaxis - green-lagrange tensor - fluid phase | diff eqns |
| durotaxis - adhesion forces | functions i can't make sense of |
| active strain of cell in durotaxis | - radial protrusion and contraction - lamellipodium in the direction of migration d |
| durotaxis - soft vs. stiff substrate | there is a difference that can only be seen in images that i can't put here. slides 58-61 |
| durotaxis (discrete approach) | - cellular potts model - boltzmann probability function to validate the trial spin - hamiltonian function - net energy difference |
| cellular potts model | - 3D regular lattice -> center (x) and label σ(x) - subdomains with same label form discrete objects: medium, cell, substrate - iterative and stochastic reduction of energy - monte carlo-boltzmann dynamics |
| iterative and stochastic reduction of energy | hamiltonian function (H) |
| monte carlo-boltzmann dynamics | behavior of biological individuals |
| each timestep with in cellular potss model | - randomly chosen lattice site (xsource) - allocation of its spin σ(xsource) to one neighbours xtarget randomly selected |
| durotaxis | does not make sense to me |