Membrane flow per unit area - 1st Fick's eqn

J = −D∇C

Membrane evolution of concentration - 2nd Fick's equation

∂C/∂t = D∇^2C = D∆C

single-cell vs multicellular organisms

- single-cell = limited functions - multicellular = specialization and multitasking

another example of cellular components that can be measured

- membrane shell mechanics - shear stress - two-dimensional liquid (rearrangement)

membrane biaxial tension and area expansion modulus are measured via

area strain equations A = L^2 Ka = Eh/2 (1 − ν) 0.1 − 10 N/m

under biaxial tension and/or area expansion modulus the membrane is ____

effectively inextensible (up to 4-6%)

membrane bending stiffness can be measured with

Kb = Eh^3/12*(1 − ν^2) 10^-19 N/m

mitochondri

- provide energy to the cell via glucose and oxygen - protein synthesis, division, motility

nucleus

- 95% of DNA - stiffest component

cilia

- short - hundreds per cell - rotational movement

flagella

- long - less than 10 per cell - wave like and sinusoidal movement

cytoskeleton composed of

- microfilaments (actin): thinnest, 6 nm diameter - microtubules: hollow cylinders, very dynamic, 10 nm diameter - intermediate filaments: more stable, 20 nm diameter

cell migration occurs

- in response to external cues - to find nutriments - positive or negative migration

external cues

- chemotaxis - electrotaxis - thermotaxis - phototaxis - positive or negative migration - mechanotaxis - durotaxis - geotaxis

an example of electrotaxis is

wound healing

an example of thermo and phototaxis is

sperm guidance and plant growth

an example of mechanotaxis is

fluid shear stress

an example of durotaxis is

stiffness gradient

an example of geotaxis is

- microstructured substrates - cellular confinement

migration requirements

motility polarity adhesion

motility

intrinsic ability to move (motility phenotype)

polarity

ability to orient towards an external cue

adhesion

ability to adhere to fibers, substrate or neighbors

migration steps

1. protrusion 2. focal adhesion at the front 3. contraction 4. focal adhesion at the back

examples of protrusion

- lamellipodia - filipodia - pseudopodia - actin polymerization

lamellipodia

projection of frontal edge of the cell

filipodia

rodlike, thin protrusions with rounded ends

pseudopodia

broad and flat appendages

actin polymerization

brownian movement

brownian movement

fluctuation of membrane = fluctuation in actin filament

brownian fluctuation of membrane

2 scenarios if the membrane fluctuates leftward = nothing happens. actin is not polymerized if the membrane fluctuates rightward = F-actin is polymerized and extended

examples of adhesion

cell-cell cell-matrix cell-substrate focal adhesions

cell-cell adhesion

- maintain epithelial tissues - facilitate directed collective migration

cellular automata models

- discrete - each point of the lattice occupied or not by the cell - probability of occupation depending on external factors

semi-discrete models

- no mesh of the domain, but of the membrane - all points on the membrane are connected to the nucleus by springs - external signals

continuum models

- partial differential equations describing mechanical equilibrium - constitutive laws - stress-strain field influencing cell shape