Lecture 7: 26/09 Flashcards
What is the formula the bulk modulus?
The Bulk Modulus is K
K = -V(dP/dV)
What does the bulk modulus measure?
The bulk modulus measures the change in volume in response to applied pressure
How can we apply a uniform compressive stress to a cell?
Osmotic stress
For PEG do higher or lower molecular weights exert greater osmotic pressures?
Higher PEG molecular weights exert a greater osmotic pressure
What does pressure scale with in terms of PEG?
Pressure scales with concentration and molecular weight of PEG
How are cell moduli and volume related?
Inverse relationship
As the cell volume decreases, the cell moduli increase
What is phi?
volume fraction (i.e., density (Vmin/V))
What is the relationship between the shear modulus and phi?
Regardless of cytoskeletal state, compressed cells have a similar moduli
Shear modulus increases with volume fraction, all treated types converge to the same shear modulus value
At low volume fractions, cytoskeletal differences impact the shear modulus
Explain how the viscosity changes as a function of the normalized volume fraction between hard spheres vs cells? How are cells similar to colloidal glass?
Viscous increase in cells follows colloidal glass transition of a jammed material
How do changes in the cell state influence compression stiffening?
Changes: substrate stiffness, actin polymerization, myosin activity, or cell spreading
All of these changes equally impact the compression stiffening
Compressing the cell volume through any means results in the same relationship with the shear modulus
What does the line on the graph with the number tell us?
It provides a scaling factor
(for instance in G’ vs cell volume, it scales G’ ~ V^(-2) )
What is the cell modulus impacted by, besides strain-stiffening?
Cell modulus is not just strain-stiffening as learned in rheology, but also impacted by volume fraction (density of polymers)
Cell Universal Scaling:
change in G’ ~ change in density^2
G’~1/V^2
How do shear and bulk moduli differ with cell volume?
Bulk modulus scale is x1000 times more than shear modulus as cell volume is changed
(i.e., shear modulus is easier to change than bulk)
How do all moduli relate to cell volume?
All moduli have the same relationship with the cell volume, just at different magnitudes
Cell moduli increases as the volume decreases
What is Poisson’s ratio?
Nu = poissons ratio
How to calculate the shear modulus from bulk modulus
Summarize what osmotic stress using PEG can be used for?
Compress object uniformly
Measure their volume change
Calculate their Bulk Modulus
This can be used to infer shear or Young’s moduli
Summarize what micropipette aspiration is used for?
Allows serial direct characterization of time-dependent bulk and shear moduli of small to large structures
(measures the time-dependent bulk and shear modulus)
What is the equation that relates shear modulus to bulk modulus?
G = 3/2 [K(1-2n)/(1+n)]
What does lamin do within the cell?
Lamins provide structural support in the cell membrane
What is the definition of compliance?
J(t) = Delta strain(t) / stress
How do A and alpha change for a stiffer elastic nucleus vs a softer more viscous nucleus?
Stiffer elastic: Low compliance -> A decreases, alpha decreases
Softer more viscous: High compliance -> A increases, alpha increases
