Lecture 7: 26/09

Question 1

What is the formula the bulk modulus?

Answer 1

The Bulk Modulus is K
K = -V(dP/dV)

Question 2

What does the bulk modulus measure?

Answer 2

The bulk modulus measures the change in volume in response to applied pressure

Question 3

How can we apply a uniform compressive stress to a cell?

Answer 3

Osmotic stress

Question 4

For PEG do higher or lower molecular weights exert greater osmotic pressures?

Answer 4

Higher PEG molecular weights exert a greater osmotic pressure

Question 5

What does pressure scale with in terms of PEG?

Answer 5

Pressure scales with concentration and molecular weight of PEG

Question 6

How are cell moduli and volume related?

Answer 6

Inverse relationship

As the cell volume decreases, the cell moduli increase

Question 7

What is phi?

Answer 7

volume fraction (i.e., density (Vmin/V))

Question 8

What is the relationship between the shear modulus and phi?

Answer 8

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

Question 9

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?

Answer 9

Viscous increase in cells follows colloidal glass transition of a jammed material

Question 10

How do changes in the cell state influence compression stiffening?

Answer 10

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

Question 11

What does the line on the graph with the number tell us?

Answer 11

It provides a scaling factor

(for instance in G’ vs cell volume, it scales G’ ~ V^(-2) )

Question 12

What is the cell modulus impacted by, besides strain-stiffening?

Answer 12

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

Question 13

How do shear and bulk moduli differ with cell volume?

Answer 13

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)

Question 14

How do all moduli relate to cell volume?

Answer 14

All moduli have the same relationship with the cell volume, just at different magnitudes

Cell moduli increases as the volume decreases

Question 15

What is Poisson’s ratio?

Answer 15

Nu = poissons ratio

How to calculate the shear modulus from bulk modulus

Question 16

Summarize what osmotic stress using PEG can be used for?

Answer 16

Compress object uniformly
Measure their volume change
Calculate their Bulk Modulus

This can be used to infer shear or Young’s moduli

Question 17

Summarize what micropipette aspiration is used for?

Answer 17

Allows serial direct characterization of time-dependent bulk and shear moduli of small to large structures

(measures the time-dependent bulk and shear modulus)

Question 18

What is the equation that relates shear modulus to bulk modulus?

Answer 18

G = 3/2 [K(1-2n)/(1+n)]

Question 19

What does lamin do within the cell?

Answer 19

Lamins provide structural support in the cell membrane

Question 20

What is the definition of compliance?

Answer 20

J(t) = Delta strain(t) / stress

Question 21

How do A and alpha change for a stiffer elastic nucleus vs a softer more viscous nucleus?

Answer 21

Stiffer elastic: Low compliance -> A decreases, alpha decreases

Softer more viscous: High compliance -> A increases, alpha increases