Lecture 3: 12/09

Question 1

Describe the term “tensegrity”

Answer 1

A mechanically stable yet dynamic structure (tension & integrity)

Question 2

How can we quantify a filament’s rigidity?

Answer 2

Persistence length, which is the length over which the tangent vector changes >1/e (66%)
–> dot product of tangent vectors

Question 3

How do we determine the overall shape of a polymer (straight or coiled??)

Answer 3

The overall shape of a polymer is determined with both persistence length and contour length. The degree of coiling depends on flexibility and length (if lp &laquo_space;L, it is flexible, if lp&raquo_space; L, it is stiff).

Question 4

Why do flexible polymers coil up into a ball

Answer 4

• External forces such as thermal forces will cause the polymer to coil
• From a statistical perspective, there are many more configurations for a polymer to be coiled up, and therefore it is entropically favorable to be in one of these configurations
  –> small r means many configurations, large r means few configurations.

Question 5

What are some filament deformations?

Answer 5

buckling, entropic spring, contour stretching.

Question 6

When a coiled polymer is pulled, a force can be calculated in the form of hookes law (f ~ lpk/L^4)x. Why must we be ~wary~ of using this equation?

Answer 6

It can only be used for small elastic deformations. For larger deformations, use the Boal equation.

Question 7

Sort microtubules, actin filaments, and intermediate filaments from most rigid to most flexible.

Answer 7

• Microtubules are very rigid
• Actin filaments are semi flexible
• Intermediate filaments are very flexible

Question 8

Describe the relations between Lp and L in flexible, semi-flexible, and rigid conditions?

Answer 8

Lp: persistence length
L: total length

Lp &laquo_space;L is flexible
Lp =~ L is semi-flexible
Lp&raquo_space; L is rigid

Question 9

What property does persistence length describe?

Answer 9

Stiffness (i.e., rigidity/flexibility)

Question 10

Describe the difference between the persistence length, contour length, and end-to-end distance?

Answer 10

Persistence length: the length over which correlations in the direction of the tangent are lost, describes the stiffness

Contour length: length of the entire contour of the polymer

End to end distance: single vector distance between the ends of the polymer

Question 11

Which biological polymer is a compressive element?

Answer 11

Rigid rods, such as microtubules

At compressive loads before the buckling threshold, no deformation is observed

Question 12

Describe which biological polymers are tensile elements?

Answer 12

Actin filaments and intermediate filaments (due to their flexibility)

Question 13

Define Elastic Modulus?

Answer 13

Elastic modulus = Stress/Strain

The unit of measurement of an object’s or substance’s resistance towards deformation elastically upon the application of stress

Question 14

Define Young’s Modulus (E)?

Answer 14

The mechanical property that measures the tensile elasticity of a solid when the force is applied lengthwise (i.e., tensile elasticity); It is a type of elastic modulus

Question 15

Define Bulk Modulus

Answer 15

The mechanical property that measures the compressional elasticity of a solid when the force is applied lengthwise; It is a type of elastic modulus

More relevant for fluids as it relates to pressure

Question 16

Define bending modulus (kappa)

Answer 16

Stress/Strain in flexural deformation, the tendency for a material to resist bending.

Also known as flexural rigidity

Question 17

Define shear modulus (G)

Answer 17

Shear stress / Shear strain

Question 18

Describe the shear or elastic storage modulus?

Answer 18

Shear storage modulus: G’
Elastic storage modulus: E’

Ratio of stress and strain under vibratory conditions (cosine in formula). The ability for the material to store energy elastically.

Question 19

Describe the shear or viscous loss modulus?

Answer 19

Shear loss modulus: G’’
Viscous loss modulus: E’’

Ratio of stress and strain under vibratory conditions (sine in formula). Related to the materials ability to dissipate stress through heat

Question 20

What are examples of two types of crosslinks?

Answer 20

• Alpha-actinin (ACTN) forms parallel actin networks
• Filamin (FLN) forms orthogonal actin networks

Question 21

How can you measure the influence of crosslinks on network mechanics?

Answer 21

Bulk rheology

Applying force in a frequency to a material to measure its storage or loss moduli, with varying ratios of crosslinkers to polymers.

Question 22

Describe the difference between solids and fluids?

Answer 22

Difference: Stress dissipation
- True elastic solids do not dissipate stress
- Viscoelastic materials dissipate stress at a certain timescale

Question 23

What is the definition of a solid-like material?

Answer 23

G’ > G”
G’: Elastic shear storage modulus
G”: Viscous shear loss modulus