Lecture 3: 12/09 Flashcards
Describe the term “tensegrity”
A mechanically stable yet dynamic structure (tension & integrity)
How can we quantify a filament’s rigidity?
Persistence length, which is the length over which the tangent vector changes >1/e (66%)
–> dot product of tangent vectors
How do we determine the overall shape of a polymer (straight or coiled??)
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 «_space;L, it is flexible, if lp»_space; L, it is stiff).
Why do flexible polymers coil up into a ball
- 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.
What are some filament deformations?
buckling, entropic spring, contour stretching.
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?
It can only be used for small elastic deformations. For larger deformations, use the Boal equation.
Sort microtubules, actin filaments, and intermediate filaments from most rigid to most flexible.
- Microtubules are very rigid
- Actin filaments are semi flexible
- Intermediate filaments are very flexible
Describe the relations between Lp and L in flexible, semi-flexible, and rigid conditions?
Lp: persistence length
L: total length
Lp «_space;L is flexible
Lp =~ L is semi-flexible
Lp»_space; L is rigid
What property does persistence length describe?
Stiffness (i.e., rigidity/flexibility)
Describe the difference between the persistence length, contour length, and end-to-end distance?
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
Which biological polymer is a compressive element?
Rigid rods, such as microtubules
At compressive loads before the buckling threshold, no deformation is observed
Describe which biological polymers are tensile elements?
Actin filaments and intermediate filaments (due to their flexibility)
Define Elastic Modulus?
Elastic modulus = Stress/Strain
The unit of measurement of an object’s or substance’s resistance towards deformation elastically upon the application of stress
Define Young’s Modulus (E)?
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
Define Bulk Modulus
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
Define bending modulus (kappa)
Stress/Strain in flexural deformation, the tendency for a material to resist bending.
Also known as flexural rigidity
Define shear modulus (G)
Shear stress / Shear strain
Describe the shear or elastic storage modulus?
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.
Describe the shear or viscous loss modulus?
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
What are examples of two types of crosslinks?
- Alpha-actinin (ACTN) forms parallel actin networks
- Filamin (FLN) forms orthogonal actin networks
How can you measure the influence of crosslinks on network mechanics?
Bulk rheology
Applying force in a frequency to a material to measure its storage or loss moduli, with varying ratios of crosslinkers to polymers.
Describe the difference between solids and fluids?
Difference: Stress dissipation
- True elastic solids do not dissipate stress
- Viscoelastic materials dissipate stress at a certain timescale
What is the definition of a solid-like material?
G’ > G”
G’: Elastic shear storage modulus
G”: Viscous shear loss modulus
