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PHYS5530M Physics of Biological Systems > Biopolymer Networks > Flashcards

Biopolymer Networks Flashcards

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1
Q

Biopolymer Networks Inside Cells

A
  • intermediate filaments
  • microfilaments
  • microtubules
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2
Q

Cytoskeleton

A
  • composed of intermediate filaments, microfilaments and microtubules
  • defines the cells mechanical properties
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3
Q

Biopolymer Networks Outside Cells

A
  • extracellular matrix which defines tissue mechanical properties
  • composed of collagen and hyaluronan
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4
Q

Collagen

A
  • self-assembles hierarchically
  • long triple stranded helix, tropocollagen, is its primary feature measuring 300nm x 1.5nm
  • most collagens form fibrils and then networks of fibrils,
  • fibrils are ~100nm in diameter and a few micrometres long
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5
Q

Hyaluronan

A
  • present in every body tissue, it has structural and biochemical functions
  • produced in enzymes in cell membrane then extruded directly into the ECM
  • linear, regular, hydrophilic polymer and negatively charged when dissolved in water
  • typically large with variable contour length, 1-10μm
  • in water it forms random coils ~100nm in diameter, an open structure that randomly wiggles around
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6
Q

Forming Networks From Collagen

A
  • collagen fibrils self-assemble on their own

- fibril organsiation varies with collagen type

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7
Q

Forming Networks From Hyaluronan

A
  • HA and other filaments (e.g. actin) DO NOT self-assemble, they stay out of solution in pure form
  • cross-link via accessory proteins
  • cross-link stability and filament connectivity can vary
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8
Q

Hierarchical Organisation

A
  • salient feature of filament networks

- molecule combine to form filaments which combine to form networks

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9
Q

Composite Networks

A
  • different filaments co-assemble into a single network

- multiple networks can interpenetrate

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10
Q

Strain Stiffening Behaviour

A

-e.g. skin is soft to touch but resistant to stretching at larger deformations, this is due to collagen networks

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11
Q

Mucus

A
  • large glycoproteins that become physically cross-linked / entangled
  • keeps lungs clean - ‘gel on brush’ organisation provides lubrication for mucus transport and pathogen/dust clearance
  • helps snails/slugs move - thixtropy, time-dependent shear property
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12
Q

Elasticity of Biopolymer Filaments - Bending

Worm Like Chain Model

A

-persistance length, Lp, quantifies the correltation length of filament axi orientation upon thermally activated fluctuations
= exp(L/Lp)
-the most general model, can be used for stiff, flexible and semi-flexible polymers:
stiff: Lp&raquo_space; Lc
semi-flexible: Lp ~ Lc
felxible: Lp &laquo_space;Lc
-where Lc is the length of the chain

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13
Q

Elasticity of Biopolymer Filaments - Bending

Freely Jointed Chain Model

A

-for flexible filaments
-model parameterises local stiffness by the Kuhn length, b, where:
Lp = b/2
-model movement of the chain as a random walk

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14
Q

Elasticity of Biopolymer Filaments - Bending

Isotropic Elastic Rod

A

-for less flexible filaments
-bending modulus, κ, determined by filament radius and Young’s modulus (E):
κ = 4π r^4 E
-where:
Lp = κ / kbT

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15
Q

Elasticity of Biopolymer Filaments - Stretching

Flexible and Semi-Flexible Filaments

A

-stretching opposed by spontaneous bending to maximise filament conformational entropy

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16
Q

Elasticity of Biopolymer Filaments - Stretching

Straight and Straightened Filaments

A

-stretching opposed by intra-filament connectivity (quantified by Young’s modulus)

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17
Q

Measuring Filament Elastic Properties

A
  • stretching force analysis by AFM
  • noise analysis of clamped filaments
  • statistical shape analysis of immobilised filaments
18
Q

Elasticity of Cytoskeleton Fiaments

A
  • microtubules - stiff, Lp>1mm
  • microfilaments - semi-flexible, Lp=3-17μm
  • intermediate filaments - flexible, Lp=0.2-1μm
19
Q

Elasticity of ECM Fiaments

A
  • collagen - semi-flexible, Lp~9μm

- hyaluronan - felxible, Lp~4nm

20
Q

Hyaluronan Elasticity

A

-the combination of local stiffness (b=2Lp»a) and global flexibility (b<

21
Q

Affine Network Model

A

-model for networks of flexible polymers
-assumes that all cross-links are displaced affinely with the whole network
-this means that changes on an individual filament level are the same as global network changes
-shear modulus:
G = nkbT / V = ρkbT / Mx ~ kb*T / ξ²
-where:
n = number of filaments in network
V = total volume of network
ρ = network density (total mass over total volume)
Mx = average mass per network strand
ξ = correlation length, so ξ³ is the volume per strand

22
Q

Volume Fraction

A

φ = r²L/ξ³

-where ξ³ is the volume of the network of unit and r²L is the volume of a filament

23
Q

Gaussian Chain and Strain-Stiffening

A

-the affine network models chains as Gaussian which negelcts finite chain extensibility - when stretching approaches the contour length, lc, stiffening occurs and eventually the chain would snap

24
Q

Contour Length and End-to-End Distance

A

lc = bN
-where b is the Kuhn length and N is the number of segments
lo = b N^(0.5)

25
Q

Freely Jointed Chain Regimes vs Gaussian Chains

A
  • linear extension: l ≤ 0.4 lc
  • linear elastic stretching: 1 ≤ l/lo ≤ 0.4 N^(0.5)
  • so Gaussian model is valid for l ≤ 0.4 lc, the linear regime
26
Q

How to make ultrasoft hydrogels?

A
  • need to reach a concentration where individual extended coils can overlap, this threshold is the overlap concentration, c*
  • for given polymer size, networks soften with increasing Kuhn length (b) as long as b<
27
Q

End-to-End Distance for Flexible Chains

A

R ∝ Lc ^(0.5)

28
Q

End-to-End Distance for Semi-Flexible Chains

A

R ∝ L

29
Q

End-to-End Distance for Rigid Rods

A

R ∝ L

30
Q

Modelling Connective Tissue

A
  • connective tissues require an adaptive reponse to strain, they need to be:
  • -soft at small deformations for homeostasis and migration / proliferation of cells
  • -stiff at large deformatoins to maintain tissue structure and prevent rupture
  • networks of semi-flexible flaments are strain-stiffening so fit these requirements
  • studying real tissues is challenging as they are made of many different molecules
  • in-vitro reconstituted networks made with defined composition (purified) are easier to analyse than real tissues
31
Q

Networks of Semi-Flexible Filaments

A
  • deformation is non-affine, network mechanics are effected by strand mechanics AND network reorganisation
  • this makes it difficult to develop simple analytical descriptions
32
Q

Networks of Semi-Flexible Filaments

Computer Simulation With Rigid Rods

A
  • with non strain, ε=0, the system is in its normal state, zero deformation
  • at low strain, ε=0.08, filaments bend
  • at high strain, ε=0.24, filaments start to align in the strain direction and stretch
33
Q

Networks of Semi-Flexible Filaments

Bending/Stretching Regime

A
  • transition from a bending to a stretching dominated regime is a plausible mechanism of strain-stiffening
  • filament orientation is the dominant mechanism for this (undulations postpone stiffening onset), this would predict k∝σ^(1/2)
  • but in real, collagen rich tissues dependence of stress on strain is given by k∝σ so transition from bending to stretching regime can’t be the full explaination of collagen network behaviour
34
Q

Differential Elasticity

A

-one way to define strain stiffening:
k = dσ/dε
-where ε is strain and σ is stress

35
Q

Coordination Number

A
  • the number of fibre segments meeting at a junction

- isostatic stretching requires z≥6 (in 3D) or z≥4 (2D)

36
Q

Networks of Semi-Flexible Filaments

Importance of Connectivity

A
  • experiments realised that connectivity must be important for strain stiffening
  • collagen networks have low connectivity with z between 3 & 4, so sub-isostatic
  • sub-isostatic means:
  • -extended strain stiffening regime with k∝σ
  • -k independent of concentration ρ
  • -in the linear elastic regime (K=G) G∝κρ²
  • these three characteristic fit experiment well
37
Q

Three Elasticity Regimes

A

1) linear elasticity (K=G∝σ^0)
2) bending dominated strain stiffening (K∝σ^1)
3) stretching dominated strain stiffening (K∝σ^0.5)

38
Q

Dimensionless Bend-Stretch Stiffness

A 
the dimensionless bend-stretch stiffness (κ~) is a key determinant for elastic behaviour across the three elasticity regimes
κ~ = κ/μL²
-where L is the segment length
-for isotropic elastic rods:
κ = r²/L² &amp; κ∝ρ
39
Q

Composite Biopolymer Networks

A
  • in biology, fibrous collagen networks in tissues are imbedded in a soft hydrated matrix of hyaluronan and proteoglycans
  • the HA matrix effects collagen network elasticity by:
  • -increasing the linear elastic modulus from HA matrix elasticity
  • -the two regimes of strain-stiffening shift to larger strains due to internal pre-stress
40
Q

Computational Models for Composite Biopolymer Networks

A

-network models can be extended to composite systems to study the physical mechanisms behind hyaluronan matrix effects
-can use a two component lattice based model
-set the proportion of HA to collagen
-programme different bending/stretching properties for the two different filament types
-

41
Q

Mapping Composite Network Models to Single Component Models

A
  • composite network reponse can be mapped onto an effective single component model:
  • -enhanced stiffness, κeff~, accounts for the hindrance of filament bending by HA matrix
  • -pre-compressed network accounts for internal stresses
  • internal stress generation is a powerful control variable to tune the onset of strain stiffening -> this could be exploited in synthetic materials with pH or temperature responsive components

PHYS5530M Physics of Biological Systems (12 decks)

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