Biopolymer Interfaces & Cell Mechanics

Question 1

Flory Radius

Answer 1

• the end-to-end distance

- for an ideal chain: Rf ∝ b N^0.5

Question 2

Radius of Gyration

Answer 2

• mean distance of all segments from the centre of mass

- for an ideal chain: Rg ∝ b N^0.5

Question 3

Hydrodynamic Radius

Answer 3

• effective size with which the polymer diffuses

- for an ideal chain: Rh ∝ b N^0.5

Question 4

Polymer Brushes in Biological Systems

Answer 4

• arrays of polymer molecules end-attached to an interface (planar or curved)
• brush thickness is given by H and the distance between polymer molecules is s giving grafting density σ = 1/s²
• polymer brushes are common in biological systems where the polymer is typically wither a hydrophobic polysaccaride (well-disolved and flexible) OR an intrinsically disordered protein
• they have various functions

Question 5

Flexible Polymer Chains in Solution - Scaling Laws

Ideal Chain

Answer 5

• also FJC or random walk
• contour length: Lc = bN
• Flory radius: Rf = bN^(1/2)

Question 6

Flexible Polymer Chains in Solution - Scaling Laws

Real Chain

Answer 6

• self-avoiding random walk

- Flory radius: Rf ~ bN^(3/5)

Question 7

Flexible Polymer Chains in Solution - Scaling Laws

Long vs Short Range Interactions

Answer 7

• short range interactions, e.g. local stiffness, only effects b
• long range interactions effect the Flory exponant

Question 8

Flexible Polymer Chains in Solution - Effective Excluded Volume
Definition

Answer 8

-chain segments in a polymer can repel or attract, this effect is described by an effective volume, v, per chain segment

Question 9

Flexible Polymer Chains in Solution - Effective Excluded Volume
v > 0

Answer 9

-excluded volume repulsion (good solvent)
-chain segments repel
-polymer coil stretches as a real chain
-most common for biological systems
Rf ~ [v/b³]^(1/5) b N^(3/5)

Question 10

Flexible Polymer Chains in Solution - Effective Excluded Volume
v = 0

Answer 10

-Θ-condition / Θ-solvent
-attraction between segments balances repulsion of chains
-polymer behaves as an ideal chain
Rf ~ bN^(1/2)

Question 11

Flexible Polymer Chains in Solution - Effective Excluded Volume
v < 0

Answer 11

-excluded volume attraction (poor solvent)
-attraction between segments is strong
-dense globule forms
Rf ~ b² |v|^(-1/3) N^(1/3)

Question 12

Effect of Grafting on Polymer Configuration

Answer 12

-when grafting one end to a surface, flexible polymers in good solvents adopt a distinct conformation depending on surface density
-when s≥Rf there is no overlap of chains, polymers retain their random coil conformation and look the same as they would in solution, ‘mushrooms’
H ~ Rf
-when s

Question 13

Alexander de Gennes Polymer Brush Model

Formula

Answer 13

H ~ σ^(1/3) b N

-where σ is the grafting density

Question 14

Alexander de Gennes Polymer Brush Model

In Terms of v

Answer 14

H ~ v^(1/3) σ^(1/3) N ∝ N

Question 15

Alexander de Gennes Polymer Brush Model

Pros. & Cons.

Answer 15

• correctly predicts scaling of brush thickness: H ∝ N
• but as it assumes all chain ends are in the same plane
• cannot provide accurate numerical pre-factor (as it is a scaling approach)

Question 16

Self-Consistent Field Theory Polymer Brush Model

Answer 16

-additionally to the Alexander de Gennes Polymer Brush Model, it provides pre-factors and correctly predicts the density profile and distance of chain ends

Question 17

Brushes of Locally Stiff Polymers

Answer 17

-locally stiff chains (a«b></b>

Question 18

Polyeclectrolyte Brushes

Answer 18

-brushes of charged polymers are sensitive to salt and pH changes
–without added salt they are highly swolen due to the osmotic pressure of trapped counterions
–salt leads to charge screening and reduces brush thickness
–reponse to pH is not well understood
-for moderate & high concentrations, effect of salt can be accoutned for by an added excluded volume:
v ~ vo + α²/4cs
-where vo is the exlcuded volume without charges, α is the fractional charge per monomer and cs is the salt concentration

Question 19

Elasticity of Polymer Brushes

Answer 19

• non-linear response to compression
• approximating as homogeneous, an elastic modulus can be derived for the initial regime of linear compression
• for small deformations (lineare elastic regime), and ignoring pre-factors, the elasticity of simple polymer gels is recovered

Question 20

Hyaluronan Brushes

Answer 20

-hyaluronan is locally stiff and charged both of which promote highly swollen and soft brushes

Question 21

Interpentration of Brushes

Answer 21

-it is NOT entropically favourable for two brushes to interpentrate

Question 22

Mechanobiology

Answer 22

• how physical forces and changes in mechanical properties of cells and tissues contribute to development, cell differentiation, physiology and disease
• ECM elasticity directs stem cell lineage specification - cells sense the mechanical properties of the ECM in order to direct specialisation to the appropriate cell type

Question 23

Mechanosignalling in Soft Connective Tissues

Answer 23

• cell and ECM are pre-stressed to facilitate mechanosensing - cells pull on ECM to determine its mechanical properties and vice versa
• at homeostasis the mechanical stresses are balanced
• these interactions are mediated by a transducer which both the cell and ECM are connected to

Question 24

Mechano-Transducers at Cell Surface

Answer 24

• focal adhesions are large dynamic protein complexes that sense and transduce forces from ECM
• transmembrane proteins (integrins) bind to ECM and connect to intracellular protein complex
• the protein complex (including talin, vincilin) sits at cell periphery and binds actin stress fibres
• actomyosin stress fibres generate tensile stress in cell

Question 25

Pre-Stress in Cells

Answer 25

- mechanical elements of cells are pre-stressed - generated by pulling of actin filaments by myosin molecular motors - this is an active process requiring ATP - pre-stress in the resting state needs to be accounted for when considering cell response to external mechanical stress

Question 26

Signal Propagation to Nucleus

Answer 26

- for specialisation as result of mechanical sensing at membrane - there are two possible mechanisms: - -direct force transduction to nucleus via cytoskeleton to nucleoskeleton (purely physical) - -force dependent signal transduction via cytosolic signalling cascades possibly involving ion channels (biochemical pathway) - these pathways are NOT mutually exclusive, it is likely that both play some role in mechanoregulation of gene expression - still an active area of research

Question 27

Methods to Characterise Cell Mechanical Properties

Answer 27

- atomic force microscopy - magenetic bead microrheometry - micropipette aspiration - laser tweezer microrheology

Question 28

Methods to Characterise Cell Mechanical Properties | Atomic Force Microscopy

Answer 28

- maps local mechanica properties (nm-μm scale) - colloidal probe run over cell which is attached to surface, laser bounced off of probe arm to optical position detector - force vs distance curve analysed with contact mechanics model (e.g. Hertz) to extract mechanical properties (e.g. Young's modulus) - can map properties - varying probe size (10nm-10μm) allows probing over a spectrum of length scales

Question 29

Methods to Characterise Cell Mechanical Properties | Magnetic Bead Microrheometry

Answer 29

- measures local mechanical properties at μm scale - micron sized magnetic bead functionalised with fibronectin and attached to apical syrface of cell adhered to cover slip - magnet brought in proximity of cell and B field used to generate force on bead - measure displcacement response of cell to applied magenetic forces

Question 30

Methods to Characterise Cell Mechanical Properties | Micropipette Aspiration

Answer 30

- measures cell mechanical properties (μm scale) - suction pressure used to some of cell down the length of a pipette - applying known pressure and measuring the length of cell in the pipette and normalising with respect to pipette radius allows for effective measure of elasticity

Question 31

Methods to Characterise Cell Mechanical Properties | Laser Tweezer Microrheology

Answer 31

- local mechanical properties inside cell - optical trap applies defined force on microbeads injected into the cell then measure concomitant displacement to infer viscosity of cytoplasm / cell elasticity - allow for direct analysis of mechanical properties inside cells - best for soft materials since the force range is limited to very small

Question 32

Models of Cell Mechanics

Answer 32

- cell cortex and cytoplasm model | - tensegrity model

Question 33

Cell Cortex & Cytoplasm Model | Description

Answer 33

- thin, elastic cortex lining attached to cell membrane, thickess ~100nm - cytoplasm is modelled as homogeneous either viscous, viscoelastic or elastic

Question 34

Cell Cortex & Cytoplasm Model | Lumped Parameter Viscoelastic Model

Answer 34

- model cell propeties using a viscoelastic circuit - the viscoelastic cell response involves a fast elastic response, viscous relaxation regime and viscous flow regime - in the cell cortex - cytoplasm model elastic properties are assigned to the cortex and viscous ones to the cytoplasm

Question 35

Cell Cortex & Cytoplasm Model | Experiment

Answer 35

- experiments on pure networks of actin and crosslinker allow us to test if the actin cortex alone can reproduce cell behaviour - if you take purified actin and crosslinkers can create invitro constituted cortex - this actin cortex recapitulates the strain stiffening of collagen in the ECM (K∝σo)

Question 36

Tensegrity | Definition

Answer 36

- tensional integrity - interaction of set of isolated compression elements with set of continuous tension elements with aim of providing a stable form in space - in cells actin stress fibres are the main tension elements - microtubules and ECM fibres are the main compression elements

Question 37

Tensegrity Model | Description

Answer 37

- depicts entire cell as mechanical network of interconnected parts with local mechanical perturbation generating global deformation - this means that nucleus deforms with the rest of the cell, a simple way to propagate signals and modulate gene expression & downstream cell responses - pre-stress is implicit in tensegrity, in tensegrity structures elasticity depends linearly on pre-stress - the same dependence of elasticity on (pre) stress as actin and collagen networks on their own (E~σo)

Question 38

Tensegrity Model | Pros & Cons

Answer 38

- a cell cannot be a fully-autonomous tensegrity structure since we known that cells sense and respond to their environment to change shape - good evidence for actin stress fibres being under tension - some evidence for microtubles under pressure BUT ECM also plays a role in balancing tension from actin stress fibres - cells in suspension tend to be spherical as mechanical external cues required for complex cell shape changes