Nanofibers

Biophysics in the Guthold lab

Why study nanofibers

• Have a physiological relevance– Extracellular Matrix – Blood Clots– Gecko feet– Spider scopula pads (setules)

• Interesting properties

• Surface area to volume ratio

Extracellular Matrix

Neural Interconnect and Cellular MatrixNerves and nerve bundles (yellow), extracellular supporting matrix

(red), and ganglion cells (blue).

Lust, University of Rochester

University of Michigan Medical School Image

Blood Clot

Colored SEM image of a whole clotBlue – Fibrin fibers

Purple – platelet aggregationRed – red blood cells

Credit: Yuri Veklich and John W. Weisel, University of Pennsylvania School of Medicine

50nm-200nm

Gecko Feet

200 – 500 nm spatula

Van der waals interactions (electrostatic)

Base on geometry not material

Sitti and Fearing, Journal of Adhesion

Science and Technology, 2003.

Our focus - 1

Native Fibrin fibers (blood Clots)Heart attack Stroke DVT Hemorrhaging Embolism

•Clots have been studied on the macroscopic level

•No good model for blood clots

•Gain a better understanding from the ground up•Model clot

The mechanical properties of native and

gamma-crosslinking deficient fibrin fibers

1. Background and Motivation

2. Mechanical Properties of Native Fibers

3. Conclusions and Fibrin Fiber Model

4. Properties of Fibrin Fiber Branch Points

Blood clots ‘perform’ the mechanical task of stemming the flow of blood

Need to understand mechanical behavior of clot and its constituents.

One goal is to build a realistic model of a blood clot, based on the physical

parameters of the fibers 1.

Another goal is to learn more about internal structure of fibers.

How does the clot perform, depending on numerous variables (mutations,

environment, crosslinking, diseases, etc).

1.1. The Major Structural Component of a Blood Clot is a Network of Fibrin Fibers*

Image: Yuri Veklich & John Weisel

*ignoring platelets for the time being

1 A. E. X. Brown et al, “Multiscale Mechanics of Fibrin Polymer: Gel Stretching with Protein Unfolding and Loss of Water” Science (2009) 325, 741-744

B

AFibrinogen

b

a

Dimensions of monomer: ~ 45 x 4.5 nm

Crystal structure (chicken), Z. Yang, et al Biochemistry 40, 12515-12523 (2001)

1.2 Formation of Fibrin Fibers

+

Fibrinopeptides A & B

Thrombin

Fibrin (protofibrils)

Protofibrilformation

Further lateral aggregation

Lateral aggregation and branching

SEM image (Roy Hantgan) of fibrin clot

(plus platelets)10 m

Major interactions:

• A:a interactions, D:D interface, B:b interactions

• crosslinks, crosslinks

20-200 nm

- The properties of the individual fibers

- The properties of the branching points

- The architecture of the network

1.2. Properties of any Fibrous Networks Generally Depend on Three Parameters

If you want to design a model/structure out of fibers, it is important:

- to know these three parameters,

- and how they affect overall properties

Thus, we need to:

- Determine fiber properties, branchpoint properties, and architecture

- Determine and test macroscopic properties of structures

- Iteratively compare experimental data, model data, improve model.

Chicken wire

Side view of set-up: Top view of set-up:

Linit

Fibrin fiber

AFM tip

Ridge

Ridge

Instrumentation set-up:

Objective lens

AFM tip

substrate

Fibrin fiber

12 m

8 m6 m

x-y-z translatorMicroscope

x-y stage

L’

L’’

A B C

Features:

• Obtain images & movies of manipulation

• Easy manipulation (nanoManipulator)

• Obtain stress-strain curves of fiber deformation

• Can apply larger force regime than in normal force measurement

• Well-defined geometry

1.3. Experimental set-up

Fstress

A

Lstrain :

L

Maximum

extension

Breaking strength

Extensibility: rupture strain = strain at which fiber ruptures.

Energy loss

Elastic limit: Greatest strain a material can withstand without any measurable permanent strain remaining upon the complete release of the load.

For elastic deformations: Y… Young’s modulus Y

For viscous fluids: … viscosity t

Polymers usually show viscous and elastic properties

1.4. Stress-Strain Curves of Single Fibrin Fibers

= 0

Fibrin fiber

A

= 183%

C

20 mUncrosslinked

batroxobin

LiniExtensibility L/Linit

100% 200% 300% 400%

Thr + X

Bat +X

Thr - X

Bat -X

Original length

332 ± 71

226 ± 52

226 ± 72

265 ± 83

0%

E

AFM tip

B

= 70%

Ridge

Groove

W. Liu et al. “Fibrin Fibers have extraordinary extensibility and elasticity” Science (2006) 313, 634

50 m

D

2.1. Extensibility of Fibrin Fibers

Partially crosslinked: max = 330%

Fully crosslinked: max = 147%

A

ED

B C

F

G

20µm

Crosslinked

thrombin

2.2. Elasticity of Fibrin Fibers

Partially crosslinked fibers: ~ 180%*

Uncrosslinked fibrin fibers: ~ 60 – 120%*

Fully crosslinked fibers: ~ 50 – 75 %*

* Difficult to measure exactly

W. Liu et al Science (2006) 313, 634

• Fibrin fibers become stiffer at around 100% strain (sigmoidal change)

• Uncrosslinked fibers stiffen by a factor of 3 (consistent)

• Crosslinked fibers stiffen by a factor of 1.9 (inconsistent)

• Slope is modulus (stiffness):

• Uncrosslinked: 4 MPa (initial); 12 Mpa (high strain)

• Crosslinked: 8 Mpa (initial); 15 Mpa (high strain)

2.3. Stress-Strain curves: Modulus and Strain Hardening

W. Liu et al. JTH (2010) “The mechanical Properties of Single Fibrin Fibers” 8, 1030-1036

Collet JP et al. PNAS (2005) 102, 9133-7

2.4. Radius dependence of Modulus (stiffness)

• Fibrin Fibers become stiffer with decreasing radius

• Thin fibrin fibers are denser than thicker fibers

W. Liu et al. JTH (2010) “The mechanical Properties of Single Fibrin Fibers” 8, 1030-1036

2.5. Energy loss in fibrin fibers

• Inscribed are in stress-strain curve corresponds to energy loss in pull cycle.

• Uncrosslinked: little energy loss at low strains, 70% energy loss at high strains.

• Crosslinked: higher energy loss at low strains, 70% energy loss at high strains.

• Again, sigmoidal (two step) shape.

W. Liu et al. JTH (2010) “The mechanical Properties of Single Fibrin Fibers” 8, 1030-1036

2.6. Incremental Stress-strain curves: Elastic and viscous components

W. Liu et al. JTH (2010) “The mechanical Properties of Single Fibrin Fibers” 8, 1030-1036

• Incremental stress-strain curves can be used to separate elastic and viscous (time-dependent) parts of modulus

• Values see summary table

• Two relaxation rates

• Relaxation rates are:

• independent of strain

• independent of cross-linking

2.7. Incremental Stress-strain curves: Relaxation times

21

210 )( tt eet

1 = 2 s

2 = 50 s

2.8. Summary Table, Mechanical properties of fibrin fibers

FiberType Uncrosslinked Crosslinked

max 226% +/- 8.7%* 147 % +/- 5%

elastic 60 -120 % * < 50 - 76 %

E0 (Mpa) 3.9 +/- 0.3 8.0 +/- 1.0

E∞ (Mpa) 2.0 +/- 0.2 4.0 +/- 0.6

1 (s) 2.9 +/- 0.5 2.1 +/- 0.2

2 (s) 54 +/- 9 49 +/- 4

h 3.2 +/- 0.4 1.9 +/- 0.3

2.9. Summary Table, Mechanical properties of fibrin fibers, Kelvin Model, and Partially Crosslinked Fibers

FiberType Uncrosslinked Crosslinked Partially Crosslinked

max 226% +/- 8.7%* 147 % +/- 5% 333 % +/- 13%*

elastic 60 -120 % * < 50 - 76 % 180 % *

E0 (Mpa) 3.9 +/- 0.3 8.0 +/- 1.0 4.6 +/- 0.7

E∞ (Mpa) 2.0 +/- 0.2 4.0 +/- 0.6 2.6 +/- 0.3

1 (s) 2.9 +/- 0.5 2.1 +/- 0.2 2.0 +/- 0.2

2 (s) 54 +/- 9 49 +/- 4 54 +/- 7

h 3.2 +/- 0.4 1.9 +/- 0.3 3.5 +/- 0.8

Eloss ≤40-70% 0-70% 0-70%

E1 (Mpa) 1.6 +/- 0.8 1.3 +/- 0.2 1.1 +/- 0.3

E2 (Mpa) 0.6 +/- 0.2 2.0 +/- 0.2 0.8 +/- 0.12

μ1 (Mpa*s) 2.5 +/- 0.6 3.2 +/- 0.6 1.0 +/- 0.4

μ2 (Mpa*s) 37 +/- 17 155 +/- 47 33 +/- 6.9

W. Liu et al. JTH (2010) 8, 1030-1036

3.1 Conclusions from Single, Native Fibrin Fiber Stress-Strain Measurements

• We determined extensibility, elasticity, energetic behavior, total and

relaxed elastic modulus (stiffness), stress relaxation behavior.

• Despite nearly crystalline structure of fibrin fiber, fibers have large

elasticities and extensibilities.

– Monomer must be able to extend while keeping interactions intact

• Crosslinking increases stiffness, reduces extensibility, little effect on

relaxation times.

• Two relaxation rates, sigmoidal strain hardening (two step), sigmoidal

energy loss (two step).

3.2 Molecular Model

Brown AEX et al. Biophys. J. (2007) 92, L30-41

Primalov PL et al. J. Mol. Biol. (1982) 159m 665-83.

Collet JP et al. Blood (2005), 106, 3824-30

Falvo MR et al. JTH (2008), 6, 1991-3

Litvinov RI et al. Biochemistry (2007) 46, 9133-42

3.3 Molecular Model, main features

• Assumes A:a interaction and D:D interface stay intact.

• 1. Mechanism: Elastic interactions of alpha C-terminal domain, even across protofibrils.

• 2. Mechanism: Alpha helical to beta strand transition, as suggested from single molecule experiments.

• 3. Mechanism: Partial unfolding of gamma domain. Energy to stretch fibrin monomer is similar to thermal melting energy of gamma domain.

• Joints are much more stable than we expected, fibers could be stretched to over 2.3 times their length, before joints broke (details, next slide).

• In about 100 experiments we never saw the fiber fully unzip.

• We often saw triangular architecture that may prevent unzipping, (perhaps originating from ‘trimolecular’ or tetramolecular junctions’1).

• Slight helical structure of protofibrils may also stabilize joints.

1 Mosesson, MW et al. Ann NY Acad Sci (2001) 936, 11-30; Mosesson MW, Blood (1993) 82, 1517-1521; Mosesson et al. Proc Natl Acad Sci U S A. (1989) 86, 1113-1117; Ryan EA, et al. Biophysical Journal. (1999);77, 2813-2826.

4.1 Properties of Fibrin Fiber Branchpoints

4.2 Properties of Fibrin Fiber Branchpoints

• Crosslinked and uncrosslinked joints ruptured at strains of 132% amd 146%.

• Crosslinked fibers rupture 40% at the joint, 60% along the fiber.

• Uncrosslinked fibers rupture 70% at the joints, 30% along the fiber.

Crosslinking stabilizes joints (makes fibers less extensible).

Overall joints are stabalizes by protofibril twisting, triangular architecture and crosslinking.

Material Stiffness (MPa) max Proposed mechanisms explaining extensibility

High extension fibers

Fibrin (crosslinked) 8-15 147 Flexible linkers, -helix -sheet transition, unfolding globular domains

Fibrin (uncrosslinked) 4-12 226 Flexible linkers, -helix -sheet transition, unfolding globular domains

Fibrin (partially crosslinked) ~ 6-12 255 Flexible linkers, -helix -sheet transition, unfolding globular domains

Spider silk (Araneus Flag silk) 3 270 Consists almost entirely of amorphous regions

Elastin (Bovine ligament) 1 150 Compact, amorphous, hydrophobic domains, which are crosslinked together, entropic, rubber-like elasticity

Resilin (Dragonfly tendon), cloned resilin

1-2 190, 313 Similar to elastin, not as well studied

Fibrillin 0.2 – 100 > 185 Unstacking pleated domains

Myofibrils(Titin, connectin)

1 200 Unfolding of PEVK and Immunoglobulin domains

Matrix-free Intermediate fiber (1mammalian, 2hagfish)

6-300 1601- 2202 Potentially ↔ transition and/or fibril sliding

Synthetic rubber 1-10 850 Alignment of randomized, crosslinked chains

Low-extension fibers

Spider silk (Araneus MA silk) 10,000 27 Modular composition; amorphous regions or beta spiral connected by crystallites

Uncrosslinked, self-assembled collagen-I

- 24-68 Sliding of collagen fibrils

Cross-linked, self-assembled collagen-I

5,000 12-16 Small, reversible molecular deformations

Fibronectin - 200 – 300 Unfolding of globular domain or extension of bent and looped molecules

Actin 2,000 ≤ 20 Highly regular, crystalline structure

Microtubules 1,500 ≤ 20 Highly regular, crystalline structure

Wet, hard -keratin in high-sufur matrix (hair, wool)

2,000 45 ↔ transition,

Fishing line (nylon) 10-10,000

Our focus - 2

Nanofibers for tissue engineering

• ECM is composed of nanofibers• Regenerative medicine -> Tissue

engineering• cell differentiation and proliferation has

been related to scaffold mechanical properties

• WFIRM – bladder from collagen and PGA• One branch with exceeding research and

promise is electrospinning of biological polymers -> to form scaffolds

Wor

king

dis

tanc

e

• Requirements for electrospinning

- High concentration polymer solution

- Volatile solvent, for example (HFP)

- Large voltage source

- Syringe and syringe pump

• Candidate for tissue engineering scaffolds (Collagen and Fibrinogen)

- Biocompatible

- Support cell proliferation

• Individual fiber properties important for design and engineering of structures with certain mechanical properties

•By changing the polymer you can change the properties of the material

Cell differentiation and proliferation have been related to mechanical matrix properties

Post Taylor cone stream – MIT 2005, J.H. Yu, S.V.

Fridrikh

1mm

Electrospinning

25 μm

0 7.5 15-5 106

0

5 106

1 107

1.5 107

2 107

2.5 107

3 107

0 5 10 15

Energy loss

Str

ess

(Pa)

Strain (%)

forwardpull

backwardpull

Stress-Strain curve of electrospun collagen

0

5 106

1 107

1.5 107

2 107

2.5 107

3 107

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Str

ess

(P

a)

Strain

Modulus dependence on radius

0

1

2

3

4

5

6

7

8

9

0 200 400 600 800 1000

Radius (nm)

Mo

du

lus

(GP

a)

Permanent deformation at all visible strains

Significant strain softening

Viscoelastic behavior such as stress relaxation

Loses integrity in buffer unless crosslinked

Large energy loss per cycle at strains over 12%

Modulus dependence on radius

A B C DE

Native Collagen8

Electrospun Collagen

Fiber Radius 75 – 250 nm 160-783 nm

Extensibility 20% 33%

Modulus (MPa)

Initial - 860 Initial – 2800

Modulus behavior

Strain hardening and softening

Strain softening

Electrospun Collagen

0

2 106

4 106

6 106

8 106

1 107

1.2 107

1.4 107

0 0.2 0.4 0.6 0.8 1

Stress versus Strain Curve

Elastic Stress (Pa)

Total Stress (Pa)

To

tal a

nd E

last

ic S

tre

ss (

Pa

)

Strain

3 106

4 106

5 106

6 106

7 106

8 106

9 106

0 20 40 60 80 100 120 140

Double exponential vs. Stretched Exponential Fit

Str

ess

(Pa)

Time(sec)

Red - Double exponential ( R=0.98262 ) Purple - Stretched exponential ( R=0.98184 )Rehydrated after spinning

Strain softening (average total modulus 16 MPa, elastic modulus 6.7 MPa)

Extensibility 133%

Stress relaxation

Relaxation fit with both double exponential and stretched exponential (convention)

Modulus decreases with increasing radius

Electrospun Fibrinogen

Electrospun fibrinogen and collagen• Collagen is soluble in buffer unless crosslinked• Fibrinogen and Collagen modulus decreases with increasing radius• Fibrinogen is more extensible• Collagen shows significant deformation at low strains• Both work well for cell seeding

Current Work• Other polymers (PCL)• Combination spinning • Orientation • Layering

Electrospinning in Tissue EngineeringHeart Valve

• Match Mechanical Properties of the tissue

• Biodegradable

• Cell adhesion

• Shape

• Function (three leaflets, prevent reverse flow)

Bioreactor

Future Final Step• Seed Cells• Durability• Strong enough to be handled by

physician during surgery; compliant enough to pump blood and degrade as cells produce their own ECM