ES228 S13 Lecture2 Biopolymers Viscoelasticity

7/29/2019 ES228 S13 Lecture2 Biopolymers Viscoelasticity

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Lecture 2 Slides!Spring 2013!ES228: Biomaterials!

LECTURE 2: Molecular raw materials andmechanical properties!


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Lecture 2 Slides!

Spring 2013!ES228: Biomaterials!

Origin of biomaterials! Naturalselec,oncreatesnewmaterial

designsbyincrementalaltera,ontogenes

(andbyextensionothermolecules)

Moleculardiversityisdependentonestablisheddesignsolu,ons

Cannotgobackwardsortransferinforma,onacrossspecies

Thereforethereisalimitedsetofbiopolymersandinorganicmaterialsusedby

biology

Thesearecombinedindifferentwaystogetnewfunc,on


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Lecture 2 Slides!


Molecular raw materials!

Lipids

Proteins

Polysaccharides

Ceramics


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Lecture 2 Slides!


Proteins! Structure! Linear polymer consisting of 20 different possible amino acids!

Sequence specific! Monodisperse! Polymer folding leads to defined 3D shape determined by linear

sequence!

Function! Highly specific biochemical recognition! Dynamic structures! Catalysis!


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Lecture 2 Slides!


Amino acids!

Most naturally occurring amino acids have (L)stereochemistry!

Peptide bond = amide bond! Stable to hydrolysis polymers do not degrade

spontaneously! Rigid limited flexibility for entire chain!

H2N

OH

O

R

NH

HN

O

R

NH

O

R n

L--aminoacids

ribosomal

transla,on


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Lecture 2 Slides!


Naturally occurring amino acids!

Non-polar

(ionizable)

Polar(non-ionizable)

Hydrophobic


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Lecture 2 Slides!


Protein biosynthesis! Intracellular

process! Translated from

genetic code! High sequence

specificity!


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Lecture 2 Slides!


Unnatural amino acids!Hackingthegene,ccode

UnnaturalAAshavebeenincorporatedinvivo

Selec,vefunc,onaliza,on Photolabilegroups Glycosyla,on Trackingdyes


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Lecture 2 Slides!


Polypeptide conformation!

Hollmoveretal.ActaCrystallographicaD200258(5)768-776

All19otheraminoacids Gly


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Lecture 2 Slides!


Secondary structure: alpha helix! 3.6 amino acids per turn, right handed helix!! 36 amino acid a-helix has 10 turns and is 5.4 nm long!! Helixpropensi,esoftheaminoacidsareasfollows(kcal/mol):

Ala=0

Leu=0.21

Arg=0.21

Met=0.24

Lys=0.26Gln=0.39

Glu=0.40

Ile=0.41

Trp=0.49

Ser=0.50

Tyr=0.53

Phe=0.54

Val=0.61

His=0.61

Asn=0.65

Thr=0.66

Cys=0.68

Asp=0.69

Gly=1

(Paceetal.Biophys.J.199875422-427)


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Lecture 2 Slides!


Secondary structure: beta-sheet! Pleated structure!

Maybeparalleloran,parallel -sheetpropensi,es:Thr>Ser>Glu>Val>Phe>Tyr>Ala

Maybeparalleloran,parallel


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Lecture 2 Slides!Spring 2013!

ES228: Biomaterials!

Secondary structure: beta-sheets!

an,parallelparallel


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Tertiary structure!

GreenFluorescentProtein

(mostly-sheet)

Hemoglobin

(mostly-helix)

Fibrin

(mixtureof-helixand-sheet)


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Proteins are EvolutionaryMaterials!Polypep,desequenceisdirectlyrelatedtoDNAinstruc,onswhichcanchange!

pointmuta,on

alterna,vesplicing

Homologousrecombina,on


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Polysaccharides!

Makeupalargepor,onofanimalandplant,ssues Mainroleinmany,ssuesistoretainwater


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Polysaccharides made up of sugars!

O

HO

HO

OH

OH

OH

GLUCOSE

Anomeric

posi3on

1

2

3

4

5

6

Generalproper,esofpolysaccharides

Hydrophilic(ManyH-bondinginterac,onssome,meselectrosta,cwithmodifica,ons)

MaybemonomericorhaveaMWofmanyMDaMorerigidthanalipha,cpolymers

STARCH

(-14-linkedglucose)

enzymes

glycosylbond


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Naturally occurring sugars!

glucose

(-D-glucopyranose)

galactose

(-D-galactopyranose)

N-acetylglucosamine

(2-acetamido-2-deoxy--D-glucose)glucuronicacid

mannose

rhamnose

O

HO

HO

OH

OH

OH

O

HO

HO

OH

OH

OH

O

HO

HO

OH

OH

OH

O

HO

HO

OH

OH

O

OH

O

HO

HO

OH

NH

OH

O

O

OH

OH

OHCH3

OH


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Carbohydrate bonding!

O

HO

HO

OH

OH

O

O

HO

OH

OH

OH

Glycosylbondhasrota,onflexibilityin2direc,ons Maybeordependingonsugarbondorienta,on

Mnemonicisshapedlikeafish(downwardorienta,onasdrawn;isforbird(upwardbondorienta,onasdrawn)

Manyopportuni,esforH-bondsbuttheymustcompetewithwaterleadingtomoreconforma,onalstates


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Examples of polysaccharides!

alginate

hyaluronicacidcellulose

chi,n


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Polysaccharide properties! Structure!

Polydisperse!Limited options for exploring sequence space !

Function!Structural materials (space fillers)!

Gels (water retention)!

Hard materials (chitin shells)!


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Unnatural sugars!

Wearenotlimitedtonaturallyoccurringfunc,onalgroupsonpolysaccharides


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Examples of bioceramics!

Eggshells

bone

Molluskshells

Seaurchinspine


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Ceramics!

Conchshell

(aragoniteCaCO3)

Diatom

(silicaSiO2)

2maintypesofinorganicbiomaterials:

Calcium-based Silica-based

Keyfeatures:

Metabolicallycheap Highs,ffness Templatedbyorganicmolecules


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Deforming materials Deforming molecules!Whyarecrystallinematerialsgenerallyhardandpolymericmaterialsgenerallyso?

Deformingabulkmaterialisonlyaccomplishedbyalteringthespacingor

packingofitscons,tuentmolecules

Atomsincrystallinematerialscannotmovewithrespectto

eachother

stressisreadilytransferredthroughoutthecrystallaceStrainislimitedtomovementofatomswithinthelace

Atomsinpolymershavemoredegreesoffreedom

Stresscangointoalteringpolymerconforma,on

Higherstrainsareaccommodatedbyunfoldingofpolymerchains


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How do materials respond to deformation?!

AtomsheldrigidlyinplaceInteratomicdistance=0.10.2nmMaximumstrain=


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Polymer conformation - The random walk!ForanidealpolymeroflengthLmadeupofmanyfreelyjointedsegments:

ContourlengthL RadiusR

R~L1/2

Theconforma,onofthepolymercanbe

referredtoasarandomwalk:


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Entropic springs!

Rf

Howmuchforce(f)isrequiredtomaintainthepolymerwithapar,cularradius(R)?

ENTROPY:

Ifeveryjointisfreelyrota,ngthereareaninfinitenumberofvaluesforthevectorR

Byapplyinganexternalforcesomeofthosevaluesarenotavailable.Bymakingthepolymermoreextendedincreasingorderisintroducedtothesystem

Thedropinentropyassociatedwithextendingthepolymerchaincausesthe

polymerchainitselftoapplyacounterforce.


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Viscoelastic theory!

What do we mean when we say amaterials is:!Stiff?!Strong?!Tough?!Resilient?!


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Definition of strain!

l

lo

eC=l

lo

Cauchystrain

(a.k.a.conven,onalnominalor

engineeringstrain)

STRAIN=Increaseinlengthperunitofstar,nglength

Thismakesforagoodes,mateifl


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Definition of stress!

=f

Ao

appliedforce

cross-sec,onalarea

hasunitsofforce/unitarea(N/m2orPa)


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Stress-strain curve!

E=

e

stress

strain

Strain(unitless)

Stress

,(Pa)

Modulus

(sameunitsasstress-Pa)

Modulus

(s,ffness)

Ul,matebreakingstress

(strength)

Ul,matebreakingstrain

(extensibility)

Energyabsorbedbymaterial

beforebreaking

(toughness)


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Stress-strain behavior of materials!

Strain

Stress

steel

rubber


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Idealized types of material behavior!elas,c plas,c

visco-elas,celas,c-plas,c

STRAIN

STRESS


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Springs and dashpots!

Strain

Stress

Hookeanregion

materialbehaveslikeaspringElas,cyougetbacktheenergyyouputintothesystem

Materialwillreturntoitsini,alform

Hookesspringmodel

F = kx

= Ee


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Springs and dashpots!

Strain

Stress

Non-Hookeanregion

Non-elas,ccomponentofmaterialcanbemodeledasadashpot

Energyyouputinisdissipatedbyviscousmaterial

Dashpot

= (de/dt)

Stressonmaterialispropor,onalto

thechangeinposi,onandviscosity

where = viscosity


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Most biomaterials are viscoelastic!Viscoelas,cmaterialscanbemodeledwithMaxwellorVoigtmodels

Maxwell Voigt

1

e1

2

e2m

1

e1

Em2

e2

v

Ev

(useforcreeptestexpt)(useforstress-relaxa,onexpt)


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Stress-relaxation experiment!Inastressrelaxa,onexptlengthisheldconstantandforceismonitoredover,me

Maxwell

(useforstress-relaxa,onexpt)

2 = mde2/dt1

e1

2

e2m

Em1 = Eme1

1

Em=

1

dt

e1

dt=

2

m

de2

dt

1=2 = AND etotal=e1 +e2

However

Thereforeaddingthetwoequa,onstogetherweget:

1

Em=

d

dt

de1

dt

m

+de2

dt+ =

detotal

dt


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Stress-relaxation experiment!Inastressrelaxa,onexptlengthisheldconstantandforceismonitoredover,me

Maxwell

(useforstress-relaxa,onexpt)

1

e1

2

e2m

Em

But

1

Em

d

dt

m

+ =

= 0

= 0

detotal

dt

detotal

dt

Therefore:

1

Em

d

dt

m

+

=d

-Em

m

dt

integrate

= o exp(-Emt/m)


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Stress-relaxation experiment!

= o exp(-t/)

= o exp(-Emt/m)

Inastressrelaxa,onexperimentstressdecaysexponen,allyover,me

Thereforelet=(m/Em) beacharacteris,c,meconstant


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Creep test!Inacreeptestaconstantforceisappliedtothematerialandthechangein

deforma,onismonitoredover,me

Usingargumentssimilartothoseusedforthe

stress-relaxa,ontest:

Voigt

(useforcreeptestexpt)

1e1

2

e2v

Ev

e = eo exp(-t/)


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More sophisticated models of viscoelasticty!

Moreaccuratemodelscanbeconstructed

frommorecomplicatedcombina,onsof

springsanddashpots

BecauseoftheirdeficienciestheVoigtandMaxwellmodelsaloneareusuallynotcomprehensiveenoughtorepresentmostrealmaterials


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Dynamic tests (Hookean)!

,me

STRESSandSTRAIN

Themostprac,calmethodtoassesstheviscoelas,cityofmostbiologicalmaterialsis

withadynamicexperiment

Appliedstrain

Measuredstress

eo

o

ThisistheresponseexpectedfromaHookeanmaterial


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Dynamic responses (Hookean)!

eo

o

STRAIN

STRESS

ForHookean(elas,c)materialsstress

varieslinearlywithstrain

ForHookean(elas,c)materialsstressvarieslinearlywithstrain

1 = Eme1


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Dynamic tests (viscous)!

,me

STRESSandSTRAIN

Themostprac,calmethodtoassesstheviscoelas,cityofmostbiologicalmaterialsis

withadynamicexperiment

Appliedstrain

Measuredstress

eo

o

Thisistheresponseexpectedfromaviscousmaterial


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Dynamic responses (viscous)!

eo

o

STRAIN

STRESS

eo

o

STRAIN

STRESS

ForHookean(elas,c)materialsstress

varieslinearlywithstrain

Forviscoelas,cmaterialsthereisa

phaseshibetweenmeasuredstress

andappliedstrain

Forviscousmaterialsmaximumstressisachievedatthehigheststrainrate

2 = mde2/dt

=lossangleanindicatorofviscoelas,ccharacter

=90ocompletelyviscous =0ocompletelyelas,c 0o


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ES228 S13 Lecture2 Biopolymers Viscoelasticity