Introduction to Polymer Physics - KU...

Introduction to Polymer Physics

Enrico Carlon, KU Leuven, Belgium

February-May, 2016

Enrico Carlon, KU Leuven, Belgium Introduction to Polymer Physics February-May, 2016 1 / 28

Polymers in Chemistry and Biology

Polyethylene: Synthetic polymer. It is the

most known form of plastic. The degree of

polymerization can be n = 107.

Cellulose: the most abundant natural

polymer on Earth. Essential component of

the cell wall in plants. The degree of

polymerization n ≈ 103.

E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 2 / 28

DNA (most common: B form, alternatives: A and Z forms)


B-DNA: some details


Some basics of DNA . . .

Two intertwined strands forming a double helix

Four bases: Adenine Thymine Guanine Cytosine

A and G are purines while T and C are pyrimidines

Complementary bases form hydrogen bonds (A=T, C≡G)

The two strands are antiparallel (5′-3′ and 3′-5′)

One full helix turn corresponds to 10 base pairs

The double helix has a major groove and a minor groove


RNA

Similar chemically to DNA but with ribose (less stable).The four bases A, U (Uracil replaces the Thymine), G and C

Usually single stranded, but can bind to form RNA/RNA and DNA/RNA helices

It can fold into itself to forma three dimensional structure

Here: transfer RNA (tRNA)


RNA

Base pairings: C≡G A=U G=U


Proteins

Building blocks 20 Aminoacids

Common chemical composition with a variable side chain R

R can be polar (hydrophilic) or non-polar (hydrophobic)

Black: α-carbon

ExamplesRed: Side chainSer and Thr polar

Cys nonpolar


Polar and non-polar aminoacids

There is an equal number of polar and non-polar aminoacids


Peptide bonds

Aminoacids are held together bypeptide bonds

These are formed between C and Nterminals with the release of a watermolecule

Typical protein ∼ 50− 2000 aa

Primary structure. . . - Ser - Glu - Gln - Ala - Val - . . .(sequence of aminoacids)


Non-covalent bonds help protein folding

Many weak bonds (hydrogen bonds, ionic bonds and van der Waals attractions) act

together to fold a protein. Add to these hydrophobic forces.


Secondary structure: α-helix

Helix period 0.54 nm(DNA 3.4 nm)

Side chains are not involvedin the structure formation

Pattern due to hydrogen bondsbetween N-H and C=O groups

Bonds between group i and

group i+ 4


Secondary structure: β-sheet

As α-helices, β-sheets are heldtogether by hydrogen bondsbetween N-H and C=O groups

Can be parallel or (as here)antiparallel

Side chains project alternately

outside and inside the sheet


Tertiary structure: a protein is biologically active whenfolded

A protein may be composed by different domains (units that fold independently from

each others). Here Src protein kinase carrying an ATP molecule.


DNA melting

Dissociation of the two strandsof the double helix by an increaseof temperature.It is a reversible phase transition!Dissociation can occur also

through a change of pH . . .

Melting experiments are rather easy to do!

They were performed since the sixties to investigate the double helix stabilities under

changes of external conditions (salt, pH . . . )


UV absorption spectrum of DNA

Single stranded DNA absorbs 30% moreUV light (260 nm) than double stranded DNAUV absorbance is used to measure dsDNAconcentration c at room temperature

A260 = lεdsDNA c

Here εdsDNA is known and

l is the thickness of the sample


DNA melting experiment

Increase of absorbanceas the temperature isincreased indicates thedissociation of the two

strands, ie DNA melting


Two state model of melting

Short sequences melt approximately as a two state process

[s1s2]↔ [s1] [s2]

[si] concentration of strand i[s1s2] concentration of duplex

Equilibrium constant Keq =[s1] [s2]

[s1s2]= eβ∆G

Free energy difference ∆G = ∆H − T∆S

Melting occurs at (ct totalsingle strand concentration) [s1] = [s2] = [s1s2] = ct/4


The melting temperature

The melting temperature is

1

TM=

∆S

∆H− R log(ct/4)

∆H

The melting temperaturedepends on the concentration!

The figure shows aplot of 1/TM vs. log(ct/4)

Precise determination of ∆Hand ∆S from experiments.


Thermodynamics of base pairing

A=T and G≡C base pairs have two and three hydrogen bonds!

Is for instance the enthalpy simply ∆HAT = 2ε and ∆HCG = 3ε?

hydrogen bondsbase stacking

No!There is also base stackingBases prefere to pile upover other specific bases

Stacking-unstacking isobserved in single-strandednucleic acids


The nearest neighbor model

The model assumes that the stability of a given base pair depends on theidentity of the adjacent base pair.

For instance

GC5 ’’ 3

CG5’’3

GG5 ’’ 3

CC5’’3

CG5 ’’ 3

GC5’’3

have all different stabilities!

However, there aresome symmetries

AG5 3’’

CT5 ’’ 3

C T53’ ’

GA5’’3


The nearest neighbor model

Experiments on melting of short RNA duplexes:

Evidence against simple model

TA = 26.5◦C, TB = 34.4

◦C(c = 10−4M , 1M NaCl)

’35’

’3

’3

5’

5’

’3

CGGC

GCC

5’G

GGCC

CCGG

A B

Evidence for the nn model

TA = 67.2◦C, TB = 65.2

◦C(c = 10−4M , 1M NaCl)

5’

’3

’3

5’

CGC

CG

CGGGGC C

A

5’

’3

’3

5’

GC

CG

CGC

G GCC G

B

From experimental data on melting of short duplexes the nn parameters∆Hij, ∆Sij are derived

∆H =∑

ij

∆Hij + ∆Hinit ∆S =∑

ij

∆Sij + ∆Sinit


Nearest neighbor parameters ∆G37◦C (DNA/DNA)

Table of nearest neighbor parameters for the hybridization free energies ∆G37◦Cin 1M NaCl expressed in kcal/mol. The orientation is 5′-3′ for the upper strand

and 3′-5′ for the lower strand. Only 10 of the 16 parameters are independent.

AATT -1.00

ATTA -0.88

ACTG -1.44

AGTC -1.28

TAAT -0.58

TTAA -1.00

TCAG -1.30

TGAC -1.45

CAGT -1.45

CTGA -1.28

CCGG -1.84

CGGC -2.17

GACT -1.30

GTCA -1.44

GCCG -2.24

GGCC -1.84


Calculating free energies from the nn model

Calculation of ∆G37◦ for a DNA/DNA duplex

A G C A C −3’

3’− T A C G T G −5’A

5’− G

C

= 11.4 kcal/mole

T T

0.88 1.451.84 1.301.45 2.24 0.88

. . . plus boundary terms!The precise knowledge of DNA melting temperatures is very useful inmany biotechnological applications!

Note: the free energy parameters also depend on salt concentration!


Comparison with experiments

The DNA base pairingthermodynamicsis well-reproduced by the nn model

T expM − Tth.M ≤ 3◦ C

Thermodynamic parameters have also been determined for RNA/RNA andRNA/DNA duplexes


Mismatches

Base pairings can occurr also for non-complementary bases.

Here: possible structure of a mismatchbetween G (left) and A (right)G·A forms two hydrogen bonds!

G·A, G·T and G·G are the most stable DNA/DNA mismatches!

Table of ∆G37◦C at 1M NaCl

for G·A mismatches expressedin kcal/mol. The orientation is

5′-3′ for the upper strand and

3′-5′ for the lower strand.

AATG 0.14

AGTA 0.02

CAGG 0.03

CGGA 0.11

GACG -0.25

GGCA -0.52

TAAG 0.42

TGAA 0.74


DNA supercoiling in cells

DNA in cells is mostlyin a supercoiled form

Here an electron

microscope image of

circular supercoiled

bacterial DNA

Supercoiling reduces the space occupied by DNA.

Supercoiling is induced/reduced by specific enzymes the topoisomerases II, which cut,turn and resealed DNA.

See: https://www.youtube.com/watch?v=T06lo8T8Pmw


https://www.youtube.com/watch?v=T06lo8T8Pmw

DNA supercoiling in MT experiments

Supercoiling can be induced in a Magnetic Tweezerexperiment

If we apply a large number of turns (n > nc) theDNA is expected to buckle and form plectonemes

The extension z decreases with the number of turnsn and the torque on the bead increases with n.

f1

f2

z(n)

stretched

supercoil

n (#turns)

Here we show a typical experimental curves (called”hat curves”) of extension vs. number of turns fortwo different forces.

At zero turns (n = 0) this is the DNA force-extensioncurve, which is well-reproduced by the WLC model.


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