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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
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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
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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.
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DNA (most common: B form, alternatives: A and Z forms)
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B-DNA: some details
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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
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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)
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RNA
Base pairings: C≡G A=U G=U
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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
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Polar and non-polar aminoacids
There is an equal number of polar and non-polar aminoacids
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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)
E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 10 / 28
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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.
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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
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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
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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.
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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 . . . )
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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
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DNA melting experiment
Increase of absorbanceas the temperature isincreased indicates thedissociation of the two
strands, ie DNA melting
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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
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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.
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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
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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
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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
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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
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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!
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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
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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
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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
E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 27 / 28
https://www.youtube.com/watch?v=T06lo8T8Pmw
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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
E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 27 / 28
https://www.youtube.com/watch?v=T06lo8T8Pmw
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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.
E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 28 / 28
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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.
E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 28 / 28