chapter 22, macromolecules and aggregates ideality and reality simplicity of small systems and...
TRANSCRIPT
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Chapter 22, Macromolecules and aggregates
Ideality and reality
Simplicity of small systems and complexity of real systems
Entropy and order
Dealing with large systems
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Proteins
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DNA
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Amyloids and Cellucoses
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Liposome
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Artificially Synthetic macromolecules
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Common synthetic polymers
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ContentsStructure and dynamics 22.1 different levels of structure 22.2 Random coils 22.3 The structure of proteins 22.4 The structure of nucleic acids 22.5 The stability of biological polymersDetermination of shape and size 22.6 Mean molar mass 22.7 Mass spectroscopy 22.8 Laser light scattering 22.9 Ultracentrifugation 22.10 Electrophoresis 22.11 Size exclusion chromatography 22.12 ViscositySelf-assembly 22.13 Colloids 22.14 Micelles and biological membranes 22.15 Surface films
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Assignment for chapter 22
• 22.1(b)
• 22.5(a)
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Structure and dynamicsConfiguration
Structural features elated toa given arrangement of chemical bonds
Spatial arrangement of the differentparts of a chain.
Conformation
It can be changed only by breakingChemical bonds and forming new ones.
It can be changed into another byRotating one part of a chain around a bond.
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Different levels of structure
Primary structure (sequence)
Secondary structure (helix, sheet etc.)
Tertiary structure (overall 3D structure)
Quaternary structure (formedby different 3D structures)
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Random coils
All bond angles are arbitrary.Free rotation.
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Random coils (a more realistic model)
Bond angle is fixed.Free rotation.
Freely jointed chain model
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Measure of size
Contour length: NlRC l
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Measure of size
N
n
eN
P 22
1 2
2
1D chain, N units, each with length l,
The probability that the ends are nl apart:
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ProofNumber of chains pointing to the right: NR
Number of chains pointing to the left: NL
!nN!nN
!N
!N!N
!NW
RL
2
1
2
1
Effective length: (NR-NL)l=nl N=NR+NL
The number of ways forming a chain with end-to-end distance nl:
N
N
RL nNnN
N
NNN
N
P
2!21
!21
!2/
)!(!
!
bonds of tsarrangemen ofnumber totalright the tobonds N with polymers ofnumber R
With Stirling’s approximation:
The probability that the ends are nl apart:
N
n
eN
P 22
1 2
2
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3D casel
nl
222
3
214 RaeRa
f
21
22
3
Nl
a
P(RR+dR)=fdR
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Measure of size
Root mean square separation:
lN
fdRRRrms
21
21
20
(classroom exercise)
222
3
214 RaeRa
f
2
1
22
3
Nl
a
0
2
134
22
a
xa dxex
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Measure of size
Radius of gyration:
21
2
2
11
ijijg R
NR
Rij: separation of atoms i and j
lN
Rg
21
6
2/3
:length of rod uniform thin longA
21lR
l
g
RRR g
21
5
3 : radius with sphere uniform Solid
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Exercise• Calculate the mean separation of the ends of a freely
jointed chain of N bonds pf length l.
RfdRR 0
fdRRR nn0
0
2/138233 )()(4 2/1
2
2/1 ldReRR Na
aRa
0
213
4
22
a
xa dxex
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Conformational entropy
Nn
kNS
/
11ln2
1 11
!nN!nN
!N
!N!N
!NW
RL
2
1
2
1
WkS ln
2/})()ln{(
ln)2/1(2ln)1()2ln(
})!(ln{})!(ln{!ln/
11
2/1
21
21
nNnN nNnN
NNN
nNnNNkS
The most probable conformation is the onewith n=0:
NNkS ln2ln)1()2ln(/ 212/1
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Constrained chains
21
1
1
cos
cosF
lNRrms 21
2 lN
Rg
21
3
For tetrahedral bonds,
)5.109( 3/1cos 0
222
3
214 RaeRa
f
FeR
af Ra 222
3
214
For polyethylene with M=56 kg/mol,N=4000, l=154 pm (C-C bond),
nm 6.5,nm 14 grms RR
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The structure of proteins
Corey-Pauling rules
Classroom question:How many standard amino acidsare most commonly found in living things?
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α helix
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Conformational energy
22
1estretchstretch RRV
22
1ebendbendV
3131 cosBcosAVtorsion
r
qqV jicoulomb 4
612 r
D
r
CVLJ
1012 r
F
r
EV bondingH
Bond stretching:
Bond bending:
Bond torsion:
Coulomb forces between partial charges:
Dispersion and repulsive forces:
Hydrogen bonding:
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anglesbonds
b KbbkRU 20
20 )(
2
1)(
2
1)(
ij
ji
ij
ij
ij
ijij r
rr 0
612
pairs nonbonded 4)()(
)(2
1)cos(1
2
1 20
improperimp
dihedrals
KnxKx
Potential Energies
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bonds
b bbk 20 )(
2
1
Kb :bond force constants
b : bond length
vibration
b
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• Kθ :angle force constant
• Θ: bond angle
angles
K 20 )(
2
1
bending
Θ
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• KX :dihedral angle force constant
• X: dihedral angle
dihedrals
nK cos12
1
torsion
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• Kimp : improper dihedral angle• Φ: improper torsion angle (e.g., angle between ab and acd)
2
02
1 impropers
imp K
Improper torsion
a
b
c
d
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• εij : Lennards-Jones well depth
• σij : Distance at the Lennards-Jones minimum between atoms i and j.• qi : Partial atomic charge• ε0 : Dielectric constant• r ij : The distance between atoms i and j
ij
ji
ij
ij
ij
ijij r
rr 0
612
pairs nonbonded 4)()(
Intermolecular forces
(van der Walls forces)
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Lower energy means more stable
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Typical distribution of torsion angles(Ramachandran plot)
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Glycyl residue
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Alanyl residue
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βsheet
Parallel and anti-parallel sheets
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Higher-order structure
Four-helix bundle
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Higher-order structure
β-barrel
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The structure of nucleic acids
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Secondary structure of DNA
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Higher-order structure of DNA
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The stability of biological polymers
Denaturation and renaturation
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Determination of shape and size
22.6 Mean molar mass
22.7 Mass spectroscopy
22.8 Laser light scattering
22.9 Ultracentrifugation
22.10 Electrophoresis
22.11 Size exclusion chromatography
22.12 Viscosity
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Mean molar masses
i
iin MNN
M1
i
iiw Mmm
M1
iii
iii
w MN
MNM
2
iii
iii
Z MN
MNM
2
3
Number-average molar mass:
Weight-average molar mass:
Z-average (mean cubic) molar mass:
Viscosity-average molar mass
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MALDI principle
21
2
zeEd
mlt
2
2
l
teEd
z
m
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A typical MALDI mass spectrum
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Laser light scattering
2
2
0 sin
r
I
IR
wCpMKR
A
Cpr,r
N
d/dnVnK
4
220
24
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Determining molecular size with light scattering
2
222
22
321
sin161
3
11
g
g
RRsP
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Ultracentrifugation
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Electrophoresis
f
zeEs
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Isoelectric point of a protein
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Size-exclusion chromatography
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Viscosity
c 10
cc limlimcc
10
00
0
0
000
t
t
aVMK
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Molar mass from viscosity
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Self-assembly
22.13 Colloids
22.14 Micelles and biological membranes
22.15 Surface films
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