Harvard-MIT Division of Health Sciences and Technology
HST.508: Quantitative Genomics, Fall 2005
Instructors: Leonid Mirny, Robert Berwick, Alvin Kho, Isaac Kohane
Biomolecular Forces and
Energies
PROTEINS
CH
Protein
CH
CH
CH
CH
CH3
CH3
CH
C
Amino-acid sequence
L
V
D
L
E
W
V
L
E
L
L
D
V
L
50..500 amino acids in length
20 Types of amino acids
STRUCTURE
Figure by MIT OCW.
Amino Acids
R
C�
,
C
O-H
H - N
C
H - N
H
O
H
GLY
,
R
ALA
R
O
�
,
C
,
O
LEU
Hydrophobic
,
εC
H
H - N
H
H
O
,
,
N ε,
�
� C γ
O
TRP
,
C
,
, �,
O H
C �
,
R
GLU
Acidic
LYS
Basic
Figure by MIT OCW.
Amino Acids
Name
(Residue)
3-letter
code
Single
Code
Relative
abundance
(%) E.C.
MW
pK
VdW
volume( A3 )
Charged, Polar,
Hydrophobic
67
H
148
C+
96
P
91
C­
86
P
109
C­
128
114
P
7.8
57
48
-
H
0.7
137
118
P, C+
ILE
I
4.4
113
124
H
Leucine
LEU
L
7.8
113
124
H
Lysine
LYS
K
7.0
129
135
C+
Methionine
MET
M
3.8
131
124
H
Phenylalanine
PHE
F
3.3
147
135
H
Proline
PRO
P
4.6
97
90
H
Serine
SER
S
6.0
87
73
P
Threonine
THR
Tryptophan
TRP
T
W
4.6
1.0
101
186
93
163
P
P
Tyrosine
TYR
Y
2.2
163
141
P
Valine
VAL
V
6.0
99
105
H
Alanine
ALA
A
13.0
71
Arginine
ARG
R
5.3
157
Asparagine
ASN
N
9.9
114
Aspartate
ASP
D
9.9
114
Cysteine
CYS
C
1.8
103
Glutamate
GLU
E
10.8
128
Glutamine
GLN
Q
10.8
Glycine
GLY
G
Histidine
HIS
Isoleucine
12.5
3.9
4.3
6.0
10.5
10.1
Figure by MIT OCW.
INTERACTIONS
Figure removed due to copyright considerations.
Review of Protein Structure
Secondary Structure:
β-sheets
Figure removed due to copyright reasons.
Please see: Figure 6-9 in Voet, Donald, Judith G. Voet, and Charlotte W. Pratt. Fundamentals of Biochemistry. New York, NY: John Wiley & Sons, 2002, p. 130. ISBN: 0471417599.
Secondary Structure:
β-sheets
Figure removed due to copyright reasons.
Secondary Structure:
α-helices
Figure removed due to copyright reasons. Please see: Figure 6-7 in Voet, Donald, Judith G. Voet, and Charlotte W. Pratt. Fundamentals of Biochemistry. New York, NY: John Wiley & Sons, 2002, p. 129. ISBN: 0471417599.
Secondary Structure:
α-helices
Figure removed due to copyright reasons.
DOMAIN STRUCTURE
Many proteins consists of several domains
Many proteins are dimers or oligomers which consist of
several polypeptide chains.
Figure by MIT OCW.
X-ray Crystallography
X-rays
2φ
Crystal
Detector
Protein
Crystal
Diffraction
Electron Density
Protein Structure
MOLECULAR DYNAMICS used to: 1) Fit structure into density
2) Refine the structure
Figure by MIT OCW.
X-ray Crystallography
X-ray Crystallography
X-ray Crystallography
X-ray Crystallography
Protein Strcutures
• Protein Data Bank
http://www.rcsb.org/pdb/
• Structural Classification of Proteins (SCOP)
http://scop.mrc-lmb.cam.ac.uk/scop/
Forces
BONDED INTERACTIONS
NON-BONDED INTERACTIONS
• van der Waals
• Hydrogen bonds
• Hydrophobic
• Electrostatic (with screening)
Amino acids
R
R
C�
,
,
C
O-H
H - N
C
H - N
H
O
H
R
O
�
,
H
H - N
,
O
O
,
,
N ε,
ε C�
,
C
,
H
� C γ
H
O
C
H
,
C
,
, �,
O H
C �
,
R
Two Steric Forms : L and D
COOH
H
C
R
NH2
COOH
R
NH2
Figure by MIT OCW.
POLYPEPTIDE UNIT
C�
O
C'
C�
N
H
O
cis: C'
C�
H
N
C�
All but PROLINE
Figure by MIT OCW.
POLYPEPTIDE UNIT
C�
O
trans : C'
N
C�
H
O
H
N
C'
cis:
C�
C�
All but PROLINE
90%
O
trans Pro: C'
C�
10%
C'
C�
C
cis Pro:
N
C
C
C'
C�
C
C
O
N
C�
C
C'
Figure by MIT OCW.
POLYPEPTIDE UNIT IS FLAT
C�
O
C'
trans:
N
C�
Sp2 Hybridization LI
C
+
N
H
=
C
Figure by MIT OCW.
N
Vibration of covalent bonds
• IR spectra of C-H : ν~ 7x1013 s-1
wave length λ = c/ν = 5 µm
• IR spectra of CH3 - CH3 : ν~ 2x1013 s-1
wave length λ = c/ν = 15 µm
• Thermal fluctuations:
ν~ 7x1012 s-1
insufficient to excite
covalent bonds
Vibration of covalent angles
• IR spectra of X-Y-Z angle :
ν~ 1012 - 1013 s-1
Thermal fluctuations:
ν~ 7x1012 s-1
Sufficient to excite
covalent angles,
but fluctuations are small ~5o
ROTATION AROUND BONDS
O
C'
ϕ
trans:
C�
C�
χ
N
H
Figure by MIT OCW.
ROTATION AROUND BONDS
Relative Energy
3
2
�E = 2.9
kcal/mol
1
0
0
0
0
60
0
120
0
0
0
0
240
180
360
300
Dihedral angle between Ha and Hb
Ha
Hb
Ha
Hb
Hb
Hb
Ha
Ha
a
a
O'
5.3
Ψ
O"
Ψ
O
c
c
Figure by MIT OCW.
ROTATION AROUND BONDS
ϕ,χ
1kcal/mol
kT
0
60
120
180
240
C
+
N
=
3600
C
15 kcal/mol
kT
300
0
60
120
C
180
240
300
3600
N
Figure by MIT OCW.
N
Forces
• Van der Waals
“London forces" (after Fritz London)
α−
α+
α−
α+
α−
α+
Original temporary Induced dipole
dipole
V(r)
α+
α−
α+
α−
α+
α−
α+
α−
α+
α−
α−
α+
α−
α+
α−
α+
α−
α+
α−
α+
α+
α−
α+
α−
α+
α−
α+
α−
α+
α−
α−
α+
α−
α+
α−
α+
α−
α+
α−
α+
Repulsive, exchange
energy
V(r) =
c
β
r
A _ B
r12 r6
-0.2 kcal/mol at 4A
Attractive, dispersion energy -C/r6
Figure by MIT OCW.
Van der Waals interactions
Interaction
E0 kcal/mol r0,A
~
~
rmin,A Atomic radii (A)
~
~
6

12


r0  
r0

A
B
V (r) =
12
−
6
= E 0
  −
  
r
r


r  
r


Forces
Hydrogen Bonds
-Anisotropic
lone pairs
δ+
N
H
δ−
Hδ+
δ+
H
δ−
δ+
H
O
H
δ+
δ+
δ−
F
δ−
δ+
H
O
δ+
H
H
δ−
δ+
hydrogen bonds
H
O
δ+
H
Figure by MIT OCW.
SOLVENT: Hydrogen bonds
Figure removed due to copyright considerations.
sions from studies of protein stability
Forces
ence changes at buried sites almost always have
much larger effects on stability
sequence changes at exposed sites. The small
sing given that these residues are likely to havechange at exposed sites is not
similar environments (ie, largely
ted) in both the denatured and native states. (See
previous figure??repressor)
on
ged residues and to a lesser extent polar residues
are disfavored at buried sites.
is expected given the large energetic cost of burying
a charge.
ence changes which reduce the amount of hydrophobic
burial are destabilizing.
• Hydrophobic
interactions
Walter Kauzmann
energetic (<1nm) and
entopic (>1nm)
Substitution
��G (kcal/mol)
Number of
examples
Low
High
Average
�Gtr
(kcal/mol)
Ile
Val
9
0.5
1.8
1.3
0.4
0.80
Ile
Ala
9
1.1
5.1
3.8
0.7
2.04
Leu
Ala
17
1.7
6.2
3.5
1.1
1.90
Val
Ala
11
0.0
4.7
2.5
0.9
1.24
-CH2­
46
0.0
2.3
1.2
0.4
0.68
Met
Ala
4
2.1
4.6
3.0
0.9
1.26
Phe
Ala
4
3.5
4.4
3.8
0.3
2.02
~10 cal/mol/A2
Figure by MIT OCW.