Modeling studies of chromatin fiber structure as a function of DNA
linker length
Supplemental material
Ognjen Perišića,∗, Rosana Collepardo-Guevaraa,∗, Tamar Schlicka,b,∗∗
Department of Chemistry, New York University,
100 Washington Square East, New York, New York 10003
b
Courant Institute of Mathematical Sciences, New York University,
251 Mercer Street, New York, New York 10012, Tel.: 212-998-3116; fax: 212-995-4152
a
∗
∗∗
These authors contributed equally to the work
Corresponding author
Email address: schlick@nyu.edu (Tamar Schlick)
Preprint submitted to Journal of Molecular Biology
July 24, 2010
ql (e)
x
y
z (nm)
ql (e)
x
y
z (nm)
ql (e)
x
y
z (nm)
ql (e)
x
y
z (nm)
-0.92
-1.39
-2.03
-2.53
-0.06
2.31
4.71
-0.63
1.50
-2.46
-1.75
-0.76
-5.03
-0.03
2.82
-2.39
-0.65
0.31
-0.74
-1.70
-1.84
5.27
-0.84
-0.65
-1.59
-1.55
-0.45
0.12
-1.84
-2.19
-1.57
-0.82
-0.79
-1.71
-0.65
0.00
-0.33
-2.94
-1.83
3.31
-3.12
-1.47
-0.70
-2.66
-3.31
2.49
-1.18
0.05
-0.08
0.11
-1.31
-2.56
-1.45
-0.85
-0.34
-3.39
1.50
-1.72
-0.71
-1.38
1.87
-1.87
-2.37
2.83
-0.72
-1.16
-0.75
-1.26
-0.58
-2.27
0.10
0.81
-1.18
-1.56
-4.07
0.68
0.12
-0.50
1.23
-1.37
0.33
-1.11
1.16
-0.51
-1.41
-0.80
1.34
0.30
-1.42
2.41
0.32
-1.51
-2.53
0.03
2.30
2.07
-0.88
-2.69
-2.16
-2.49
1.06
4.12
3.81
1.80
-2.54
-1.69
-3.90
-3.61
-1.25
0.01
2.52
3.47
3.41
3.00
0.95
-2.26
-3.53
-3.21
-3.35
-2.67
-1.74
-0.93
0.62
5.15
4.07
4.92
4.17
3.83
1.54
-0.76
-1.36
-2.24
-4.00
-4.02
-2.75
-2.03
0.48
1.78
1.85
4.97
5.90
4.96
2.76
0.61
-0.24
-2.14
-3.26
-4.24
-4.56
-3.16
-0.17
0.72
-0.51
0.81
-0.74
-1.16
0.62
-0.27
1.96
-0.24
-1.73
2.38
1.66
1.54
1.21
2.58
2.66
-0.42
-2.37
0.14
2.14
2.66
0.95
0.36
-2.30
-2.09
0.53
1.78
2.98
2.14
1.29
0.34
-1.46
-3.29
-3.48
-1.03
-0.05
1.05
1.90
3.00
3.25
1.84
0.22
-0.82
-1.59
-2.39
-4.17
-3.00
-1.27
-1.05
1.01
1.42
2.95
4.13
4.25
3.46
2.60
1.02
-2.19
-3.71
-3.25
-4.36
-3.26
-0.94
-0.33
0.03
2.10
3.86
3.92
3.33
4.11
2.86
1.77
-0.22
-2.72
1.94
2.84
2.01
2.16
2.86
1.34
2.37
0.86
2.90
2.10
2.18
2.88
1.97
2.62
2.21
2.54
3.11
2.59
1.89
1.47
2.26
2.46
2.55
2.01
2.69
1.45
2.52
2.64
2.38
2.52
1.71
2.88
2.76
2.26
2.12
1.46
1.73
1.90
1.97
1.93
2.50
2.53
2.13
2.17
1.92
1.76
2.31
1.52
2.75
2.12
2.29
1.97
2.25
-2.18
2.24
1.97
1.86
2.19
2.29
2.22
1.82
1.93
1.55
0.78
2.18
2.18
2.03
1.88
1.65
1.71
2.06
1.90
2.06
1.95
1.75
0.28
-1.98
2.75
-0.01
-0.11
-2.40
-0.78
3.14
-0.85
-0.93
-1.28
-1.22
-1.46
-1.79
-1.49
-1.69
1.02
-0.93
-1.47
1.52
-1.58
-2.53
-1.99
-1.94
-0.66
-2.24
-2.13
-1.65
-0.76
-2.23
-1.49
-0.39
-0.23
-2.06
-0.63
-0.79
-0.80
-2.96
-1.40
-0.81
-0.78
0.82
-0.30
-2.64
-2.62
-2.08
-0.65
0.16
-1.71
0.05
-2.07
-0.78
-3.13
-1.78
-2.54
-1.23
-1.22
-0.70
-1.08
-0.68
0.30
-0.69
0.92
-1.36
0.89
-0.89
-0.14
2.43
-2.40
-1.33
-1.56
-2.75
-1.02
-0.86
-0.86
-1.57
-0.43
1.54
4.97
3.50
4.97
4.47
3.22
1.05
-0.39
-1.44
-3.20
-3.67
-3.88
-3.28
-2.42
1.00
2.68
3.03
2.27
5.73
4.96
4.02
2.16
0.25
-2.14
-3.67
-4.57
-3.99
-1.88
0.57
1.47
2.31
2.89
4.45
6.06
4.99
2.78
0.99
-1.07
-2.84
-3.67
-4.38
-2.88
-0.99
2.01
3.62
5.47
5.27
5.24
4.09
3.57
1.91
-0.33
-1.99
-4.08
-4.05
-0.07
3.05
3.61
4.07
4.69
2.49
0.65
-1.33
-3.21
-4.88
-3.55
0.96
1.70
4.21
4.97
4.98
1.63
-0.58
-4.04
-4.73
-2.64
-1.26
-0.95
0.31
2.67
3.03
4.73
4.15
4.80
3.95
2.16
-1.48
-3.54
-3.94
-3.90
-3.79
-2.59
-1.93
-0.76
1.40
3.32
4.68
4.83
4.51
3.33
0.80
-2.62
-4.15
-5.12
-4.79
-3.09
-1.17
-1.15
0.11
2.35
3.89
5.34
4.47
4.02
2.66
-0.57
-3.63
-4.78
-4.08
-3.37
-1.37
-0.41
0.62
2.67
3.50
4.20
4.96
4.09
1.62
-1.85
-4.92
-4.17
-1.97
-1.34
1.65
3.89
4.79
4.31
3.31
0.33
-2.91
-4.90
-4.58
-2.78
-0.98
-0.07
4.95
4.54
1.71
1.77
1.08
1.87
1.30
1.45
1.63
1.37
1.70
1.47
1.71
1.76
1.49
1.44
1.54
1.45
1.14
1.31
1.08
-0.76
-1.69
1.16
1.27
1.26
1.23
1.30
1.31
1.22
1.22
1.12
1.23
1.10
0.79
0.61
1.06
0.98
0.88
0.80
0.98
0.83
0.90
0.87
0.79
0.77
0.78
0.68
0.78
0.91
0.88
0.47
0.50
0.47
0.45
0.51
0.47
0.53
0.44
0.49
0.44
0.33
0.39
0.17
0.11
0.13
0.19
0.16
0.13
0.17
0.16
0.11
0.15
0.11
-0.17
-0.19
-0.22
-1.04
-0.60
-1.41
-0.50
-0.26
-1.72
-2.04
-1.11
-0.76
-0.98
-2.11
-0.91
-2.29
-2.07
-0.68
-0.57
-0.27
-1.24
-0.67
-0.60
-0.85
0.72
-1.22
-1.45
0.23
-1.08
-2.58
-0.74
-1.49
-0.33
-1.77
-0.61
-2.32
-1.43
-1.09
-1.96
-2.26
-2.19
-0.73
-0.66
-3.75
-0.69
-0.74
0.50
-3.39
-0.76
-1.15
-3.52
-1.14
-0.96
-1.91
0.31
-0.37
-1.74
-2.75
-0.85
-1.03
-4.17
-0.48
2.85
4.63
-1.56
-1.05
2.45
-3.06
-1.21
-2.01
-2.62
-2.56
0.62
-0.09
-3.11
-0.67
-0.96
-0.95
-4.14
-4.38
-4.84
-4.88
-2.25
2.22
3.42
4.28
4.31
3.24
-2.44
-4.70
-4.96
-4.13
-3.31
-0.51
1.29
1.29
2.94
4.77
5.10
1.01
-1.48
-3.68
-4.47
-4.58
-3.57
-1.57
0.45
1.31
2.18
4.17
4.95
4.00
2.34
-0.05
-4.29
-4.84
-5.13
-4.58
-2.51
-0.75
0.22
1.53
3.20
4.39
5.04
4.37
3.09
-0.86
-2.71
-4.08
-3.80
-4.17
-4.08
-3.17
-1.94
0.07
1.12
1.38
2.58
3.82
4.84
3.17
1.41
0.54
-1.95
-3.46
-4.03
-3.43
-4.07
-3.11
-2.80
0.48
0.32
2.60
1.15
-0.98
-2.14
-4.44
-3.52
-3.46
-1.94
2.42
3.47
3.78
1.95
-0.14
-2.30
-3.82
-5.55
-5.72
-2.96
-4.01
-1.41
0.99
4.21
4.43
3.54
0.57
-1.58
-2.98
-4.95
-5.20
-3.96
-2.63
-3.00
0.05
3.22
4.21
4.49
2.72
1.32
-0.80
-2.45
-4.22
-4.98
-5.94
-4.84
-2.41
-2.10
-0.87
1.73
3.60
4.44
3.12
1.84
0.00
-0.89
-1.76
-3.51
-5.15
-5.09
-5.52
-1.70
-1.51
-0.59
0.83
2.26
3.86
4.50
4.01
2.58
0.85
-0.68
-2.63
-2.51
-4.17
-5.85
-3.26
-0.24
-0.22
-0.24
-0.25
-0.22
-0.18
-0.20
-0.20
-0.55
-0.55
-0.57
-0.64
-0.61
-0.50
-0.59
-0.61
-0.63
-0.35
-0.52
-0.53
-0.91
-0.85
-0.95
-1.04
-0.90
-0.92
-0.83
-0.94
-0.69
-0.67
-0.57
-0.87
-1.19
-1.30
-1.27
-1.25
-1.44
-1.42
-1.43
-1.40
-1.24
-1.25
-1.46
-1.16
-0.93
-1.14
-1.22
-1.45
-1.51
-1.64
-1.55
-1.66
-1.38
-1.55
-1.58
-1.61
-1.80
-1.61
-1.77
-0.61
-0.86
-1.17
-1.90
-1.57
-1.78
-1.99
-2.03
-1.99
-1.90
-1.61
-1.98
-1.73
-2.08
-2.25
-1.25
-0.45
-1.30
-1.23
-1.20
-2.59
-2.01
-5.40
-0.20
-2.47
-3.24
-3.31
-1.29
-1.35
1.41
-5.07
-0.82
-0.38
0.16
-0.04
-0.29
-0.40
1.25
-0.43
-0.46
-3.22
0.06
1.55
-0.02
-1.41
-0.81
-2.26
1.29
0.03
1.36
-1.48
-0.81
-1.05
-2.84
-1.11
1.36
-0.04
-2.30
1.14
-0.56
0.64
-0.75
-0.66
1.71
0.78
-0.31
1.86
-0.53
-0.20
-1.51
-4.17
-0.72
-0.90
3.12
0.55
-2.46
2.57
-4.04
-2.25
0.65
2.44
-1.97
-2.01
0.16
-0.30
-0.55
-2.71
-4.99
-5.50
1.26
4.14
1.34
3.64
3.27
4.36
3.67
3.58
2.20
0.34
-1.25
-2.38
-3.07
-3.09
-3.23
-1.94
-1.24
0.26
0.73
1.59
1.19
2.87
4.11
2.76
1.95
-0.07
-0.96
-2.13
-3.12
-3.77
-2.14
-1.01
-0.60
0.32
0.73
0.69
1.86
3.30
2.70
1.25
0.84
-0.21
-1.22
-1.77
-2.86
-2.37
-0.57
2.57
1.90
1.91
0.47
-0.86
-2.86
-2.04
-1.41
2.54
1.27
-2.37
-2.60
-1.11
1.85
-0.27
-1.86
-1.44
-1.61
0.54
-0.97
-0.59
1.33
-1.76
0.29
0.95
-1.10
0.41
-0.53
-0.35
0.77
-4.08
-2.01
-1.25
-0.27
0.83
3.02
3.18
3.22
3.02
2.08
1.23
0.32
-1.56
-2.79
-4.05
-4.10
-4.81
-5.07
-2.48
0.01
1.30
1.33
3.89
4.19
3.81
3.05
1.91
1.61
-3.53
-4.62
-3.22
-2.42
-3.47
-1.81
-1.12
1.53
2.46
2.73
3.51
2.40
1.89
2.28
-0.42
-2.05
-2.34
-1.26
1.57
2.27
2.59
2.76
0.89
0.20
-2.89
0.57
2.08
1.72
-1.15
-2.22
-0.22
1.29
0.97
-0.76
-1.50
1.79
1.12
-1.43
0.64
0.17
-1.58
-0.95
0.03
0.69
-0.45
0.43
-0.12
-1.56
-1.48
-1.27
-1.98
-1.74
-2.29
-1.96
-1.76
-1.85
-1.83
-1.90
-1.78
-1.92
-1.72
-2.05
-1.84
-2.26
-2.39
-1.19
-1.49
-2.33
-1.71
-2.59
-2.61
-2.41
-2.47
-2.38
-2.69
-2.36
-2.58
-1.83
-1.23
-1.86
-0.94
-1.02
-2.29
-2.47
-2.17
-2.52
-1.91
-1.88
-2.32
-2.19
-2.26
-1.58
-1.57
-1.88
-2.37
-2.30
-2.63
-2.72
-1.99
-2.52
-2.08
-2.24
-3.07
-2.77
-2.19
-1.56
-1.83
-2.73
-2.01
-2.48
-2.54
-2.40
-1.79
-1.87
-3.02
-1.71
-1.12
-2.36
-1.90
-1.82
-2.82
-1.57
Table S1: Nucleosome pseudo-charges and relative postions on the nucleosome surface at CS = 0.15 M
obtained with the DiSCO approach.
2
Parameter
T
CS
l0
Lp
h
g
s
θ0
2w0
r0
σtt
σtc
σcc
σtl
σcl
σgLHc
σgLH1
σcLHc
σcLH1
kev
kevt
qgLH
qcLH
σLHLH
Description
Value
Temperature
Monovalent salt concentration (NaCl)
Equilibrium DNA segment length
Persistence length of linker DNA in monovalent salt
Stretching rigidity of linker DNA
Bending rigidity of linker DNA
Torsional rigidity constant of linker DNA
Angular separation between linker segments at core
Width of wound DNA supercoil
Radius of wound DNA supercoil
Excluded vol. distance for tail/tail interactions
Excluded vol. distance for tail/core interactions
Excluded vol. distance for core/core interactions
Excluded volume distance for tail/linker DNA interactions
Excluded vol. distance for core/linker DNA interactions
Excluded vol. distance for globular link. hist./core interactions
Excluded vol. distance for globular link. hist./link.DNA interactions
Excluded vol. distance for C-term. link. hist./core interactions
Excluded vol. distance for C-term. link. hist./link.DNA interactions
Excluded vol. energy param for all components except for tail beads
Tail/tail excluded volume interaction energy parameter
Charge on the globular linker histone bead
Charge on the C-terminal linker histone bead
Excluded volume distance for link.histone/link.histone interactions
293.15◦ K
0.15 M
3.0 nm
50 nm
100kB T/lo2
Lp kB T/lo
3.0×10−12 erg.nm
108◦
3.6 nm
4.8 nm
1.8 nm
1.8 nm
1.2 nm
2.7 nm
2.4 nm
2.2 nm
3.4 nm
2.4 nm
3.6 nm
0.001 kB T
0.1 kB T
13.88e
25.62e
2.0 nm
Table S2: Parameters employed in mesoscale modeling/simulation.
3
Tail
N-ter H3
N-ter H4
N-ter H2A
C-ter H2A
N-ter H2B
Bond
i-j
1-2
2-3
3-4
4-5
5-6
6-7
7-8
1-2
2-3
3-4
4-5
1-2
2-3
3-4
1-2
2-3
1-2
2-3
3-4
4-5
kb
(kcal/mol/AA)
0.09
0.06
0.07
0.07
0.07
0.07
0.11
0.10
0.10
0.06
0.20
0.08
0.09
0.03
0.07
0.07
0.08
0.10
0.08
0.08
Average
[Å]
15.6
15.0
15.6
16.1
16.1
15.1
14.9
14.1
15.2
14.8
14.7
14.1
15.3
14.5
15.7
13.7
14.7
14.1
16.2
15.1
SD
[Å]
2.3
3.0
2.9
2.6
2.6
2.9
2.4
2.6
2.4
2.8
1.8
2.6
2.5
3.4
2.6
2.6
3.1
2.3
2.4
2.7
Table S3: Protein bead stretching parameters.
Tail
N-ter H3
N-ter H4
N-ter H2A
C-ter H2A
N-ter H2B
Angle
i-j
1-2-3
2-3-4
3-4-5
4-5-6
5-6-7
6-7-8
1-2-3
2-3-4
3-4-5
1-2-3
2-3-4
1-2-3
1-2-3
2-3-4
3-4-5
kθ
(kcal/mol/AA)
1.1
1.0
1.7
1.2
1.2
1.5
1.0
1.1
0.5
1.1
0.6
1.0
0.9
0.6
1.6
Average
[Å]
108.6
108.1
111.3
117.6
110.4
110.5
103.2
106.0
103.6
108.5
100.1
100.7
104.9
103.9
113.8
SD
[Å]
28.8
28.6
25.4
27.8
29.3
27.2
25.4
25.8
35.5
29.0
29.3
31.8
35.1
28.4
26.7
Table S4: Protein bond-angle parameters.
4
(a) Interdigitated solenoid
1
6
7
11
2
5
8
10
3
9
4
(b) zigzag
6
4
1
2
3
5
7
Figure S1: Initial configurations and their interaction patterns.
5
ï400
40
(a) Energy, 182 bp
ï600
zigzag start
solenoid start
30
25
deg
kcal/mol
ï800
(b) Bending angle, 182 bp
35
ï1000
20
15
ï1200
10
120
140
0
5
(c) Triplet angle, 182 bp
110
100
100
80
deg
deg
90
80
60
70
40
60
20
50
40
0
5
10
15
20
25
million MC steps
30
0
35
ï1000
0
5
10
15
20
25
million MC steps
30
35
90
(e) Energy, 218bp
ï1200
(f) Bending angle, 218 bp
80
70
ï1400
ï1600
deg
kcal/mol
(d) Dihedral angle, 182 bp
120
ï1800
60
50
40
ï2000
30
ï2200
120
120
20
(h) Dihedral angle, 218 bp
(g) Triplet angle, 218 bp
100
100
80
deg
deg
80
60
60
40
40
20
20
0
10
20
30
million MC steps
40
50
0
0
10
20
30
million MC steps
40
50
Figure S2: Convergence of different quantities for 24-core 182-bp (top half) and 218-bp (bottom half)
oligonucleosome trajectories simulated with LH.
6
I’(i,j)
0.9
0.8
5
0.7
0.6
10
j
0.5
0.4
15
0.3
0.2
20
0.1
5
10
15
20
0
i
Figure S3: Internucleosome interaction matrix I $ (i, j).
7
Figure S4: Triplet, dihedral, and bending angles cartoons.
8
CS = 0.01 M
without LH
CS = 0.15 M
without LH
CS = 0.15 M
with LH
CS = 0.2 M
with LH
CS = 0.15 M
with Mg and LH
Short NRL
Medium NRL
Long NRL
Figure S5: Space filling model for representative 48-core arrays (short NRL: 173 bp, medium NRL: 209 bp,
and long NRL: 226 bp) at different salt concentrations. Nucleosomes, DNA linkers, and LH are colored as
in Figure 2.
9
Figure S6: Description of the fiber axis calculation for 24-unit oligonucleosome. (a) Cyan - nucleosome cores,
Red lines - connections between consecutive nucleosomes, Green line - fiber axis, as estimated by the least
squares procedure; (b) Fiber axis decomposition into three separate curves for three vectors (x, y, and z);
Blue dots - nucleosome centers, Green line - fiber axis, Red dots - separators between line segments of the
fiber axis.
10
Figure S7: Geometry of the mesoscale oligonucleosome showing (a) assembly of oligonucleosome components
into a chain, (b) entering/exiting linker DNA, and (c) individual coordinate systems for the linker DNA
beads and nucleosome core, and Euler angle β depicting the linker DNA bending. For nucleosome core i,
ai and bi lie in the nucleosome core plane, with ai pointing along the tangent at the attachment site of the
entering DNA, and bi in the direction normal to this tangent. For linker DNA bead i, the vector ai points
from the geometric center of i to either the center of the following DNA bead or to the attachment point in
points from the attachment point of the exiting linker
the nucleosome (if i + 1 is a core). The vector aDNA
i
−
DNA to the center of the following DNA linker bead. The vectors a+
i and ai represent the local tangents
on the nucleosome cores at the exiting and entering points of attachment, respectively.
11