I. Chromosome structure and dynamics

Biological Physics of
DNA, protein-DNA interactions,
and Chromosomes
Part I. Micromechanics of DNA
and its interactions with proteins
DNA and DNA-protein micromechanics
(emphasis on single-DNA studies)
DNA supercoiling and knotting
Part II. Chromosomes
bacterial chromosome – structure and dynamics
eukaryote chromosome – structure and mechanics
DNA-protein interactions
DNA folding (packaging)
looping < 1 pN
contacts > few pN
DNA processing (transcription, replication, recombination
and repair)
RNApol 40 pN
Micromechanics important part of the story
Molecular-biological forces
work done ~ kBT
reaction distances ~ nm
4 × 10
Joule
work
=
force =
-9
distance
10
meter
-21
= 4 × 10
-12
Newton = 4 pN
B-DNA
double helix
stiff polymer
genetic memory element
1 base-pair = 0.34 nm
1 helix turn = 10 bp = 3.5 nm
polyelectrolyte (2e-/bp)
[but 150 mM ion conc so
range of electrostatic
interactions ~ 2 nm]
Chemical bonds in dsDNA
C
G
T
A
G
A
T
C
T
A
C
G
NDB ID:
BDL042
TBP binding to dsDNA
D.B. Nikolov, H. Chen,
E.D. Halay, A. Hoffman,
R.G. Roeder, S.K. Burley
PNAS 1996
Bending Energy of an Elastic Rod
L
R
Bending Energy = ?
Bending Energy of an Elastic Rod
L
R
Bending
kT AL 1
kT AL 2
=
=
κ
2
Energy
2 R
2
For dsDNA A = 50 nm
How long a DNA is bent 1 rad by kT?
L
R=L
kT A L kT
Bending Energy =
=
2
2 L
2
DNA bends 1 rad about every
A = 50 nm or 150 bp
kT
Entropic force scale =
= 0.1 pN
A
DNAs longer than 150 bp (L >> A)
A
Every A along the
molecule its tangent
direction changes
DNAs longer than 150 bp (L >> A)
A
Every A along the
molecule its tangent
direction changes
Correlation in tangent
direction decays away
over contour length A
DNAs longer than 150 bp (L >> A)
A
Every A along the
molecule its tangent
direction changes
Correlation in tangent
direction decays away
over contour length A
Average end-to-end distance
= (2AL)1/2
L = 3 kb = 1µ circular DNA, ∆t=2 msec
step length
b=2A=100 nm
Random walk
overall size
R = 2 AL
= 300 nm
L = 50 kb = 16 µ DNA in aqueous solution
b=2A=100 nm
R = bL
R = 2 AL
= 1300 nm
This is only 1/90 of a 4.5 Mb E. coli chromosome
Micromanipulation of a single dsDNA
(S. Smith et al, Science 1992)
exploits AT and GC base pairing
49 kb λ dsDNA
ss overhangs on ends
ssDNA
+DIG
antiDIG
microscope slide
≡
ssDNA
+biotin
avidin
+3 µ
bead
5’-GGGCGGCGACCT-biotin
5’-GGGCGGCGACCT---------------CCCGCCGCTGGA-5’
49140 bp
dig-CCCGCCGCTGGA-5’
DNA single-molecule elasticity
Entropic regime:
kBT/A = 0.08 pN
z/L = 0.5
Elastic regime:
f = kBT/A to 3 kBT/nm
1 kBT/nm = 4 pN
z/L = 0.9
> 3 kBT/nm = 12 pN
Single-DNA elasticity
Smith, Bustamante, Finzi
Science 1992, 98 kb
These data from
Strick et al
Science 1995, 50 kb
Cluzel, Chatenay et al,
Science 1996, 50 kb
see also
Cui et al
Science 1996
Entropic elasticity of dsDNA
dr
du
κ=
u=
ds
ds
E
1
 2 f 
=
 u ⊥q
 Aq +
∑
kT 2 L q 
kT 
(suitable for
u⊥q
2
=
f > k BT / A)
L
Aq 2 + f / kT
k BT
z / L = 1−
4 Af
fit to expt data gives
A = 50 nm (150 bp)
1 kBT/nm = 4.1 pN (300 K)
2
Science (1994)
Macromolecules (1995)
PRE (1995)
A,B: Single-DNA polymer elasticity
k BT
f =
A
z

1
 +
− 1
2
 L 4(1 − z / L)

A = 50 nm
Regimes A,B sensitive to
DNA deformation by protein
‘effective persistence length’
Proteins that organize DNA can
easily be studied by micromanipulation
naked DNA
+ loops
+ sharp bends
Study the action of these proteins via mechanical
response of the DNA they are binding to
Build chromosome-like protein-DNA complexes
LEF-1 (Mouse)
HU
(E. coli)
HMGD (Human)
IHF (E. coli)
DNA-bending proteins: simple compaction effect
Yan and JM, PRE 2003
z
k BT / A
= 1−
+L
L
4f
2
k BT  1 
f =

 +L
4A 1− z / L 
NHP6A
HU
Effective persistence length
reduced by protein-generated
Bends
Easy to detect bends A = 150 bp
apart
20 kD DNA-bending proteins roughly
2 nm in size, cover 10 to 20 bp
DNA-bending proteins:
compaction effect
Yan and JM, PRE 2003
Skoko et al, Biochem 2004
NHP6A
HU
DNA-bending proteins:
compaction effect
Yan and JM, PRE 2003
Dame et al, PNAS 2004
Skoko et al, Biochem 2004
NHP6A
3,5,10,33,75 nM
HU
“bimodal”
C: Double helix stretching elasticity
z
f = f0
L
f 0 = 1100 pN
f0
Y = 2 = 300 MPa
πr
A,B vs C: Bending vs stretching elasticity
Y = 300 MPa
b = 100 nm
π Y r4
b=
2 k BT
D,E: Overstretching of DNA (S-DNA)
60 pN = 15 kBT / nm
= 5 kBT / bp
Work done
~ 3 kBT / bp
DNA melting
protein binding
thermal
fluctuation
RecA protein polymerizes onto DNA
and elongates it by 1.5x
Stasiak, Di Capua, Koller JMB 1981
h Rad51
Sc Rad51 Ec RecA
9.1 nm/turn
6.16 RecA/turn
18 DNA bases/turn
0.5 nm/base
Yu et al PNAS 98, 8419 (2001) EM data
lengthening in microns
RecA binding to DNA under tension
Leger et al, PNAS 1998
DNA Topology
dsDNA shape and free energy
depends on values of topological ‘charges’
DNA Supercoiling
Interlinking of two DNAs
Knotting of a DNA
Lk strand links
Ca molecule links
knot type
Cells control DNA topology (topoisomerases)
Statistical mechanics of polymers
with constrained topology is interesting physics
Double helix
linking number Lk
two strands are RH-linked
once every 10.5 bp
Lk0 = N / (10.5 bp)
= L / (3.5 nm)
σ = (Lk − Lk0) / Lk0
Energy cost to twist dsDNA
θ
L
E
C 2
=
θ
kT 2L
θ
2
L
=
C
-C = 75 to 100 nm
-one thermal twist every ~300 nm or 1000 bp
-linkage changes |σ| < 0.01 have small effect
on DNA conformation
σ = − 0.033
σ = − 0.062 (in vivo)
σ = 0.000 (relaxed)
σ = − 0.016
Boles, White, Cozzarelli JMB 1991
Plectonemic Supercoiling ( |σ| > 0.01 )
Separation of helix repeat (3.5 nm) and self-crossing
distance (~ A = 50 nm) allows separation of local
(twisting) and nonlocal (writhing) contributions to ∆Lk
Lk = Tw + Wr
Wr ≈
-1
-1
-1
-1
-1
dsDNA crossings can soak up ∆Lk, reducing Tw and
therefore “screening” the twisting energy
(RH)
Plectonemic Supercoiling ( |σ| > 0.01 )
E
C 2 A
2
=
θ + ∫ ds κ
kT 2L
2
θ = 2π (∆ Lk − Wr)
-1
-1
-1
-1
-1
Wr ≈ n for n-crossing tight plectoneme
Free energy extensive F ~ L f(σ)
(Experiments: F ≈ 10 kT Nbp σ2)
RH
Plectonemic Supercoiling ( |σ| > 0.01 )
E
C 2 A
2
=
θ + ∫ ds κ
kT 2L
2
θ = 2π (∆ Lk − Wr)
+1
+1
+1
+1
+1
Wr ≈ n for n-crossing tight plectoneme
Free energy extensive F ~ L f(σ)
(Experiments: F ≈ 10 kT Nbp σ2)
LH
Branching of Plectonemic Supercoils
is Entropically Favored
One ‘Y’ branch point per 2 kb
Large supercoiled DNA is annealed branched
polymer, R ~ L1/2
Internal ‘Slithering’ Dynamics
Internal ‘slithering’ motion in addition to
usual polymer bending modes - changes
branching & juxtapositions of distance sequences
No-branching slithering time ~L3
Slithering relaxation time ~ L2 (JM Physica A 1997)
Control of plectonemic supercoiling (E. coli):
1. DNA gyrase – injects ∆Lk = – 2, ATP-powered
+1
-1
2. Topoisomerase I – cuts one strand, Lk relaxes thermally
3. Transcription – generates + (ahead) and – supercoils
(behind)
Also, Lk of DNA is modified when bound to proteins
(contributes -0.02 to net σ in E. coli)
Knotting probability for
phantom circular Gaussian polymer
Punknot = e
− L /( 260 b )
L >> b
Characteristic length for a (trefoil) knot is 260 segments
(520 persistence lengths = 78 kb for ds DNA)
Where does this big polymer length scale come from?
Unknotting probability is exponential in chain
length for Gaussian and SA polymers
SA
u
ga
i an
ss
dsD
NA
Koniaris & Muthukumar
PRL 1991
‘Knotting length’ drastically increases with
self-avoidance
(gaussian)
(dsDNA)
(denatured
RNA or protein)
(Self-avoiding)
Koniaris & Muthukumar PRL 1991
(n.b. collapsed polymer case)
DNA Equilibrium Knotting
Probability
5.6 kb
8.6 kb
0.005
0.015
SW expt, SW expt,
theory
Theory
10 kb
0.02
RCV expt,
theory
100 kb
~ 0.5 (?)
theory
0.1 M NaCl ionic conditions, ring closure
Knots are rare on < 10 kb dsDNAs
Pknot = 0.01
Punknot = 0.99
Fknot − Funknot = 4.5 kT
Cellular control of knotting topology:
Topoisomerase II ∆Lk = ± 2, ATP-powered (Roca lect)
+1
-1
(Topo II in eukaryotes, Topo IV in E. coli)
Topo II is small (10 nm) compared to the size of a 10 kb
plasmid (500 nm) or a whole chromosome and cannot
determine topology by itself…
Topo II+ATP steady-state vs thermal equilibrium
(Rybenkov et al, Science 1997)
ea
t
s
e
at
t
-s
y
d
=
(
)2
m
u
i
r
li ib
u
eq
Entanglement-reducing effect of
plectonemic supercoiling
•experimentally observed (Zechiedrich et al 1997)
•simulations show this effect (Vologodskii & Cozz. BJ 1998)
•can be discussed in terms of free energy (Marko PRE 1999)
Local DNA compaction can reduce
entanglement
Punknot
e − L /( 300b ) L >> b
=
−8π 2b/L
L<b
1 − e
Make L smaller, b bigger
by local compaction
DNA
DNA + protein
DNA + many proteins = chromosome
bp, genes, chromosomes
1 bp = 0.34 nm
1 gene ~ 103 to 104 bp
1 chromosome ~ 103 to 104 genes ~ 106 to 109 bp
E. coli chromosome (1) ~ 4.5 106 bp (1.5 mm)
human chromosomes (23) ~ 108 bp each (3 cm)
newt chromosome (11) ~ 3 109 bp each (1 m)
Bacterial Chromosome
1. Folding scheme
-loops and supercoiling
2. Communication processes
-slithering over >10 kb distances
3. Chromosome is laid out linearly
E. Coli - one chromosome
4.5 Mb = 1.5 mm
2 microns
E. Coli - one chromosome
4.5 Mb = 1.5 mm
Random walk estimate of free coil size:
2A L = 0.1 µm × 1500 µm
= 13 µm
2 microns
dsDNA is at high concentration inside E. coli
E. coli chromosome = 4.5 Mb = 15,000 segments
nucleoid volume < 1 µm3 = 1000 segments3
so >15 segments per segment-length-cubed
(concentration of DNA ~ a few mg/ml)
Wang, Possoz, Sherratt Genes Dev 2005 E. coli (phase contrast)
J Struct Biol 2001, Bar 5 um
E. coli chromosome dragged out of lysed cell into gel
Bars 20 µm
Classical loop domain model
50 to 100 loops
Typical loop
60 to 100 kb
20 to 30 µm
Loop anchors?
‘Star Polymer’
L=1500 µm DNA
n=100 loops
L/(2n) DNA per
`bristle’
Chromosome size
= (2AL / 2n )1/2
~ 1 µm
(2A = 0.1 µm)
Plectonemic
Supercoiling
One branch/2 kb
‘branched star’
Chromosome
size still roughly
= ( 2AL / 2n )1/2
≈ 1 µm
DNA near DNA
DNA condensation
Short unconstrained DNA segment
< 1000 bp (300 nm)
DNA-DNA adhesion
(polyions)
Loop domain
elements (proteins?)
Bending/coiling
(HU, IHF, SMC)
Condensed DNA ‘disappears’ from total L in random-walk estimates
Self-avoidance increases
Studies of communication on the bacterial
chromosome and dynamics of supercoiled “domains”
Slithering
Random
collision/bending
“Random coil” collisions
Contour length between sites = L
Typical distance
d = (AL)1/2
Diffusion constant D= kT/ (ηd)
Time to diffuse distance d
τ = d2/D
τ = (η A3 / kT) (L/A)3/2
τ = (30 µsec) (L/A)3/2
≈ 20 msec for 10 kb
Typical time to first collsion
(Doi 1976)
τ = (η A3 / kT) (L/A)3/2 ln(L/A)
Effective viscosity for random collision?
“Slithering” inside a supercoil
Entire coil of length L must move
on order of distance L
Diffusion constant D= kT / (ηL)
Time to diffuse distance L
τ = L2/D
τ = (η A3 / kT) (L/A)3
τ = (30 µsec) (L/A)3
e.g. for L = 2 kb, L/A = 20
gives
τ = 0.2 sec
Branching of superhelix neglected in this
simple argument
PRE 1995
Slithering inside a supercoil + branching
One Y every 2 kb. Large supercoil is
‘living branched polymer’.
More complicated due to possibilities of:
branch birth/death
branch & branch-clump ‘sliding’
Scaling behavior (L is intersite distance)
τ = (200 µsec) (L/A)2
≈ 1 sec for 10 kb
100 sec for 100 kb
Physica A 1998, 2001
Resolvase only
acts on scDNA targets
separated by 3 RH nodes
Resolvase cuts efficiently
over 10 kb in vivo
Barriers to supercoil motion
are stochastic
Deng, Stein, Higgins Mol Micro 2005
Rapid growth
Higgins, Yang, Fu, Roth, J Bact 1996
Not growing
100 nm
500 nm
Postow, Hardy, Asuaga, Cozzarelli, Genes Dev 2004
Visualization of
small E. coli loop
domains
Teleman AA, Graumann PL, Lin DCH,
Grossman AD, Losick R Curr Biol 1998
(B. subtilis)
Rapid and sequential movement of individual chromosomal loci
to specific subcellular locations during bacterial DNA replication
(Caulobacter)
Viollier, Thanbichler, McGrath, West, Meewan, McAdams, Shapiro PNAS 2004
Chromosome and Replisome Dynamics in E. coli (E. coli)
Bates, Kleckner Cell 2005
Progressive segregation of the E. coli chromosome
Nielsen, Li, Youngren, Hansen, Austin
Mol Micro 2006
“Linear” nucleoid
One Y branch/2 kb
200 20 kb clumps
along ~1000 nm
One clump/50 nm
Chromosome
size determined by
inner “circuit”
Still question of
what are cross-linkers
Eukaryote Chromosomes
1. Chromosomes are made of a DNA-protein
fiber, one nucleosome/200 bp (‘chromatin fiber’)
2. Between cell divisions chromosomes are dispersed
3. During cell division chromosomes are formed into
isolated bodies (‘mitotic chromosomes’)
4. ‘Condensin’ SMC protein complexes play a vital
role in this process
5. Combined micromechanical-biochemical
properties of mitotic chromosomes
Nucleosome
(8 ‘histone’ proteins + 146 bp DNA)
basic organizational unit of chromosomes
K. Luger, A.W. Maeder, R.K. Richmond,
D.F. Sargent, T.J. Richmond, Nature 1997.
String of Nucleosomes
= Chromatin Fiber
10 mM
NaCl
10 nm
100 mM
NaCl
30 nm
•octamer+146 bp DNA + linker histone+20-50 bp DNA,
repeated every 180-200 bp
•extensible polymer (Cui & Bustamante, PNAS 2000)
•cm-long DNAs, mm-long chromatin fibers
•compaction factor, physical properties not clear
•cell-cycle dependence of chromatin structure
•enzyme modifications of chromatin structure
NSB 2001
Xenopus egg extract + λ DNA
(48.5 kb = 16.5 µm)
Ladoux et al PNAS 2000
Compacted chromatin ~ 1/10 DNA length
Nucleosome pop-off (buffer)
> 15 pN
Force constant ~ 10 pN
Persistence length ~ 30 nm (?)
WD ~ 50 nm x 15 pN = 180 kT = 120 kcal/mol
Nonequilibrium crossing of
large free energy barrier to nucl removal
In-plane magnetic tweezer (Yan Jie)
97 kb 32.8 µm dimer of λ
•micropipette holds left 3 µm bead
•right bead under 1 pN tension applied by magnet to right
Chromatin (nucleosome)
assembly onto 97 kb DNA against 1 pN, Yan Jie
(collab. Tom Maresca, Rebecca Heald, UC Berkeley)
•Xenopus high-speed interphase extract, diluted w/ buffer
(Ladoux et al PNAS 2000, Bennink et al NSB 2001)
•32.8 m DNA becomes 3.6 m fiber (400 nucl) in 600 sec
•Starting point for chromatin structure studies ‘in extractio’
Force-controlled nucleosome assembly/disassembly, -ATP
(a) 2.8 pN
(c) 3.5 pN
(b) 2.8 pN
(d) 4.5 pN
79 kb bare DNA
40
(f) 9.6 pN
15 kb
36
(g)
32
28
3.9
Count
(e) 15 pN
Length (µm)
4.0
3.8
24
20
16
12
8
4
3.7
0
0
50
100
150
200
250
Time (sec)
0
20 40 60 80 100 120 140 160 180 200 220
Step size (nm)
Nucleosome open-close equilibrium (extract) ~ 3 pN
∆G ~ 50 nm x 3 pN = 35 kT = 25 kcal/mol
N
+ATP stimulates processive opening/closing events
(a) -ATP 3.5 pN
(b) +ATP
3.5 pN
What ATPase is responsible for this?
Plan to use antibodies to deplete specific enzymes
(ISWI family chromatin remodeling enzymes)
Add purified enzymes to assembled fibers
Chromatin organization - between cell divisions
Attachments/loops every ~100 kb
(Jackson et al 1990)
Territories
(T. Cremer et al
CSHSQB 1993
JMB 1999)
Self-contact map
consistent with RW, b~60 nm
(J. Dekker et al Science 2002)
Random-walk structure
R = (bL)1/2
at two scales, suggesting
both b = 60 nm and
Mbp loop structure
(Sachs et al PNAS 1995)
Diffusive ~1 µm
motions in vivo
suggesting polymer
motion of loops of
chromatin
(Marshall et al
Curr. Biol. 1997)
(1.5 µm)2/Mbp = (50 nm)2/kb
+ larger-scale loop structure
Sachs, Trask, Yokota, Hearst
PNAS 1995
(also JMB 1995)
Levi, Ruan, Plutz, Belmont, Gratton BPJ 2005
+ATP
2x10-4 µm2/s
3x10-3 µm2/s
-ATP
Bar: 20 µm
Paulson & Laemmli Cell 12, 817 1977
Stack & Anderson
Chromosome Res. 9, 175 (2001)
Compacted Mitotic Chromatid
A
•Suggested by observed
loops released from
de-proteinized metaphase
chromosomes
(Laemmli et al, 1977)
B
•Suggested by other
EM studies
(Belmont et al, 1987)
New development in 1990s - SMCs
•ATPase essential for chromosome compaction during mitosis
•Introducing antibodies to block leads to chromosome disassembly
(Hirano and Mitchison Cell 1994)
•Related proteins involved in a
variety of chromosome dynamics
•Basic structure is long (0.1 µm)
heterodimeric (2 x 1200 aa)
hinged stick
•Thought to be able to switch conformation
possibly from open to closed
•Homologues found in eubacterial
(E. coli MukB)
(Nasmyth, Haering ARBiochem 2005)
SMCs are essential to form and maintain mitotic
chromosomes (Hirano and Mitchison JCB 1993)
−XCAP-C
before
assembly
Native extract
−XCAP-C after (10’)
(30’)
10 µm
+ATP
Strick, Kawaguchi, Hirano Curr Biol 2004
-ATP
+AMP-PNP
http://www.npwrc.usgs.gov/
narcam/idguide/rsnewt.htm
Extraction of a mitotic
chromosome from a newt cell
M.G. Poirier Ph.D. `01
Native mitotic chromosomes are elastic
Y=300 Pa
Elastic regime: x < 5
f0 = 1 nN
Y = 300 Pa
Poisson ratio
= +0.08
Poirier et al
Mol Biol Cell
2000
Shifting local ionic conditions
100 mM MgCl2 in culture buffer
Ionic strength shifts can unfold mitotic chromosome in < 1 sec
Reversible for short (< 100 sec) exposures
Swelling and condensation isotropic
Na+
< 50 mM : decondensed (Coulomb repulsion opens chromatin fiber)
50 to 200 mM : native
>500 mM : decondensed (‘puffed’ - screening of interactions)
Mg++ (added to 100 mM NaCl of extracellular buffer)
10 to 100 mM : condensed (bridging)
>100 mM
: decondensed (screening)
(NH3)6Co+++ (added to 100 mM NaCl of extracellular buffer)
~1 to 150 mM : condensed (bridging)
> 150 mM
: decondensed (screening)
Microscopic network version of experiments on actin, DNA
(J. Cell. Biochem. 2002)
What happens when we cut DNA only?
MC nuclease digestion, 0.1 nN initial tension
Force (nN)
Force vs time, spray w/ 1 nM MNase
Time (sec)
Extension after light MC nuclease
digestion at zero tension
Invisible fibers cut by puff of 1 nM MNase
Structural element of chromosome is chromatin
Non-DNA components not tightly connected
Restriction enzymes cut up chromosomes
Longer recog sequences suppress cutting
Buffer with no enzyme
Dra I
TTT^AAA
Hinc II GT(T/C)^(A/G)AC
Cac8 I
Alu I
GCN^NGC
AG^CT (1/256)
Network with node spacing of around 50 kb
Proteolysis reduces but does not eliminate elastic response
a
0s
b
30
90
270
390
0s
Increasing trypsin digestion
c
120
180
250
Increasing proteinase K digestion
d
100 nM trypsin
0s
60
500 nM proteinase K
0s
30
90
270
30
60
390
90
120
L.H. Pope MBC 2006, see also experiments of Maniotis 1997, Almagro 2004
Proteolysis leads to a strong swelling of the mitotic chromosome
but never breaks or dissolves it
Chromosome still elastic with well-defined shape
after >30 min proteolysis
0s
30
60
120
240
480
Enhanced contrast
840
Extensive proteinase K digestion
1320
L.H. Pope MBC 2006
1320
Problems to work on:
What molecules and organizational principles
define bacterial chromosome domains,
and how dynamic and fluid are those domains in the cell?
What is the mechanism of condensin SMCs, and how
does that mechanism contribute to mitotic chromosome
shape and structure?
How does large-scale (> 10 kb) Brownian motion of
chromosomal domains affect biologically relevant
chromosome dynamics?
Michael Poirier, Abhijit Sarkar
Chee Xiong, Dunja Skoko, Yan Jie
Hua Bai, Botao Xiao, Lisa Pope
University of Illinois at Chicago
Rebecca Heald, Tom Maresca UCB
Reid Johnson UCLA
NSF-DMR, Whitaker Foundation,
ACS-PRF, Research Corporation,
Johnson & Johnson