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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. Chromosomesbacterial chromosome – structure and dynamics
eukaryote chromosome – structure and mechanics
DNA-protein interactionsDNA folding (packaging)
DNA processing (transcription, replication, recombinationand repair)
Micromechanics important part of the story
RNApol 40 pN
looping < 1 pNcontacts > few pN
Molecular-biological forces
work done ~ kBTreaction distances ~ nm
pN 4 Newton 104
meter10
Joule104
distance
work force
12-
9-
-21
=×=
×==
B-DNA
double helixstiff 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
GNDB 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
?Energy Bending =
R
Bending Energy of an Elastic Rod
L
nm 50 A dsDNA For
κ 2
LA kT
R
1
2
AL kT
Energy
Bending 2
2
=
==
R
How long a DNA is bent 1 rad by kT?
L
pN 1.0A
kT scale force Entropic
bp 150or nm 50 A
everyabout rad 1 bends DNA
2
kT
L
L
2
A kTEnergy Bending
2
==
=
==
R = L
DNAs longer than 150 bp (L >> A)
AEvery A along the
molecule its tangent
direction changes
DNAs longer than 150 bp (L >> A)
AEvery 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)
AEvery 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
step length
b=2A=100 nm
ALR 2== 300 nm
Random walk
overall size
L = 3 kb = 1µ circular DNA, ∆t=2 msec
L = 50 kb = 16 µ DNA in aqueous solution
b=2A=100 nm
bLR =
ALR 2== 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 dsDNAss overhangs on ends
ssDNA
+DIG
ssDNA
+biotin
antiDIGavidin
+3 µbeadmicroscope slide
≡
5’-GGGCGGCGACCT-biotin
5’-GGGCGGCGACCT----------------CCCGCCGCTGGA-5’49140 bp
dig- CCCGCCGCTGGA-5’
DNA single-molecule elasticity
kBT/A = 0.08 pN
z/L = 0.5
1 kBT/nm = 4 pN
z/L = 0.9
Entropic regime: f = kBT/A to 3 kBT/nm
Elastic regime: > 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
Science (1994)
Macromolecules (1995)
PRE (1995)
bp) (150 nm 50A
gives dataexpt fit to
41/
/u
)/for suitable(
u2
1
uru
2
2
22
=
−=
+=
>
+=
==
⊥
⊥∑
Af
TkLz
kTfAq
L
ATkf
kT
fAq
LkT
E
ds
d
ds
d
B
q
B
q
q
κ
1 kBT/nm = 4.1 pN (300 K)
A,B: Single-DNA polymer elasticity
nm 50
1)/1(4
12
=
−
−+=
A
LzL
z
A
Tkf B
Regimes A,B sensitive to
DNA deformation by protein
‘effective persistence length’
Proteins that organize DNA caneasily be studied by micromanipulation
naked DNA
+ sharp bends
Study the action of these proteins via mechanicalresponse of the DNA they are binding to
Build chromosome-like protein-DNA complexes
+ loops
HMGD (Human)
HU(E. coli)
LEF-1 (Mouse)
IHF (E. coli)
DNA-bending proteins: simple compaction effect
HU
Yan and JM, PRE 2003
NHP6A
L
L
+
−=
+−=
2
/1
1
4
4
/1
LzA
Tkf
f
ATk
L
z
B
B
Effective persistence lengthreduced by protein-generatedBends
Easy to detect bends A = 150 bpapart
20 kD DNA-bending proteins roughly2 nm in size, cover 10 to 20 bp
DNA-bending proteins: compaction effect
HU
Yan and JM, PRE 2003Skoko et al, Biochem 2004
NHP6A
DNA-bending proteins: compaction effect
HU“bimodal”
Yan and JM, PRE 2003Dame et al, PNAS 2004Skoko et al, Biochem 2004
NHP6A
3,5,10,33,75 nM
C: Double helix stretching elasticity
MPa 300 π
pN 1100
2
0
0
0
==
=
=
r
fY
f
L
zff
A,B vs C: Bending vs stretching elasticity
nm 100=b
MPa 300=Y
Tk
rYb
B
4
2
π =
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
RecA binding to DNA under tension
lengthening in m
icrons Leger et al, PNAS 1998
DNA Topology
dsDNA shape and free energy
depends on values of topological ‘charges’
DNA Supercoiling Lk strand links
Interlinking of two DNAs Ca molecule links
Knotting of a DNA 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
L
θ
C
L θ θ
2L
C
kT
E 2 == 2
-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 = 0.000 (relaxed)
σ = − 0.062 (in vivo) σ = − 0.016 Boles, White, Cozzarelli JMB 1991
Plectonemic Supercoiling ( |σ| > 0.01 )
WrTwLk +=
Wr ≈ -1 -1 -1 -1 -1 (RH)
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
dsDNA crossings can soak up ∆Lk, reducing Tw and
therefore “screening” the twisting energy
Plectonemic Supercoiling ( |σ| > 0.01 )
Wr)Lk∆(2πθ
κ ds2
A θ
2L
C
kT
E 2
−=
+= ∫2
Wr n for n-crossing tight plectoneme
Free energy extensive F ~ L f(σ)(Experiments: F 10 kT Nbp σ2)
≈
≈
-1 -1 -1 -1 -1 RH
Plectonemic Supercoiling ( |σ| > 0.01 )
Wr)Lk∆(2πθ
κ ds2
A θ
2L
C
kT
E 2
−=
+= ∫2
+1 +1 +1 +1 +1 LH
Wr n for n-crossing tight plectoneme
Free energy extensive F ~ L f(σ)(Experiments: F 10 kT Nbp σ2)
≈
≈
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
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)
+1 -1
Knotting probability for
phantom circular Gaussian polymer
bLeP bL >>= − )260/(
unknot
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
Koniaris & Muthukumar
PRL 1991
dsDNA
gaussian
SA
‘Knotting length’ drastically increases with
self-avoidance
Koniaris & Muthukumar PRL 1991
(n.b. collapsed polymer case)
(gaussian)
(Self-avoiding)
(dsDNA)
(denatured
RNA or protein)
DNA Equilibrium Knotting
Probability
5.6 kb 8.6 kb 10 kb 100 kb
0.005
SW expt,
theory
0.015
SW expt,
Theory
0.02
RCV expt,
theory
~ 0.5 (?)
theory
0.1 M NaCl ionic conditions, ring closure
Knots are rare on < 10 kb dsDNAs
kT 5.4
99.0 01.0
unknotknot
unknotknot
=−==
FF
PP
Cellular control of knotting topology:
Topoisomerase II ∆Lk = ± 2, ATP-powered (Roca lect)
(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…
+1 -1
Topo II+ATP steady-state vs thermal equilibrium
(Rybenkov et al, Science 1997)
steady-state = (equilib
rium)2
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
Make L smaller, b bigger
by local compaction
<−>>
=−
−
bLe
bLeP
b/L
bL
2π8
)300/(
unknot1
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
2 microns
mµ 13
mµ 1500 mµ 1.0L2A
=×=
Random walk estimate of free coil size:
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 Loop domain Bending/coiling
(polyions) elements (proteins?) (HU, IHF, SMC)
Condensed DNA ‘disappears’ from total L in random-walk estimates
Self-avoidance increases
Random
collision/bending
Slithering
Studies of communication on the bacterial
chromosome and dynamics of supercoiled “domains”
“Random coil” collisionsContour 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 onlyacts on scDNA targetsseparated by 3 RH nodes
Resolvase cuts efficiently over 10 kb in vivo
Barriers to supercoil motionare stochastic
Deng, Stein, Higgins Mol Micro 2005
Rapid growth Not growing
Higgins, Yang, Fu, Roth, J Bact 1996
Postow, Hardy, Asuaga, Cozzarelli, Genes Dev 2004
Visualization of
small E. coli loop
domains
500 nm
100 nm
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
basic organizational unit of chromosomesK. Luger, A.W. Maeder, R.K. Richmond,
D.F. Sargent, T.J. Richmond, Nature 1997.
Nucleosome
(8 ‘histone’ proteins + 146 bp DNA)
String of Nucleosomes= Chromatin Fiber
10 mMNaCl
10 nm
100 mMNaCl30 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
Nucleosome pop-off (buffer) > 15 pN
WD ~ 50 nm x 15 pN = 180 kT = 120 kcal/molNonequilibrium crossing oflarge free energy barrier to nucl removal
Xenopus egg extract + λ λ λ λ DNA(48.5 kb = 16.5 µµµµm)Ladoux et al PNAS 2000
Compacted chromatin ~ 1/10 DNA length
Force constant ~ 10 pN
Persistence length ~ 30 nm (?)
NSB 2001
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’
0 20 40 60 80 100 120 140 160 180 200 2200
4
8
12
16
20
24
28
32
36
40
Cou
nt
Step size (nm)0 50 100 150 200 250
3.7
3.8
3.9
4.0
Leng
th (
µm)
Time (sec)
(a) 2.8 pN (b) 2.8 pN(d) 4.5 pN
(e) 15 pN
(c) 3.5 pN
79 kb bare DNA
(f) 9.6 pN15 kb (g) N = 188
Force-controlled nucleosome assembly/disassembly, -ATP
Nucleosome open-close equilibrium (extract) ~ 3 pN
∆∆∆∆G ~ 50 nm x 3 pN = 35 kT = 25 kcal/mol
(a) -ATP 3.5 pN (b) +ATP
3.5 pN
+ATP stimulates processive opening/closing events
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 divisionsAttachments/loops every ~100 kb
(Jackson et al 1990)
Territories
(T. Cremer et al
CSHSQB 1993
JMB 1999)
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)
Self-contact map
consistent with RW, b~60 nm
(J. Dekker et al Science 2002)
(1.5 µm)2/Mbp = (50 nm)2/kb
+ larger-scale loop structure
Sachs, Trask, Yokota, Hearst
PNAS 1995
(also JMB 1995)
+ATP
-ATP
2x10-4 µm2/s
3x10-3 µm2/s
Levi, Ruan, Plutz, Belmont, Gratton BPJ 2005
Bar: 20 µm
Paulson & Laemmli Cell 12, 817 1977
Stack & Anderson
Chromosome Res. 9, 175 (2001)
Compacted Mitotic Chromatid
A
B
•Suggested by observed
loops released from
de-proteinized metaphase
chromosomes
(Laemmli et al, 1977)
•Suggested by other
EM studies
(Belmont et al, 1987)
•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)
New development in 1990s - SMCs
SMCs are essential to form and maintain mitotic
chromosomes (Hirano and Mitchison JCB 1993)
Native extract
−XCAP-Cbefore
assembly
−XCAP-C after (10’) (30’)10 µm
+ATP
-ATP
+AMP-PNP
Strick, Kawaguchi, Hirano Curr Biol 2004
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 elasticY=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 isotropicNa+
< 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 vs time, spray w/ 1 nM MNase
Time (sec)
Force (nN)
Extension after light MC nuclease digestion at zero tension
Invisible fibers cut by puff of 1 nM MNaseStructural element of chromosome is chromatin
Non-DNA components not tightly connected
Restriction enzymes cut up chromosomes
Longer recog sequences suppress cutting
Network with node spacing of around 50 kb
Buffer with no enzyme
Dra I TTT^AAA
Hinc II GT(T/C)^(A/G)AC
Cac8 I GCN^NGC
Alu I AG^CT (1/256)
0 s 30 90 390270 0 s 60 120 180 250
c
a b
Increasing trypsin digestion Increasing proteinase K digestion
Proteolysis reduces but does not eliminate elastic response
0 s30
90
270
390
100 nM trypsin
0 s
3060
90120
500 nM proteinase Kd
L.H. Pope MBC 2006, see also experiments of Maniotis 1997, Almagro 2004
Proteolysis leads to a strong swelling of the mitotic chromosomebut never breaks or dissolves it
Chromosome still elastic with well-defined shape after >30 min proteolysis
0 s30
60
120 240
480840
1320
Enhanced contrast
1320
Extensive proteinase K digestion
L.H. Pope MBC 2006
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 UCBReid Johnson UCLA
NSF-DMR, Whitaker Foundation,
ACS-PRF, Research Corporation,
Johnson & Johnson