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