„virtuelle strahlen-biophysik: einflüsse der zellkernarchitektur„

Kirchhoff-Institute for Physics, University of Heidelberg

G. Kreth, SKIP, Heidelberg, 05.08.2004

„Virtuelle Strahlen-Biophysik: Einflüsse der Zellkernarchitektur„

• Monte Carlo modeling of the genome structure of the cell nucleus

• Virtual radiation biophysics

• Comparison with experimental data



Fixed cells

Chromosome Painting experiments

I. Solovei, F. Habermann, M. Cremer, T. Cremer

(Institute of Anthropology and Human Genetics University of München)

Living cells

H. Bornfleth, D. Zink, T. Cremer



Spherical 1-Mbp Chromatin Domain (SCD) model

Scheme

1-Mbp domain

Bead i-1

Bead i

Bead i+1

Bead i+2ui-1 ui

ui+1

"Entropic" spring potential between neighbored 1-Mbp domains

nm600LL2l

,ll2

kT3)l(U

0p0

220

s

A

B

0FB FA

0 0.2 0.4 0.6 0.8 1Abstand der 1-Mbp Domänen in Einheiten von D

0

0.2

0.4

0.6

0.8

1

En

erg

ie in

U0k B

T ,

Kra

ft in

4k B

T/D

4 KraftPotential

KT

nmD

kTU

D

rDrUrU

e

ee

300

500

5.1

,2

1)(

0

4

2240

"Excluded Volume" Interaction between domains

N

iicc

genome

chromosomenucleusterr

terrterre

terr

t

rN

rrrrc

cRR

aRrfüraRra

kTU

aRrfürrU

1

3

1

0

1,,

1.0

0)(

Weak enveloping spherical potential barrier around each territory

1-Mbp Domäne

Bead i-2

Bead i-1

Bead i

Bead i+1Bead i+2

Bead i+3

rcRTerr

a



„Importance Sampling“ Monte Carlo method

x

x)x()x(x)x(1

)x(

/)x(

/)x(

deZ

dApdAeZ

A

TkH

TkH

B

BTkH Be

Zp /)x(1

)x(

normalized Boltzmann factor

Simple Sampling Monte Carlo method:

choose randomly N states x1, x2, ...., xN

from phase space

N

iii ApA

1

)x()x()x(

Importance Sampling Monte Carlo method:

choose states x1, x2, ...., xN with a probability P(xi) from phase space

with P(xi)~exp(-H(xi)/kBT)

Expectation value of a canonic ensemble

N

ii

i

i AP

pA

1

)x()x(

)x()x(

N

iiA

NA

1

)x(1

)x(

idea of Metropolis: consecutive states are generated by a transition probability (Markov process). The choice of the transition probability has to be made in such a way that the probability function P(xi) of the states convergence against the equilibrium distribution

TkHGli

BieZ

P /)x(1)x(



„Metropolis algorithm“

1. Choose randomly a state from phase space .

2. An accessible state from phase space is chosen.

4. The energy difference H between the new and the old state is computed.

4. If H<0 the new state will be accepted.

5. If H>0 the new state is accepted with the probability exp(- H/kT).

That means, when a random number from [0;1] < exp(- H/kT) than the new

state is accepted.

6. Go back to 2.



Monte Carlo Relaxation (no real time dependency)

0 MC

1000 MC

20m0 1e+05 2e+05 3e+05 4e+05

Monte Carlo Cycle

0

500

1000

1500

2000

2500

3000

gyr a

ti on

r ad

ius

[nm

]

chromosome 1chromosome 12chromosome 24

N

1i

ic

N

1n

2

cn2g r

N

1r,rr

N

1r



Additional constraints of the higher order nuclear architecture:

•distribution of chromosome territories in the nuclear volume

•the morphology of the active and inactive X-chromosome



Positioning of chromosomes in

lymphocyte cell nuclei



Positioning of chromatin homologous to human CTs #18(red, gene poor) and #19(green, gene rich) in lymphocyte nuclei of higher primates (Tanabe et al. 2002)

Human

Chimpanzee

Gorilla

Marmoset

Orangutan

Tamarin



3D mapping algorithm



differential DNA-content of chromosome territories # 18 versa # 19 in 31 human lymphoblastoid nuclei in 3D

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70 80 90 100 110relativ radius

dif

fere

nti

al D

NA

-co

nte

nt

wit

h S

DM

in %

o

fch

rom

atin

of

the

co

nce

rnin

g

chro

mo

so

me

# 18

# 19

counterstain distr.

differential DNA-content of chromosome territories # 18 versa # 19 in 41 Chimpanzee (PTR) nuclei in 3D

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70 80 90 100 110relativ radius

dif

fere

nti

al D

NA

-co

nte

nt

wit

h S

DM

in %

o

fch

rom

atin

of

the

co

nce

rnin

g

chro

mo

so

me

# 18

# 19

counterstain distr.

differential DNA-content of chromosome territories # 18 versa # 19 in 30 Gorilla (GGO) lymphoblastoid nuclei in 3D

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70 80 90 100 110relativ radius

dif

fere

nti

al D

NA

-co

nte

nt

wit

h S

DM

in %

o

fch

rom

atin

of

the

co

nce

rnin

g

chro

mo

so

me

# 18

# 19

counterstain distr.

differential DNA-content of chromosome territories # 18 versa # 19 in 31 Orang Utan (PPY) lymphoblastoid nuclei in 3D

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70 80 90 100 110relativ radius

dif

fere

nti

al D

NA

-co

nte

nt

wit

h S

DM

in %

o

fch

rom

atin

of

the

co

nce

rnin

g

chro

mo

so

me

# 18

# 19

counterstain distr.

Mapping of CTs: comparison (#18) and (#19)

Human Chimpanzee

Gorilla Orang Utan



Summary of primate #18 and #19 sequencies distribution in lymphocyte nuclei

<r18> sd <r19> sdSquirrel Monkey 75,4 10,8 55,5 11,7Common Marmoset 76,9 6,0 53,0 8,9Tamarin 80,7 8,2 60,2 6,6White Handed Gibbon 72,0 11,2 52,8 10,3Orang Utan 73,8 8,1 46,8 11,6Gorilla 75,2 7,3 56,5 10,0Chimpanzee 72,0 11,2 52,8 10,3human 79,2 9,0 48,8 8,3

Mean of mean: 75,7 +- 3,2 | 53,3 +-4,3

<r18>,<r19> : mean value of radial distributions of #18, 19sd : standard deviation



Virtual Microscopy

15874nm

chromosome 3 territories

Simulation of the human genome structure

digitization(62x62x248nm)

convolution with a measured PSF(FWHM:204x245x793nm)

photon noise(100 photons in the maximum)

mid sections

Virtual microscopy



simulated gene density correlated distribution

#17

#22

nucleolus

nucleus

#19

#17

#22

nucleolus

nucleus

#17#19

statistical gene density correlated

Virtual microscopy reconstructions

of simulated CTs #18(red)

and #19 (green)



Radial distribution of chromosome territories

Simulation (statistical distribution) Experiment (lymphocyte cell nuclei)

Experiment (37 nuclei)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110

relative radius

dif

fere

nti

al D

NA

-co

nte

nt

counterstain distribution# 18

# 19

Experiment (31 nuclei #12 and 30 nuclei #20)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110

relative radius

dif

fere

nti

al D

NA

-co

nte

nt


# 20

Simulation (statistical,ncbi; 50 nuclei)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110relative radius

dif

fere

nti

al D

NA

-co

nte

nt

counterstain distribution.# 18

# 19

Simulation (statistical,ncbi; 50 nuclei)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110

relative radius

dif

fere

nti

al D

NA

-co

nte

nt

counterstain distribution.# 12# 20



Radial distribution of chromosome territories

Simulation (gene density correlated distribution) Experiment (lymphocyte cell nuclei)

Experiment (37 nuclei)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110

relative radius

dif

fere

nti

al D

NA

-co

nte

nt


# 19

Experiment (31 nuclei #12 and 30 nuclei #20)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110

relative radius

dif

fere

nti

al D

NA

-co

nte

nt


# 20

Simulation (probabilistic,ncbi; 50 nuclei)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110

relative radius

diff

ere

nti

al D

NA

-co

nte

nt

counterstain distribution.# 18 # 19

Simulation (probabilistic,ncbi; 50 nuclei)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100 110

relative radius

dif

fere

nti

al D

NA

-co

nte

nt

counterstain distribution.# 12

# 20



Morphology of X-chromosomes

amniotic fluid cell

volume rendering optical section

Xa

Xi Xi

Xa

Visualization: C. Dartu, W. Jäger

( IWR, University of Heidelberg)



Simulation of the Xa and Xi chromosome

XaE x p e r im e n ta l :( E i l s e t a l . 1 9 9 6 )

V o lu m e r a t io : V o l ( X a ) / V o l ( X i )S u r f a c e r a t io : A e n v ( X a ) / A e n v ( X i)

V ir t u a l : T r u e :a f te r c o n v o lu t io na n d s e g m e n ta t io n w i th a g lo b a l

t h r e s h o ld ( 1 0 - 1 3 % )

s e g m e n ta t io n w i th a

t h r e s h o ld ( 0 .4 % )

S im u la t io n :

2.1~(Xi) Vol

(Xa) Vol

4.1~(Xi) Aenv

(Xa) Aenv

2.1~(Xi) Vol

(Xa) Vol

2.1~(Xi) Aenv

(Xa) Aenv

7.1~(Xi) Vol

(Xa) Vol

8.1~(Xi) Aenv

(Xa) AenvConvolution with the measured PSF Segmentation,

Visualization

Convolution with the measured PSF

I

globalthreshold

Xa

Xi

Xa

Xi



Interchange frequencies:

comparison of Observation and Simulation



Virtual radiation algorithm

• Random distribution of DSBs within DNA

• number of DSBs increases linearly with dose and is proportional to the DNA content

• probability p n of an individual modeled 1Mbp domain containing n DSBs:

!n

ebp

bn

n

qDb

D - dose of radiation in (Gy)

q - size of a domain (=1000000bp)

- yield of DSBs (=8.07 ·10-9Gy-1bp-1)

• interchange is counted when the distance d of two DSBs in two directly neighbored domains followed:

4.1

4.1

[1;0[d

rpd

1Mbp domain

d

DSB

Intra-change

Inter-change

Chromosome territory i

Chromosome territory j



Influence of chromosome distribution on interchange frequencies

absolute interchange frequencies in %, examples:

(4;18) (4;19) (19;18)

Exp. (1600 cells): 0.3% 0.3% 0.1%

statis. Simul. (50000cells): 0.6% 0.7% 0.3%

gendens. corr. Simul. (50000cells): 0.6% 0.2% 0.1%



Influence of chromosome distribution on interchange frequencies

Relative one-chromosome yield (normalized to 1000)

individual autosome yields

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Chromosome number

rel.

on

e-c

hro

mo

som

e y

ield

simul. statistical distribution (1600 cells)

simul. gene density correlated distribution (1600 cells)

exp. Cornforth et al. (1587 cells)

Error bars: E ± (E)1/2

E



Influence of chromosome distribution on interchange frequencies*

Relative one-chromosome yield (normed to one)irradiation of lymphocyte cells (3 Gy)

y = 0.0022x0.6273

R2 = 0.9059

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 50 100 150 200 250 300

DNA content

rel.

on

e-c

hro

mo

so

me

yie

ld exp. Cornforth et al. (1587 cells)

irradiation of simulated nuclei (3 Gy)(gene density correlated distribution of CTs )

y = 0.0015x0.6837

R2 = 0.91130

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 50 100 150 200 250 300

DNA content

rel.

on

e-c

hro

mo

so

me

yie

ld

simul. gene density correlateddistribution (1600 cells)

irradiation of simulated nuclei (3 Gy)(statistical distribution of CTs )

y = 0.0012x0.7372

R2 = 0.9597

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 50 100 150 200 250 300

DNA content

rel.

on

e-c

hro

mo

so

me

yie

ld

simul. statistical distribution(1600 cells)

*1,600 cells (50simulated nuclei

were virtually iradiated 32 times)

scattered (experimental)

scattered (simulated)

Regression: t-rate~(DNA content)2/3



Heinz Eipel

Claudia Batram

Johann von HaseHans

Mathée

Constance GrossmannChristia

n CarlNick Kepper

Werner Stadter

Senthilkumar PazahanisamyAndreas

SchweitzerMargund BachStefan

Stein

Udo SpöriDavid

Baddeley

Gregor KrethJutta

FinsterleChristian Wagner

Helmut Schneider

Susanne FenzJürgen

Reymann

„virtuelle strahlen-biophysik: einflüsse der zellkernarchitektur„

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