~30 min talk at APCTP, 2017 January,

1. Polymer meets stochasticity:
DNA looping &Transcription
1
Jaeoh Shin
Max-Planck-Institute for the Physics of Complex Systems, Dresden, Germany
— APCTP, Pohang, January 23rd 2017 —

2. Biological physics of cell
• A number of biological materials are soft, e.g., DNA, proteins, membranes
• Soft matter can be easily deformed by external stresses
• Thermal fluctuations play important roles
2
Soft matter Stochastic process
Biophysics
Polymer, …
Random walk, …
Biology
~10 µm

3. Central dogma of biology:DNAàRNAàProteins
3
Image: https://www.khanacademy.org/

4. Processes of interests
DNA looping
RNA transcription
4
~10 nm

5. Part I:DNA looping in“cellular” environment
• Nonequilibrium fluctuations are abundant
• Cells are highly crowded with macromolecules
5
Cytoplasm model
S R Mcguffe & A H Elcock, PLoS Comp. Biol. (2010)
~10 nm

6. Recent experiments show that
● A small tension (~100 fN) on a substrate DNA increases the looping time by
factor of 10
● In the presence of a fluctuating tension, the looping time is decreased significantly
6
[Y-F Chen, J N Milstein, & J-C Meiners, PRL(2010)x2]
cf.) Motor protein~10 pN
L=110 nm

7. Coarse-grained simulation of DNA
7
US
=
k
2
(|
!
ri+1
−
!
ri
|−l0
)2
i=1
N−1
∑
1
2
22
N
B i
i
U
κ
θ
−
=
= ∑
DNA is modeled as a bead-spring
L=110 nm
A small tension (~100 fN) greatly changes
looping time
r
f (t)
JS & W Sung, JCP (2012)

8. Analytical description
Polymer looping can be considered as a one-dimensional barrier crossing process
8
A Szabo, K Schulten, & Z Schulten, JCP (1980)
γ
2
!r(t) = −
∂F0
(r)
∂r
+ξr
(t)
0 ( ) log ( )BF r k T P r= −
T(r0
) = drexp(βF0
(r))
1
Dlc
r0
∫ d ʹr exp(−βF0
( ʹr ))
r
L
∫
r
Looping time=Mean first-passage time

9. Comparison with experiments
● Relative looping time as a function of tension
● Mean first-passage time shows a good agreement with the exp. data
9
Red: Experimental data
Blue: MFPT calculation
JS & W Sung, JCP (2012)
Why looping time is so sensitive with tension?
Chain connectivity!

10. 2
/ (2 )r L Dτ :
Fluctuating tension
We consider dichotomically fluctuating tension as a simple example of a non-
equilibrium noise
10
● Looping time has a minimum at an optimal
àResonant activation in polymer looping
Y-F Chen et al. showed that the looping time
decreases in the presence of a fluctuating tension
( )f t
r
Y. -F. Chen et al., PRL(2010)
+
- + -
τ
τ

11. Crowded & confine environment
11
JS, A Cherstvy & R Metzler, Macro Lett (2015) JS, A Cherstvy, WK Kim & R Metzler, New J Phys (2015)
Active fluid
Other important aspects of the cellular environment

12. Summary of Part I
ü DNA (polymer) looping is a ubiquitous process in the cell
ü We study the looping in „cellular environment“- fluctuating/ crowded/ confined
ü Our studies provide insights on the DNA looping in vitro/ in vivo
12
• JS & W Sung, JCP (2012)
• JS, A Cherstvy & R Metzler, Soft Matt (2015)
• JS, A Cherstvy & R Metzler, Macro Lett (2015)
• JS, A Cherstvy, WK Kim & R Metzler, New J Phys (2015)

13. 13

14. Part II:RNA transcription
• Synthesise mRNA from DNA template
• Use NTPs (A, C, G, U) as material and as energy source
14
~10 nm
RNA polymerase II (Pol II)
“copy machine with motors”

15. DNA is packed into chromatin
DNA is wrapped around histone
15
11 nm
In large fraction of time, nucleosomal DNA is
still accessible due to thermal fluctuations!
G Li et al., Nat Struc Mol Biol (2005).
Human DNA ~2 m, nucleus size !!~ 5 µm

16. Transcription through nucleosome
• Pol II can move forward while the downstream DNA is transiently unwrapped
• Q:What is effects of neighboring nucleosome?
16
[C Hodges et al., Science (2009) ]
linker DNA : 45, 50, 99 bp
(1 bp= 0.34 nm)
“Copy machine moving through
paper blocks”
1st
2nd

17. [Stephan Grill’s lab, Dresden]
Experimental setup
17
~10 pN

18. Transcription dynamics:Position of Pol II
18
- Pol II elongation is interrupted by pauses
- In nucleosome, Pol II pauses more often and for
longer periods & pause-free velocity decreases
End of the DNA
Pause

19. Origin of pauses:backtracking
19
M. Depken et al., BPJ (2009); A. Lisica et al., PNAS (2016).
“If paper is jammed, copy machine is
just moving back and forth”

20. Transcription dynamics
20
• Pause-free vel. & Passage prob. show non-monotonic behaviour!
• Q: How these two quantities are correlated?
γ =
vnucl
vbare

21. Model: Important features
1. Active elongation & Backtracking
2. Forward-motion of Pol II is slowed down ( ) in nucleosome
3. Assisting force biases diffusion of Pol II in backtracked state
21
γ

22. Stochastic model:Random walk in 2D lattice
22
Active elongation
a = 0.34 nm
: # of transcribed RNA
: # of backtracking steps
Assisting force F
Possibility of moving backward in nucleosome:
n
b
ke
γke
γkf
kb
kf
kb
nucleosomalDNA

23. Important parameter:
ratio between forward & backward rates
23
χ = kf
/ kb
=γ exp(Fa / kB
T)
χ >1
χ <1
Depending on , backtracking dynamics changes dramatically
If , Pol II can easily recover to elongation mode
If , Pol II prefers to move backward à long pauses
χ
n
b
ke
γke
γkf
kb
kf
kb
nucleosomalDNA

24. Comparison with experimental data (i)
24
Only for the case of 50 bp linker
DNA, is smaller than 1, which
results in the lowest passage prob.
1.46 1.32 0.89 1.28B
0
0.2
0.4
0.6
0.8
Probabilitytopasswithin145s
1
data theory
*** / ***
*** / ***
1xN
ucl
2xN
ucl(45)
2xN
ucl(99)
bareD
N
A
C
2xN
ucl(50)
V Fitz, JS, … V Zaburdaev & S Grill, PNAS (2016)
χ

25. Comparison with experimental data (ii)
25
• Residence times show broad distribution,
which is due to the stochasticity of the
process
V Fitz, JS, … V Zaburdaev & S Grill, PNAS (2016)

26. Nucleosome arrangement
• 3D distance between two nucleosomes varies
non-monotonically due to the helical structure
of DNA
26
DNA helix: ~10.4 bp/turn
45 bp50 bp99 bp
*In yeast, nucleosomes placed on opposite
sides of the DNA helix

27. Summary of Part II
ü Transcription is the first step of gene expression; how Pol II transcribe along
the chromatin structure is not well understood
ü We show that, by using experiments and a stochastic model, the nucleosome
arrangement affects Pol II transcription dynamics
ü Relative strength of nucleosomal barrier & assisting force dramatically changes
backtracking dynamics, hence the transcription dynamics
27
V Fitz, JS, C Ehrlicha, L Farnungd, P Cramerd, V Zaburdaev, & S Grill, PNAS (2016)

28. Acknowledgements
Prof.Wokyung Sung (POSTECH)
Prof. Ralf Metzler (U Potsdam)
Dr.Andrey Cherstvy (U Potsdam)
Dr.Vasily Zaburdaev (MPI-PKS)
Prof. Stephan Grill (TU Dresden, MPI-CBG, MPI-PKS)
Dr.Veronika Fitz (TU Dresden, MPI-CBG)
28

29. Future research plan
Polymer dynamics in viscoelastic
active environment
Softening transition of coiled-coil
29
Exp.: Prof. Grill’s group