2038-7
Conference: From DNA-Inspired Physics to Physics-Inspired Biology
1 - 5 June 2009
DNA Bending by Bound Proteins
Yitzhak RABIN
Bar-Ilan University, Department of Physics
52900 Ramat Gan
Israel
DNA Bending by Bound Proteins
(Elastic Effects on Adsorption of Small Molecules)
Trieste, June 2009
Shay Rappaport
Phys. Rev. Lett. 101, 038101 (2008)
DNA Compaction in Bacteria - by different proteins:
HU, H-NS, IHF, FIS, …
HU, high concentration
H-NS
HU, low conc.
Dps
IHF
FIS
AFM images of DNA-HU complexes on surface
Bare DNA
18 nm HU
sharp bends
900 nm HU
stretched
Force-extension curves:
Extension first decreases then increases back, with increasing HU concentration
FRET transfer efficiency between donor and acceptor bound to ends of 55bp long DNA
(Stavans)
Fluorescence from donor is quenched when the acceptor is close (<5 nm)
donor
acceptor
Donor-acceptor distance goes down and then up again with increasing HU concentration
(3 different DNA sequences)
DNA
Standard Model of DNA - Worm-like Chain:
lp
(0)
Inextensible rod with bending elasticity
! 50 nm
Bustamante et al., Science 265, 1599 (1994)
2
Eel 1 ( 0 ) L
! l p $ ds"% ( s )#
0
k BT 2
Elastic bending (free) energy of WLC:
local curvature
Discrete WLC:
step size &s '' l p
&s
Eel 1 ( 0 )
2
! l p * (% n )
k BT 2
n
lengths scaled by &s
tˆn
Relationship between local curvature and bending angle
% n ! 2(1 , tˆn - tˆn .1 ) ! 2(1 , cos + n )
% n / lim % ( s )&s ! &+
In the continuum limit:
&s /0
and
(0)
% (s) !
d+
ds
+n
tˆn .1
Binding of HU protein introduces spontaneous curvature in DNA
The polymer fluctuates about a bent zero energy conformation!
Eel 1 ( 0 )
2
! l p * (0% n )
k BT 2
n
Deviations of curvature from spontaneous value:
0% n ! % n , % n ( 0)
The model: binding of HU protein defines the bending angle of a dimer
(each segment – 9 bp)
lowest energy
conformation
1% 2
(0)
n
Spontaneous curvature
Site occupancy
% n ( 0) ! % 0 (3n . 3n .1 , 23n3n .1 )
3n ! 10, 12
H ! * Hn
“Hamiltonian” :
n
H n 1 (0)
1
(0) 2
! l p (% n , % n ) , : (3n . 3n .1 )
kT 2
2
with effective chemical potential
9 <b
: 0 (T ) 6
: ! 7 . ln ; .
4
kT 5
8 kT
binding energy
reference chemical potential
bulk concentration of protein
Partition function
Z ! =$
n
D{tˆ }e
*
3
n ! 0 ,1
n
,
*
Hn
n kT
tangent vector of n-th segment
1d problem : diagonalize 2x2 transfer matrix (i,j=0,1)
Tij ! 2>e
: (i . j ) / 2 2
$
0
d%%e
, l p ( 0 ) [% ,% 0 ( i . j , 2 ij )]2 / 2
where we used d (cos + ) ! ,%d% and integrated over the angle d;
%0 ! 0
%0 ! 0.1
%0 ! 0.3
@!
lp
lp
%0 ! 1/ 2 (45! )
(0)
Effective persistence length versus effective chemical potential
: ? log( HU concentration)
(a) Mean site occupancy
3 ! 3n
Deviations from Langmuir isothermElastic effects on binding?
:
(b) Cooperativity
A ! 3n3n .1 , 3n 3n .1
%0 ! 0
Occupancy at neighboring sites
is suppressed!
% 0 ! 0.1
% 0 ! 0.3
%0 ! 1/ 2
What is the origin of elastic effects on binding ?
(deviations from Langmuir isotherm for % 0 B 0 )
Effect of spontaneous curvature on elastic entropy and energy of WLC
(0)
H el l p
(% , % 0 )2
!
2
k BT
Probability distribution of curvature
9 l p (0)
6
2
P(+ )d (cos + ) ! exp 7,
(% , % 0 ) 4%d%
78 2
45
Density of states increases with curvature!
As % 0 increases, % follows and the density of states grows
Increase of entropy with % 0 , trivial consequence of 3d geometry!
% 2 ! 2(1 , cos + )
+ increases with % (and thus with % 0 ) in the interval [0, > /2]
Element of area on unit sphere ! sin+ d+ d3
Elastic entropy and energy:
S el
E el
Fel
In our model – elastic entropy first increases and then decreases with adsorption
(as spontaneous curvature first increases and then decreases)
Conversely- elasticity enhances adsorption at small site occupations and
suppresses it at large ones!