modeling fluctuations in the force-extension single-molecule experiments alexander vologodskii new...
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Modeling fluctuations in the force-extension single-molecule experiments
Alexander Vologodskii
New York University
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Diagram of the force-extension experiment
F
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0.0 0.2 0.4 0.6 0.8 1.00
20
40
60
80- Experimental data of Smith et al.
chainWorm-like
Extension, <x>/L
The force-extension dependence for DNA is well studied
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The force has entropic nature
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From: J. W. Shaevitz1, E. A. Abbondanzieri, R. Landick & S. M. Block. Backtracking by single RNA polymerase molecules observed at near-base-pair resolution. Nature, 426, 684-687.
The entropic force from extended DNA molecule is used in many single-molecule experiments
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DNA model for Brownian dynamics simulations
The intersegment interaction is specified by the Debye-Hückel potential
Segments are stretchable
Virtual beads of a certain diameter placed at chain vertices specify hydrodynamic interaction with solution and between the beads
Discrete wormlike chain with some modifications:
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Dynamics of the chain is described by the Langevin equations
midvi
dt ij
j v j Fi ij
j f j
ij
where
is a configuration-dependent friction tensor
is a force acting on beadFi i
represents the randomly fluctuating force resulting from the thermal motion of the surrounding fluid
ijj f j
is the mass of bead imi
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How accurate is Brownian dynamics simulation of DNA properties?
Comparison of measured and simulated diffusion coefficients of knots along stretched DNA moleculeshows that simulation is quite accurate
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Tying knots by optical tweezers
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Experimental measurement of knot diffusion
X. R. Bao, H.J. Lee and S.R. Quake, Phys. Rev. Lett., 91, 265506 (2003)
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Brownian dynamics simulation of knot diffusion
Typical simulated conformations of knotted model chains
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Comparison of the measured and computed diffusion coefficients of knots
Knot type
Computed diffusion
coefficient, m2/s
Measured diffusion
coefficient, m2/s
8.6 ± 1
12.5 ± 0.5
6.0 ± 1
7.9 ± 0.3
2.5 ± 0.3
4.8 ± 0.2
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Simulated values of the force fluctuate strongly
Time, ns
0.0 0.2 0.4 0.6 0.8 1.0
For
ce,
Fb/
kT
-10
-5
0
5
10
Time, ns
0.0 0.2 0.4 0.6 0.8 1.0
x/L
0.79
0.80
0.81
0.82
0.83
0.84
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Time, ns
0 20 40 60 80 100
For
ce,
pn
-20
-10
0
10
The force fluctuations do not depend on its average value
Each point is the averaging over 1 ns
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The force averaging does not occur over 0.1 s
Each point is the averaging over 100 ns
Time, s
0 2 4 6 8 10
For
ce,
pn
-4
-2
0
2
4dt = 400 psdt = 4 ps
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Time, ms
0.0 0.2 0.4 0.6 0.8 1.0
For
ce,
pn
-1.0
-0.5
0.0dt = 400 ps
The force averaging does not occur over 10 s
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Time, ms
0 20 40 60 80 100
For
ce,
Fb/
kT
-0.7
-0.6
-0.5
-0.4
-0.3
A good averaging of the force is achieved by averaging over 1 ms
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Fluctuations of the force do not depend on DNA length
DNA length, bp
1000 10000
x, p
n0
20
40
60
80
f = 0.5 pn
f = 2.5 pn
f = 8.3 pn
DNA length, bp
1000 10000
f, pn
0
1
2
3
4
5
f = 0.1 pn
f = 0.5 pn
f = 2.5 pnf = 8.3 pn
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Presence of a protein-induced bend decreases DNA extension
Can the extension measurement be used to determine the bend angle?
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Simulated values of the extension reduction resultingfrom DNA bending by angle
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Time
Ext
ensi
on
No bound protein No bound proteinOne protein is bound
Large fluctuations of the extension and a finite time of the protein-bound state create a problem
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DNA length, bp
0 1000 2000 3000
, n
m
0
50
100
150F = 0.1 pn
F = 1 pn
The variations of the extensions are large
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Extension of a single DNA molecule by force
ForceForce
These are actual proportions for 1500 bp DNA
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time, ms
0 20 40 60 80
Ext
ensi
on,
nm
0
100
200
300
400L = 500 nmF = 0.1 pn
No beadBead radius 500 nm
Fluctuations of DNA extension averaged over 0.4 ms
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Fluctuations of DNA extension averaged over 40 ms
Time, ms
200 400 600 800
Ext
ensi
on, n
m
200
400L = 500 nmF = 0.1 pn
No beadBead radius is 500 nm
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Interval of averaging, ms
0.01 0.1 1 10 100 1000
Ext
ensi
on v
aria
tion,
nm
10
100
L = 500 nmF = 0.1 pn
With bead R = 500 nmNo bead
What averaging interval do we need?
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The work was supported by NIH
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Displacement of unknotted part of the model chain eliminates the chain length restriction