Origin of the Electrophoretic
Force on DNA in a Nanopore
Stijn van Dorp 1
Ulrich F. Keyser 2,*Nynke H. Dekker1, Cees Dekker1,
Serge G. Lemay1
1Kavli
Institut of Nanoscience, Delft University of Technology, NL
2Institut für Experimentelle Physik I, Universität Leipzig, D
*Present Address: Cavendish Lab, University of Cambridge, UK
Outline
• ‘Early’ experiments revisited (Nature Physics 2 473 (2006))
• Force on DNA in nanopores:
numerical modeling and new experiments
Ulrich F. Keyser
DNA Tug of War
• Idea: put DNA in a nanopore and pull on it –
how cool is that ?
U. F. Keyser et al., Nature Physics 2 473 (2006)
Ulrich F. Keyser
First Measurements
40
Time (ms)
30
Controlled
insertion of
DNA strands
one by one
DNA in
Pore
20
10
0
3.55 3.50
Current (nA)
Ulrich F. Keyser
0 -0.1 -0.2
Position (µm)
F = k × ( Z1 − Z 0 )
Exact number
of DNA in the
nanopore is
known from
ionic current
measurement
U. F. Keyser et al. Nature Physics 2, 473 (2006)
Time-Resolved Events
• Conductance step
indicates capture
of DNA in
nanopore
• Only when DNA is
pulled taut the
force changes
• Time to pull taut ∆t
is consistent with
translocation of
DNA
Ulrich
U.
F. Keyser
F. Keyser
et al., Nature Physics 2, 473 (2006)
Force on DNA
• Linear force-voltage
characteristic
• Force does not
depend on distance
nanopore-trap
• Extract the gradient
and vary salt
concentration
Ulrich
U.
F. Keyser
F. Keyser
et al., Nature Physics 2, 473 (2006)
Slo pe (pN/mV )
Salt Dependence of Force
0.3
0.2
0.1
Nanopore diameter
around ~6 - 10 nm
0.0
0.01
0.1
1
KCl concentration (M)
• Force is constant
as ionic strength is
varied
• From literature
force is expected
to decrease with
increasing salt
concentration
• Force/voltage
conversion
0.23±0.02 pN/mV
See e.g. Manning Q Rev Biophys 11, 179-246 (1978), Laue et al.
J.Pharm. Sci. 85, 1331-5 (1996), Long, Viovy, and Ajdari Biopolymers
(1996), Keyser et al. Nature Physics 2, 473 (2006)
Ulrich F. Keyser
Effective Charge
• Potential drops over
nanopore
∆V = ∫ E ( z )dz
• Force on DNA
F = ∫ (qeff / a ) E ( z )dz
F = (qeff / a )∆V
qeff effective charge/bp
• Slope Ù effective charge
• Yes but …
Ulrich F. Keyser
…
U. F. Keyser et al., Nature Physics 2, 473 (2006)
What is missing here ?
The role of the nanopore (walls)...
Ulrich F. Keyser
Lots of Interest Recently
Analytical calculations
S. Ghosal
•
•
•
Phys. Rev. E 74, 041901 (2006)
Phys. Rev. E 76, 061916 (2007)
Phys. Rev. Lett. 98, 238104 (2007)
Molecular dynamics simulations
A. Aksimentiev et al.
•
•
Phys. Rev. E (2008) in press
Talk yesterday
Ulrich F. Keyser
Vary Nanopore Diameter
•
Task: increase nanopore diameter by at least a factor of ten
Ulrich F. Keyser
Increase Nanopore Diameter
relative DNA area ~ 1:1600
relative DNA area ~ 1:25
10 nm
80 nm
DNA
• Detection of a single DNA molecule still possible?
• Yes should be at low salt concentration see Smeets PNAS (2008)
Ulrich F. Keyser
DNA in a D=80 nm Nanopore
2
20
1
current (nA)
-1
-20
-30
-2
-3
-4
applied voltage (mV)
0
-60
-4.0
data
20 point
average
0
2
4
6
8
time (s)
10
12
14
• Nanopore diameter ~80 nm
• Salt concentration 0.033 M KCl
Ulrich F. Keyser
current (nA)
-5
-4.1
-4.2
5.5 6.0 6.5 7.0 7.5
time (s)
Force Measurements
16
24
pN/mV
0.24
pN/mV
force (pN)
12
0.11
pN/mV
11
pN/mV
2 in
8
4
0
1 in
0 10 20 30 40 50 60 70 80
voltage (mV)
• Force on two DNA strands is doubled as expected
• DNA strands do not interact in large pores R > 15 nm
Ulrich F. Keyser
Change in Conductance ∆G
• Nanopore diameter ~80 nm
• Salt concentration 0.033 M KCl
• Usually 100 events are measured
Ulrich F. Keyser
S. van Dorp et al. submitted
Change in Conductance ∆G
• Pore radius varied from 3 nm – 45 nm
• Large pores: ∆G is constant and lower
• Consistent with free translocation (open symbols )
Ulrich F. Keyser
S. van Dorp et al. submitted
Forces Dependence on Radius
• Force is proportional to voltage as expected
• For larger nanopore force is roughly halfed
Ulrich F. Keyser
S. van Dorp et al. submitted
Numerical Modeling
• Solve Poisson-Boltzmann equation numerically in 1D
• Electrostatic potential Φ and distribution of ions n± :
with
as reduced potential
• Boundary conditions:
insulating nanopore walls (uncharged)
on DNA surface
• Simplification: access resistance is neglected
Ulrich F. Keyser
Potential Distribution
• Potential depends on radius of nanopore
• Calculated for bare charge of DNA 2e/bp
• In small nanopores a finite potential is observed
despite boundary condition of zero charge
Ulrich F. Keyser
Co- and Counter-ion Distribution
•
•
•
•
Counter-ions accumulate near DNA
In small nanopores counter-ion cloud is compressed
Co-ions are almost completely depleted
In large nanopore almost bulk numbers
Ulrich F. Keyser
Flow Velocity
• We assume a no-slip boundary conditions
• Nanopore wall is uncharged
• Maximum flow velocity depends on distance between
nanopore wall and DNA
• Drag force depends on nanopore radius Ù
Fmech=-Felec=Fbare-Fdrag depends on pore radius R
Ulrich F. Keyser
Relating Model to Experiments
• Combining Poisson Boltzmann and Stokes equation:
Potential Φ(a) on DNA surface, Φ(R) Nanopore wall
S. Ghosal PRE 76, 061916(2007)
• Logarithmic dependence of Fmech on nanopore radius
explains slow variation with pore diameter
Ulrich F. Keyser
Nanopore Diameter Matters
• Force on DNA
depends on pore
diameter
• Change in pore
diameter by factor
10 increases drag
by a factor of two
Ulrich F. Keyser
S. van Dorp et al. submitted
Main Conclusion
• Potential on DNA surface and pore wall depend on
pore radius R although DNA charge remains constant
Ulrich F. Keyser
S. van Dorp et al. submitted
Comparison: Model Ù Data
• Force depends
on nanopore
radius R
• Our full PB
model fits data
when ion
mobility is
reduced
Ulrich F. Keyser
S. van Dorp et al. submitted
Summary
• Experimental prove that force on DNA depends on
geometry of nanopore
• Hydrodynamic interactions have to be considered
• Numerical model qualitatively explains experiments
• For quantitative fitting mobility of counter ions have to
be known Ù MD simulations Aksimentiev et al.
Ulrich F. Keyser
1/f-Noise Sources in Nanopores
• Not only one origin of 1/f noise in nanopores
• Identified Nanobubbles (de-wetting) as ONE source of
1/fa -noise
Smeets et al. PRL 2006
• General Hooge relation for 1/f noise holds in
nanopores
Smeets et al. PNAS (2008)
• Sources of 1/f-noise
see webpage with collection of papers
http://www.nslij-genetics.org/wli/1fnoise/
Ulrich F. Keyser
Funding
Delft University of Technology
FOM NWO
DFG Emmy Noether Program
Universität Leipzig
Ulrich F. Keyser
FOGU 877