Electrokinetic-flow-induced viscous drag on a tethered DNA inside a nanopore
Sandip Ghosal
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA

Received 31 May 2007; revised manuscript received 23 August 2007; published 26 December 2007
Recent work has shown that the resistive force arising from viscous effects within the pore region could
explain observed translocation times in certain experiments involving voltage-driven translocations of DNA
through nanopores Ghosal, Phys. Rev. E 71, 051904
2006; Phys. Rev. Lett. 98, 238104
2007. The
electrokinetic flow inside the pore and the accompanying viscous effects also play a crucial role in the
interpretation of experiments where the DNA is immobilized inside a nanopore Keyser et al., Nat. Phys. 2,
473
2006. In this paper the viscous force is explicitly calculated for a nanopore of cylindrical geometry. It
is found that the reductions of the tether force due to viscous drag and due to charge reduction by Manning
condensation are of similar size. The result is of importance in the interpretation of experimental data on
tethered DNA.
DOI: 10.1103/PhysRevE.76.061916 PACS number
s: 87.15.Tt, 87.14.Gg
The interaction of charged polymers such as DNA with
nanometer-sized natural and artificial pores has received con-
siderable attention recently 1–7. Such studies are partly
motivated by the desire to understand how polymers cross
internal membranes of cells 8. The possibility of develop-
ing devices capable of detecting properties of biopolymers at
the single-molecule level for applications such as rapid DNA
sequencing 9 is also a motivating factor for such studies.
In a recent paper 10 Keyser et al. reported experimental
measurements in which a single molecule of double-stranded
DNA was immobilized while threaded inside a nanopore by
the application of a pulling force to counteract the electrical
force on the DNA. This was achieved by attaching one end
of the DNA strand to a Streptavidin-coated polystyrene bead
and holding the bead in a laser optical trap. The displacement
of the bead from its equilibrium position could be detected
and used to measure the pulling force on the DNA. The
measured value was found to be about 75% of the maximum
electric force on the DNA within the pore based on its bare
charge, irrespective of the electrolyte
KCl concentration.
This pulling force is, however, determined by a complex
interplay between electric forces and hydrodynamics, as
noted by Keyser et al. 10. The point of this calculation on
an idealized physical model is to understand the relative im-
portance of hydrodynamics and the reduction of effective
charge on the DNA due to Manning condensation in deter-
mining the observed pulling force. Since the DNA as well as
the internal walls of the pore are charged, the pore region has
a cylindrically symmetric distribution of oppositely charged
counterions. In the presence of a strong electric field an
electro-osmotic flow 11 is therefore generated in this region
that flows in a direction opposite to the direction in which the
DNA would move if it were not immobilized
Fig. 1. This
flow produces a hydrodynamic drag on the DNA, partially
balancing the applied electrical force. In this paper, a simpli-
fied geometry of the pore region is used to calculate the
viscous drag explicitly. It is shown that the drag is a signifi-
cant fraction of the total force acting on the DNA and needs
to be taken into account for a proper interpretation of experi-
mental data on DNA-nanopore interactions.
A simplified model is adopted in which the nanopore is
regarded as a cylinder of radius R
5.0 nm and length L

60 nm. The part of the DNA inside the nanopore is re-
garded as a uniformly charged cylinder of radius a
1.1 nm
along the axis of the pore. The DNA has a linear charge
density

two electron charges every 0.34 nm—the distance
between adjacent bases and a lower “effective” charge den-
sity of
e=
/qB due to the Oosawa-Manning 12,13 phe-
nomenon of counterion condensation on its surface. The fac-
tor qB is the Oosawa-Manning factor; it has the value of qB
=4.2 for an ideal model of an infinite line charge in an un-
bounded electrolyte. Referring to the system sketched in Fig.
1, the fluid velocity in the pore is axially directed and is
described by some function u
r where r is the distance from
the central axis. The electric potential is −E0z+
r, where
the first term is due to the externally applied axial electric
field E0 along the pore
the z direction. The functions u and
 are governed by the Stokes equation for viscous flow
with
zero pressure gradient and an electric body force term and
the Poisson equation of electrostatics, respectively.

1
r
d
dr
r
du
dr 
+ e
rE0 = 0,
1
z = 0
z = L
Substrate
2R
2a
z
Electrolyte
DNA
∆V
Bead/Optical Trap
FIG. 1. Sketch illustrating the tethered nanopore experiment
with a cylindrical pore.
PHYSICAL REVIEW E 76, 061916
2007
1539-3755/2007/76
6/061916
3 ©2007 The American Physical Society061916-1