Biomedical Engineering Reference
In-Depth Information
Both
DI
b
and
t
d
(Fig.
6.1c
) also depend on the geometry and electrical properties of
a nanopore, on the properties of solution, and the bias potential.
The distribution function for the translocation time can be derived from the
Fokker-Planck equation equivalent to Eq. (6.2) [
13
].
2
e
ð
d
t
uÞ
4
tD
ðd þ tuÞ
P
fpt
ðtÞ¼
p
4
(6.4)
t
ptD
Here
d
is the distance to be translocated. For a long polymer with
l
m
>>H
eff
,
d ¼ l
m
+H
eff
; for a small spherical particle
d ¼ H
eff
. In this formulation, the
width of the distribution arises due to thermal fluctuations. Equations (6.3) and
(6.4) are appropriate for uniformly charged polymers and particles that behave as a
point charge. The prediction under these assumptions is that the translocation time
should decrease when electrostatic bias across the nanopore is increased.
When a protein molecule is unfolded and it passes a nanopore as a linear amino
acid chain, very different translocation kinetics is expected due to the inhomoge-
neous charge distribution. A protein molecule that has neutral regions bracketed by a
positively charged and a negatively charged region can experience a net zero
electrical force when the net charge of the local segment chain in the pore is zero.
At this stall point the unfolded protein molecule is electrostatically trapped; increas-
ing the voltage only serves to increase the electrostatic trap barrier height. The
molecule can escape the trap by thermal fluctuations, thus an inhomogeneous charge
polymer translocation could be thermally activated if it has zero net charged regions.
Since larger applied bias voltages,
C
, would result in deeper traps, the dwell time,
t
d
,
is predicted to increase with
, the opposite prediction from the uniformly charged
translocation model of Eqs. (6.3) and (6.4). The consequences of unfolded protein
translocation are discussed below, in context with the experimental evidence.
C
6.3 Experimental Setup and Sample Preparation
6.3.1 Experimental Setup
The results discussed in this chapter were measured with a solid-state nanopore
sensing system as illustrated in Fig.
6.2a
. The main components of this system
include a nanopore chip, two PDMS chambers (
cis
and
trans
), a pair of Ag/AgCl
electrodes, and an Axopatch (200B) single channel recording system. The nanopore
chip has a dimension of 3 mm by 3 mm and is sandwiched between two PDMS
chambers. A freestanding silicon nitride membrane widow supported by a silicon
substrate contains a single nanometer size pore at the center of the chip.
The thickness of the freestanding membrane is ~275 nm as illustrated in the
expanded view of the region around the pore in Fig.
6.2b
. The nanopore is the
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