Biomedical Engineering Reference
In-Depth Information
Fig. 2.8 Net electrical forces on a captured dsDNA. (a) Diagram of forces on dsDNA (
center
)ina
nanopore (
black
), showing that measured force
F
meas
is balanced by a combination of the
electrophoretic force (
F
ep
) and the drag force caused by electroosmotic flow (
F
eo
). Flow direction
and qualitative magnitude are indicated by the vertical arrows. (b) Calculated force curve slope for
dsDNA under various ionic concentrations and nanopore radii [
2
]
where
is the dielectric constant of water,
a
and
R
are radii of the molecule and the
nanopore, respectively, and F
(a)
and F
(R)
are the surface potentials of the mole-
cule and the nanopore, respectively [
17
]. A
ln
1
(R/a)
size dependence is therefore
predicted, explaining why the measured force is affected by nanopore dimension as
observed. Furthermore, the surface potentials are dependent on the distribution of
ions surrounding those surfaces; a higher concentration of counterions causes
greater screening of surface charge, thereby reducing the surface potential. This
is correlated to the overall ion concentration, indicating the source of the observed
force dependence on the measurement solution salt concentration.
Comparison of this description to experimental results is achieved by creating a
computer model wherein the nanopore is represented by an annulus and the captured
molecule by a cylinder, each of uniform charge density. For a designated salt
concentration, this allows the ion distribution between the two entities to be calcu-
lated numerically. The distribution can then be used to solve the Stokes equation and
describe the fluid flow profile, which can subsequently be used to yield the viscous
drag acting on the molecule at a given voltage [
16
]. This can be combined with pure
electrophoresis (
F
EP
¼QDV
) to result in a total prediction of the measured force per
unit voltage on a captured molecule for any combination of pore diameter and salt
concentration (Fig.
2.8b
).
The trends of the size and salt dependences are captured well by the model
(Fig.
2.7b, c
), but the values do not agree quantitatively; the measured force is
apparently overestimated by ~50%. This quantitative difference, while trouble-
some, has a physical explanation that becomes clearer by comparing these
dsDNA measurements to ones on a second type of molecule with different physical
properties.
e
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