Biomedical Engineering Reference
In-Depth Information
From Eqs. (8.6) and (8.7), one can give a quantitative constraint on the feasibility
of DNA sequencing using HANS approach.
Imagine two ssDNAs, as shown in Fig.
8.10
, each has two probes hybridized to
it, with their 5
0
ends attached to beads. Assume both molecules have a probe (oligo)
at the same distance away from the free 3
0
ends. However, the oligos near the 5
0
ends differ by a distance of
dx
. The distance between the two probes in lower
DNA is
x
.
In order to resolve
dx
in the temporal signals from the translocation data, the
change
d <t>
in the mean-first-passage time
<t>
must be greater than the variance
in the mean-first-passage time, i.e.
p
<t
2
d<t>
> <t>
2
:
(8.8)
Condition (8.8) can be re-written as,
d
x
2
2
D
x
v
:
(8.9)
This says that, in order to resolve the location of a probe to precision
dx
, the time it
takes for thermal diffusion to occur over distance
dx
has to be greater than the time
it takes to translocate across distance
x
. This condition makes physical sense:
thermal diffusion is always there, but one can still resolve the location of the
probe accurately as long as the translocation is fast enough. A similar conclusion
was reached by Jene Golovchenko [
25
] using a different argument.
Another way to look at condition (9) is that the diffusion length over time
x/v
has
to be less than
dx
,or
r
2
D
x
v
dx
:
(8.10)
In fact, Eq. (8.10) is the same principle as that in gel electrophoresis: the separation
between two bands (due to two different lengths of DNA fragments) grows linearly
with time, due to the electric-field driven drift, but the spread of each band due to
thermal diffusion grows as
t
1/2
. Thus after long enough time, the travel distance
between the bands will exceed the width of each band.
Next, a simple back-of-envelope calculation will show that it is not trivial to
satisfy condition (8.10) in standard DNA translocation experiment. For
x ¼
40 nm
(100 bases apart between two adjacent probes),
0.4 nm (single-base resolu-
tion),
D
~10
8
nm
2
/s (using that for single-base nucleotides in water), the transloca-
tion velocity,
v >
dx ¼
dx
2
, would have to be greater than 50 m/s, or 200 kb/
s. This
is 10,000 times faster than that in typical nanopore experiments (Storm et al. [
26
])
using Si
3
N
4
pores. Besides, at this high translocation speed, the existing patch-clamp
electronics will not be able to detect the current signals. A simple solution to this
problem is to use the “reverse translocation” concept (Peng and Ling, [
27
]). If the
DNA is held under tension, the DNA moves with the bead, the effective diffusion
2
Dx
/
m
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