Biomedical Engineering Reference
In-Depth Information
Fig. 10.16 The dependence
of bath temperature on DNA
transport dynamics through
4 nm pores. The
top graph
shows a semi-log plot of
t
1
for
selected DNA lengths
<
6 kbp. The Arrhenius slope
of the
t
1
timescale (~12
K
B
T
)
is length independent,
suggesting that the dynamics
are governed by interactions
within the pore. In contrast,
the
t
2
timescale (
lower graph
)
exhibits increasing
temperature dependence for
increasing DNA lengths,
suggesting external
interactions of the DNA coil.
Reproduced with permission
from Wanunu et al. [
49
],
Copyright Elsevier Inc
3,500 bp, the prominent timescale (
t
1
) follows a power-law dependence on
N
, where
the power is equal to 1.40. For longer polymer lengths where
t
2
dominates, a much
stronger power-law dependence emerges:
t
2
< N
2.28
. The striking shift from
t
1
-dominated to
t
2
-dominated transport dynamics can be attributed to additional
interactions external to the pore that occur for longer DNA coils, either with the
silicon nitride membrane or with itself.
Temperature dependence studies of biopolymers' dynamics provide further
evidence for the dominant role of interaction in determining translocation timescales.
A study of the temperature dependence of translocation time for selected DNA lengths
revealed nearly a tenfold increase in the characteristic
t
1
and
t
2
timescales when the
temperature was varied from 30 to 0
C[
49
]. Figure
10.16
shows a semi-log plot of
their mean transport time as a function of
T
1
. A simplified Arrhenius model for the
temperature dependence
t
D
ΒΌ Ae
DGk
B
T
=
yields similar effective energy barriers for all
DNA lengths studied:
DG
~12.0
0.5
k
B
T
,or7.1
0.3 kcal/mol for
t
1
. The invar-
iance of
DG
with
N
for the
t
1
timescale suggests that interactions within the pore
dominate its dynamics, since these are not expected to depend on the external coil
length. In contrast, the
t
2
timescale displays increasing
DG
values for increasing
N
;
with
2
k
B
T
for 1200, 3500, 8000 and
20,000 bp, respectively. Notably, the slowing down observed with reduced tempera-
ture in both
t
1
and
t
2
cannot
be attributed to increased fluid viscosity, as the viscosity
was expected to increase by only a factor of ~2.7 over the same temperature range.
DG
~18
1, 25.5
1, 48
4, and 45
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