Capture and Translocation of Nucleic Acids into Sub-5 nm Solid-State Nanopores - Nanopores: Sensing and Fundamental Biological Interactions - page 235

is cr g in the absence of VðrÞ

, the presence of VðrÞ enhances this probability by the

is a constant related to the fact that not
all phosphates on the DNA are ionized due to Onsager-Manning condensation.
2. When the DNA coil is placed at the pore mouth, the probability of successful end
threading into the pore is determined by the internal dynamics of the coil. While
the coil relaxation time may be estimated by its Zimm time (

exponential factor exp ðNea = k B TÞ , where a

t Zimm ), its dynamics

are affected by the potential VðrÞ , which provides further bias of DNA segments

towards the pore and thus, enhances the attempt rate of DNA end threading.
Together, these two effects result in an increased capture rate R bar :

" s

N
4 N p

#
:

r g
t

k B T a d 2

q D V U
k B T þ

eDV

R bar ¼ exp (10.4)

al

8 la d 2 Here, 150 is the number of base

pairs in a dsDNA persistence length, and a is the length per base pair of dsDNA. We
consider ( 10.4 ) to be valid only for sufficiently long DNA, i.e. N>

t is proportional to t Zimm ðkT eDVÞð Þ , N p

4 N p . Since
t Zimm / r g , the only dependence on DNA length in ( 10.4 ) appears in the second
term of the exponent, R bar e C

p

N 4 N p

=

. Thus in the threading-limited regime, the
translocation rate should increase with DNA length [ 50 ].
To summarize, the dynamics determining capture rate of double-stranded DNA
into small nanopores involves two steps: first, a transition from pure diffusion to
biased diffusion that funnels DNA coils toward the pore region driven by VðrÞ
( 10.1 ), and second, a threading stage occurring at the mouth of the pore, which
involves crossing an energy barrier [ 50 ]. Equation ( 10.3 ) predicts that the first step
is DNA length-independent , while ( 10.4 ) shows that in the second step the translo-
cation rate grows with increasing DNA length . Since the DNA capture rate
measured in experiments is limited by the slower process of the two steps, these
equations predict that when the overall rate is limited by the diffusion, the capture
rate will be length-independent and the rate will grow linearly with the applied
voltage DV . In contrast, if the overall rate is limited by crossing the energy barrier

associated with threading, then we expect to see a growing capture rate with length,
and exponential growth with

DV .

10.2.2 Experiments Measuring the DNA Capture Rate

DNA translocation data are typically acquired using custom software that either
collects a continuous current recording, or detects and records only the current pulses
in real time [ 3 ]. ADNA sample is typically characterized by statistical analysis of the
square translocation pulse depths (current blockage level, I B ) and widths (dwell-
times, t D ) for thousands of molecules, as shown in Fig. 10.4 [ 49 ]. Capture rates were
calculated for each experiment from the mean time-delay between two successive
events (

dt in Fig. 10.4 ). To obtain a reliable measure of the capture rate, thousands of