Sensing Single Protein Molecules with Solid-State Nanopores - Nanopores: Sensing and Fundamental Biological Interactions - page 144

6.6 Comparison of Time Histograms

For a linear amino acid chain translocation as shown in Fig. 6.5a , if there are neutral
regions or stall points, Eq. (6.3) is no longer valid. If the potential wells are deep
enough, Kramers reaction rate theory [ 40 ] predicts that the distribution of sojourn
times should be multi-exponential according to the number of barriers present.
When there is only one barrier present, using a simple one dimensional transition
state theory, the predicted escape time from one electrostatic trap with barrier
height ( DU z ) will be

ðDU z =k B TÞ t 1

/ exp (6.6)

This neglects protein conformational changes that could provide alternate lower-
barrier pathways.
As shown in Fig. 6.5c , there is one stall point for Hpr and two for LGa. The

time histograms measured for these two proteins under denaturing conditions show
that the t d histogram of Hpr (Fig. 6.7a ) fits well with a single exponential, and the t d
histogram of

b

LGa (Fig. 6.7b ) fits better with two exponentials. This is consistent
with the presence of no more than two stall points during translocation of these
two proteins.
It is enlightening to compare the time histograms of heterogeneously charged
polypeptides with homogeneously charged dsDNA. Without any stall points,
due to their uniform charge density, the time histograms shown for a 2.7 kb
(Fig. 6.7c ) and a 7 kb (Fig. 6.7d ) DNA fit well to the analytical model predicted in
Eq. (6.4).
The DNA molecules translocate through a nanopore moving on average at the
molecule's terminal velocity with variance increasing linearly with t d according to
<x 2

b

2(k b T/)t d . In this case, the most probable time will be the length
divided by its average velocity, t d ¼l m / v ( l m >>H eff ). Thus a longer t d is expected
and observed for the 7 kb DNA (Fig. 6.8d ) compare to the 2.7 kb.
The time distribution described in Eq. (6.4) derived for a charged particle is
appropriate to fit the time distribution of BSA. In this case, l m ~14 nm

>¼ 2Dt d ¼

<H eff ¼ 20 nm,

d¼H eff ¼ 20 nm. Indeed the Eq. (6.4) fits well for the time histograms of BSA at

pH 7 (Fig. 6.7e ) and pH 4.5 (Fig. 6.7f ). These time histograms of the native state
BSA at pH 7 (Fig. 6.7e ) and at pH 4.5 (Fig. 6.7f ) are from the cluster one events in
Fig. 6.4d, e , respectively. These fits suggest that native state BSA translocation can
be treated under the simple charged particle model.
The above analyses have made many simplifying assumptions and neglected
many complex issues including neglect of: conformational changes during the
translocation process, protein interactions with the nanopore wall, dynamics of
long, floppy segments of the molecule outside of the pore, the surface charge of a
nanopore and electroosmosis. Nevertheless, the simple models have thus far been
able to quantitatively explain the protein translocation data.