Biomedical Engineering Reference
In-Depth Information
direction when the net charge of the local segment changes sign, which could drive
the protein back and forth near the electrically neutral charged region. The poly-
peptide chain could be transiently stalled or trapped in an electrical potential well
due to protein heterogeneous charge sequence.
The variability of protein physical properties influences the behavior of the main
translocation observables derived from nanopore resistive pulse measurements.
The complexity in the translocation physics of proteins is reflected in both the
mean current drop and current blockage duration (translocation time).
6.2.3 The Mean Current Drop Amplitude of an Event
The intrusion of a protein or a polypeptide segment into the nanopore reduces its
current flow capacity. To relate the transient current blockage amplitude
DI
b
to the
physical properties of protein molecules, Ohm's law can be exploited based on the
volume displacement of the electrolyte solution from the pore [
17
-
20
]. A translo-
cating molecule that is much smaller than an idealized cylindrical nanopore will
cause a transient drop in current that can be written as
DI
b
ðtÞ¼I
0
LðtÞ
H
eff
A
p
½
1
þ f ðd
m
D
p
; l
m
H
eff
Þ
(6.1)
when the nanopore accounts for nearly all the resistance in the circuit. Here
A
p
H
eff
¼V
p
, the volume of the pore and
f
(
d
m
/
D
p
,
l
m
/
H
eff
) is a correction factor that
depends on the shape of a protein molecule and the relative values associated with the
dimensions of a molecule and a nanopore. (Note, this equation neglects nanopore
surface charge effects, which might be significant at low salt concentrations [
21
].) The
correction,
f
, contains higher order terms in the ratios of the molecule to pore diameter
(
d
m
/
D
p
) and molecule to effective pore length (
l
m
/
H
eff
)[
18
]. For example,
f
(
d
m
/D
p
,
l
m
/
H
eff
)
(4/5)(
d
m
/
D
p
)
2
for a spherical shaped particle that is smaller than the pore but not
at the small particle limit [
18
]. For short molecules that fit entirely inside the length of
the pore like small folded proteins, these ratios are less than one and contribute little to
the current drop [
18
,
22
-
24
]. For molecules such as polynucleotides and unfolded
proteins that are much longer than the pore, a different derivation based on Ohm's law
produces a relation that contains only the first term for the absolute,
¼
DI
b
I
0
(
L
/V
p
), or
DI
b
/
I
0
L
relative current drop,
/V
p
. These equations relate the measured current drop
amplitude to the volume of the molecule transiently blocking the pore.
Equation (6.1) shows that the instantaneous excluded volume of a molecule,
(
t
),
can be estimated by measuring
DI
b
(
t
), however the correction term will vary
depending on the conformation of the protein during the translocation which can
vary as shown in Fig.
6.1b
. A folded globular protein will require a correction
appropriate for a spherical or ellipsoidal particle (Fig.
6.1a
) and the expected current
drop is larger than for a linear particle with the same volume inside the nanopore.
The partially unfolded, and completely unfolded protein translocations will be
L
Search WWH ::
Custom Search