Biomedical Engineering Reference
In-Depth Information
2
1.5
J
k
/J
0
1
0.5
0
1
2
3
4
5
6
7
8
9
10
special binding site position,
k
Fig. 2
The ratio of molecular fluxes for different positions of the special binding site k for the
channel with N
D
10 binding sites.
Circles
are for "=k
B
T
D
5,
u
=
u
0
D
0:1,and
D
0:5.
Squares
are for "=k
B
T
D
5,
u
=
u
0
D
0:1,and
D
0:5.
Triangles
are for "=k
B
T
D
5,
u
=
u
0
D
10,and
D
0:5.
Diamonds
are for "=k
B
T
D
5,
u
=
u
0
D
0:1,and
D
0:0
current is reached when the binding site is at the exit from the pore (
k
D
N
), while
it is better to have the repulsive site closer to the entrance (
k
1
) to accelerate the
D
transport. It can be shown rigorously from (
6
)that
@J
k
.N /
@k
>0
for positive
"
,and
J
k
.N /
is always a decreasing function for negative
"
.
These observations can be understood in the following way. Putting the attractive
binding site near the exit increases the probability of finding the particle there,
which leads to higher chances to complete the translocation by exiting the nanopore.
The repulsive site at the entrance serves as a barrier for the particles that have
already passed it, lowering the probability of unsuccessful excursions without
the translocation. These results are in full agreement with recent single-molecule
experiments on translocation of polypeptides [
14
,
15
]. In these experiments, the
mutation in the biological nanopore that increased the molecule/pore interaction
have led to faster transport when the mutation site was near the exit. These
theoretical results might also shed the light on experimental observations, showing
that many biological channels have their binding sites at the entrance and/or at the
exit positions, that have not been fully understood so far. To have special binding
at these locations will optimize the overall flux [
34
]. These results can be easily
extended to more complex potentials with several attractive and repulsive sites, and
it can easily be shown that the most optimal flux is reached when several repulsive
sites cluster together near the entrance, while attractive sites must stay closer to the
exit to optimize the overall particle flux through the channel.
Search WWH ::
Custom Search