Biomedical Engineering Reference
In-Depth Information
We characterize the water-mediated signal multiplication, by computing the
probability of occurrence in the range of 10
ı
<
N
'<70
ı
, denoted by
P
(
t
). We
can expect that
P
(
t
) approaches 1 in both BTs when the water orientations in the
MT are downward (after a sufficiently long time). In contrast,
P
(
t
) approaches 0.5
in both BTs when the water orientations in the MT are upward, since the water
orientations in both BTs fluctuate between upward and downward with a roughly
equal probability. If we set
P
C
as a value between 0.5 and 1, we expect that
P
>
P
C
in
the BTs corresponds to the downward water orientations in the MT and that
P
<
P
C
in the BTs implies the upward water orientations in the MT after a sufficiently
long time. Considering the rapid convergence of the case for the downward water
orientations in the MT,
P
C
D
0.8 is set, which is a little larger than the average value
of 0.5 and 1. From Fig.
1.46
, we can see that
P
>
P
C
in both BTs for any time
t
> 1ns
for the downward water orientations in the MT, while
P
<
P
C
in both BTs for any
time
t
> 8 ns for the upward water orientations in the MT. Thus, the charge signal at
the MT can be readily distinguished from the value of
P
(
t
) in each BT within a time
interval of 8 ns with an appropriate threshold
P
C
D
0.8.
In the following, we further examine the water orientations inside the branched
tubes (BTs). Let us first consider a single channel without any external charge. There
is a hydrogen atom pointing out at the upmost (or bottommost) end when water
molecules inside the channel have a concerted upward (or downward) orientation
inside the single channel. One upward
!
downward switch of the water orientations
inside the nanochannel will result in an “apparent” transportation of an upward-
pointing hydrogen atom at the upmost-end of the tube to a downward-pointing
hydrogen atom at its bottommost-end.
However, there is a different situation in Y-shaped nanochannels. Let us think
about what happens to the water orientations inside a Y-shaped nanochannel. In the
MT, there is the similar bottom
!
upper transportation of only one hydrogen atom,
after the downward
!
upward switch of its concerted water orientation. But this
transportation causes a different situation in the BTs. There is the transportation of
only half a hydrogen atom on the average in each BT, due to the conservation of
the hydrogen atom (the total number of the hydrogen transportation is also one for
both BTs). Different from the above simple single-tube case, this creates asymmetry
for the Y-shaped tube, since the average half hydrogen atom “transported” in BTs
can be either zero or one at any moment. Thus, the situation will not be always a
simple upward
!
downward (or downward
!
upward) orientation switch in each
BT following that in the MT. In other words, if the water orientations in both BTs
follow the
downward
water orientations as in the MT, these same water orientations
in both BTs might not follow the
upward
water orientations as in the MT on the
other hand.
Interestingly, our simulations exactly reproduce this situation. For example, the
downward water orientations in both BTs are observed when the water orientations
in the MT are downward (corresponding to a negative monitored charge), while the
upward water orientation in the MT (corresponding to a positive monitored charge)
results in a fluctuation of the water orientations between the downward and upward
