Page 138 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 3 – Internet of Bio-Nano Things for health applications

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 3

whose integration yields the closed-form solution: biological reason.
2
2
( ) = [− ∫ ( + + [1 − 2 ]) ]
0
( )

With = and by specifying the upper limit by

“T” the net charge that is transported by the bacteria
2
with the change ( ) = + + [1 − 2 ], then Eq. 32
2
can be written in compact form as:

( , ) = [− ( )]. ( )

With this result, now the electric current that Fig. 4 – The instantaneous current as a function of radial
involves a more general electric description of distance (Eq.36), expressed in in arbitrary units. Two phases
bacteria aggregation transporting ions is given by can be perceived.
the instantaneous derivative of Eq. 33 and written Below in Fig. 5 the simplest scenario of Eq. 35
as: written as I(t)=tExp(-t) is illustrated. The
qualitative shape of electric current indicates its
( , )
( = , ) = − [− ( )]. ( ) maximal value. Clearly, it is directly interpreted as

the inverse scenario of Fig. 4 establishing a kind of
On the other hand in the simplest case by which " " complementarity with it. This triggers logic
does not depend on time, then the integration over scenario establishing that organization is first and
the time variable inside the exponential in Eq. 32 is disruption is after.
trivial. In this manner the resulting electric current
can be written in a simplified form as:
( )
= ( ) = − ( ) [− ( )]. ( )

Actually the variable “ ” can be understood as the
period in the which the bacteria aggregation
behaves as an electric current.

3.1 Biophysics Interpretation of Electrical
Currents
Eq. 34 is displayed in Fig. 4 exhibiting a minimum
for ≈ a.u. For this plotting it was used as a
numerical expression for Eq. 34 in the form of:
Fig. 5 – RC Discharge: The instantaneous current and period of

( = , ) = . ( + . + ) [− . ( ^ + electric interaction of bacteria as a function of radial distance,
( )^
both expressed in in arbitrary units. This plot as well as Fig. 1,
. + ( − ))]. (36) Fig. 2, Fig. 3 and Fig. 4 were done with the usage of Wolfram
( )^
[13].
As indicated at Fig. 4, bacteria aggregation would
exhibit a kind of disruption as seen in the minimum In this manner, one can see that from Fig. 4 and Fig.
value of current distribution. In this manner, one 5 the possible existence of well-defined phases. This
can wonder if it is an inherent property of bacteria would characterize the BKS model. These possible
aggregation or if it is a pure speculative theoretical phases would emerge from the fact that the Eq. 5
result that might not be matched with experiments. exhibits a kind of electric discharge as a RC-circuit.
It should be noted that all these procedures have It is in accordance to the negative exponential of Eq.
been done under the assumption of a 1-Dimension 35. Therefore, bacteria aggregation and their social
model. Of course, realistic simulations might be manifestations would be disrupted. In Fig. 5 the
necessary in order to identify rupture of electrical instantaneous current falls down as a fact that
properties. As done in [14], memory-based bacteria have “finshed” a social action leaving them
chemotaxis would exibit drift velocities. So that one to break down the possible molecular
can argue that this drift dynamics might appear communications between them.
from electric phenomena more than a pure

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