Page 133 - 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

ELECTRIC MANIFESTATIONS AND SOCIAL IMPLICATIONS OF BACTERIA AGGREGATION
FROM THE BESSEL-KELLER-SEGEL EQUATION

Huber Nieto-Chaupis
Universidad Autónoma del Perú

Panamericana Sur Km. 16.3 Villa el Salvador, Lima PERÚ
NOTE: Corresponding author: hubernietochaupis@gmail.com

Abstract – This paper proposes a fair extension of Keller-Segel equation based in the argument that
bacteria exhibit proporties electric in their composition. The new mathematical form of this extension
involves the integer-order Bessel functions. With this one can go through the electrodynamics of the
representative scenarios in order to understand the social behavior of bacteria. From the theoretical side
this paper demonstrates that, charged electrically, aggregation of bacteria would give rise to electric
currents that hypothetically are the reasons for social organization and disruption among them. The
electrical properties of bacteria from this mathematical proposal might be relevant in a prospective
implementation of so-called Internet of Bio-Nano Things network, that aims to be characterized for having
a very high signal/noise.

Keywords – Bessel, classical electrodynamics, Keller-Segel, nanonetwork

1. INTRODUCTION reason of the Keller-Segel equation, in the sense that
bacteria can deplete substrate in an efficient manner.
Evelyn Keller and Lee Segel in 1971 reported in [1] For example, Unluturk, Balasubramanian and Akyildiz
that bacteria exhibit some relative preference to [3] have used the Keller-Segel model in the study of
move through the highest concentrations of social behavior of bacteria inside the framework of
substrate instead of the lowest ones. This molecular communications as part of the fundamental
phenomenon was projected onto the equation postulates of the prospective Internet of Bio-Nano
known as the Keller-Segel equation and it is written Things (IoBNT) [4]. Clearly one can appeal to physics
as: of Eq. 1 for a robust application inside the molecular
( , ) ( , ) and phenomena at the nano-level. Since bacteria is
= [ ( ) ] − [ ( , ) ( ) ] ( )
transporting a net electric charge, then a plethora of
whose meaning of elements of this reads as follows: ways to search their behavior represents an option to
use theoretical scenarios of physics interactions and
• ( , )= bacteria density, the implcations that would rise in a scenario of bio-
• ( , ) = substrate density, nano technology. Thus, Eq. 1 opens various paths to
understand both the physics and biophysics of
• ( ) = chemotactic coefficient,
bacteria dynamics. Of course, Eq. 1 can also be seen
• ( ) = motility parameter. as a fair extension of diffusion equation [5].
In effect, Eq.1 to some extent can also be written as
Eq.1 can be seen actually as a kind of compensation.
In effect, one can see that by putting ( , ) and ( , ) = D ( , ) + G(s,t) with D the diffusion

( ) as constants, then the positive change constant and G(s, t) enclosing a set of operations based
( , ) > 0 demands that: at both spatial and time derivatives. Thus, emerges the

questions: Are bacteria fully diffusive? What are then

( , ) ( , )
> . ( ) the physics of this possible diffusion? Here one can
answer in terms of physics laws in: (i) Electricity, (ii)
That is valid over the allowed periods of bacteria Thermodynamics, and (iii) Space-time propagation.
substrate interaction. This has interesting The purpose of this paper is to extend Eq.1 when
consequences in the discipline of bacteria dynamics bacteria are composed by electrical material such as
[2]. Clearly one can see that it encompasses the ions for instance, so that concrete electric interactions
would take place.

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