Page 40 - 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

where is the initial concentration of chiral
molecules, is the initial concentration of achi‑
ral molecules and ( , ) represents the Brownian
particles at time at point , with irst moment as:
2
= 2 , (4)
Fig. 3 – Chirality transfer property of chiral molecules (black circles) to‑ and standard deviation:
wards achiral molecules (light blue molecules).
√
= 2 . (5)
show an optical activity, and become a chiral molecule. As
aresult, thechiralitytransferworksaspoint‑to‑pointdata In Eq. (3), we account for the achiral molecules that are
forwarding among heterogeneous molecules (i.e., from “inducted” to become chiral with a certain probability
chiral to achiral molecules). that is proportional to the helical twisting power of the
Speci ically, when a chiral molecule encounters an achiral chiral molecules, i.e.:
component, it forms a non‑covalent bond and the chiral‑ ( → ) ∽ , (6)
ity effect is transferred into the achiral molecule, which
becomes chiral. Finally, the chirality transfer propagates where is the helical twisting power and is expressed
in the whole system. as [24]
Fig. 3 depicts the chirality transfer feature of chiral Δ
molecules in a heterogeneous channel (i.e., comprised of = 8 , (7)
both chiral and achiral molecules). In this scenario, the 2
chiral molecules are used as messenger molecules re‑ where Δ is the chemical potential difference between a
leased by a transmitter nanomachine (e.g., a eukaryotic chiral molecule and its enantiomer when they are placed
cell) through the medium via diffusion (i.e., Brownian mo‑ in the solution, is twist elastic constant, the wavevec‑
2
tion). They are used as messengers, since they allow tor = 2 / and is the elical pitch, which is inversely
the transmission of a light signal applied to a transmitter proportional to the concentration of chiral molecules in‑
molecule and transferred from a molecule to the neigh‑ jected by the transmitter.
bors through the chiroptical properties when the system
will reach a steady state. The motion is basically driven 4. CHIRAL OPTICAL CHANNEL
by diffusion, meaning that the particles move from areas In the context of molecular communication, we envision
of higher concentration to areas of lower concentration, that chiral molecules will be expected to be largely ex‑
and the displacement of messenger molecules follows a ploited [25]. Due to the feature of changing the polariza‑
normal distribution with zero mean. tion plane of an impinging optical signal, data information
The overall chiral molecule concentration lux is given can be encoded into chiral molecules, and carried out via
by the sum of the chiral molecules concentration gra‑ the chiral transfer mechanism. Speci ically, when an opti‑
dients, with as the number of apertures of the Tx
cal pulse impinges a (biological) chiral channel, an optical
nanomachine. The lux of chiral molecule concentration
activity as output of the channel will be observed. The op‑
depends on both time and position through the Fick’s irst
tical activity is expressed as a rotation of the polarization
law i.e.,
plane of the impinging EM wave. On the other side, if no
( , ) = − ∑ ∇ , ( , ), (1) pulse impinges the chiral channel, no optical activity will
=1 be observed at the output of the chiral channel, and then,
where ∇ is an operator used in vector calculus as a vec‑ there will be no rotation of the polarization plane of the
3
tor differential operator, , [mol/cm ] is the ‑th chi‑ EM wave.
ral molecule concentration with = {1, 2, … , }, and In Fig. 4 we show how the chiral molecules are arranged
2
[cm /s] is the diffusion coef icient, assumed as a constant after the diffusion process, in a steady state. We assume
value for a given luidic medium as: that a certain concentration of chiral molecules is injected
in the system and these molecules diffuse in the solution

= , (2) and “transfer” their chirality to other achiral molecules.
3 Speci ically, a Tx nanomachine releases a concentration
where is the Boltzmann constant equal to 1.38 × of chiral molecules that transfer chirality to neighboring
10 −23 [ / ], is the temperature [ ], is the viscosity of achiral molecules, which become chiral as well. Blue cir‑
the liquid [ ⋅ ], and is the size of the chiral molecules cles represent chiral molecules (both enantiomers), while
expressed in [ ]. Finally, Eq. (1) can be rewritten as: gray circles are the achiral molecules. In this work, we
treat chiral molecules as chiral optical antennas and we
+ ( → ) 2 focus on some speci ic parameters allowing the charac‑
( , ) = − 4 (3) terization of the chiral optical ield generated. In particu‑
3
√ (4 ) lar, as demonstrated in [26], we consider the chirality lux

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