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Enabling Energy Efficient Molecular Communication
via Molecule Energy Transfer
Yansha Deng, Member, IEEE, Weisi Guo, Member, IEEE, Adam Noel, Member, IEEE,
Arumugam Nallanathan, Senior Member, IEEE, and Maged Elkashlan, Member, IEEE.
Abstract—Molecular communication via diffusion (MCvD) is in-
herently an energy efficient transportation paradigm, which requires
no external energy during molecule propagation. Inspired by the
fact that the emitted molecules have a finite probability to reach
the receiver, this paper introduces an energy efficient scheme for the
information molecule synthesis process of MCvD via a simultaneous
molecular information and energy transfer (SMIET) relay. With this
SMIET capability, the relay can decode the received information as
well as generate its emission molecules using its absorbed molecules
via chemical reactions. To reveal the advantages of SMIET, approx-
imate closed-form expressions for the bit error probability and the
synthesis cost of this two-hop molecular communication system are
derived and then validated by particle-based simulation. Interestingly,
by comparing with a conventional relay system, the SMIET relay
system can be shown to achieve a lower minimum bit error probability
via molecule division, and a lower synthesis cost via molecule type
conversion or molecule division.
Index Terms—Molecular communication, energy transfer, chemical
reaction, SMIET relay.
I. INTRODUCTION
Recently, molecular communication has been proposed as the
potential enabler for nano-scale communication between nanoma-
chines via the transmission of chemical signals in very small
dimensions or in specific environments, such as in salt water,
tunnels, or human bodies. Among all types of molecular communi-
cation paradigms, molecular communication via diffusion (MCvD)
allows the information molecules to propagate freely via random
Brownian motion, and it is the most simple, general and energy
efficient transportation paradigm, since it does not require external
energy or infrastructure.
Even though the propagation of information molecules in M-
CvD does not need external energy, molecule synthesis at the
transmitter is energy consuming, and currently nano-batteries for
nanomachines do not exist. Moreover, supplying power externally
via acoustic or electromagnetic waves to nanomachines operating
in vivo can be difficult due to high penetration loss and its small
dimensions. Hence, how to reduce the molecule synthesis cost to
improve energy efficiency in molecular communication becomes
an important question to answer.
One way to reduce the synthesis cost is to collect the information
molecules arriving at the nanomachine not only for received signal
Manuscript received Jul. 18, 2016; revised Oct. 03, 2016 and Oct. 31, 2016;
accepted Dec. 01, 2016. The editor coordinating the review of this manuscript and
approving it for publication was Dr. Vasileios Kapinas.
Y. Deng and A. Nallanathan are with King’s College London, London, WC2R
2LS, UK (email:{yansha.deng, arumugam.nallanathan}@kcl.ac.uk).
Weisi Guo is with University of Warwick, West Midlands, CV4 7AL, UK (email:
weisi.guo@warwick.ac.uk).
A. Noel is with University of Ottawa, Ottawa, ON, K1N 6N5, Canada (email:
anoel2@uottawa.ca).
M. Elkashlan is with Queen Mary University of London, London, E1 4NS, UK
(email: maged.elkashlan@qmul.ac.uk).
decoding, but also for its own information transmission use. This
process is the so called simultaneous molecular information and
energy transfer (SMIET) process [1]. In fact, SMIET-like processes
can be found at the cellular level in biology; one example is
the γ-Aminobutyric acid (GABA) metabolism and uptake, which
is usually found in all regions of the mammalian brain [2].
In this mechanism, GABA, which is generated and released by
the presynaptic neuron cell (i.e., source), can be harvested and
converted to Glutamine inside the neighbouring Glial cells (i.e.,
SMIET relay) for further transmission. The SMIET process can
also be engineered in a cell by using genetic circuits with chemical
reactions facilitated by catalysts [3].
To construct an energy efficient system, we propose and study
a two-hop molecular communication system with an absorbing
SMIET relay, where the relay has the capability of converting
the absorbed molecules to another type of molecule via chemical
reactions for its own transmission to save its synthesis cost. To
showcase the benefits of the proposed system, we derive closed-
form expressions for the approximate bit error probability at the
destination and the system synthesis cost. These are verified by
particle-based simulations. Our results show that with the help
of the SMIET relay in the two-hop molecular communication
system, the minimum bit error probability can be greatly improved,
whereas the synthesis cost with molecule type conversion and
that with molecule division are reduced compared to that of a
conventional relay system.
II. SY ST EM MO DE L
We propose a two-hop SMIET molecular communication system
with a point source, an absorbing decode-and-forward (DF) relay
with radius RR, and an absorbing destination with radius RD.
Here, we limit ourselves to the full absorption receiver case as
in [4], which can be extended to the partial absorption receiver
[4]. In this two-hop SMIET molecular communication system, the
relay can absorb the type A molecules transmitted by the source
located at a distance dRaway from the surface of the relay. With
the absorbed type A molecules, the relay operates in SMIET mode
to decode the information as well as to convert type A molecules to
type B molecules, then the relay transmitter emits the generated
type B molecules for the intended destination at a distance dD
away from the surface of the destination.
The type A information molecule and the type B information
molecule are molecules with an arbitrary shape and effective radius
rAand rB(rA, rBRR, RD), respectively. We assume that
rA=lrB,(l > 0). The diffusion coefficient is generally inversely
proportional to the radius [5], [6], thus we have the diffusion
coefficient of type A molecule DAand the diffusion coefficient of
type B molecule DBfollowing the relationship DB=lDA. We
2
assume that the relay has specific receptors that only absorb type
A molecules transmitted by the source, and the destination has
different receptors that only absorb type B molecules transmitted
by the relay for information decoding. Otherwise, each receiver is
transparent to the non-specific molecule type.
A. Source to Relay Link
In the source to relay link, the source transmits the jth bit
at time t= (j−1)Tbby modulating the number of type A
molecules with binary concentration shift keying (BCSK), where
the source emits NAtype A molecules to transmit bit-1 and emits
0 molecules to transmit bit-0. Tbis the single bit interval time, and
Tb=TR+TD, where TRand TDare the first hop and second hop
time intervals, respectively. As in [7]–[9], we decode using the net
number of absorbed molecules in the current interval. Thus, the
relay measures the number of absorbed type A molecules Nnew
R[j]
during the first hop interval [(j−1)Tb,(j−1)Tb+TR].Nnew
R[j]is
used for information decoding of the jth bit and molecular energy
transfer and for powering the second hop transmission.
B. SMIET Relay
The SMIET relay receiver is capable of performing division
from a type A molecule into one or more type B molecules via
a chemical reaction in a short time with the help of a reaction
catalyst, and one example is the protein degradation of type A
molecule into subunits [10]. We express this reaction as [11]
A→mB,(1)
where each absorbed type A molecule is instantaneously decom-
posed1into m type B molecules inside the relay. We idealistically
assume that this reaction only occurs during the interval of the
first hop. However, the implementation of time-varying reaction
kinetics is outside the scope of this work.
C. Relay to Destination Link
In the model, a barrel transmitter with negligible radius is
located on the surface of the relay. It is placed at the point closest
to the destination. We assume that there is no interaction between
the type A molecules and the type B molecules outside the relay,
due to the lack of catalyst, and transformation of type-A to type-B
only occurs inside the relay. The type B molecules transmitted by
the relay will not be absorbed by the relay (since the relay only
absorbs type A molecules), and the relay can be treated as a point
transmitter during the transmission process.
In the relay to destination link, the relay forwards the decoded
signal by modulating on the number of converted type B molecules
at the relay. If the received signal at the relay ˆxR[j]is bit-1, then
the relay transmitter emits mNnew
R[j]type B molecules to the
destination at t= (j−1)Tb+TR; if the received signal at the relay
ˆxR[j]is bit-0, then the relay transmitter emits zero molecules.
The destination then decodes the signal ˆxD[j]based on the net
number of type B molecules absorbed at the destination during
[(j−1)Tb+TR, jTb].
1Fast enzymatic reactions can occur at timescales of 1µs or less, which is much
faster than the diffusion times considered in Section IV. By assuming instantaneous
conversion, the derived error probability is a lower bound and the synthesis cost
is an upper bound to that in the finite reaction rate scenario.
III. ERRO R PROBABILITY AND SYNTHESIS COST
In this section, we examine the bit error probability and the
synthesis cost in the two-hop molecular communication system
with the proposed SMIET mechanism.
A. Bit Error Probability at the Relay
For multiple bit transmission, the net number of absorbed type
A molecules received at the relay in the jth bit interval can be
modeled as [7, Eq. (26)] [12, Eq. (8)]
Nnew
R[j]∼Pois(NAΨR[j]),(2)
where
ΨR[j] =
j
X
i=1
xS[i]RdR, rR, DA,(j−i)Tb,(j−i)Tb+TR,
(3)
R(dR, rR, DA, T, T +TR) = rR
rR+dR
herfcndR
p4DA(T+TR)o−erfcndR
√4DAToi,(4)
xS[i]is the ith transmitted bit at the source, and Pois is the Poisson
distribution. The Poisson approximation is accurate for sufficiently
large NAand sufficiently small ΨR[j].
The received signal at the relay is decoded as follows: if
Nnew
R[j]< NR
th, then the received signal ˆxRat the relay is bit-0;
otherwise, ˆxRis bit-1, where NR
th is the decision threshold at the
relay. The error probability of the jth bit is
PR
e[j] =P1PR
ehˆxR[j]=0
xS[j]=1, xS[1 :j−1]i
+P0PR
ehˆxR[j]=1
xS[j] = 0, xS[1 :j−1]i,(5)
where
PR
ehˆxR[j] = 0
xS[j]=1, xS[1 :j−1]i
≈exp n−NAΨ1
R[j]o
NR
th
−1
X
n=0
NAΨ1
R[j]n
n!,(6)
and
PR
ehˆxR[j] = 1
xS[j]=0, xS[1 :j−1]i
≈1−exp n−NAΨ0
R[j]o
NR
th
−1
X
n=0
NAΨ0
R[j]n
n!,(7)
respectively [7, Eqs. (32), (33)]. In (6) and (7), Ψ1
R[j]and Ψ0
R[j]
are given in (3) with xS[j]=1and xS[j] = 0, respectively. In
(5), P1and P0denote the probability of sending bit-1 and bit-0,
respectively.
B. Bit Error Probability at the Destination
Each absorbed type A molecule is converted to mtype B
molecules for transmission at the relay, thus, the net number of
absorbed type B molecules received in the jth bit interval during
3
[(j−1)Tb+TR, jTb]is described as a binomial distribution
Nnew
D[j]∼
j
X
i=1
BmNnew
R[i],ˆxR[i]
×RdD, rR, DB,(j−i)Tb,(j−i)Tb+TD,(8)
where ˆxR[i]is the ith detected bit at the relay.
According to the fact that Y follows a Poisson distribution
Y∼Pois(λp)when we have the conditional binomial distribution
Y|(X=x)∼B(x, p)and X∼Pois(λ)2[14], we approximate
Nnew
D[j]as
Nnew
D[j]∼
j
X
i=1
PoismNAΨR[i]ˆxR[i]
×RdD, rD, DB,(j−i)Tb,(j−i)Tb+TD
∼Pois(NAΨD[j]),(9)
where
ΨD[j] =
j
X
i=1
mΨR[i]ˆxR[i]R(dD, rD, DB,
(j−i)Tb,(j−i)Tb+TD,(10)
and ΨR[i]is given in (3). We note that Nnew
D[j]is dependent on
constant parameters and the detected signals at the relay, but not
on Nnew
R[i].
The destination decodes the received signal by comparing the
net number of absorbed molecules in the second hop interval
Nnew
D[j]with the destination decision threshold ND
th . Thus, the
error probability of the jth bit at the destination is
PD
e[j] =P1PD
ehˆxD[j]=0
xS[j] = 1, xS[1 :j−1]i
+P0PD
ehˆxD[j] = 1
xS[j]=0, xS[1 :j−1]i,(11)
where
PD
ehˆxD[j]=0
xS[j] = 1, xS[1 :j−1]i
= exp n−NAΨ1
D[j]o
ND
th
−1
X
n=0
NDΨ1
D[j]n
n!,(12)
and
PD
ehˆxD[j] = 1
xS[j]=0, xS[1 :j−1]i
= 1 −exp n−NAΨ0
D[j]o
ND
th
−1
X
n=0
NDΨ0
D[j]n
n!,(13)
respectively. In (12) and (13), Ψ1
D[j]and Ψ0
D[j]are given in
(10) with xS[j] = 1 and xS[j] = 0, respectively. As can
be seen in (10), the bit error probability is a function of the
detected bits at the relay ˆxR[1 :k]. To calculate (11) with low
computational complexity, we average the bit error probability
over many realizations of ˆxR[1 :k]to obtain an approximation.
Each realization of ˆxR[1 :k]is obtained by tossing a biased
coin for each bit. Specifically, given xS[k] = νS∈ {0,1}, we
2Here, the approximation mNnew
R[j]∼Pois(mNAΨR[j]) is obtained from
that for the sum of correlated Poisson variables in [13, pp. 63-64].
toss a biased coin to determine whether the detected bit at the
relay is ˆxR[k] = xS[k], which occurs with probability equal to
1−PR
ehˆxR[k] = |1−νS|
xS[k] = νS, xS[1 :j−1]igiven in (6)
and (7). Our simulation results in Section IV confirm the accuracy
of this approximation.
C. Synthesis Cost at the Source
We now present the energy model for the proposed SMIET
relay system. In biological cells, most energy-requiring reactions
are powered by the Gibbs free energy released by the hydrolysis of
Adenosine triphosphate (ATP) [11]. Thus, ATP is useful in many
cell processes, such as photosynthesis, active transport across cell
membranes (as in the electron transport chain), and synthesis of
macromolecules (e.g., DNA).
To quantify the synthesizing energy cost of the type A molecule
and type B molecule, we use the amount of Gibbs free energy G0
released from hydrolysis of ATP as [11]
AT P +H20→ADP +PI,∆G0=−30.5kJ/mol,(14)
where ADP is adenosine diphosphate, and PIis phosphate. We
assume that the synthesis of a single type A molecule requires gA
ATPs, and that of single type B molecule requires gBATPs. As
such, the synthesizing energy cost of a single type A molecule,
GA, and that of a single type B molecule, GB, are calculated as
GA=gA
30.5
NAvo
kJ,and GB=gB
30.5
NAvo
kJ,(15)
respectively, where NAvo = 6.022 ×1023mol−1is Avogadro’s
constant. For multiple bit transmissions, the synthesis cost of type
A molecules at the source is
Esyn
S=
nbit
X
j=1
xS[j]NAGA,(16)
where nbit is the total number of bits emitted at the source.
D. Synthesis Cost at the Relay
The chemical reactions are a type of thermodynamic process.
The Gibbs free energy is a thermodynamic potential that can be
used to calculate the amount of energy required for a reaction to
happen in a thermodynamic system [15]. The reactions at the relay
require the energy released from hydrolysis of ATP. For one type A
molecule converting to mmolecules of type B, the standard-state
free energy of reaction is given as [16, Ch. 7 Eq. (20)]
A→mB,∆GAB = (mGB−GA)kJ,(m≥1) (17)
where ∆GAB is the difference between the free energy of a
substance and the free energies of its constituent elements at
standard-state conditions, and GAand GBare given in (15).
The expected synthesis cost of type B molecules from type A
molecules at the SMIET relay is calculated as
Esyn
R=
nbit
X
j=1
ˆxR[j]NAΨR[j] (mGB−GA)kJ,(mGB> GA).
(18)
We note that the synthesis cost at the relay is zero for mGB≤
GA, thus (18) provides the maximum synthesis cost at the SMIET
4
0 5 10 15 20 25 30 35 40
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
ND
th
Bit Error Probabilility
Analytical
Simulation
m = {1, 2, 3}
No Relay
SMIET:
Fig. 1. Bit Error Probability versus the detection threshold at the destination.
relay. As shown in (18), the maximum synthesis cost increases
with increasing the expected number of absorbed molecules at the
SMIET relay.
E. Synthesis Cost of Molecular Communication System
For the random nbit bits emitted at the source, the expected
maximum synthesizing cost of the two-hop molecular communi-
cation system can be written as
Esyn
tot =P1Esyn
ET xS[nbit] = 1
xS[1 :(nbit −1)]
+P0Esyn
ET xS[nbit]=0
xS[1 :(nbit −1)],(19)
where
Esyn
ET xS[nbit]=(·)
xS[1 :(nbit −1)]
=NA
nbit
X
j=1 xS[j]GA+ ˆxR[j]ΨR[j] (mGB−GA).(20)
IV. NUMERICAL RES ULT S
In this section, we present the simulation and analytical results.
In the figure and the table, we set NA= 100,nbit = 4,dR=
dD=RR=RD= 4 µm, TR=TD= 0.5Tb= 0.14 s, P0=
P1= 0.5,NR
th = 10,DA= 158.8µm2/s, DB=lDA,l≈
m,gA= 6000,gB= 4000, the simulation step is 10−5s, and
simulations were repeated 103times3. The “Simple Relay” case
corresponds to the relay not having SMIET capability, such that it
must synthesise type B molecules directly, whereas the “No Relay”
case corresponds to no relay in the system4.
Fig. 1 plots the bit error probabilities at the destination, where
the analytical curves are plotted via Eq. (11), and the simulation
points are plotted by extending the particle-based simulation
algorithm in [7]. Table I presents the synthesis cost corresponding
to each case in Fig. 1. We observe that with the SMIET relay,
increasing the reaction factor mimproves the minimum bit error
probability, but increases the synthesis cost, which can be seen
3We use l≈mas a first approximation without considering the specific shapes
of A and B. The value of gAcorresponds to the typical amount of ATP required
to synthesize a protein with 100 −200 amino acids.
4To make these comparisons fair, the distance between the source and the center
of destination in the “No relay” case is equal to dR+dD+RD.
TABLE I
SYNTHESIS COST OF THE MOLECULAR COMMUNICATION SYSTEM (×10−16)KJ
Simple Relay SMIET SMIET SMIET No Relay
m= 1 m= 2 m= 3
1.3121 1.0604 1.1464 1.3121 1.0604
from (20). The “No relay” case has the worst minimum bit error
probability. The “Simple Relay” and “m= 1” cases achieve the
same bit error probability, but the “m= 1” case has a much
lower synthesis cost, which demonstrates the energy efficiency
of the SMIET relay system via molecule type conversion. With
the same synthesis cost for the “m= 3” and “Simple Relay”
cases, the “m= 3” case achieves a much lower minimum bit
error probability, which showcases the performance enhancement
brought by the SMIET relay.
V. CONCLUSIONS
In this paper, we proposed and modeled an energy efficient
molecular communication system with a SMIET relay. We have
examined the bit error probability and synthesis cost of the two-
hop molecular communication system with the SMIET relay. Im-
portantly, our results showed that the minimum bit error probability
can be greatly improved with low synthesis cost in the SMIET
relay system. The extension to a finite reaction rate inside the
SMIET relay with counting noise can be considered in future work.
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