Content uploaded by Yansha Deng

Author content

All content in this area was uploaded by Yansha Deng on Feb 19, 2019

Content may be subject to copyright.

1

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.

REFERENCES

[1] W. Guo, Y. Deng, H. B. Yilmaz, N. Farsad, M. Elkashlan, C. Chae, A. W.

Eckford, and A. Nallanathan, “SMIET: simultaneous molecular information

and energy transfer,” CoRR, 2016.

[2] L. Iversen and J. Kelly, “Uptake and metabolism of γ-aminobutyric acid

by neurones and glial cells,” Biochemical pharmacology, vol. 24, no. 9, pp.

933–938, 1975.

[3] C. J. Myers, Engineering genetic circuits. CRC Press, 2016.

[4] H. B. Yilmaz, A. C. Heren, T. Tugcu, and C.-B. Chae, “Three-Dimensional

Channel Characteristics for Molecular Communications with an Absorbing

Receiver,” IEEE Commun. Lett., vol. 18, no. 6, Jun. 2014.

[5] E. L. Cussler, Diffusion: mass transfer in ﬂuid systems. Cambridge University

Press, 2009.

[6] Y. Ma, C. Zhu, P. Ma, and K. T. Yu, “Studies on the diffusion coefﬁcients

of amino acids in aqueous solutions,” Journal of Chemical & Engineering

Data, vol. 50, no. 4, pp. 1192–1196, May 2005.

[7] Y. Deng, A. Noel, M. Elkashlan, A. Nallanathan, and K. C. Cheung, “Mod-

eling and simulation of molecular communication systems with a reversible

adsorption receiver,” IEEE Trans. Mol. Biol. Multi-Scale Commun., vol. 1,

no. 4, pp. 347–362, Dec. 2015.

[8] Y. Deng, A. Noel, W. Guo, A. Nallanathan, and M. Elkashlan, “Stochastic

geometry model for large-scale molecular communication systems,” Proc.

IEEE GLOBECOM, 2016.

[9] Y. Deng, A. Noel, M. Elkashlan, A. Nallanathan, and K. C. Cheung,

“Molecular communication with a reversible adsorption receiver,” Proc. IEEE

ICC, Jun. 2016.

[10] A. J. Cornish-Bowden and D. Koshland, “The quaternary structure of proteins

composed of identical subunits,” Journal of Biological Chemistry, vol. 246,

no. 10, pp. 3092–3102, Oct. 1971.

[11] G. Zubay, Biochemistry. New York: Macmillan Publishing Company, 1988.

[12] A. Ahmadzadeh, A. Noel, and R. Schober, “Analysis and design of multi-hop

diffusion-based molecular communication networks,” IEEE Trans. Mol. Biol.

Multi-Scale Commun., vol. 1, no. 2, pp. 144–157, Jun. 2015.

[13] G. Bohm and G. Zech, Introduction to statistics and data analysis for

physicists. DESY, 2010.

[14] M. Evans, N. Hastings, and B. Peacock, Statistical Distributions, 3rd ed.

Wiley-Interscience, Jun. 2000.

[15] W. Greiner, L. Neise, and H. St¨

ocker, Thermodynamics and statistical

mechanics. Springer Science & Business Media, 2012.

[16] P. Atkins and L. Jones, Chemical principles: The quest for insight. Macmil-

lan, 2007.