Novel Modulation Techniques using Isomers as Messenger Molecules for Molecular Communication via Diffusion

0.48 MB·English

by  Na-Rae Kim

1
Novel Modulation Techniques using Isomers as
Messenger Molecules for Molecular
Communication via Diffusion
Na-Rae Kim and Chan-Byoung Chae
School of Integrated Technology
Yonsei University, Korea
Email: {nrkim, cbchae}@yonsei.ac.kr
2
1
0
2 Abstract—In this paper, we propose novel modulation tech- no inorganic harmful materials. Moreover, driven by chemical
niquesusingisomersasmessengermoleculesfornanocommuni- reactions, molecular communication is energy efficient. For
n cationviadiffusion.Toevaluateachievablerateperformance,we
these reasons, molecular communication is the main focus of
a compare the proposed techniques with concentration-based and
J this paper.
molecular-type-based methods. Analytical and numerical results

3 confirmthattheproposedmodulationtechniquesachievehigher The authors in [6], [7] have extensively studied the fun-
data transmission rate performance than conventional insulin damentals of molecular communication via diffusion. A new

] based concepts. energy model has been investigated to understand how much
M
Index Terms—Nano communication network, molecular com- energy is required to generate messenger molecules in [6]
Q munication, modulation technique, isomer, diffusion, messenger andconcentration-basedandmolecular-type-basedmodulation
. molecule. techniques have been introduced in [7]. By using a simple
o
i symmetric binary channel model, the achievable transmission
b
- I. INTRODUCTION rate(achievableratehereafter)hasbeenextensivelycompared.
q In analyzing their modulation techniques, however, [6], [7]
Since R. Feynman’s talk in 1959, people have eagerly
[ did not clearly suggest concrete structures for the messenger
pursued practical work on smaller and smaller scales, notably
molecules. They considered insulin-based nano networks but
1
through nanotechnology [1]. Nanotechnology, recently, pro-
v it is unclear how these could be utilized for molecular-type-
duced a new branch of research called nano communication
3 based modulations. In this paper, to maximize the achievable
1 networks (NCNs). NCNs interconnect several nanoscale ma- ratewithlesstransmitpower/energy,weproposeusingisomers
9 chines (nanomachines in short) to carry out more complex
asmessengermolecules.Toconsiderthepropertiesofisomers,
0 tasks in a cooperative manner, or to perform simple tasks [2].
we slightly modify the energy model described in [6]. To
.
1 These networks are not just smaller versions of traditional
the best of our knowledge, the proposed method is the first
0 communication networks; they have their own features and
attempt to design appropriate messenger molecules for NCN
2 areapplicableinmanyfields,includingbiomedical,industrial,
1 via diffusion.
military, and environmental [3].
: This paper is organized as follows. Section II describes the
v NCNs can be realized by several methods. We can rely on
channel and energy models under consideration. Section III
i
X traditional communication systems that use electromagnetic
explains isomers for messenger molecules and also proposes
fields or ultrasonic wave. We have to overcome, however,
r two modulation techniques, i) concentration-based and ii)
a someradiofrequency(RF)devicebarriers[2].Onthepractical
molecular-type-based. We present the numerical results in
front, researchers are considering new materials, such as
Section IV, and Section V offers our conclusions.
carbon-nano tubes (CNTs) and graphene [4]. Little research,
however, has focused on channel models and human body
absorptionwithterahertzbands.Inadditiontothesesactivities,
II. SYSTEMMODEL
a new concept utilizing diffusion especially for short range
communication has been introduced [5].
For simplicity, we consider a nano communication system
Thisnewparadigmofcommunication,molecularcommuni-
consisting of a single transmitter and a single receiver, as
cation,sends/receivesinformation-encodedmoleculesbetween
illustrated in Fig. 1. For this system, the messenger molecules
nanomachines. One of its advantages is its biocompatibility.
diffuse through the medium1 (i.e. water) at body temperature.
Biocompatibility is the most important and challenging issue
This paper assumes that no collisions occur among the prop-
confronting intra-body applications. By using biomolecules
agating messenger molecules and/or the molecules and the
we can create inherently biocompatible systems that require
medium.
ThisworkwasinpartsupportedbytheMinistryofKnowledgeEconomy
underthe“ITConsilienceCreativeProgram”(NIPA-2010-C1515-1001-0001) 1Inourfuturework,bloodwillbeconsideredasthemediumtogetmore
andtheYonseiUniversityResearchFundof2011. reasonableresults.
2
total number of molecules during a symbol duration becomes
different depending on the current and previous symbol.
Binomial(n,P (d,T )),
hit s
N ∼N(np ,np (1−p )),
c 1 1 1
N ∼Nnp ,np (1−p ))−N(np ,np (1−p ))
p 2 2 2 1 1 1
where, N denotes the number of molecules transmitted and
c
received during the current symbol duration, and N is the
p
number of molecules transmitted from the previous symbol
Fig. 1. System model of nano communication via diffusion with a single duration but received during the current symbol duration. For
transmitterandasinglereceiver. simplicity,weusep forP duringT andp forP during
1 hit s 2 hit
2T .
s
A. Channel Model
B. Energy Model
Theparticlesormessengermoleculesreleasedfromatrans-
mitter nanomachine spread out through the medium by Brow- Weuseanenergymodeltothatdescribedin[6].Toprevent
nian motion [6]. Such motion is basically driven by diffusion, them from interacting with others during propagation, the
meaningtheparticlesmovefromareasofhigherconcentration messengermoleculesareencapsulatedinvesicles.Thevesicles
region to areas of lower concentration. A random process, are then carried to the boundary of the machine (e.g. the
the displacement of messenger molecules follows a normal eukaryotic cell), and released into the propagation medium.
distributionwithzeromean.Thus,thestandarddeviationσ of Here we use r to denote the machine radius size.
unit
the displacement can be obtained as follows: The energy needed in these steps are calculated. Moreover,
(cid:52)X ∼N(0,σ2), we can obtain the cost of synthesizing messenger molecules
(hexoses as an example) by the enthalpy of formation ∆H.
∂c ∂2c
=D , (1) Then the final energy model can then be presented as fol-
∂t ∂x2
lows [6]:
1
c(x,t)= e−x2/4Dt, (2) n
(4πDt)1/2 E =nE + (E +E +E ),
T S c V C E
x2 =2Dt, v
√ E = ∆Hhexose J per messenger molecule,
σ = 2Dt, S 6.02×1023
D = KbT (3) EV =83×5(4πrv2)zJ,
6πηrmm E =83×(cid:20)runit/2(cid:21)zJ,
where, c indicates the concentration of Brownian particles at C 8
time t at point x, and D represents the diffusion coefficient E =83×10zJ,
E
of the particles calculated from the Boltzmann constant (Kb), (cid:18) r (cid:19)3
temperature (T), the viscosity of the medium (η) and the c = v√
v
radius of a messenger molecule (rmm). Eq. (1) is Fick’s rmm 3
second law of diffusion. By solving this partial differential where,E isthetotalenergycostrequiredtotransmitnnum-
T
equation,weobtainthegeneralequationfortheconcentration ber of molecules, E is the synthesizing cost of one hexose
S
of the particles represented in (2). The first moment of (2) molecule calculated from the sum of bond energy (e.g., the
is zero, which indicates the displacement has a zero mean, enthalpy change), E is the vesicle-synthesizing cost having
V
and the second moment becomes the var√iance. Hence, the a radius of rv. EC is the cost of intra-cellular transportation,
displacement has a standard deviation of 2Dt, and finally E is for membrane fusion, and c is the capacity of one
E v
we have vesicle that is related to the radius of messenger molecules
r .
(cid:52)X ∼N(0,2Dt). (4) mm
When n messenger molecules are transmitted by the trans-
III. MODULATIONTECHNIQUES
mitter nanomachine, the molecules have a probability of hit-
tingthereceivernanomachine.Werepresentthisasabinomial Inmolecularcommunicationviadiffusion,theuniqueprop-
distribution of n times of trials with a probability of P for erties of the messenger molecules can determine modulation
hit
each. P is determined by the symbol duration (T ) and the techniques. Two such techniques that have been proposed
hit s
distancebetweenthetransmitterandthereceiver(d),whichare include the use of concentration and type of messenger
bothaffectedbythediffusioncoefficient.Ifnislargeenough, molecules [7]. A usable messenger molecule itself, however,
and nP is not zero, binomial can be approximated as a has yet to be proposed. Thus this paper proposes practical
hit
normal distribution. In addition, we have to take into account messenger molecules, as well as analyzes and compares their
the overflow molecules from the previous symbol [6]. The achievable rates by applying different modulation techniques.
3
H O H O H O H O H O H O H O H O
C C C C C C C C
H C OH HO C H H C OH HO C H H C OH HO C H H C OH H C OH
H C OH H C OH HO C H HO C H H C OH H C OH HO C H HO C H
HO C H HO C H H C OH H C OH H C OH H C OH HO C H HO C H
H C OH H C OH H C OH H C OH H C OH H C OH H C OH H C OH
CHOH CHOH CHOH CHOH CHOH CHOH CHOH CHOH
2 2 2 2 2 2 2 2
D-Allose D-Altrose D-Glucose D-Mannose D-Gulose D-Idose D-Galactose D-Talose
Fig.2. D-formisomersofaldohexoses.
Mirror α- form, and if a cis-structure, β- form. They interconvert
H O H O each other in solution through a process called mutarotation.
C C
Therefore, by deploying hexoses group in the system, there
H C OH HO C H are a total of 32 different isomers. This means that we can
HO C H H C OH increase a modulation order up to 32, i.e., 5 bits per symbol.
H C OH HO C H
H C OH HO C H B. Molecular Concentration Based
CHOH CHOH
2 2 When the concentration of messenger molecules is used,
D-Glucose L-Glucose
the technique is known as concentration-based modulation,
Fig.3. MirrorimageofD-andL-glucose.Theyareenantiomers. originally introduced in [7]. It is also referred to as CSK
(concentration shift keying). In binary CSK (BCSK), one
threshold exists, and a receiver nanomachine decodes the
A. Isomers for Messenger Molecules symbol as ‘1’ if the number of received messenger molecules
The most important thing we have to be careful when exceeds the threshold, ‘0’ otherwise [6]. Generally, 2n-CSK
designing messenger molecules is that has to be non-toxic systemstransmitnbitspersymbol,andrequires2n-1number
to human body. The messenger molecule suggested in [6], of thresholds. In this system, there is, theoretically, no limit
however, is highly flammable (i.e., hydrofluorocarbon), which in the modulation order. As the modulation order increases,
means it may be inappropriate as a messenger molecule. however, so does the error probability since the minimum
For several reasons, potential candidates for messenger distancebetweentwoneighboringthresholdsdecreases.Itonly
molecules are isomers, molecules with the same number and uses one kind of molecule, and D-glucopyranose is used for
types of atoms [8]. First of all, they consist of the same type analysis here. Below is a probabilistic analysis for BCSK
of atoms, lightening the burden on the transmitter nanoma- systems:
chine synthesizing the messengers. For numerical analysis, P (0,0)=P (0,0,0)+P (1,0,0)
a b b
this paper uses the isomers known as hexoses, especially
1
aldohexoses. Note that we can select from the aldoses family, = 4[P(Nn <τ)+P(Np+Nn <τ)]
hexoses, pentoses, tetroses, or trioses based on the required (cid:34) (cid:32) (cid:33)(cid:35)
1 (cid:16)τ(cid:17) τ −n(p −p )
modulation order. = 2−Q −Q 2 1 ,
(cid:112)
Aldohexoses are monosaccharides with the chemical for- 4 σ n[p2(1−p2)+p1(1−p1)]+σ2
mula C H O . They have four chiral carbon atoms that give
6 12 6
them 16 (=24) stereoisomers. Fig. 2 illustrates eight kinds of P (0,1)=P (0,0,1)+P (1,0,1)
a b b
D- form diastereomers. The enantiomers of each molecule 1
are another set of eight L- form diastereomers. Therefore, = 4[P(Nn ≥τ)+P(Np+Nn ≥τ)]
aldohexoses have 16 different shapes. Here, diastereomers are (cid:34) (cid:32) (cid:33)(cid:35)
1 (cid:16)τ(cid:17) τ −n(p −p )
stereoisomersthatarenotenantiomers(mirror-imageisomers). = Q +Q 2 1
(cid:112)
For example, D-glucose and L-glucose as shown in Fig. 3 4 σ n[p2(1−p2)+p1(1−p1)]+σ2
are enantiomers. D-glucose and D-galactose, isomers but not
where, P (X,Y) indicates the probability of X sent and Y
a
mirror images, are diastereomers.
received, and P (Z,X,Y) is the probability of X sent, Y
b
When each isomer is dissolved in aqueous solution, it
received, and Z previously sent. Q(·) is the tail probability of
mostly exists as a cyclic form. D-glucose, for instance,
the normal distribution.
undergoes nucleophilic addition reaction generating four
cyclic anomers, α-, β- forms of D- glucopyranose and D-
C. Molecular Type Based
glucofuranose [9]. We consider, however, only two pyranose
forms since they predominate with 36 and 64 percentages. If When different types of molecules represent different sym-
the functional groups attached to carbon number 1 (C1) and bols, the technique is known as molecular-type-based modu-
the C5 shown in Fig. 4 have a trans-structure, it is called lation, referred to as molecule shift keying (MoSK). Unlike
4
TABLEI
H C1 O SIMULATIONPARAMETERS.
2
H C OH Parameters Values
HO C3 H Phit forTs 0.6097
4 Phit for2Ts 0.7208
H C OH Radiusofthehexoses[12] 0.38nm
5 D ofhexoses(3) 597.25µm2/sec
H C OH
6 (cid:52)Hhexose 1271kJ/mol
CH2OH Ts [6] 5.9sec
Viscosityofthewater 0.001kg/sec·m
OH OH Temperature(bodytemperature) 36.5◦C =310K
α β
4 6 4 6
HO 5 O HO 5 O
HO 2 HO 2 1 OH
3 1 3
OH OH error term. Thus, P (α,β) can be calculated as
a
OH
R −R 0.99
tα eq =− t +1,
Fig. 4. D-glucose and its α- and β- anomers. They undergo rapid R −R 3600 s
α eq
interconversioninwater,whichiscalledmutarotation.
αR +βR αR +(n−α)R
R = α β = α β,
tα α+β n
(R −R )n
α= tα β , β =n−α.
the work in [7], we here use a set of isomers. We thus R −R
α β
name it IMoSK (isomer-based MoSK). IMoSK requires only
β
one threshold, making it simpler than the CSK system. For If β ≥τ, Pa(α,β)=Pa(α,β)AWGN + n
systematic analysis, we can choose one among the several
where, R = 52.7◦, R =112.2◦, and R =18.7◦ [10]. The
aforementioned isomer sets; a modulation order can be de- eq α β
parameters α and β indicate the number of α- form and β-
termined by the sets used. For example, hexoses have a
form molecules, respectively, and n is the number of total
modulation order of up to 32, trioses of 4. For simplicity,
moleculestransmitted.Opticalspecificrotationofthechemical
we apply, as did in [7], the addictive white Gaussian noise
compound is defined as the observed angle of optical rotation
(AWGN) model. The mutarotation effect is also considered.
whenplane-polarizedlightpassesthroughD-glucopyranoses.2
1) B-IMoSK-AWGN: Only AWGN considered,
3) 32-IMoSK: When using hexoses, the system has the
maximummodulationorderof32.ProbabilitiesofX sentand
P (α,α) =P (α,α,α)+P (β,α,α)
a AWGN b b Y received for all X and Y values are obtained similarly and
1
= [P(N +N +N ≥τ)P(N <τ) thus omitted here (see [13]).
4 p c n n
+P(N +N ≥τ)P(N +N <τ)],
c n p n IV. NUMERICALRESULTS
P (α,β) =P (α,α,β)+P (β,α,β)
a AWGN b b Assume that all hexoses have the same physical properties;
1
= 4[P(Nn ≥τ)P(Np+Nc+Nn <τ) sviazleu,ediisffucasilocunlacteodeffibcyietnhte, asnamdeenntuhmalepryicaolfcfaolrcmulaattiioonn. uPsheidt
+P(N +N ≥τ)P(N +N <τ)].
p n c n in [6]. We approximate the valuefor the hexoses by assuming
it to be proportional to the diffusion coefficient. Therefore,
we have the hitting probabilities shown in Table I and apply
Note that P (β,β) and P (β,α) can also be calculated
a a
theseintotheproposedschemeexplainedinSectionIII.Here,
similarly. Due to the page limit, we omit it here.
we define the achievable rate R that maximizes the mutual
2) B-IMoSK-MutarotationConsidered(α-D-glucopyranose information I(X;Y) as follows
⇔ β-D-glucopyranose): When α- and β- D-glucopyranose
(cid:88) P(X,Y)
are chosen, there is a possibility of incorrect decoding, such I(X;Y)= P(X,Y)log ,
as α- sent, β- received, or β- sent, α- received due to 2 P(X)P(Y) (5)
mutarotation. Thus we derive an error probability considering R=maxI(X;Y)
τ
the mutarotation process. The α- or β- form sent varies its
where, P(X,Y) denotes the joint probability of X and Y
number with time [10], and the number can be calculated by
while P(X) and P(Y) are the probabilities of events X and
observing the specific optical rotation. R or R (observed
tα tβ
Y. In (5), the threshold values vary from 1 to 1000.
specific optical rotation at time t) minus R (at equilibrium)
eq
Fig.5comparestheachievablerateoftheproposedmethod
divided by R or R (at time 0) minus R has a linear
α β eq
using hexoses with the conventional insulin based method in
relationship with time (T ) at about 36.5◦C. R and R
s tα tβ
BCSK and B-IMoSK systems. It is remarkable that we obtain
values are calculated by R and R , and R cab be found
α β eq
about8dBofSNRgaininbothBCSKandB-IMoSKsystems.
in [10]. The number of α- and β form existed after time T
s
is obtained as below. If the number of β- form exceeds the
2It could be measured by a polarimeter, and there is a linear relationship
thresholdvalueafterTs whenα-sent, nβ valueisaddedtothe betweentheobservedrotationandtheconcentrationofthecompound[11]
5
Fig.5. Achievableratecomparisonsoftheconventionalinsulinbasedand Fig.7. Achievableratecomparisons.Trioseandhexoseused.
theproposedmethodsusingtwokindsofaldohexoseisomers.
messenger molecules. We first introduced energy and channel
models for our system. Next we proposed several modulation
methodsabletosupportupto5bitspersymbol.Wealsocom-
pared the achievable rate performance with existing modula-
tionmethods(concentration-basedandmolecular-type-based).
This work differs from prior work in that it proposes practical
messenger molecules and provides guidelines for selecting
fromamongseveralpossiblecandidates.Futurework,wewill
consider, to achieve more modulation degrees of freedom,
the ratio of enatiomers. To increase the transmission data
rate further, we will also consider multiple sets of messenger
molecules.
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work proposed novel modulation techniques using isomers as preparationforjournalpublication.