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IEEE TRANSACTIONS ON NANOBIOSCIENCE, VOL. 13, NO. 3, SEPTEMBER 2014 315

FRET-Based Nanoscale Point-to-Point and BroadcastCommunications With Multi-Exciton Transmission

and Channel RoutingMurat Kuscu , Student Member, IEEE, and Ozgur B. Akan, Senior Member, IEEE

Abstract—Nanoscale communication based on Förster Reso-nance Energy Transfer (FRET) enables nanoscale single moleculardevices to communicate with each other utilizing excitons gener-ated on fluorescent molecules as information carriers. Based on thepoint-to-point single-exciton FRET-based nanocommunicationmodel, we investigate the multiple-exciton case for point-to-pointand broadcast communications following an information theoret-ical approach and conducting simulations through Monte Carloapproach. We demonstrate that the multi-exciton transmissionsignificantly improves the channel reliability and the range of thecommunication up to tens of nanometers for immobile nanonodesproviding high data transmission rates. Furthermore, our analysesindicate that multi-exciton transmission enables broadcasting ofinformation from a transmitter nanonode to many receiver nanon-odes pointing out the potential of FRET-based communication toextend over nanonetworks. In this study, we also propose electri-cally and chemically controllable routing mechanisms exploitingthe strong dependence of FRET rate on spectral and spatial char-acteristics of fluorescent molecules. We show that the proposedrouting mechanisms enable the remote control of informationflow in FRET-based nanonetworks. The high transmission ratesobtained by multi-exciton scheme for point-to-point and broad-cast communications, as well as the routing opportunities makeFRET-based communication promising for future molecularcomputers.

Index Terms—FRET, nanoscale communications, nano-networks, broadcast networks, routing, channel capacity, ISI,error probability, transmission rate, fluorescent molecules, QCSE,interlocked molecules.

I. INTRODUCTION

N ANOTECHNOLOGY has enabled manufacturing ofnano-size machines which are capable of performing

simple actuating, sensing and computing tasks. A number ofnanomachines communicating with each other is envisioned

Manuscript received April 12, 2013; revised May 24, 2014; accepted July 07,2014. Date of publication July 30, 2014; date of current version September 23,2014. This work was supported in part by the Turkish Scientific and TechnicalResearch Councilunder Grant #109E257, by the Turkish National Academyof Sciences Distinguished Young Scientist Award Program (TUBA-GEBIP),and by IBM through IBM Faculty Award. An earlier version of this work waspresented at IEEE MoNaCom’12, Ottawa, Canada. Asterisk indicates corre-sponding author.*M. Kuscu is with the Next-generation and Wireless Communications Lab-

oratory (NWCL), Department of Electrical and Electronics Engineering, KocUniversity, Istanbul, 34450, Turkey (e-mail: mkuscu, [email protected]).O. B. Akan is with the Next-generation and Wireless Communications Lab-

oratory (NWCL), Department of Electrical and Electronics Engineering, KocUniversity, Istanbul, 34450, Turkey (e-mail: mkuscu, [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TNB.2014.2342712

as a nanonetwork. Nanonetworks allow nanomachines to co-operatively exchange information to achieve more complextasks ranging from nuclear defense to in-body drug deliveryand disease treatments [1]. The exchanged information amongnanomachines might be an output of a sensing process or alogic operation, as well as a control signal sent by a remoteinformation source that intends to control the operation ofnanomachines. Modeling the potential information sharingmechanisms among nanomachines and investigating themethods for controlling the route of the information flow atnanoscale are crucial for the design of fully functional nanoma-chines with networking capabilities. Several approaches havebeen proposed in order to achieve communication at nanoscalesuch as electromagnetic, acoustic, nanomechanical or molec-ular, some of which are inspired by nature [2], [3]. In additionto the existing techniques, recently, we have proposed and in-vestigated a novel and radically different nanoscale molecularcommunication method exploiting a well-known phenomenonFRET [4].FRET is a pairwise non-radiative energy transfer process

observed among fluorescent molecules, i.e., fluorophores, suchas organic dyes, fluorescent proteins, as well as semiconductornanoparticles, e.g., Quantum Dots (QDs), which have spectralsimilarities, and are located in a close proximity such as 0–10nm [9]. The phenomenon has been widely used in studies ofbiotechnological research including fluorescence microscopy,molecular biology, and optical imaging, since it provides asignificant amount of structural and spatial information aboutmolecules by means of optical signals with nanoscale resolu-tion [10], [11]. Several chemical and biological nanosensorsbased on FRET, some of which utilize DNA as the scaffold forfluorophores, have been developed [12], [13]. Furthermore innanomedicine, exploiting FRET, QDs have been employed asthe photosensitizing agents for photodynamic therapy (PDT) incancer treatment [14], [15]. Moreover, the quantum coherencebehavior of FRET in short distances has been widely studiedshowing the potential usage of FRET for future quantumcomputer designs [16].Using FRET as a communication mechanism for

single-molecular nanonodes has been first proposed in [4].In that study, we have modeled point-to-point and multi-stepFRET-based communication channels between immobilesingle-molecular nanonodes, and analyzed their informationtheoretical capacity for varying internal and environmentalparameters. In that basic model, communication betweennanonodes was realized via the transfer of single excited

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316 IEEE TRANSACTIONS ON NANOBIOSCIENCE, VOL. 13, NO. 3, SEPTEMBER 2014

state, i.e., single exciton, generated by a remote informationsource (IS) on a donor fluorophore acting as the TransmitterNanonode (TN) to an acceptor fluorophore acting as the Re-ceiver Nanonode (RN). It has been shown that FRET-basednanoscale communication outperforms the other short rangecommunication methods in terms of reliability and commu-nication rate as well as controllability. We also investigatedthe multi-step FRET-based long-range nanocommunicationchannel [5], FRET-based mobile molecular ad hoc nanonet-works [6], [7], and graphene plasmon-assisted FRET-basednanocommunication channel [8] to derive their information the-oretical models, and evaluate the communication performance.In this study, based on the channel model given in [4], we

investigate the feasibility and performance of FRET-basedbroadcast communication channel between one TN and manyRNs from the network perspective. Furthermore, exploitingQuantum Confined Stark Effect (QCSE) observed in semicon-ductor nanoparticles, we propose an electrically controllablerouting mechanism for FRET-based nanonetworks. In thispaper, we also extend our preliminary work in [17]. Differingfrom our previous work, we propose encoding informationinto multiple excitons, instead of single-excitons, in orderto improve the reliability of the communication. We analyzethe performance of FRET-based point-to-point and broadcastcommunication channels with multi-exciton transmission.Additionally, we propose another chemically controllablerouting method based on the nanoscale shuttle-like movementof [2]rotaxane macrocycle between two nodes with acid/basetreatment. We conclude that information flow can be directedin an FRET-based nanonetwork by either external control, i.e.,electric field, or depending on environmental conditions, i.e.,acid/base condition. Performance evaluations of the commu-nication channels and routing methods are carried out throughsimulations with Monte Carlo algorithms based on the compet-itive behavior of multiple excitons.The remainder of this paper is organized as follows.

In Section II, we briefly review the basics of FRET andFRET-based nanoscale communications. In Section III, wemodel FRET-based point-to-point and broadcast communica-tion channelswithmulti-exciton transmission.The electrical andchemical routing mechanisms for FRET-based nanonetworksare proposed and investigated in Section IV. In Section V, weevaluate the performance of the proposed communication androuting schemes by means of information theoretical capacity.Finally, the concluding remarks are given in Section VI.

II. BACKGROUND

A. FRET Theory

FRET defines the non-radiative energy transfer from a donormolecule (D) to a proximal acceptor molecule (A). It is observedamong the fluorescent molecules with chromophore units thatare able to be excited by optical, electrical or chemical energyat a specific range of wavelength and emit that absorbed energyat a different wavelength.Theodor Förster postulated the governing equations of

FRET theory in his seminal work [18]. The main equations

are then validated experimentally [11]. As Förster stated, thereare mainly two requirements for FRET to occur between twomolecules; spectral similarity and proximity [18]. The spectralcharacteristics of donor and acceptor must have significantsimilarity, i.e., the overlapping area of the emission spectrumof the donor and the absorption spectrum of the acceptor mustbe large enough. The spectral similarity is proportional to theresonance probability of the molecule transition dipoles. Inaddition, the molecules must be in a close proximity such as0–10 nm. When these conditions are satisfied, FRET competeswith fluorescence process. The probability of FRET can begiven in terms of process rates as

(1)

where and are the fluorescence and FRET rates, respec-tively. is the reciprocal of the mean of excited state lifetimeof the donor in the absence of a nearby acceptor, i.e., .denotes the time that the excited donor molecule stays in the

excited state before relaxing through fluorescence, and it is anexponential random variable [9]. The mean lifetime is shortenedwhen there exists different pathways for the donor to relax in-cluding FRET. In case there exists an acceptor in the proximityof the donor, the mean of the donor lifetime is given as

(2)

is also an exponential random variable [9]. FRET rateis given in terms of fluorescence rate as

(3)

where is the Förster radius denoting the distance between themolecules when is 0.5, and defines the intermoleculardistance between the transition dipole centers of the molecules.relates the FRET rate with environmental and intrinsic pa-

rameters and can be expressed by

(4)

where is the relative orientation factor, is the quantumyield of the donor, and is the refractive index of the medium.The integral part of (4) denotes the degree of the overlap of thedonor emission spectrum and the acceptor absorption spectrum,and is denoted by

(5)

where is the normalized fluorescence emission intensity,and is the acceptor molar absorptivity. The orientationfactor can be given as

(6)

where and are the angles determined by the emis-sion and absorption transition dipoles of the fluorophores [9]

KUSCU AND AKAN: FRET-BASED NANOSCALE POINT-TO-POINT AND BROADCAST COMMUNICATIONS 317

Fig. 1. Point-to-point FRET-based nanocommunication channel model.

as shown in Fig. 1. Assuming isotropic and unrestricted distri-butions for all three angles, the distribution of can be givenas [19]

(7)

Due to the strong dependence of the transfer efficiency onthe spatial parameters of the participating molecules, FRET iswidely exploited as an experimental tool in biotechnologicalresearch to observe the molecular events of conformation,association, separation and diffusion. There are numerousmethods to exploit FRET in fluorescence microscopy such asfluorescence-detected excited state lifetime (FLIM), biolumi-nescence RET (BRET), and photobleaching FRET (pbFRET)[10]. Among these methods, single-molecule FRET (smFRET),which defines the use of single pair of donor and acceptor formicroscopic observations, is continuously being advancedparallel to the developments in nanotechnology and gainingincreased popularity, since it provides radically higher temporaland spatial resolution compared to the bulk solution FRETmethods. Recently, smFRET has been proposed to increasethe spatial resolution and sensitivity of apertured ScanningNear-field Optical Microscopy (SNOM) which is limited bythe size of the aperture for light transmission, e.g., a typicalvalue of 50 nm [21]. In the same study, the first microscopicimages with a spatial resolution of the order of Förster radiuswere obtained using smFRET SNOM.

B. FRET-Based Nanoscale Communications

The point-to-point FRET-based nanoscale communicationsystem proposed in [4] consists of three main parts; a Trans-mitter Nanonode (TN) which is a single donor fluorophore, acommunication channel, and a Receiver Nanonode (RN) whichis a single acceptor fluorophore.The system utilizes a pulsed laser as IS that can generate pi-

cosecond-duration excitation pulses, and implements ON-OFFkeying (OOK) modulation with two bits available; bit-0 andbit-1. When IS intends to transfer bit-1, a single laser pulsewhich has a wavelength near to the excitation maximum of thedonor is sent to TN at the beginning of a fixed-duration timeslot. The donor fluorophore acting as TN is excited by this pulseand after some time it relaxes through either fluorescence or

FRET by transferring its excited energy to a nearby acceptorfluorophore, i.e., RN, and making the acceptor excited. If FREToccurs following the excitation of the donor, RN detects bit-1.In the bit-0 case, IS does not send any pulse to TN and keepsit silent in a time slot duration. Therefore, RN also stays in theground state, detects bit-0. The time slot determines the bit in-terval, i.e., bit period, .A fluorophore in its excited state cannot be re-excited until it

relaxes to the ground state [9]. If slot durations are not arrangedproperly, this fact results in InterSymbol Interference (ISI) suchthat when IS sends successive bit-1’s to TN, some of the bitscannot be transmitted through the channel if the donor or ac-ceptor is in the excited state due to the preceding bit-1 trans-mission. We have to consider the worst-case in determining theminimum bit interval , i.e., minimum slot duration, re-quired to avoid ISI. In the worst case, the exciton generated byIS stays on the donor for time , and then it is transferredto the acceptor where it stays for time . Here,and are the maximum donor lifetime in the presence ofa nearby acceptor, and the maximum acceptor lifetime, respec-tively. After a time of , the exciton is removedfrom the system. Therefore, is expressed as follows

(8)

Since themolecule lifetimes are modeled as exponential randomvariables, setting equal to results in an ISIprobability below that might be enough to neglect ISI insome cases.If the bit interval satisfies the no-ISI criteria, assuming that the

donor is guaranteed to be excited by each laser pulse, and ne-glecting the direct excitation of the acceptor by the laser pulse,the successful transmission probability of bit-1, i.e., , is equalto . Assuming there is no another excitation source thatcan excite the acceptor independently, the successful transmis-sion probability of bit-0 is equal to 1. Therefore, the channel ismodeled information theoretically as a Z-channel.Using fluorescent molecules at the single molecular level,

i.e., without a bulk solution, for FRET-based communicationsbrings some crucial challenges originated from the photo-chemical properties of the molecules. Fluorescent moleculesundergo photochemical destruction and lose their fluorescenceability after a number of excitation-relaxation cycles underillumination. Their resistance to the photobleaching event,which depends on the intrinsic molecular characteristics, theexcitation wavelength and intensity, determines their photo-stability [9]. Therefore, photostability of the employed singlemolecules acting as communication nodes is one importantparameter setting a limit for the lifetime of the whole system.Dye molecules are extensively used in fluorescence mi-

croscopy, and thus, their photochemical and spectral character-istics are well-known. As most of the theoretical FRET-basedstudies, we based our work on the properties of widely-usedorganic dyes, to derive the theoretical framework, and basicallyevaluate the communication performance. However, we knowthat most of the dye molecules are not sufficiently photostableand undergo photobleaching after excitation/relax-ation cycles [9], therefore, it may lead to feasibility problems


for FRET-based communications depending on the applica-tion. To establish communications for the applications requiringlong-time operability, more stable fluorescent molecules need tobe employed. Semiconductor QDs with inorganic surface layersshielding the core material are proved to be 100 times morestable than conventional organic dyes [22], and find increasingnumber of applications in fluorescence microscopy includingFRET-based imaging techniques. However, QDs suffer fromphotoblinking, i.e., photoluminescence intermittency, and theirtoxicity limits their usage for in vivo applications [9]. Recently,Nitrogen-Vacancy (NV) centers in nanodiamonds have beenproposed as highly-stable local fluorescence probes with nearlyinfinite lifetime and proved to be suitable for FRET-basedapplications including quantum information processing [23].Therefore, they may provide more convenient alternative toorganic dyes and QDs to overcome the photostability problemfor FRET-based communications.

III. MULTI-EXCITON TRANSMISSION

FRET-based communication can be very unreliable if theinternodal distance is greater than the Förster radius of themolecules [4], or there are more than one RN communicatingwith TN. In order to reduce the error probability, one mightcome up with the idea of transmitting the signal many timesthrough the channel. However, without a feedback mecha-nism, i.e., without the knowledge of the TN about the successof the transmission, this method has to be applied for eachtransmission with the number of repetitions determined priorto communication. For the case of single pair TN-RN com-munication with fixed repetitions, the bit interval required fornegligible ISI is multiplied with the number of repetitions,

(9)

Assuming, , and are constant for each transmission, thetransmission probability of bit-1 becomes

(10)

is again equal to 1 for repeated transmission. As can be seenintuitively, this transmission scheme significantly reduces theerror probability of bit-1. Therefore, the capacity is expectedto increase with increasing . However, high bit durationrequired for negligible ISI significantly reduces the transmissionrate.Since the excited state lifetimes of the molecules are random

variables with exponential distributions, it is very possible foran exciton to be removed from the system in a duration smallerthan . This makes it inefficient for IS to send fixed periodpulses to TN. An alternative way to reduce the error probabilityof transmission with relatively small bit intervals is to increasethe pulse duration sent by IS into nanoseconds range and allowmany excitations to be generated on TN in one pulse durationwith a probabilistic manner. In this scheme, for the representa-tion of bit-1, IS continuously sends photons or electrons to TNin a pulse duration. TN is expected to be excited by the firstphoton or electron coming from IS. After a duration of ,TN relaxes through FRET or fluorescence. If is smaller

than the pulse duration, then TN is excited again as soon as itrelaxes, and this continues until the pulse duration ends. In otherwords, multiple excitons are transmitted during a pulse durationto represent bit-1.In the following sections, multi-exciton transmission scheme

is applied to FRET-based point-to-point and broadcast chan-nels; and we obtain the channel capacities through Monte Carlosimulations.

A. FRET-Based Point-to-Point Communication WithMulti-Exciton Transmission

In this section, we revisit our point-to-point communicationchannel model in order to investigate the communication perfor-mance of the channel with multi-exciton transmission scheme.Here, IS sends an optical or electrical pulse with dura-tion to TN in the beginning of a -duration time slot to makeit transmit bit-1. In order for TN to transmit bit-0, IS does notsend any pulse during the time interval . In one slot time in-terval, i.e., bit interval, TN can be excited and relaxed throughFRET or fluorescence many times. When RN is excited throughFRET, bit-1 is detected by RN, and then the transferred excitonis removed from the system after a random occupation time, ,which is also an exponential random variable with mean .Once RN detects bit-1, it neglects other excitations until the cur-rent bit interval ends. If RN is not excited in a bit duration, itdecides that bit-0 is sent.Assuming that there is no other excitation source except IS,

the successful transmission probability of bit-0, i.e., , equalsto 1. The transmission probability of bit-1 can be written as

(11)

where is a random variable which defines the number of ex-citons generated by the pulse with duration . Note that inthis scheme, TN is always in the excited state during ,such that, when it is relaxed through fluorescence or FRET, itis immediately excited by another photon or electron comingfrom IS. Therefore, the generation time of the th exciton on thedonor is expressed by

(12)

where denotes the excited state lifetime of the donor forthe th exciton, i.e., the occupation time of the th exciton on thedonor. is an exponential random variable with a mean thatdepends on the state of the acceptor at time . The acceptorcan be in the excited state at time due to the transfer of apreceding exciton. Therefore, can be expressed as

(13)

where is the FRET rate for the th exciton that can be givenas follows

(14)


where . depends onthe random variable which defines the relative orientationof the fluorophores during the generation and relaxation of theth exciton. Assuming that molecules are isotropically free,

are independent and identically distributed (i.i.d.)random variables with the probability distribution definedin (7).Accordingly, the th exciton on the donor fluoresces or is

transferred to the acceptor through FRET at time. If the exciton is transferred to the acceptor at , it occu-

pies the acceptor until the acceptor fluoresces at time .Note that the emission spectrum of the acceptor and the ab-sorption spectrum of donor are assumed to be non-overlapping,therefore, fluorescence is the only way for the excited acceptorto relax. denotes the occupation time of the th exciton onthe acceptor, and it is an exponential random variable with mean

. The exciton , stays in the system for , if it results influorescence of the donor; and for , if it results influorescence of the acceptor.The FRET probability for the th exciton, i.e., , is

a random variable that depends on the state of the acceptor attime

(15)

The randomness of and is originated from therandom nature of relative orientations and occupation times.Due to high degree of stochasticity, we simulate the transmis-sion of bit-1 following aMonte Carlo approach to obtain numer-ical expressions for and ISI probability. Using the obtainedvalues, we analyze the channel capacity and achievable rates inSection V-A.

B. FRET-Based Broadcast Communication With Multi-ExcitonTransmission

FRET occurs when the transition dipole moments of two flu-orophores come into resonance. Therefore, FRET is a pairwiseenergy transfer, such that it is not possible for an excited donormolecule to transfer its excited energy to more than one accep-tors at the same time. However, if the donor is excited and re-laxed continuously for a sufficiently large time interval, as inthe case of multi-exciton transmission, it is possible that eachof the acceptor molecules is excited through FRET by differentexcitons.FRET-based broadcast communication can be realized with

one TN surrounded by many RNs in a close proximity as seen inFig. 2. TN sends the same binary information come from IS toeach of RNs. The information theoretical capacity of this broad-cast communication channel is limited by the performance ofthe worst point-to-point channel in the network. If we assumethat RNs are located by the same distance from TN, the broad-cast channel capacity equals to the capacity of one of the TN-RNpoint-to-point channels. Therefore, we investigate the binarytransmission probabilities through single TN-RN channel in thebroadcast network to determine the overall broadcast channelcapacity.Assuming that TN communicates with number of RNs, the

successful transmission probability of bit-1 to the th RN, ,

Fig. 2. Demonstration of FRET-based broadcast communication with a singleTN communicating with three RNs in close proximity.

is the probability that th RN gets excited via FRET in a bitinterval , when TN is continuously excited by IS in a timeduration of . Note that , and begins atthe beginning of . Assuming that the length of guaranteesthe no-ISI condition, can be given as

(16)

, i.e., the non-excitation probability of the th RN during, when IS sends no pulse, is 1 assuming that there is no other

excitation source. Here, is a random variable that rep-resents the probability of FRET between TN and the th RN forthe th exciton. is a random variable indicating the numberof the excitons generated by one pulse. Note that the donor isalways in the excited state, and the generation time of the thexciton is given as in (12). , i.e., the occupation time ofthe exciton on the donor, is an exponential random variableand its mean can be expressed as

(17)

where is a random variable which defines the FRET ratebetween TN and the th RN for the th exciton, and is theindicator function defined on the set of the acceptor molecules.

, if the th acceptor is available at time , and, if is in the excited state at time . in

terms of the orientation parameter can be expressed by

(18)

where is the distance between the centers of the transitiondipole moments of TN and the th RN. is the overlap be-tween the emission spectrum of the donor and the absorptionspectrum of . and , as well as , are assumed tobe constant during the communication. is the relative ori-entation factor of the donor and during the generation andrelaxation of the exciton . For isotropically free molecules,

, as well as are i.i.d. random vari-ables with the probability distribution defined in (7).At time , the exciton is either removed from the

system by the fluorescence of TN, or is transferred to one of the


RNs. The probability of the transfer for the th exciton to interms of process rates is given as

(19)

where when is available at time , andwhen is excited at time .The transmission of bit-1 is simulated following a Monte

Carlo approach. We numerically obtain , and then, inves-tigate the broadcast channel capacity and ISI probability inSection V-B.

IV. INFORMATION ROUTING IN FRET-BASED NANONETWORKS

The ability of controlling the route of the information flowin a nanonetwork comprising many nanonodes with varioussensing, computing and actuating capabilities brings the advan-tage of making the nanonodes cooperatively perform severalcomplex tasks. In this section, we propose electrically andchemically active routing mechanisms to control the infor-mation flow in an FRET-based nanonetwork exploiting theremarkable dependence of FRET on spectral and spatial pa-rameters of fluorophores.

A. Electrical Routing

Semiconductor nanoparticles are extensively used in fluores-cence-based applications owing to their exceptional propertieswhich are mainly originated from the effect of quantum confine-ment, such as size-dependent tunable emission, high quantumyield and broad absorption spectrum as well as narrowbandemission [24]. Another distinctive property of semiconductornanoparticles is Quantum Confined Stark Effect (QCSE) thatdefines the Stark Shift in the emission spectrum of the particlewith varying internal or external electric field [25]. QCSE bringsanother dimension to the spectral tunability of the emission al-lowing post-synthesis tuning of the optical characteristics.In a quantitative sense, the shift of a semiconductor nanopar-

ticle in terms of electric field is approximated as a sum of linearand quadratic functions [25] as

(20)

where is the shift in the energy spectrum; is the projectionof excited-state dipole; is the polarizability along the electricfield, and is the magnitude of the applied electric field.The tunability of the emission with an electric field is ex-

ploited as a control mechanism over the FRET efficiency in[26]. Becker et al. investigate the FRET between CdSe/CdSQuantum Rods (QR) and Cy5-derivative dye molecules ex-posed to an external electric field, and the switch behavior ofthe mechanism over FRET is experimentally demonstratedfor cryogenic temperatures, i.e., at very low temperatures,obtaining a typical 10 nm wavelength shift [26]. At cryogenictemperatures, the inhomogeneous broadening observed in themolecules’ emission and absorption spectra are removed, andthus, the spectrum of single fluorescent molecules becomesvery narrower such that the typical spectral shifts (0–20 nm)resultant from the QCSE become comparable to the spectraloverlap between the molecules. The idea of electrical control

Fig. 3. Demonstration of electrically controllable routing of the communica-tion between a single RtN and two RNs.

over FRET is based on tuning the degree of the spectral overlapbetween donor CdSe/CdS and acceptor Cy5 by altering themagnitude of the applied electric field. As the electric fieldincreases, the emission spectrum of CdSe/CdS is red-shifted,however, the absorption spectrum of the dye molecule is notaffected by the electric field. Thus, the overlap either increasesor decreases depending on the relative positions of the emissionand absorption spectra of CdSe/CdS and Cy5, respectively. Asa result, efficiency is tuned with electric field.In this study, we further develop the idea introduced in

[26] by approaching from the communication perspective andexploiting QCSE in order to enable a nanoscale communicationnetwork which is capable of altering its state depending onthe magnitude of the applied electric field. Using a semicon-ductor nanoparticle as a network node brings the selectiverouting capability to the node such that it becomes able toroute the incoming information packets from IS or a precedingnode, through one of the FRET channels making the selectionaccording to the magnitude of the applied electric field. Em-ploying this type of routing mechanism brings the advantageof directing the information flow at nanoscale by controlling itat macroscale.In the considered scenario, a single quantum rod CdSe/CdS

as the Router Nanonode (RtN) is the first destination of the in-formation coming from an IS. Two spectrally distinct acceptorsas RNs with different absorption characteristics are located inthe opposite sides of RtN with a distance to RtN as demon-strated in Fig. 3.In order to investigate the performance of the routing mech-

anism in terms of communication capacity, we approximate thenormalized emission of the router CdSe/CdS, i.e., , andthe absorption spectra of the RN dye molecules, i.e., and

, as Gaussian distributions given as

(21)

where is the center wavelength at which emission or absorp-tion is maximum, and is the fitting parameter which gives themeasure of the spectral broadening about the mean wavelength,i.e., linewidth of the spectrum. For a single CdSe/CdS, is605 nm under zero electric field condition and it is shifted inthe red direction with the application of an electric field, thus,

is equal to nm, where is the amount ofthe spectral shift in nanometers. is set according to the spec-tral linewidth 1.6 nm of CdSe/CdS at 50 K [26]. At the samecryogenic temperatures, the vibrational broadening of the emis-sion spectrum of single dye molecules is frozen out, and spec-tral linewidth becomes very narrow compared to the spectrum


Fig. 4. Approximated emission spectrum of single CdSe/CdS and absorptionspectra of the hypothetical dye molecules at different spectral shifts: (a), (b) nm, (c) nm.

of dye’s bulk solution. However, the absorption spectra of singledye molecules, which we need to approximate, cannot be mea-sured directly. Fortunately, the emission spectrum of a dye setsan upper limit for the absorption spectrum’s linewidth. Basedon this, and in parallel to assumptions in [26], the absorptionspectra of the dye molecules and are designed hypothet-ically with nm, nm and linewidthsequal to 7 nm and 9 nm, respectively.The approximated emission spectrum of CdSe/CdS and the

absorption spectra of hypothetical dye molecules for differentspectral shifts are demonstrated in Fig. 4. Under zero electricfield condition, the spectral shift of CdSe/CdS is also zero andand CdSe/CdS have a significant spectral overlap, however,

the overlap of and CdSe/CdS is negligible. As the spectralshift increases with increasing electric field, the spectral overlapof CdSe/CdS and decreases with increasing spectral shift;conversely, the spectral overlap of CdSe/CdS and increases.The Förster radius is related to the spectral overlap as follows

(22)

As a consequence, and spectral overlap vary proportionally.We analyze the resultant deviation of the capacity for eachchannel with varying spectral shift in Section V-C.

B. Chemical Routing

Mimicking the macroscopic machine-like actuating capabil-ities on the molecular scale is of great interest for nanotech-nology. For this aim several artificial molecular machines in-spired by the nature, e.g., charge separation in photosynthesis ormuscle movement, have been designed [27]. Mechanically in-terlocked molecules providing controllable and reversible mo-tion can be considered as the most simplest molecular machineswith the electrochemically or photochemically active compo-nents that undergo basic translational or rotational movements[28]. Here, we focus on a specific kind of synthetic interlocked

Fig. 5. Demonstration of chemically controllable routing.

molecules, namely [2]rotaxane, that can be employed for selec-tive routing of information in an FRET-based communicationnetwork.[2]rotaxane is an interlocked supramolecule consisting

of a macrocyclic ring trapped onto a dumbbell componentcontaining two separate recognition sites and two stoppermolecules at the both end of the dumbbell as seen in Fig. 5. Thering undergoes a reversible translational movement betweentwo recognition sites on the dumbbell axes when [2]rotaxane isinduced by a chemical or optical signal [28], [29]. Therefore, thering acts as a bistable molecular shuttle between two stations.There are several studies which combine the ring displacementin [2]rotaxane and the strong distance dependence of FRET inorder to develop a mechanical switch that outputs an opticalsignal. Some of the studies concerning FRET and [2]rotaxanefollow a way through replacing the [2]rotaxane componentswith photoactive molecules [30], and some of them covalentlybinding the fluorophores onto the ring and stopper components[31]. In both ways, the fluorescence intensity of the donormolecule located at the end of the axis is altered when the ringacting as acceptor or bearing an acceptor molecule is movingthrough the axis.In our proposedmodel, two acceptor fluorophores of the same

kind as the receiver nanonodes are immobilized through cova-lent binding on the stoppers of a chemically active [2]rotaxane,and a donor fluorophore as the routing node, i.e., RtN, is cova-lently bound to the macrocycle DB24C6 [29] as demonstrated inFig. 5. The length of the [2]rotaxane axis is assumed to be 5 nm.The recognition sites consist of dialkylammonium center and4,4 -bipyridinium unit as in the configuration proposed in [29].The recognition sites are assumed to be located at 1 nm insidefrom the stopper molecules. The center of the transition dipolemoments of the donor and acceptor molecules are assumed to bealigned linearly on a second axis parallel to the [2]rotaxane axis.The donor molecule on the ring is the first destination of the in-formation coming from IS. In the stable case, i.e., state 0, themacrocycle with the donor molecule is expected to be locatedaround the dialkylammonium center because of the strong hy-drogen bonding interactions between the cycle and the center.Upon the protonation, the macrocycle moves from the ammo-nium station to the bipyridinium station and is located aroundit, therefore, the system goes into state 1 [29]. The reversible


Fig. 6. Monte Carlo algorithm for the simulation of the transmission of bit-1through the point-to-point communication channel.

displacement of the macrocycle is based on an electrochemicalstimuli such as acid/base treatment [29]. We do not go into de-tail about the chemical reactions, but analyze the effect of ringdisplacement on the capacity of the channels established amongthree nodes located on the [2]rotaxane system in Section V-D.

V. INFORMATION THEORETICAL ANALYSIS

In this section, we investigate the performance ofFRET-based point-to-point and broadcast communicationsin terms of information theoretical capacity and ISI probabilityfor varying system parameters. Furthermore, we simulatethe electrical and chemical routing scenarios, and derive thechannel capacity for each state of the routers in order to evaluatethe performance of each routing scheme.

A. Analysis of FRET-Based Point-to-Point CommunicationsWith Multi-Exciton Transmission

The degree of randomness over the transmission probabilityof bit-1 makes it hard to find an analytical expression for theinformation theoretical capacity of the channel. Therefore, wesimulate the channel model for the transmission of bit-1 fol-lowing a Monte Carlo approach.1) Simulation Algorithm: Fig. 6 demonstrates the algorithm

used in the simulations operating through the following steps:1) The pulse length and the internodal distance be-tween TN and RN are set. The simulation time is set toits initial value 0.

2) The algorithm checks whether simulation time reaches at.

3) If is not reached, a new exciton is generated ondonor, i.e., TN, with the index at time . If

, then the simulation ends with the failure ofthe transmission of bit-1.

4) For the time that the new exciton is created, the relative ori-entation of the isotropically free molecules is determined

randomly according to the distribution (7). The Förster ra-dius between the donor and the acceptor for the thexciton is calculated accordingly.

5) FRET rate is determined using . The algorithmchecks the availability of the acceptor at , andcalculates mean lifetime accordingly. The lifetimeis determined randomly from the exponential distributionwith mean . The simulation time is proceeded as ,i.e., , since it is not possible for another exciton tobe generated until the donor relaxes.

6) At time , the algorithm checks the availabilityof the acceptor, and calculates using the relation(15). A probability mass function (p.m.f.) for the possiblepathways is constructed. The pathway that will be followedby the exciton is selected randomly according to the con-structed p.m.f.

7) In the case that the exciton undergoes fluorescence, thedonor is relaxed through fluorescence at , andthe exciton is removed from the system. The simulationcontinues at Step 2.

8) In the case that the exciton is transferred to RN throughFRET, the donor is relaxed, and the acceptor is excited attime . Therefore, the simulation ends with thesuccessful transmission of bit-1.

The simulation is carried out for two hypothetical moleculeswith the typical parameters; ns, ns, andnm for the mean orientation factor [9], and with varyingand . is calculated as the number of the successful trans-missions divided by the total number of the simulation runs.Note that the simulation is repeated until converges to a finitevalue.2) Channel Capacity: The channel capacity is derived in-

formation theoretically from the obtained value of , given thatin all of the cases. Since the transmission of bit-0 is al-

ways successful and the transmission of bit-1 is problematic, thechannel information theoretically shows Z-channel characteris-tics [32]. The channel capacity of Z-channel for each parameteris derived as the maximum mutual information between inputand output alphabets over all input distributions. By omittingthe calculations, the results are demonstrated in Fig. 7. As ex-pected, the capacity significantly decreases with increasingafter a critical distance due to the sixth power dependence ofthe on . For low values of , the critical distanceis approximately equal to . However, as increases, thenumber of excitons employed in the transmission of bit-1 in-creases, therefore, the capacity is considerably improved overinternodal distances larger than .3) ISI and Achievable Rates: If the bit period is not set

carefully, the resultant communication might be ambiguous,such that, the excitons created during might arrive the RNat a time greater than , i.e., in the next bit interval. Since thegoverning time parameters are exponential random variables,it is not possible to completely remove ISI, however, the ISIprobability might be reduced to negligible values by settingover some threshold value. In order to determine the ISI

probabilities for varying , we observe the maximum removaltimes of the excitons that reaches to RN conducting the MonteCarlo simulations and recording the time data for the last-arrive


Fig. 7. Channel capacity with varying and .

Fig. 8. Removal times with Gaussian fit for different and .

excitons. The histograms of the obtained data are demonstratedin Fig. 8 for four different typical combinations of andwith Gaussian fits. According to the data, we conclude that,

for the same , varying only changes the mean of thedistribution of the removal times in proportion, and the varianceof the removal times is not affected considerably. However, forconstant , varying results in a significant variation ofthe distribution of the removal times. This is due the fact thatthe variation in has no effect on the excited state lifetimesof the molecules, however, the variation in alters the processrates significantly, and finally results in the variation of thetime parameters. Therefore, ISI probabilities are analyzed fora constant and varying . Setting ns and

, the resultant ISI probabilities for varyingare demonstrated in Fig. 9. ISI considerably decreases with

increasing for different values of , and setting asgreater than ns results in negligible ISI for allvalues.The upper bound for reliable communication rate can

be expressed by . Neglecting ISI by settingns, the achievable rate for different pulse lengths

over varying internodal distances is shown in Fig. 10. Weconclude that nanomachines can reliably communicate at a

Fig. 9. ISI probability for several with varying .

Fig. 10. Achievable rates for several with varying .

rate up to 33 Mbps over 5-nm distance, and at a rate up to300 kbps over 35-nm distance. Note that, for short-range com-munication, using shorter pulses results in higher data rates,however, over longer distances, we can get higher data rateswith long-width pulses. With these results, we can certainlyconclude that FRET-based communication strongly outper-forms other molecular communication methods by means ofcommunication rate.

B. Analysis of FRET-Based Broadcast Communications WithMulti-Exciton Transmission

In this section, we analyze the information theoretical ca-pacity and investigate the ISI problem for FRET-based broad-cast communication channel of which principles are expressedin Section III-B. The transmission of bit-1 from TN to the thRN out of RNs through the broadcast channel is simulatedusing the algorithm described in Fig. 11. The transmission prob-ability of bit-1 between TN and the th RN, i.e., , is ob-tained following a Monte Carlo approach. The algorithm usedfor broadcast communication differs from the single pair com-munication algorithm basically in Step 9 and Step 10, such thatthe simulation does not end in success until the th RN is ex-cited. If th RN with is excited, the simulation continueswith Step 10, where the th exciton on the th RN is removedby fluorescence after a random occupation time.In the simulations, we assume all of the RNs have the same

optical characteristics and are at the same distance from TN.We employ the same hypothetical molecules as in Section III-A,with the typical values of the intrinsic parameters, such that,


Fig. 11. Monte Carlo algorithm for the simulation of the transmission of bit-1through the broadcast communication channel.

ns, ns and nm for the mean rela-tive orientation [9]. is calculated as the proportion of thenumber of successful transmissions of bit-1 from TN to the thRN over the total number of simulation runs, and the simulationis repeated until converges. The information theoretical ca-pacity of the resultant Z-channel is determined as the maximummutual information between the input and output alphabets overall input distributions [32]. The derived capacity of the channelbetween TN and th RN gives the capacity of the overall broad-cast communication channel.1) Channel Capacity: The obtained capacity values for typ-

ical and combinations are plotted in Fig. 12. A re-markable result of the analysis is that the critical distance wherethe capacity begins to significantly decrease does not alter no-tably with varying number of RNs if is set sufficientlylarge. Therefore, the capacity of point-to-point communicationchannel can be achieved in a broadcast network with appropri-ately selected pulse lengths. However, for low values of ,addition of extra RNs into the network reduces the capacity forthe same internodal distances, since the number of excitons gen-erated with a short pulse might not be sufficient to excite all ofRNs. Furthermore, we observe that the slope of the capacity de-crease for distances greater than the critical distance is sharp-ened as increases. This is because as the number of RNs in-creases, the FRET processes that contribute to the relaxation ofthe donor increases. As a result, the sixth power dependence ofmany FRET processes combine improving the distance effecton the capacity expression.2) ISI and Achievable Rates: The ISI probability is analyzed

using the last exciton removal times on the acceptor, and weconclude that the distribution of the removal times does not alternotably for varying , however, the variation of signifi-cantly effects the characteristics of the distribution as in the caseof point-to-point communications. By setting ns

Fig. 12. Broadcast channel capacity for several with varying and .(a) , (b) , (c) .

Fig. 13. ISI probability of broadcast communication for different andwith varying .

and , the result of the analysis is plotted fordifferent combinations of and in Fig. 13. As is seen, theISI probability decreases with increasing and the increasingnumber of RNs. Setting the offset time as ns results ina negligible probability of ISI as in the point-to-point communi-cations. Therefore, the achievable rates for broadcast communi-cation are approximately the same as that of the point-to-pointcommunication with sufficiently large .

C. Analysis of Electrical Routing

The performance of the electrical routing scheme for thenanonetwork demonstrated in Fig. 3 is analyzed informationtheoretically in terms of communication capacity. We assumethat bit-1 is represented with a pulse of duration , andbit-0 is represented as silence during a time slot of durationwhich is assumed to be long enough to overcome ISI. The

distance of RtN to both RNs is set to which is theFörster radius of CdSe/CdS-A pair when the electric fieldis zero. The molecules on the nanomachines are assumed tobe isotropically free, therefore orientation factor has theprobability distribution defined in (7) independently for eachexciton. The configuration is similar to that of the broadcastcommunication investigated in Section III-B except thatchanges also with varying spectral shift. The transmission prob-ability of bit-1 through the individual channels, i.e., channelRtN-RN and RtN-RN , for varying spectral shift is obtainedusing the broadcast simulation algorithm described in Fig. 6and following a Monte Carlo approach. The varying channel


Fig. 14. Channel capacity of individual channels, i.e., and for varying spectral shift .

capacity is then derived using the obtained value of for bothchannels.The resultant capacity for different pulse lengths and varying

level of wavelength shift is plotted in Fig. 14. As is seen for eachvalue of , RtN-RN channel capacity is maximum underzero electric field condition and decreases to negligible valueswith increasing shift; conversely, RtN-RN channel capacity isnegligible at zero electric field, however, it increases to its max-imum as shift increases to 10 nm. Therefore, around the zeroelectric field, the information is transmitted only to RN ; con-versely, RtN transmits only to RN , when the shift is around10 nm. Additionally, we conclude that increasing de-creases the wavelength shift required for full switching betweentwo channels, therefore, larger provides faster routingperformance.

D. Analysis of Chemical Routing

In order to investigate the performance of the chemicalrouting method proposed in Section IV-B, we analyze the devi-ation of the communication capacity of the channels RtN-RNand RtN-RN with varying position of the ring. The transitionprobability of bit-1 through the individual communicationchannels is simulated using the broadcast simulation algorithmdescribed in Fig. 11. Here, we assume the transition dipolemoments of the molecules are in-line with the secondary axis,the relative orientation factor is deterministic with . TheFörster radius of the donor-acceptor pairs is assumed to be 2nm for in-line orientation and constant during the transmissionof the information bits. Although the relative orientation factoris maximized, is taken as relatively small in order to showthat one can pick the donor and acceptor pair from a large set offluorophores which are not required to have significant spectralsimilarity [9]. Bit-1 is represented with a -duration op-tical pulse coming from IS at the beginning of a time slot withduration that is assumed to be enough for avoiding ISI, andbit-0 is represented as silence during the time slot. We assumethat the effective volume of the laser beam uniformly covers thewhole trajectory traveled by the donor molecule, such that, thedonor is excited with the same probability at each point that it islocated. The transmission probabilities of bit-1, i.e., , for theindividual channels are calculated as the number of successfultransmissions divided by the total number of simulations.Using the obtained values, and given , the infor-

mation theoretical capacities of the individual channels are cal-culated for different locations of the donor, i.e., the ring. The

Fig. 15. Channel capacities of individual channels, i.e., and , withvarying displacement of macrocycle.

results are plotted for two different values in Fig. 15. Asis seen in the figure, when the ring is at its initial position, i.e.,

, RtN transmits the incoming information only to RNwith the capacity bit/use. At this position, the channelRtN-RN is in the closed state with , such that, RNcannot receive any information from RtN. As with the protona-tion, the macrocycle slightly moves in the direction of station2, and increases while decreases with about sixth degreedependence on the displacement. If the communication is estab-lished when the displacement of the macrocycle is around 1.5nm, both channels are in the transition states, and RtN broad-casts the incoming information to both of the RNs in a relativelyunreliable manner. When the macrocycle reaches at the station2, the channel 2 enters into open state with the communicationcapacity bits/use, while channel 1 becomes closed. Notethat for different , the displacement required for the transi-tion between two states of the channels does not change signif-icantly, however, the capacity of the broadcast communicationin the transition state, i.e., when is around 1.5 nm, increasesnotably for large pulse lengths.

VI. CONCLUSION

In this study, FRET-based communication is investigatedfor point-to-point and broadcast cases utilizing multiple exci-tons as information carrier. The conducted simulations usingMonte Carlo algorithms demonstrate that the multi-excitontransmission brings a remarkable performance improvement bymeans of channel reliability and coverage area, and makes thebroadcast communication realizable with notably high channelcapacities over the same coverage as in the point-to-point case.


The proposed routing schemes point out the possibility ofcontrolling the route of the information flow in FRET-basednanonetworks by electrical and chemical stimulations. Aswith the further advances in nanotechnology, we believe thatFRET-based nanocommunication and nanonetworking con-cepts, some of which are proposed in this study, will pave theway for the design of future molecular computers.

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Murat Kuscu (S’11) received his B.Sc. degree inelectrical and electronics engineering from MiddleEast Technical University, Ankara, Turkey, in July2011, and his M.Sc. degree in Electrical and Elec-tronics Engineering Department of Koc University,Istanbul, Turkey, in September 2013. He is currentlya research assistant at the Next-generation andWireless Communications Laboratory and pursuinghis Ph.D. degree in electrical and electronics en-gineering at Koc University, Istanbul, Turkey. Hiscurrent research interests include nanoscale and

molecular communications.

Ozgur B. Akan (M’00–SM’07) received his Ph.D.degree in electrical and computer engineering fromthe Broadband and Wireless Networking Laboratory,School of Electrical and Computer Engineering,Georgia Institute of Technology, Atlanta, GA, USA,in 2004. He is currently a full professor with the De-partment of Electrical and Electronics Engineering,Koc University, Istanbul, Turkey, and the director ofthe Next-generation and Wireless CommunicationsLaboratory. His current research interests are inwireless communications, nanoscale and molecular

communications, and information theory. He is an Associate Editor of theIEEE TRANSACTIONS ON COMMUNICATIONS, the IEEE TRANSACTIONS ON

VEHICULAR TECHNOLOGY, the International Journal of CommunicationSystems (Wiley), Nano Communication Networks (Elsevier), and the EuropeanTransactions on Technology.

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