Lecture Notes of the Institute for Computer Sciences...

Lecture Notes of the Institutefor Computer Sciences, Social-Informaticsand Telecommunications Engineering 20

Editorial Board

Ozgur AkanMiddle East Technical University, Ankara, Turkey

Paolo BellavistaUniversity of Bologna, Italy

Jiannong CaoHong Kong Polytechnic University, Hong Kong

Falko DresslerUniversity of Erlangen, Germany

Domenico FerrariUniversità Cattolica Piacenza, Italy

Mario GerlaUCLA, USA

Hisashi KobayashiPrinceton University, USA

Sergio PalazzoUniversity of Catania, Italy

Sartaj SahniUniversity of Florida, USA

Xuemin (Sherman) ShenUniversity of Waterloo, Canada

Mircea StanUniversity of Virginia, USA

Jia XiaohuaCity University of Hong Kong, Hong Kong

Albert ZomayaUniversity of Sydney, Australia

Geoffrey CoulsonLancaster University, UK

Alexandre Schmid Sanjay Goel Wei WangValeriu Beiu Sandro Carrara (Eds.)

Nano-Net

4th International ICST Conference,Nano-Net 2009Lucerne, Switzerland, October 18-20, 2009Proceedings

13

Volume Editors

Alexandre SchmidSwiss Federal Institute of Technology EPFLMicroelectronic Systems Laboratory STI-LSM1015 Lausanne, SwitzerlandE-mail: [email protected]

Sanjay GoelSchool of Business, University of AlbanyState University of New YorkAlbany, NY 12222, USAE-mail: [email protected]

Wei WangState University of New YorkCollege of Nanoscale Science and EngineeringAlbany, NY 12203, USAE-mail: [email protected]

Valeriu BeiuUAE University, College of Information TechnologyAl Ain, Abu Dhabi, United Arab EmiratesE-mail: [email protected]

Sandro CarraraSwiss Federal Institute of Technology EPFL1015 Lausanne, SwitzerlandE-mail: [email protected]

Library of Congress Control Number: 2009936482

CR Subject Classification (1998): C.1, B.7.1, C.3, C.5, J.2, B.2, B.4, I.6

ISSN 1867-8211ISBN-10 3-642-04849-8 Springer Berlin Heidelberg New YorkISBN-13 978-3-642-04849-4 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting,reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publicationor parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,in its current version, and permission for use must always be obtained from Springer. Violations are liableto prosecution under the German Copyright Law.

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© ICST Institute for Computer Science, Social-Informatics and Telecommunications Engineering 2009Printed in Germany

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Preface

A warm welcome to Nano-Net 2009, and to the city of Lucerne, Switzerland.

Following up a series of successful international events in Lausanne, Catania,and Boston, Nano-Net settled in Lucerne for its fourth edition. Through theyears, the focus of the conference has evolved, as well as its format, therebyreflecting the evolving concerns of the scientific community, as well as the civilsociety. The major focus of Nano-Net remains related to discovering and re-vealing a new exciting domain emerging at the cutting-edge overlap of twowell-established and highly innovative disciplines, which are information andcommunication science and nano-technologies. No one doubts that this field ofresearch will gain in prominence as the promises of nanotechnology fabricationbecome true, and novel applications with unprecedented performances emerge.The Nano-Net technical program widened its scope, this year, to include novelconcerns such as ethical and “green” aspects, reliability, and nano-bio paradigms.

Sanjay Goel prepared an exceptional technical program for Nano-Net 2009,covering the many aspects and issues mentioned above. Sanjay did an outstand-ing job presiding over the review process used to select the papers. This high-quality program was presented in technical sessions, and is further described inthe Table of Contents. These conference proceedings, including invited and reg-ular papers, have been published by Springer, as a volume of the Lecture Notesof the ICST.

Bradley Nelson, from ETH, Zurich, accepted our invitation as keynote speakerand presented an outstanding talk entitled Towards Nanorobots.

Though Nano-Net did not present any annual headline topic, this year sawa prominent focus on applications and technologies conjugating nanotechnolo-gies and biotechnologies. Two tutorials were held and included into the regularconference program. Valeriu Beiu and Peter M. Kelly gave a tutorial on Brain In-spired Interconnects for Nano Electronics, and Jian-Qin Liu and Kazuhiro Oiwagave a tutorial on Networking Science and Information Processing Technology forNano-Biological Systems in the New Millennium. Two exciting pre-conferenceworkshops enriched Nano-Net 2009. These were held on Sunday, October 18,2009. Sandro Carrara chaired the workshop on Nano-Bio-Sensing Paradigmsand Applications. Valeriu Beiu and Walid Ibrahim chaired the workshop enti-tled Toward Brain Inspired Interconnects and Circuits.

I wish to express my deepest gratitude to Sanjay Goel and the members ofthe Technical Program Committee, Alexander Sergienko, Andrei Vladimirescu,Gabriel Molina-Terriza, Sorin Cotofana, Maggie Cheng, Alhussein Abouzeid,Sylvain Martel, Nikolaus Corell, and Costin Anghel, for their efforts in preparinga high-quality technical program, along with many anonymous reviewers. Themembers of the Organizing Committee worked countless hours to guarantee

VI Preface

a successful Nano-Net 2009, and deserve my profound gratitude: Wei Wang,Publication Chair, Annabel Bush, Webmaster, Beatrix Ransburg and GabriellaMagyar, Conference Coordinators, and all of the staff at ICST.

I hope that you found Nano-Net 2009 an enriching professional event, theoccasion of stimulating discussions, and a memorable conference.

October 2009 Alexandre SchmidSanjay Goel

Wei WangValeriu Beiu

Sandro Carrara

Organization

Steering Committee

Imrich Chlamtac Create-Net, ItalyGian Mario Maggio COST-ICT, Belgium

General Chair

Alexandre Schmid EPFL, Switzerland

Technical Program Chair

Sanjay Goel U. Albany, USA

Technical Program Co-chairs

Alexander Sergienko Boston U. USAAndrei Vladimirescu ISEP, FranceGabriel Molina-Terriza ICFO, SpainSorin D. Cotofana Delft U. of Technology, The NetherlandsMaggie Cheng Missouri U. Science & Techn., USAAlhussein Abouzeid Rensselaer Polytechnic Institute, USASylvain Martel Ecole Polytechnique Montreal, CanadaNikolaus Corell MIT, USACostin Anghel ISEP, France

Workshop Chairs

Sandro Carrara EPFL, SwitzerlandValeriu Beiu, Walid Ibrahim UAEU, UAE

Publication Chair

Wei Wang U. Albany, USA

Conference Coordinators

Beatrix Ransburg ICSTGabriella Magyar ICST

VIII Organization

Webmaster

Annabel Bush annabelwebdesign.com, USA

Conference and Workshops’ Technical Chairs andCo-chairs

Emerging Nano-Devices and FabricationTechnologies Alexander Sergienko

Modeling and Simulation of Nano-Devicesand Systems Andrei Vladimirescu

Nano-Materials, Nano-Photonics Gabriel Molina-TerrizaNano-Electronics and Architectures Sorin D. CotofanaReliability and Fault-Tolerance Sorin D. CotofanaNano-Networks Maggie Cheng

Alhussein AbouzeidNano-Bio Paradigms and Applications Sylvain MartelNanosensor Self-Organization Nikolaus CorellNano-Mechatronics Nikolaus CorellEmerging Topics in Nano-Technologies Costin AnghelWorkshop on Nano-Bio-Sensing Paradigms

and Applications Sandro CarraraWorkshop Toward Brain Inspired Valeriu BeiuInterconnects and Circuits Walid Ibrahim

General Technical Program Committee

Ian Akyildiz, GatechDavid Atienza, EPFLSasitharan Balasubramaniam, TSSGValeriu Beiu, UAEUYaakov (Kobi) Benenson, Harvard U.Haykel Ben Jamaa, EPFLSubir Biswas, Michigan State U.Atul Borkar, Intel Corp.Dimitri Botvich, TSSGDarren K. Brock, Lockheed MartinPaul Bogdan, CMUFeng Cheng, U. PotsdamAna Del Amo, General ElectricChris Dwyer, Duke U.Andrew Eckford, York U.Fabrizio Granelli, U. TrentoDanilo Gligoroski, NTNUSatoshi Hiyama, NTT DoCoMo

Ronald Knepper, Boston U.Gyorgy Korniss, RPIAlvin Lebeck, Duke U.Jian-Qin Liu, KARCJames Lyke, AFRLRajit Manohar, Cornell U.Constantinos Mavroidis, NEUKevin Mills, NISTYuki Moritani, NTTShaker Mousa, ACPKota Murali, IBMTadashi Nakano, UC IrvineBradley Nelson, ETHZAristides Requicha, USCGuillermo Rueda, Intel Corp.Michael Shur, RPIMetin Sitti, CMUMarina K. Thottan, Alcatel-Lucent

Organization IX

Selim Unlu, Boston U.Paul Sotiriadis, Johns Hopkins U.Milos Stanisavljevic, EPFLTatsuya Suda, UC IrvineSuresh Venkatachalaiah, Accenture

Technology Solutions

Bulent Yener, RPIHan Yiliang, Xi’an Jiaotong U.Wei Yu, CiscoMurat Yuksel, UNRTong Zhang, RPI

Sponsoring Institutions

Sponsors

The Institute for Computer Sciences, Social-Informatics andTelecommunications Engineering (ICST), Gent, Belgium

The Center for Research And Telecommunication Experimentation forNetworked communities (CREATE-NET), Trento, Italy

nanopaprika.euFundation NANONET, nanonet.pl

In Cooperation with

ACM Special Interests Groups SIGARCH, SIGDA, SIGMICRO

Table of Contents

Nano-Net 2009Full Papers and Invited Papers

The Impact of Persistence Length on the Communication Efficiency ofMicrotubules and CNTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Stephen F. Bush and Sanjay Goel

Single and Multiple-Access Channel Capacity in MolecularNanonetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Baris Atakan and Ozgur B. Akan

Timing Information Rates for Active Transport MolecularCommunication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Andrew W. Eckford

Information Transfer through Calcium Signaling . . . . . . . . . . . . . . . . . . . . . 29Tadashi Nakano and Jian-Qin Liu

Quantitative Analysis of the Feedback of the Robust Signaling PathwayNetwork of Myosin V Molecular Motors on GluR1 of AMPA inNeurons: A Networking Approach for Controlling Nanobiomachines . . . . 34

Jian-Qin Liu and Tadashi Nakano

RF Control of Biological Systems: Applications to Wireless SensorNetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Hooman Javaheri, Guevara Noubir, and Sanaa Noubir

Sub-micrometer Network Fabrication for Bacterial Carriers andElectrical Signal Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Gael Bringout, Sajjad Saeidlou, and Sylvain Martel

Pulse-Density Modulation with an Ensemble of Single-ElectronCircuits Employing Neuronal Heterogeneity to Achieve High TemporalResolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Andrew Kilinga Kikombo, Tetsuya Asai, and Yoshihito Amemiya

Carbon Nanotube Nanorelays with Pass-Transistor for FPGA RoutingDevices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Ming Liu, Haigang Yang, Sansiri Tanachutiwat, and Wei Wang

Quantum-Like Computations Using Coupled Nano-scale Oscillators . . . . 64Nikolai Nefedov

XII Table of Contents

Optimization of Nanoelectronic Systems Reliability by Reducing LogicDepth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Milos Stanisavljevic, Alexandre Schmid, and Yusuf Leblebici

Coherent Polarization Transfer through Sub-wavelength Hole Arrays . . . 76Martin P. van Exter, Erwin Altewischer, and J.P. (Han) Woerdman

Study on Electrical and Optical Properties of the HybridNanocrystalline TiO2 and Conjugated Polymer Thin Films . . . . . . . . . . . . 84

Le Ha Chi, Nguyen Nang Dinh, Pham Duy Long,Dang Tran Chien, and Tran Thi Chung Thuy

Through Silicon Via-Based Grid for Thermal Control in 3D Chips . . . . . . 90Jose L. Ayala, Arvind Sridhar, Vinod Pangracious,David Atienza, and Yusuf Leblebici

Can SG-FET Replace FET in Sleep Mode Circuits? . . . . . . . . . . . . . . . . . . 99Marius Enachescu, Sorin Cotofana, Arjan van Genderen,Dimitrios Tsamados, and Adrian Ionescu

Functional Model of Carbon Nanotube Programmable Resistors forHybrid Nano/CMOS Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Weisheng Zhao, Guillaume Agnus, Vincent Derycke,Ariana Filoramo, Christian Gamrat, and Jean-Philippe Bourgoin

Designing Reliable Digital Molecular Electronic Circuits . . . . . . . . . . . . . . 111Ci Lei, Dinesh Pamunuwa, Steven Bailey, and Colin Lambert

Creating Nanotechnicians for the 21st Century Workplace . . . . . . . . . . . . . 116Michael Burke, Kristi Jean, Cheryl Brown, Rick Barrett, andCarrie Leopold

Chances and Risks of Nanomaterials for Health and Environment . . . . . . 128Michael Riediker

Fabrication of Elastomeric Nanofluidic Devices for Manipulation ofLong DNA Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Elena Angeli, Chiara Manneschi, Luca Repetto, Giuseppe Firpo,Corrado Boragno, and Ugo Valbusa

Repeater Insertion for Two-Terminal Nets in Three-DimensionalIntegrated Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Hu Xu, Vasilis F. Pavlidis, and Giovanni De Micheli

Workshop on Nano-Bio-Sensing Paradigms andApplication Full Papers and Invited Papers

Nanophotonics for Lab-on-Chip Applications . . . . . . . . . . . . . . . . . . . . . . . . 151Peter Seitz

Table of Contents XIII

Highly Sensitive Arrays of Nano-sized Single-Photon Avalanche Diodesfor Industrial and Bio Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Edoardo Charbon

A Cancer Diagnostics Biosensor System Based on Micro- andNano-technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Pedro Ortiz, Neil Keegan, Julia Spoors, John Hedley, Alun Harris,Jim Burdess, Richie Burnett, Margit Biehl, Werner Haberer,Thomas Velten, Matthew Solomon, Andrew Campitelli, andCalum McNeil

Nanoelectrochemical Immunosensors for Protein Detection . . . . . . . . . . . . 178Alessandro Carpentiero, Manuela De Leo, Ivan Garcia Romero,Stefano Pozzi Mucelli, Freimut Reuther, Giorgio Stanta,Massimo Tormen, Paolo Ugo, and Martina Zamuner

Quantum Dots and Wires to Improve Enzymes-Based ElectrochemicalBio-sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Sandro Carrara, Cristina Boero, and Giovanni De Micheli

Ultra Low Energy Binary Decision Diagram Circuits Using FewElectron Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

Vinay Saripalli, Vijay Narayanan, and Suman Datta

Organic Memristors and Adaptive Networks . . . . . . . . . . . . . . . . . . . . . . . . . 210Victor Erokhin, Tatiana Berzina, Svetlana Erokhina, andM.P. Fontana

Nanostencil and InkJet Printing for Bionanotechnology Applications . . . 222Kristopher Pataky, Oscar Vazquez-Mena, and Juergen Brugger

Workshop Toward Brain Inspired Interconnects andCircuits - Full Papers and Invited Papers

A New Method for Evaluating the Dynamics of Human Brain NetworksUsing Complex-Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Jian-Qin Liu, Shigeyuki Kan, Takahiko Koike, and Satoru Miyauchi

On Two-Layer Hierarchical Networks How Does the Brain Do This? . . . . 231Valeriu Beiu, Basheer A.M. Madappuram, Peter M. Kelly, andLiam J. McDaid

Reduced Interconnects in Neural Networks Using a Time MultiplexedArchitecture Based on Quantum Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

Peter M. Kelly, Fergal Tuffy, Valeriu Beiu, and Liam J. McDaid

On the Reliability of Interconnected CMOS Gates ConsideringMOSFET Threshold-Voltage Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

Mawahib Hussein Sulieman

XIV Table of Contents

On Wires Holding a Handful of Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . 259Valeriu Beiu, Walid Ibrahim, and Rafic Z. Makki

Improving Nano-circuit Reliability Estimates by Using NeuralMethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

Azam Beg

A Bayesian-Based EDA Tool for Nano-circuits ReliabilityCalculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

Walid Ibrahim and Valeriu Beiu

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

A. Schmid et al. (Eds.): Nano-Net 2009, LNICST 20, pp. 1–13, 2009. © Institute for Computer Science, Social-Informatics and Telecommunications Engineering 2009

The Impact of Persistence Length on the Communication Efficiency of Microtubules and CNTs

Stephen F. Bush1 and Sanjay Goel2

1 GE Global Research, Niskayuna, NY, 12309 2 University at Albany, SUNY Albany, NY 12222 [email protected], [email protected]

Abstract. There are similarities between microtubules in living cells and carbon nanotubes (CNTs). Both microtubules and carbon nanotubes have a similar physical structure and properties and both are capable of transporting informa-tion at the nanoscale. Microtubules and carbon nanotubes can also self-organize to create random graph structures, which can be used as communication networks. The behavior of microtubules can be understood by investigating the behavior of their synthetic counterparts, namely, carbon nanotubes (CNT). At the same time, networks of CNTs may be used for molecular-level transport in the human body for treatment of diseases. This paper seeks to examine the basic properties of the networks created by CNTs and microtubules. This behavior depends strongly on the alignment of bond segments and filaments, which in turn depends on the persistence length of the tubes. Persistence length is also important in analyzing other structures such as DNA; however, the focus in this paper is on nanotube structures and microtubules. We use graph spectral analy-sis for analyzing a simulated CNT network in which a network graph is extracted from the layout of the tubes and graph properties of the resultant graphs are examined. The paper presents the results of the simulation with tubes of different persistence lengths.

Keywords: Biology, Networks, Microtubules, Molecular Communication, Car-bon Nanotubes, Communication Networks, and Sensor Networks.

1 Introduction

One of the most promising applications of nanotechnology is nanomedicine in which nanoscale devices are used for improved therapy and diagnosis. Nanodevices have the potential to deliver therapeutic agents, serve as detectors for disease, and correct metabolic pathways to prevent diseases. Given their size, they can also seek out specific cells or invading viruses, release localized drugs to minimize potential side effects of generalized drug therapy, or bind to a target preventing further activity. Significant research is being conducted to examine the impact of nanomaterials in biological applications [1], [2], [3], [4], [5], [6]. Despite the significant investment in this research, use of nanotechnology for therapeutic applications still lags the promise. Fundamental properties of such structures need to be established prior to conception of practical applications. One of the most promising nanostructures is the carbon

2 S.F. Bush and S. Goel

nanotube (CNT). Unique mechanical and electronic properties of these materials have enabled a variety of applications ranging from novel composites [7] to electronic circuits [8] and sensors [9]. Due to their small size, nanotubes can reach deep into their environment without affecting the natural behavior of the environment. For example, a single CNT is small enough to penetrate a cell without triggering the cell’s defensive responses.

Networks of CNTs can be used as a substrate to generate, route, and transport in-formation when a subset of tubes are functionalized (e.g. with quantum dots) just as networks of microtubules serve as a substrate for the transportation of molecular motors (where molecular motor cargo is considered as information) within the body. Microtubules are cytoskeletal biopolymers, which are a close biological counterpart to nanotubes that perform these functions in living organisms. Microtubules and CNTs have [10] similar structures; both are hollow, thin-walled tubes with a high aspect ratio and are very efficient for bearing loads. Microtubules provide mechani-cal stability for the cell, including holding its shape during cell migration, and pro-viding tracks for intracellular transport. Microtubules are one hundred times stiffer than other cellular components and have a high degree of resilience. CNTs are extremely stiff, with a Young’s Modulus five times higher than steel. Similar to microtubules, they are also highly resilient. While the chemical composition of microtubules, which is comprised of proteins and non-covalent bonds, differs from CNTs, which are comprised of carbon and covalent bonds, their mechanical behavior is quite similar. Both microtubules and CNTs spontaneously assemble into bundles. In addition, microtubules and CNTs share electrical properties, namely, both have conductances that have been carefully measured. The flow of current through micro-tubules and CNTs is a different process, namely microtubules use an ion channel while CNTs are either semi-conducting or metallic. Current flow through micro-tubules was measured in [11] to be approximately 9 nS (nano-Siemens) at a rate of approximately 1.0 m/s and exhibits an amplification effect. Also, both are impacted by magnetic fields and free-floating microtubules can be steered via a magnetic field. Microtubules naturally self-assemble, while controlled self-assembly of CNTs is possible by amino acid coating [12], [13].

Individual CNTs are weak and unable to perform complex tasks, however, through self-organization; networks of CNTs can exhibit sophisticated behavior and perform complex tasks. Self-organization typically occurs in microtubules and CNTs through supra-molecular interactions, which are short-range forces between the molecules that are too weak to cause intermolecular changes or bond formation, but sufficient to cause elastic deformations of microtubules and CNTs [14], [15]. The persistence length and isotropy of nanotubes is directly correlated to such forces and is a major factor in determining graph properties resulting from self-organization of CNTs. CNT networks can be used as a substrate to transmit information across nano-sensors and thus, provide connectivity across sensors. Analogously, microtubule structures are used for transport of molecules across the network. In a cell, small molecules such as gases and glucose diffuse to where they are needed. Large molecules synthesized in the cell body, intracellular components such as vesicles, and organelles such as mito-chondria, are too large to diffuse to their destinations. Motor proteins transport these large structures to their required destinations. Motor proteins such as kinesins walk along microtubule tracks carrying their cargo.

The Impact of Persistence Length on the Communication Efficiency 3

The stepping motion of molecular motors on microtubule rails is due to a small conformational change in a molecular complex powered by ATP hydrolysis. In sim-ple terms, the motor has two heads (more like feet, but they are known as heads) that alternately bind and release from microtubule binding sites. The binding sites are like steps on a ladder. When a head releases from the microtubule binding site, it swings forward, landing on the next binding site on the microtubule. The process is then repeated with the other head releasing and swinging forward while the current head remains attached. More specifically, a head is bound to the microtubule via ATP. The loss of the γ-phosphate group from ATP leaves a space of approximately 0.5 nm. This is thought to cause a rearrangement of structural elements flanking the ATP-binding site [16]. Ultimately, this loosens the head from its binding to the microtubule allow-ing it to swing forward along a lever comprised of an α-helix of variable length. The lever swings the head through an angle of up to 70˚. The lever swing is believed to be the ultimate cause for the working stroke; motors with longer necks take larger steps and move faster.

By investigating the behavior of these networks, we hope to understand the behavior of naturally occurring microtubule networks within the human body. Understanding the nanotube network properties within the context of individual nanotube attributes will assist in the design of nanotube networks. For instance, changing the persistence length of the tubules can control the connectivity of nanotube networks. Such custom-designed networks will help us control the latency and bandwidth of transmission of information in nanotube network applications. We are examining the behavior of general nanotube networks, both CNT and biological microtubules with regard to in-formation transport. The next section describes the simulation results that examine the nanotube network properties in context of the attributes of individual nanotubes.

There are several interesting applications associated with CNT networks and nano-bio applications such as detection of cancer cells, delivery of drugs, and slow-ing propagation of diseases. We investigate four specific problems associated with the design of CNT networks and through them the behavior of microtubule networks. 1) The impact of network topology (whether CNT or microtubule) on the efficiency of information flow, i.e. maximizing bandwidth. We specifically examine properties such as isotropy and persistence length of individual CNTs on the behavior of the resultant network. This will help in design of ad-hoc nanoscale networks and under-standing the behavior of microtubule communication networks within the human body. 2) Maximizing sensitivity to change, i.e. making a sensitive detector. We en-visage using a CNT network as a substrate to nano-sensors for transmitting sensor information. The expectation is that an activated sensor will release energy that will alter the resistance of the CNT network preferentially in a localized area within the substrate. By analyzing the behavior of the CNT network, we will be able to discern the activation of different sensors. The change in transport of molecular motors based upon changes to microtubule topology can also be used for detection of mi-totic catastrophe in cancer treatment (microtubule malfunction). We look at the rate of change of measurable network properties (resistance and graph walks of molecu-lar motors) corresponding to the persistence length of the nano-networks. 3) Infor-mation capacity of a CNT network with a given topology. A CNT network can be used to encode and store information within the network topology. This information could be use to process the sensor information obtained by the network and perhaps


for computation of self-organization based upon the information content of the to-pology. For this, we introduce a graph entropy measure. 4) Latency of transport within a network. The goal is to understand the behavior of molecular motors such as kinesin on microtubules within the cell with a goal to use these molecular motors as part of a nanoscale Internet within the human body. The topology of the network will have an impact on the latency and rate of delivery of information as well as targeted drugs in the body.

2 The Nanotube Network Simulation

In this work, the impact of persistence length and isotropy of CNTs on graph proper-ties is initially examined and subsequently latency and bandwidth of such networks in molecular transport. Metrics, namely autocorrelation and persistence area are pro-posed to help characterize and analyze nanotube network structures. This work is based upon prior work by Bush and Goel [17] that shows the impact of random tube characteristics of location and angle on the behavior of a CNT network. In the previ-ous work, single-walled carbon nanotubes (SWNT) are modeled as linear tubes posi-tioned in two dimensions via central coordinates with a specified angle. A network graph is extracted from the layout of the tubes and the ability to route information at the level of individual nanotubes is considered. A similar approach for examining the impact of CNT properties on the graph attributes is used here.

Persistence length quantifies the degree of bending in microtubules. Briefly, the persistence length is the rate at which the tangents taken along each segment of a microtubule become decorrelated from one another. If R(s) is a point on a segment s, then let u(s) be the unit tangent vector,

( )R

u ss

∂=∂

. (1)

The orientations of the unit tangent vectors for all segments s is quantified by the inner product,

/( ) (0) = psu s u e ξ−⟨ ⋅ ⟩ , (2)

where ξp is the persistence length. For longer persistence lengths, or for shorter tubes, the microtubules will be straighter. For longer tubes or shorter persistence lengths, the impact of de-correlation along the chain tangent becomes more significant. We can approximate the curved microtubules as many smaller random chains that happen to be connected end-to-end, but with de-correlated alignment. Thus, shorter persistence lengths will tend to decrease the percolation threshold, which is important in the ex-planation of network conductance that follows. Persistence length becomes important in applications of nanotubes in photovoltaics, fuel cells and electronic components such as transistors, primarily due to longer lengths having greater electrical resistance. The persistence length of a microtubule has been estimated to range from 0.2 to 5.2 mm, while the persistence length at the tip of a microtubule has been found to be much shorter [18]. The rigidity and persistence length of microtubules has been found to be sensitive to various chemicals and related to various diseases [19], [20], [21].


In Figure 1, networks of tubes with different persistence lengths have been simu-lated. Networks of tubes with low persistence length tend to be tightly curled and contain a high density of tube segments. Networks comprised of tubes with higher persistence lengths cover a larger area and the tube segments are less dense. The tubes are positioned on a two-dimensional coordinate system. The mean persistence length of each tube is used to characterize the entire network. A source contact in green (vertical line at x = 0) and drain contact in blue (vertical line at x = -10) are also shown. The electrical resistance from the source to the drain is measured for each nanotube network. As shown in the figures, the position of the source and drain re-main constant in each network. The tubes are positioned randomly within an area centered between the source-drain contacts. When the tubes are perfectly straight, they are parallel to one another across the source-drain contacts.

In the network simulation, tubes that overlap in two-dimensional space create a network vertex. Figure 2 shows the number of vertices in the graph due to intersecting tubes as a function of persistence length. An observation of interest is that our simula-tions show a decreasing trend for connectivity versus persistence length.

Specifically, with very low persistence length, the total network connectivity is high due to a tendency for the individual tubes to coil up. As the persistence length increases, it reaches a point where the tubes are nearly linear and aligned, the net-works lose connectivity again. The impact of persistence length on connectivity be-comes important when designing CNT networks to control the rate of dissemination and transmission within the network. It’s interesting to note the relationship between persistence length and the autocorrelation function, which is shown in Equation 3 where τ represents lag. Note that with zero lag and without the denominator, the auto-correlation reduces simply to the variance. In relation to persistence length, the ran-dom variable is the tube segment angle. As the variance is reduced, the tubes become longer, spread out over a larger area, and there is a lower density of tube segments per unit area.

( )

2

( )( )( )

t tE X XR

τμ μτ

σ+⎡ ⎤− −⎣ ⎦= . (3)

The autocorrelation of one of the tube’s angles is shown in Figure 3. The exponential decline in the autocorrelation as the lag is increased corresponds to the mean change in angle correlation as distance increases, where the distance is as defined in persis-tence length.

A key component of the tube layout is the overall directionality of the tubes, that is, the angle of each tube relative to all other tubes. Isotropy is a global measure of this directionality. Isotropy quantifies the directionality of the tubes and is defined in Equation 5, where l is the tube length and α is the tube angle. Tubes that are almost aligned have a high isotropy and tubes that are randomly oriented have a low isotropy. Isotropy measures the alignment of all segments within the network and differs from persistence length, which was developed to measure the alignment of segments comprising individual tubes. In this paper, we introduce a new measure, known as persistence area, which is similar in nature to persistence length, but op-erates in two-dimensions instead of one. Persistence area is defined as shown in


(a) Low persistence length (b) Moderate persistence length

(c) High persistence length (d) Very high persistence length

Fig. 1. Networks as a function of increasing persistence length


Fig. 2. Number of network vertices as a function of persistence length

Fig. 3. The autocorrelation of a tube’s angles

Fig. 4. Isotropy as a function of persistence length


Equation 4, where both r and αν are radii of circular areas extending from each point in the area of interest.

/( ) (0) = pru r u e α−⟨ ⋅ ⟩ . (4)

cos( )

= sin( )

lisotropy

l

αα

∑∑

. (5)

A combination of isotropy and persistence length can be used for controlling the con-nectivity of the CNT network. The number of network vertices, due to connected or overlapping tube segments is shown in Figure 5 as a function of both persistence length and isotropy. Having two measures of control makes manufacturing of CNT networks to specification easier.

Fig. 5. Number of network vertices as a function of persistence length and isotropy

Fig. 6. Resistance as a function of persistence length (Lp)


Resistance is another key attribute for a CNT network since it is often used as a measure of change in sensor devices. Especially important is the rate of change of resistance to stimuli in the network, which determines the resolution of network. In Figure 6, the resistance to current flow is plotted as a function of the persistence length and shows an almost linear monotonically decreasing function (except for an initial spike). This makes the sensing more accurate and reliable.

The resistance of the network as a function of persistence length and the isotropy is shown in Figure 7. Again these two levers can be used to effectively control the resis-tance range of the CNT network.

Fig. 7. Resistance as a function of persistence length and isotropy

Let us switch our focus from resistance to molecular motors operating on the same set of networks that were used to obtain the resistance measurements. The operation of molecular motors was discussed in the introduction. However, we should note here that a precise understanding of how molecular motors choose which direction to take when confronted with an intersection is still an open research problem. We choose to take a maximum entropy approach (that is, assume as little a priori knowledge as possible) and simulate the motors with a random walk. The motor chooses whether to proceed forward or turn at any road of intersection with equal likelihood. In Figure 8, a molecular motor performs a random walk along the network. The initial location of the motor is randomly chosen from a set of vertices at one end of the network, and the target destination for the motor is randomly chosen from a set of nodes at the opposite end of the network. A highly connected network should allow for a rapid traverse of the distance from source to destination. The expected percent distance from source to destination is shown after 1000 steps, where a step is a movement from one intersec-tion to another. Clearly, shorter persistence length networks allowed for more effi-cient transport.


Fig. 8. The percent of distance traveled from the source to the target as a function of persistence length

3 Graph Information Theory

A network contains information within its structure, as well as potentially transports information over its structure. A new field of graph information theory has been sug-gested in the past and could provide useful techniques for reasoning about and analyz-ing the information content of network structures. There have been attempts to define graph entropy in the past via different approaches, namely, Korner’s graph entropy [22] and others based upon the Shannon capacity of a graph [23]. However, these approaches are primarily based upon using graphs as an aid to advancing information theory. Here we suggest the reverse, using information theory to aid the understand-ing of graph structure. As we mentioned, there is information embodied within the structure of a graph that could reveal better insight into the topics we’ve examined in this paper.

Let us assume the tractable case of a normal distribution of tube angles. Equation 6 shows the information entropy of a normal distribution. It should be noted that a maximum entropy probability distribution is a probability distribution whose entropy is at least as great as that of all other members of a specified class of distributions. Thus, if little is known about a distribution, then, by default, the maximum entropy distribution is often chosen. This is known as the principle of maximum entropy. Maximizing entropy minimizes the amount of a priori information assumed by the distribution and it’s interesting that physical systems tend to move toward maximal entropy configurations over time, which is perhaps a form of self-organization.

( ) = ln( 2 )normalH eσ σ π (6)

It is conjectured that the information entropy within the tube chain and network struc-ture can be captured in this manner. In this case, σ is the standard deviation of the tube angles. The information content of each tube is its variance from the mean, or its amount of decorrelation from neighboring tubes. As the graph entropy as defined here approaches zero, a network becomes unlikely to exist, as tubes are not likely to


overlap as they become parallel. As the graph entropy increases, more tubes are likely to overlap and the network structure becomes more complex (see Figure 9). As the graph entropy defined here increases further, the information in the graph begins to level out, that is, as the graph becomes fully connected, each additional tube connec-tion adds less overall information.

This includes the notion that information may not only be conveyed in the tube network, but also hidden via steganographic means. The autocorrelation of a signal can reveal hidden periodic signals, thus autocorrelation of a tube chain can reveal hidden information within the tube angles.

Fig. 9. Graph entropy of network versus number of tubes and tube angle

In Figure 10, Equation 6 is used to compute the entropy of the graphs simulated in this paper versus the expected persistence length of the tubes in each graph. As ex-pected, the entropy is greater for shorter, more tightly curled – thus, random networks, and decreases as the tubes align.

Fig. 10. Graph entropy of networks used in this paper


4 Conclusion

Rapid advances in nanotechnology have enabled science to operate at the cellular level with promise for improved therapy and diagnosis. There is remarkable similarity between nanostructures and cellular components. Fields of cellular biology and nanotechnology can both benefit from shared congruent objectives of human medi-cine. In this paper, we examine the analogy between microtubules, which form the skeletal structure of cells, and carbon nanotube networks. By examining the behavior and properties of CNT structures we seek to understand the natural behavior of micro-tubules and also develop artificial structures for sensing and drug delivery in the hu-man body. We extract a network graph from a random CNT structure to examine its properties such as connectivity and resistance in relation to the persistence length and isotropy of CNTs that are used to construct these networks. We also examine the behavior or molecular motors in a random walk along CNT structures analogous to the locomotion of kinesin across microtubules in a living cell. Finally, we examine the information capacity of CNT networks in relation to individual CNT properties. We believe that computation, storage, and transmission will all come embedded in the CNT network. Understanding the behavior of individual CNT properties in relation to the resultant CNT network will assist in development of novel applications based on CNT networks.

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Single and Multiple-Access Channel Capacity inMolecular Nanonetworks

Baris Atakan and Ozgur B. Akan

Next generation Wireless Communications LaboratoryDepartment of Electrical and Electronics Engineering

Middle East Technical University, 06531, Ankara, Turkey{atakan,akan}@eee.metu.edu.tr

http://www.eee.metu.edu.tr/∼nwcl

Abstract. Molecular communication is a new nano-scale communica-tion paradigm that enables nanomachines to communicate with eachother by emitting molecules to their surrounding environment. Nanonet-works are also envisioned to be composed of a number of nanomachineswith molecular communication capability that are deployed in an envi-ronment to share specific molecular information such as odor, flavour,light, or any chemical state. In this paper, using the principles of naturalligand-receptor binding mechanisms in biology, we first derive a capac-ity expression for single molecular channel in which a single TransmitterNanomachine (TN) communicates with a single Receiver Nanomachine(RN). Then, we investigate the capacity of the molecular multiple-accesschannel in which multiple TNs communicate with a single RN. Numer-ical results reveal that high molecular communication capacities can beattainable for the single and multiple-access molecular channels.

Keywords: Molecular communication, Nanonetworks, Single molecularchannel, Molecular multiple-access channel.

1 Introduction

Molecular communication is a new communication paradigm that enablesnanomachines to communicate with each other using molecules as a commu-nication carrier [1]. A number of nanomachines with molecular communicationis envisioned as a nanonetwork to cooperatively share molecular information andto achieve a specific task from nuclear, biological, and chemical attack detectionto food and water quality control [2]. In a nanonetwork, we define the single andmultiple-access molecular channels as follows [7]:

– Single molecular channel is a molecular communication channel between asingle Transmitter Nanomachine (TN) and a single Receiver Nanomachine(RN).

– Molecular multiple-access channel is a molecular communication channel inwhich multiple TNs transmit molecular information to a single RN.

A. Schmid et al. (Eds.): Nano-Net 2009, LNICST 20, pp. 14–23, 2009.c© Institute for Computer Science, Social-Informatics and Telecommunications Engineering 2009

Single and Multiple-Access Channel Capacity in Molecular Nanonetworks 15

In the literature, there exist several conceptual studies on the molecularcommunication paradigm [1,2,3]. However, these studies do not investigate themolecular communication from the communication theory perspective. In [4,5],achievable information rate is investigated in the molecular communication chan-nel that is modeled as a timing channel. The channel model considers Brownianmotion as a main mechanism to deliver emitted molecules to the receiver sidewithin a time delay. However, it does not include any realistic physical parame-ter such as environment temperature, molecular mass, and diffusion coefficientsthat are main determinant for the molecular delivery time and its fluctuations.Moreover, the molecular communication channel modeled as the timing channelmay necessitate the nanomachines to strictly synchronize with each other andalso incur high computational burden for the nanomachines, which may also beimpractical for low-end nanomachines.

In our previous work [6], we model the single and multiple-access molecularchannels as a binary symmetric channel with two molecular communication bitscorresponding to a specific molecule concentration delivered to RN by TNs. Thisapproach severely restricts the molecular communication capacity to one bit pertransmission. However, the single and multiple-access molecular channels maydeliver more than one concentration level corresponding to higher molecularcommunication rates instead of a specific concentration level and two corre-sponding molecular communication bits. Therefore, the capacity of the singleand multiple-access molecular channels need to be further investigated to findout their actual capacity expressions. In this paper, using the principles of nat-ural ligand-receptor binding mechanisms in biology, we first derive the capacityof the single molecular channel in Section 2. Then, we find out the capacity ofthe molecular multiple-access channel in Section 3. In Section 4, we give thenumerical results on the capacity of the single molecular channel and molecularmultiple-access channel. Finally, we give concluding remarks in Section 5.

2 Single Molecular Communication Channel

In nature, biological entities communicate with each other via the ligand-receptorbinding mechanism, in which ligand molecules are emitted by one biological phe-nomenon then, the emitted ligand molecules bind to the receptors of anotherbiological phenomenon. According to the bound molecule concentration, the bi-ological phenomenon perceives the biological information to fire an action po-tential. Hence, biological molecular channel can be envisaged as a concentrationchannel. In this paper, we use the natural ligand-receptor binding mechanismto model the molecular communication between TN and RN1 and we considerthis molecular communication channel as a concentration channel. In the litera-ture, artificial ligand-receptor binding schemes have been previously introduced[8], [9], [10]. In this paper, we assume an artificial ligand-receptor binding modelintroduced in [10].1 Here, we assume that TN and RN are analogous to the biological mechanisms such

as a single cell or a bacteria and have spherical shape with radius r0.

16 B. Atakan and O.B. Akan

We assume that TN emits one kind of molecule called A with concentrationX (μmol/liter) and X is a random variable with the mean μx and the varianceσ2

x. Furthermore, we assume that RN has the receptors called R on its surfacewith constant concentration N (μmol/liter). The receptors enable RN to receivethe molecules which bind to their surface. When TN emits molecules A withconcentration X , some of molecules bind to these receptors and generate boundmolecules with a concentration. Using the ligand-receptor binding model givenin [10], the concentration of these bound molecules, i.e., B, can be given as

B =k1NX

k−1(1)

where k1 and k−1 are the constant binding and release rate, respectively. Thebinding rate k1 indicates the ratio of the molecules binding to the receptorson RN while the release rate k−1 indicates the ratio of the molecules releasingfrom the receptors. Here, we assume that k−1 is a constant which is affected byphysical properties of the receptors on RN and it does not change as long as thephysical properties of the receptors on RN do not change. However, k1 is affectedby the several environmental factors such as molecular diffusion coefficients,temperature, and distance between TN and RN. In the literature, there areseveral realistic models for k1 that are experimentally tested for certain bio-chemical reactions [11], [12], [13]. In this paper, we use the following model [11]for k1,

k1 =4πDr0β

1 − (1 − β) r0r∞

(2)

where D is the diffusion coefficient of the emitted molecules, r0 (A◦) is the radiusof RN and r∞ (A◦) is the radius of the spherical shaped environment in whichTN and RN communicate. β is the fraction of the molecule trajectories thatallow the molecules emitted by TN to bind the receptors on RN. If we assumethat the distance between TN and RN is α, the probability that a moleculeemitted by TN will be captured by RN can be given as r0

α [12]. Therefore, weset the fraction of the molecule trajectories that allow the molecules to bind thereceptors on RN, i.e., β, as β = r0

α .Since the emitted molecules A continuously diffuse in the environment and

the diffusion process can have some natural variations as many natural events,we assume the concentration of bound molecules (B) is exposed to a noise leveldenoted by Z. Thus, the concentration of molecules delivered to RN by TN, i.e.,Y , can be given as

Y = B + Z =k1NX

k−1+ Z (3)

where we assume that Z is a random variable with the normal distributionN(μz, σ

2z). Many events in nature can be approximated with the normal distri-

bution corresponding to the central limit theorem. Therefore, this assumption isreasonable to effectively investigate the molecular channel capacity.

Single and Multiple-Access Channel Capacity in Molecular Nanonetworks 17

Hence, assuming that X and Z are independent random variables, the mutualinformation of the single molecular channel between TN and RN, i.e., I(X ; Y ),can be expressed as

I(X ; Y ) = H(Y ) − H

([k1NX

k−1+ Z

]|X)

= H(Y ) − H(Z) (4)

In order to maximize the mutual information I(X ; Y ) for providing the capacityof the single molecular channel, H(Y ) should be maximized. Y is considerablyaffected by the distribution of random variables X and Z since k1N

k−1is a constant.

Z has the normal distribution N(μz, σ2z) and the entropy of Z can be given as

H(Z) = ln(σz

√2πe). The normal distribution has maximum entropy among all

real-valued distributions with specified mean and standard deviation. Therefore,to maximize H(Y ) we assume that X is a normally distributed random variablewith the distribution N(μx, σ2

x). This makes Y a normally distributed randomvariable with the distribution N(μy, σ2

y) since the summation of two normal dis-tributions is also a normal distribution. Hence, H(Y ) can be maximized since ithas the normal distribution. Using the linearity of mean and standard deviationof normal distributions, μy and σ2

y can be given as a linear function of mean andstandard deviation of X and Z as follows

μy =k1N

k−1μx + μz , σ2

y = (k1N

k−1σx)2 + σ2

z (5)

Hence, the entropy of Y , i.e., H(Y ), can be given as [15]

H(Y ) = ln(σy

√2πe)

= ln

(√2πe

[(k1N

k−1σx)2 + σ2

z

])(6)

Hence, using H(Y ) and H(Z), the capacity of the single molecular channel be-tween TN and RN, i.e., Cs, can be expressed as

Cs = max

(I(X ; Y )

)= H(Y ) − H(Z) =

12ln

(1 +

(k1Nk−1

σx)2

σ2z

)(7)

Since X is the molecule emission concentration of TN, the minimum value of Xis equal to 0. In any normal distribution, % 99.7 of the observations fall within3 standard deviations of the mean. Therefore, μx and σx can be approximatedas μx −3σx ≈ 0 and σx = μx/3 can be assumed. Similarly, Y cannot be negativeand its minimum value is equal to 0. Therefore, μy and σy can be approximatedas μy − 3σy ≈ 0 and σy = μy/3 can be assumed [6].

Next, we introduce the capacity of a molecular multiple-access channel basedon the capacity expression of the single molecular channel given in (7).

18 B. Atakan and O.B. Akan

3 Capacity of Molecular Multiple-Access Channel

In the molecular multiple-access channel, a number of TNs (TN1...TNn) com-municate with a single RN. Each nanomachine has a self-identifying label2 andadheres the label to the emitted molecules. This mechanism provides a simpleaddressing scheme to allow RN to distinguish the molecules emitted by eachcommunicating TN [7]. Here, we also assume that TNi is located to the distanceαi from RN and transmits molecules A with concentration Xi using the bindingand release rate k1i and k−1, respectively. Xi is a random variable with the meanμxi and the variance σ2

xi.In [10], a model is proposed to find concentration of bound molecules (deliv-

ered molecules) for the case in which different molecules bind to a single kindof receptors with a constant concentration. Using this model introduced in [10],the concentration of molecules emitted by TNi and bind to the receptors on RN,i.e., Bi, can be given as

Bi =XiNk1i

k−1

1 +∑n

j �=iμxjk1j

k−1

(8)

where N is the concentration of the receptors on RN. Similar to the singlemolecular channel, we assume that the molecules emitted by TNi and bind tothe receptors on RN, i.e., Bi is exposed to a noise level denoted by Zi. Thus, theconcentration of the bound molecules delivered by TNi, i.e., Yi, can be expressedas

Yi = Bi + Zi =XiNk1i

k−1

1 +∑n

j �=iμxjk1j

k−1

+ Zi, i = 1, ..., n (9)

where Zi is a normally distributed random variable with distribution N(μzi, σ2zi)

and has the entropy H(Zi) = ln(σzi

√2πe). Similar to the single molecular chan-

nel, in order to maximize the entropy of Yi (H(Yi)), the emitted concentrationXi should have a normal distribution such that this maximization provides themaximum of mutual information I(Xi; Yi) so as to provide the capacity of themultiple-access channel between TNi and RN. Therefore, to obtain the capacity,we assume that Xi is a normally distributed random variable with the distribu-tion N(μxi, σ

2xi). Using the linearity of mean and standard deviation of normal

distributions, the mean μyi and the variance σ2yi of the delivered bound molecules

(Yi) can be expressed as

μyi =Nk1i

k−1μxi

1 +∑n

j �=iμxjk1j

k−1

+ μzi, σ2yi = (

Nk1i

k−1σxi

1 +∑n

j �=iμxjk1j

k−1

)2 + σ2zi (10)

2 To experimentally investigate the ligand-receptor interactions, three kinds of labelingprocess called as radio, enzymatic, and fluorescent labeling are mainly used [14].Here, we assume that each nanomachine has self-identifying labeled molecules usedfor the molecular communication.

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