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Capacity and Delay of Bacteria-Based Communication
in Nanonetworks
Albert Mestres Sugrañes
Advisor: Ian F. Akyildiz
10/02/2012
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Introduction
Motivation and Contribution
Effect of mutations
Propagation model of bacteria
Communication schemes
Concluding Remarks
Table of Contents
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Introduction
Motivation and Contribution
Effect of mutations
Propagation model of bacteria
Communication schemes
Concluding Remarks
Table of Contents
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Nanotechnology is enabling the development of devices which can operate at the nanoscale.
Introduction: Nanotechnology and Nanodevices
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I. F. Akyildiz, F. Brunetti, and C. Blázquez, "Nanonetworking: A New Communication Paradigm," Computer Networks (Elsevier) Journal, Vol. 52, pp. 2260-2279, August, 2008.
A nanodevice is the most basic functional unit, which is divided into independent nanoscale components and it is able to perform specific tasks at nanolevel, such as sensing, computing, data storing, or actuation.
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WHY? Due to the reduced size of the nanodevices, their limitations
are clear:
Actuation range
Capabilities
Nanonetworks expand the possible applications of single nanodevices by a collaborative effort among them.
HOW?
Bacteria-based Communication
Introduction: Interaction between Nanodevices
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Basic concept: Use bacteria as carriers of encoded DNA packets
How do bacteria move? Chemotaxis: bacteria random walk which follows the concentration gradient of specific substances (attractants) in the environment.
How do bacteria reach the receiver? Nanodevices stimulate the chemotaxis of bacteria towards themselves by releasing attractants.
Introduction : Bacteria-based Communication (I)
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Gregori, M. & Akyildiz, I. “A new nanonetwork architecture using flagellated bacteria and catalytic nanomotors” Selected Areas in Communications, IEEE Journal on, 2010, 28, 612 -619
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Introduction: Bacteria-based Communication (II)
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ND ND
ND
RX
ND
Environment
Nanodevice
Bacterium
1-10mm ~100µm
TX
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Communication scheme
Relaying process
The range of the attractant is limited: Multi-hop is needed
Introduction: Bacteria-based Communication (III)
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Cobo, L. C. & Akyildiz, I. F. “Bacteria-based communication in nanonetworks” Nano Communication Networks, 2010, 1, 244 - 256
ENCAPSULATION ENCODING PROPAGATION DECAPSULATION DECODING
• DNA synthesis • Bact. Conjugation
• Modify chemotaxis
• Chemotaxis • Bacterial
Conjugation
• DNA sequencing
RELAYING
TRANSMITTER BACTERIAL CARRIER RECEIVER
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Introduction
Motivation and Contribution
Effect of mutations
Propagation model of bacteria
Communication schemes
Concluding Remarks
Table of Contents
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To complete an analytical model for the previous work.
The propagation of bacteria was only simulated.
The capacity model was approximated.
The delay was based on the simulated results.
Motivations
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An analysis of the effect of the mutations during the communication process.
A theoretical study of the propagation of bacteria.
Definition of two different communication schemes based on bacteria.
The study of the capacity and the delay of these systems.
Contributions
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Introduction
Motivation and Contribution
Effect of mutations
Propagation model of bacteria
Communication schemes
Concluding Remarks
Table of Contents
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The information is encoded in a DNA molecule called plasmid.
The basic information unit is the base pair (bp).
A plasmid can contain up to 1.6 Mbp (millions of base pairs)
Effect of mutations: Introduction
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Effect of mutations: Errors in the information
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During the communication process, multiple copies of the plasmid are done.
In each copy, mutations may alter the information.
DPU
A
C
G
T
RELAYING
DNA Encoding DNA copies (BCs)
DNA
A
C
G
T
DPU
A
C
G
T
DNA
A
C
G
T
DNA Decoding
peENC peDEC pePROP
ENCODING ENCAPSULATION/DECAPSULATION DECODING
Drake, J. W.; Charlesworth, B.; Charlesworth, D. & Crow, J. F. “Rates of Spontaneous Mutation” Genetics, 1998, 148, 1667-1686
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Effect of mutations: Probability of error
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Probability of error during the communication:
2 23 4
( ) 1 14 3
N
e mutp N p
N: Number of hops pmut: Mutation rate
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Effect of mutations: Capacity
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Capacity of a base pair (quaternary symmetric channel):
2 1 , , ,
3 3 3
e e ee
p p pC H p
Shannon, C. E. “A Mathematical Theory of Communication” The Bell System Technical Journal, 1948, 27, 379-423
H: Quaternary entropy
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Introduction
Motivation and Contribution
Effect of mutations
Propagation model of bacteria
Communication schemes
Concluding Remarks
Table of Contents
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Chemotaxis
Bacteria random walk which follows the concentration gradient of specific substances (attractants) in the environment.
How does it work?
Bacteria move in series of “runs” and “tumbles”.
Without attractant, bacteria move randomly in the medium, like a particle.
With attractant, the movement of bacteria is biased according to the attractant concentration.
Propagation model: Chemotaxis
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Berg, H. C. “Random Walks in Biology” Princeton University Press, 1993
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How to study?
Diffusion theory.
Flux of bacteria (J):
Where:
Propagation model: Diffusion theory
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Schnitzer, M. J. “Theory of continuum random walks and application to chemotaxis”, Phys. Rev. E, American Physical Society, 1993, 48, 2553-2568
( , ) ( ) ( , )driftJ D c x t v x c x t
2
0
2
0
1 1
1
1 1
rot
drift
rot
vD
n n D
v g Cv
n n D
v: velocity of bacteria n: number of dimensions α0: tumble rate Θ: angular correlation Drot: Rotational diffusion g: Attractant sensing gain C: Attractant gradient
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Partial Differential Equation
Initial conditions:
Drift velocity:
Attractant concentration:
Propagation model: Solution
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2( , )( , ) ( ) ( , )x drift x
c x tD c x t v x c x t
t
( , ) , 0
( ,0) ( )TX
c x t t
c x x x
driftv C
( )4
QC r
D r
Q: Releasing rate D: Attractant diffusion coefficient
Bacterial flux equation:
Continuity principle:
( , ) ( ) ( , )driftJ D c x t v x c x t
( , )c x tJ
t
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With c(x, t), the probability distribution of bacteria in the medium, the distribution of the arrivals can be calculated:
Propagation model: Arrivals distribution
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( ) ( , )darrRx
F t c x t Vol
<Rx>: Volume of the receiver
( ) ( , )dRx
arr t c x t Vol
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Introduction
Motivation and Contribution
Effect of mutations
Propagation model of bacteria
Communication schemes
Concluding Remarks
Table of Contents
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Communication schemes
Synchronous scheme
Asynchronous scheme
Comparison
Communication schemes: Synchronous scheme
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Characteristics
The time is divided into slots (duration T).
In each time slot we release N bacteria encoding the same information.
Only one bacterium has to reach the receiver during the T to receive that data.
If no bacteria reach the receptor in T, the data is lost.
We wait a delay d, to maximize the probability of receiving one bacterium.
Synchronous scheme: Introduction
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System delay:
Synchronous scheme: Delay
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Encode N bact N Tx
d T Decode 1 bact
Rx
( ) ( ) 1tx hop rxdelay t N S d T S t t
d T Thop N’ H1
d T Thop N’’ H2
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Capacity:
Probability of receiving at least one bacterium in one hop:
Maximization of the capacity:
Synchronous scheme: Capacity
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1 ( , , , )( , , , , ) Rx bac
bp
P d T N SC B d T N S B C
T
1 1
1
( , , , ) 1 1 ( , )
( , ) ( ) ( )
SN
Rx bac Rx
Rx
P d T N S P d T
P d T arr T d arr d
, , ,max ( , , , , )
d T B NC B d T N S
( , )
[0, ]
encT T B N
B BactCap
N
conditions:
B: Base pairs encoded Cbp: Capacity base pair
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Capacity:
Synchronous scheme: Capacity
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System delay:
Synchronous scheme: Delay
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Communication schemes
Synchronous scheme
Asynchronous scheme
Comparison
Communication schemes: Asynchronous scheme
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Characteristics
The transmitter is continuously releasing bacteria at the encoding speed.
The information goes from the transmitter to the receiver using other nanodevices.
If the bacterium do not reach any of the nanodevices, the data is lost.
The bacterium can use a Tout in each hop or not.
Asynchronous scheme: Introduction
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System delay:
Asynchronous scheme: Delay
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( ) ( 1)tx prop hop rxDelay t t S S t t
( ) ... [ ]prop
S
t arr arrf S f f pdf
Encode 1 bact Tx
Encode 1 bact
H1 Thop Thop
Tprop Tprop
H2 Thop Thop Tprop Tprop
Rx
Tprop
Decode 1 bact
Decode 1 bact
Tprop
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Average system delay:
Asynchronous scheme: Delay
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Capacity:
Probability of receiving at least one bacterium in one hop:
The optimal capacity can be achieved when the plasmid encodes the maximum of information.
Asynchronous scheme: Capacity
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( ) 1Tout Out OutP T arr T
( )bp encode RxC C r B p
1S
Rx Toutp P
rencode: effective encoding rate
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Capacity:
Asynchronous scheme: Capacity
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Communication schemes
Synchronous scheme
Asynchronous scheme
Comparison
Communication schemes: Comparison
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Capacity
Comparison of both schemes: Capacity
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Delay
Comparison of both schemes: Delay
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The synchronous system is appropriate when:
The order of the information is important
The delay has to be known and constant
The number of hops is high
The asynchronous system is appropriate when:
Neither the order nor the exact moment when a packet is received is important
The number of hops is small
Comparison of both schemes
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Introduction
Motivation and Contribution
Effect of mutations
Propagation model of bacteria
Communication schemes
Concluding Remarks
Table of Contents
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A theoretical study of the effect of the mutations has been performed and validated.
An analytical solution for the bacteria propagation has been found and validated.
Two different communication schemes have been proposed and the capacity and the delay have been calculated.
Synchronous scheme Constant delay and high performance in long range transmissions
Asynchronous scheme High performance in short range transmissions
Concluding Remarks
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Thank you very much for your attention.
Any question?
Thank you!
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