Simulating Molecular Motor Uni-castInformation Rate for Molecular Communication

Michael J. Moore∗, Akihiro Enomoto∗, Shun Watanabe∗, Kazuhiro Oiwa†‡, and Tatsuya Suda∗∗Bren School of Information and Computer Science

University of California - Irvine, Irvine, CA 92697 USAEmail: mikemo, enomoto, shun, suda @ics.uci.edu

†National Institute of Information and Communications Technology (NICT), JapanEmail: oiwa@nict.co.jp

‡Graduate School of Life Science, University of Hyogo,Harima Science Park City, Hyogo 678-1297, Japan

Abstract—For Workshop on Biological and Bio-Inspired Infor-mation Theory. Future applications may require communicationmechanisms for nanomachines to coordinate with other nanoma-chines. Nanomachines are artificial or biological macromoleculesthat perform simple computing, sensing, or actuation. A molec-ular communication system is one method for communicationamong nanomachines: a nanomachine(s) releases molecules torepresent information (sending), the information molecules prop-agate through the environment, and another nanomachine(s)reacts to the molecules as information (receiving). Developingadvanced molecular communication systems may be simpler withgeneric uni-cast and broadcast mechanisms for transmission fromone nanomachine to one or more nanomachines(s).

All communication processes (encoding, sending, propagating,receiving, decoding) impact the design of a communicationsystem. In this paper, we improve the design of a molecularcommunication system by characterizing several techniques forsending, propagating, and receiving information molecules. First,we measure the probability of receiving information molecules forthree propagation techniques (diffusion-only, directional molecu-lar motors, and a hybrid using both diffusion and motors). Next,we model bit transmission to measure signal, noise and informa-tion rate. Finally, we model techniques to modify signal and noisesuch as noise dissipation, sending multiple information molecules,and receiving multiple information molecules. We compare theinformation rates of the various techniques to identify promisingapproaches for uni-cast and broadcast transmission.

Index Terms—molecular communication, information rate,kinesin molecular motor,

I. INTRODUCTION

A molecular communication system transmits informa-tion by releasing molecules that represent the informationfrom a sender nanomachine(s) to a receiver nanomachine(s)[1]. Nanomachines are nano-scale or micro-scale devicesthat should be capable of performing sensing, actuation, orlogic [2][3]. In biological systems, nanomachines often usemolecules since nanomachines are limited in size and powerand thus cannot readily communicate through computer com-munication mechanisms (e.g. computer networks using wiredor wireless communication). Molecular communication has 5key processes (figure 1). In molecular communication, a sendernanomachine (referred to as a ”sender” in the remainder ofthis paper) encodes information and sends out information

molecules into the environment. Information molecules prop-agate through the environment and a receiver nanomachine(referred to as a ”receiver” in the remainder of this paper)receives the information molecules and chemically reacts toproduce decoded information [4]. In this paper, we focuson uni-cast transmission, the most simple communication incomputer networks, which is transmission from a single senderto a single receiver.

Advances in molecular biology and nanotechnology haveenabled researchers to engineer or re-engineer biological sys-tems to produce new functionality. Molecular communica-tion is an important design aspect in these systems. Fu-ture engineered molecular communications may include uni-cast transmission of information molecules for medical de-vices [1][5][6], molecular computing [7][8], synthetic biology[9][10], or self-organization to perform nano-scale manufac-turing [11].

Unlike traditional digital communication, molecular com-municate involves molecules that propagate in a more stochas-tic manner. In short-range digital communication (e.g. electri-cal optical) the environment absorbs the signal (e.g. electronsor photons) after a short period of time (e.g. milliseconds toseconds). On the other hand, in molecular communication,information molecules have a much greater variance in arrivaltime at the receiver and molecules may persist in the envi-ronment for a long amount of time (e.g. some bio-moleculespersist for minutes whereas others persist for days). Receiversreact quickly to information molecules and thus propagationtime generally determines the delay of transmission.

In this paper we borrow propagation processes from biologyand design a uni-cast molecular communication system withthe goal of transmitting information at a maximal rate. Weevaluate approaches for propagating molecules to identifypromising approaches in terms of the physical layer of digitalcommunication [12]. These techniques include propagationmethods (free diffusion-only, molecular motor, and a hybriddiffusion). We perform modeling and simulation of thesevarious techniques to measure the rate of information andto improve our knowledge about how to design molecularcommunication systems.

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Fig. 1. Conceptual molecular communication system with five communica-tion processes. Information molecules propagate through the system passively(top) by diffusion and/or actively (bottom) using molecular motors and proteinfilaments.

II. SIMULATION MODEL OF PROPAGATION

A. Simulation Modeling

It is difficult to design a molecular communication throughbiology experiments since performing many biology experi-ments is time-consuming and costly experiments. Therefore,we first experimentally characterize the components of themolecular motor system in terms of parameters that affectpropagation. Then, we perform simulations to characterizea system engineered from the components. This paper onlydescribes the resulting simulation model.

B. Components in the Simulation Model

The sender, receiver, and information molecules are mod-eled as 200 nm diameter spheres. The sender produces aninformation molecule at its location and subsequently doesnot interact with the information molecule. The informationmolecule is 200 nm so that many molecular motors can bind toit. If an information molecule touches the receiver, the receiveris considered to have reacted to the information molecule.This is a simplified model of receiving that maximizes theprobability of receiving.

The environment is modeled as an aqueous solution similarto experimental conditions with viscosity equal to that ofwater (0.001 Pa·sec) and with the simulated volume as twoparallel surfaces of infinite length and width separated by adistance of 10 μm. We chose this environment since it issimilar to the arrangement in the biology experiments forcharacterizing the information molecules and microtubules.All senders, receivers, and microtubules are bound to onesurface. Microtubules can be polymerized or depolymerizeddynamically under some experimental conditions [14][15];however, in this paper, microtubules are assumed to be stati-cally formed and to be stiff, straight rods with constant length.

C. Propagation in the Simulation Model

In the simulations, we consider three cases of propagation.In (D), no protein filaments exist in the environment andinformation molecules experience only diffusion by random

SSender:Diffusion (D)

NoMotor (M)Connected

Hybrid (H)Microtubule Aster

RReceiver:

Microtubule:S R

Microtubule

S R

ConnectedMicrotubule

Microtubule Aster

S RS S S

Fig. 2. Propagation simulated for uni-cast transmission. All uni-castpropagations (D, M, H), have a sender and receiver some fixed distance apart(1, 8, 64 μm apart) and attached to the same surface.

thermal noise. In (M), a microtubule directly connects thesender to the receiver and information molecules are deliveredby motors from the sender to the receiver. In (H), severalmicrotubules lead to the receiver, but the receiver is notnecessarily directly connected to the sender, thus informationmolecules diffuse from the sender onto protein filaments thatguide the information molecule to a receiver. The receiverin (H) is in a plus-centered aster of protein filaments (star-shaped with uniform random-angled arms) so that the kinesinmotors guide information molecules to the receiver at thecenter. [20][21] describe techniques to form asters and plus-oriented microtubules. Figure 2 illustrates propagation (D, M,H) for the uni-cast case. In molecular communication systems,biological components may be located with some randomness.Propagation (D) and (H) are more adaptive to a mobile sendersince the sender is not directly connected to the receiver.In systems with time to self-organize the system, it may bepossible to form protein filaments for propagation (M) usingself-organization techniques.

In the simulation, information molecules propagate by dif-fusion when not interacting with a microtubule. When aninformation molecule is diffusing, it displaces independently inthree dimensions following a Gaussian distribution accordingto the diffusion coefficient of the sphere (coefficient deter-mined by size of the sphere, viscosity of the environment, andtemperature).

In these simulations, we model the molecular motor kinesinwhich walks along microtubules. If the information moleculecontacts a microtubule in the simulation, the informationmolecule no longer diffuses and instead walks along themicrotubule at a fixed velocity of 800 nm/s, which has beenobserved in experiment [16]. A single kinesin motor has arelatively short walking distance and disassociates from themicrotubule stochastically with an average run length of lessthan one μm. However, when many motors are attached to thesame cargo, the probability that all motors disassociate fromthe microtubule at the same time is low, and run length is muchlonger, up to 100’s of μm [17][18]. In these simulations weassume a fixed number of motors and the expected run lengthis 100 μm. Information molecules may contact multiple mi-crotubules and switch probabilistically between microtubulesdepending on the positions of the microtubules [19].

For all cases, we assume that the diffusion and microtubulewalking of an information molecule is not affected by the

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Fig. 3. The cummulative probability of receiving versus time for (D), (M),and (H). Uni-cast diffusion case (D). Waiting even much longer (simulatedup to 36000 seconds, but not illustrated) does not significantly changeprobabilities. The probability of receiving greatly decreases with distance (1m, 8 m, 64 μm). Uni-cast connected case (M). Cumulative probability ofreceiving versus time. The information molecule has some initial delay to walkto the receiver, depending on distance between sender and receiver (1, 8, 64μm). While walking there is some probability of falling off the microtubule,thus the probability of reaching a receiver is lower at longer distances. Uni-casthybrid-aster case (H). Cumulative probability of receiving versus time. Theaster is 4 microtubules of 20 μm length (4x20μm) in uniformly distributedorientations parallel to the glass surface. The hybrid-aster has properties ofboth (D) and (M), however at longer range (64μm), the diffusion propertiesdominate.

sender, receiver, or other information molecules. Note that inthe simulation, information molecules persist indefinitely. Thetime step of the simulator is 0.001 seconds and total simulatedtime for each configuration is 36,000 seconds.

III. UNI-CAST RECEIVING PROBABILITY

For each propagation method (D), (M), and (H), 1200information molecules were independently propagated throughthe environment. Figure 3 depicts the cumulative probabilitythat an information molecule has contacted the receiver bya given simulated time. Figure 3 does not show the entiresimulated time; however, there is little change in cumulativeprobability at times after the range depicted. Figures 3 alsoincludes some distances between the sender and receiver (1,8, 64 μm) which is a significant simulation parameter affectingthe probability of receiving.

When applying diffusion (D), the probability of an infor-mation molecule contacting the receiver at a given time isproportional to the probability density of the location of theinformation molecule (resulting from diffusion) which can beapproximated by a normal distribution with deviation σ (ineach of 3 dimensions):

σ =√

2Dt (1)

where t is the time elapsed since the sender released theinformation molecule with diffusion coefficient D. Thus, astime increases, the probability of subsequently contacting thereceiver is decreasing. As a result, a single sender releasing alimited number of information molecules is unlikely to suc-cessfully perform diffusion-based uni-cast to a single, distantreceiver even if the sender waits a relatively long time forpropagation.

Connecting a sender to receiver (M) greatly increases theprobability of reaching the receiver (figure 3). However, the

cumulative probability that the information molecule falls offbecomes larger as the molecular motors walk further. Theinformation molecule would be unlikely to reach a receiverat much longer distances. In effect, connecting the senderto receiver increases the effective distance of propagationfor which there is a reasonable probability of contacting thereceiver. On the other hand, there are few existing experimenttechniques for connecting a sender to a receiver, especiallyover relatively longer distances.

An alternative configuration that may be experimentally eas-ier to produce is the star-shaped aster for hybrid-propagation(H). In (H), the probability that an information moleculecontacts the receiver is relatively greater than (D). When aninformation molecule contacts any of the microtubules in theenvironment, the information molecule will likely reach thereceiver. In (H) there is some probability that the microtubulesdirectly connect the sender to the receiver.

The probability of a single microtubule connecting is illus-trated in figure 4. If a microtubule is angled within the rangedefined by angle Θ, then propagation (H) becomes almostequivalent to (M). Angle Θ can be approximated as:

θ = 2arcsin

(rs + 2ri + rm

d

)(2)

Where rs, ri, rm are the radii of the sender, informationmolecule, and microtubule, respectively, and d is the distancefrom the sender to receiver. From equation 2, we can calculatethe probability of connecting with respect to distance d (figure5). The probability for (H) to form a direct connection at 8μm is around 0.05. However, in figure 3, the probability for(H) to reach the receiver is around 0.5 in the 8 μm case. Also,the information molecule is unlikely to directly diffuse (nowalking) to the receiver at 8 μm according to the diffusion (D)in the figure 3 (probability ¡ 0.02). Thus for propagation (H),the majority of propagation begins as diffusion followed bybinding onto the microtubules. However, (H) performs betterthan (D) in diffusion since (H) has a larger target (receiverand microtubules) to bind to.

IV. INFORMATION RATE

A. Information Rate Model

The information rate determines how much information istransmitted per unit time. In this paper, we use a simplifiedbinary digital signal model to measure information rate. Thesender has an ordered set of 0’s and 1’s, sequence U, totransmit to the receiver. At the receiver, the receiver reactsto information molecules and decodes the type of reactioninto an output sequence of 0’s and 1’s, sequence V. In theith interval of duration L (communication interval), the sendertransmits the ith bit of information from sequence U. If the bitis a ”1” the sender emits a molecule(s). If the bit is a ”0”, thesender emits no information molecules. If the receiver reactsto an information molecule before the start of the next timeinterval, a ”1” is appended to sequence V; otherwise, a ”0” isappended to sequence V.

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rs+2ri+rm

d

/2

iS R

Fig. 4. Probability of a microtubule in (H) directly connecting a sender Sto receiver R is dependent on geometry. If a microtubule in (H) is withinangle Θ, then an information molecule i may directly contact the sender asin propagation method (M).

0

0.2

0.4

0.6

0.8

1

0 20000 40000 60000

Prob

abili

ty o

f con

nect

ion

with

4 m

icro

tubu

les

in a

ster

Distance from sender to aster center

Fig. 5. Probability of propagation (H) forming a connection as in case (M).The probability at 8 μm is around 0.05. Thus, the majority of successfultransmissions in (H) occur from diffusion followed by binding.

In these simulations, the sender is assumed to release oneinformation molecule with molecular motors already attached.The receiver is assumed to immediately decode when the infor-mation molecule is received. The simulation of the proposedsystem is similar to [22] in which the sender generates infor-mation molecules, and a receiver reacts to single informationmolecules. This is unlike [23][24][25] in which the receiverdetects information as the concentration of many informationmolecules.

To simplify analysis of this system, the sender is ideallysynchronized with the receiver (as a result, no bit insertion ordeletion errors occur in the output sequence). In practicality,synchronization may be possible through external signalsthat oscillate at regular intervals (e.g. molecular oscillationsin molecular computing systems or external electromagneticwaves). Also to simplify analysis, the sender does not pipelinetransmission from sequence U (i.e. does not begin sending thenext bit before the transmission of a previous bit is complete).In cases of diffusion, pipelining is less likely to be beneficialsince variance in arrival times is relatively large comparedto propagation time. When decoding, the receiver ignoresduplicate information molecules in the same time interval.From the nanomachine perspective, this would require thereceiver to enter an ”off” state in which it receives informationmolecules (similar to neuron signaling in biology [3]), but doesnot decode those information molecules into sequence V.

We measure probabilities of signal and noise to determinethe mutual information C transmitted (from the sender to the

receiver) following the mutual information formula:

C =∑y∈Y

∑x∈X

p (x, y)(

logp (x, y)

p (x) p (y)

)(3)

p(x) and p(y) are the marginal probabilities of sending x (a”1” or a ”0”) and receiving y (a ”1” or a ”0”). p(x,y) is thejoint probability of x and y. In the model in this paper, onebit of information is transmitted per interval L, thus the rateof information is C / L. Conditional probabilities to calculateinformation rate are as follows:

p (x = 0) = p (x = 1) = 0.5 (4)

p (y = 1 | x = 0) = n (5)

p (y = 0 | x = 0) = 1 − n (6)

p (y = 1 | x = 1) = s + n − sn (7)

p (y = 0 | x = 1) = 1 − (s + n − sn) (8)

s and n, representing signal and noise respectively, are cumu-lative probabilities measured from simulation data in figures 3.For a given interval of duration L, s is the cumulative probabil-ity of the receiver receiving information molecules before timeL and n is the cumulative probability of receiving after timeL. 0’s and 1’s are assumed to be sent with equally probability(both have 0.5 probability in equation (5). Equations (6) and(9) represent errors in transmission. For example in (6), thesender transmits a ”0” but the receiver detects a ”1” due noise.Equations (7) and (8) represent successful transmission. Notethat noise is beneficial in equation (8) since the probability ofsuccessfully transmitting a ”1” is the OR of s and n.

B. Uni-cast Information Rate

Figures 6, 7, and 8 illustrate the information rates calculatedfrom simulation data for (D), (M), and (H). Information rate ishighly affected by distance between sender and receiver (e.g.d in figure 4) and the frequency of information transmissionfrom the sender. Thus, in addition to the three propagationmethods (D), (M), and (H), we vary distance d from senderto receiver (1 μm, 64 μm) and possible I values. Thus, we areable to determine the optimal choice of I for a given d.

According to the information rate model, noise from previ-ous bit transmissions may significantly impact the rate of in-formation transmission. Therefore, we compared the followingtwo cases: (N) determination of information rate with noiseequal to n, and (F) information rate for an ideal noise-freetransmission in which n is always zero. It should be possibleto identify techniques to produce information rates betweenthese two curves (e.g. noise reduction techniques), but we donot consider such techniques in this paper.

In the case of diffusion (D), some information can betransmitted at a short distance of 1 μm (figure 6 left); however,at 64 μm both signal and noise are relatively low (figure6 right). Thus, diffusion in this case can be appropriate forvery short range transmission. In the case of a connectingmicrotubule (M), information can be transmitted at both 1 μm

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Fig. 6. Diffusion (D) uni-cast using 1 information molecule. Distancebetween sender and receiver is 1 μm (left) and 64 μ m (right). For 1 μm (left),noise free (F) has high capacity at ¡ 1 second (quick diffusion to receiver withsome probability), but perfect removal of noise is likely impractical at such atime-scale. Information rates decrease with interval since interval determineshow long to wait between single-bit transmissions. Probability of diffusing toa receiver 64 μm (right) away is very low, thus information rate is low evenwith all noise removal.

Fig. 7. Connected (M) uni-cast using 1 information molecule and with 1 μm(left) and 64 μm (right) between sender and receiver. For 1 μm, signal is highprobability since motors are unlikely to fall off within 1 μm walking. With64 μm walking, there is still a 70% chance of reaching receiver. Informationmolecules dissipate quickly, so the probability of acting as noise is only fora short time after receiving. Thus, all noise dissipation techniques performsimilarly. Information rate is significantly lower in 64 um since there is greaterpropagation delay.

and 64 μm. Since the expected walking distance in (M) is100 μm, many information molecules are able to walk to thereceiver. However, since there is a longer delay in walking,the information rate is significantly lower according to theinformation model in this paper.

Hybrid propagation (H) is similar to (M) in that it is alsoable to transmit some information at both 1 μm and 64 μm.(H) has only a few times lower information rate than (M) at1 μm; however, (H) is 2 orders of magnitude lower at 64 μm.Thus, (H) may be appropriate for mid-range communication(less than 64 μm). (H) has significantly higher noise than(M) in both cases as evidenced by the gap between the allnoise (N) and noise-free (F) curves in figure 8. This occurssince an information molecule is likely to repeatedly arriveat the receiver (through rebinding microtubules after already

Fig. 8. Hybrid propagation (H) using 1 information molecule. Distancebetween sender and receiver is 1 um (left) and 64μm (right). The largegap between (F) and (N) indicates that there is significant noise in thehybrid propagation system (H). The information rate at longer distances iscomparable to diffusion-only (D). In the best-case, all noise is removed and(H) does better than (D), however (H) still only achieves two orders ofmagnitude lower information rate than the connected microtubule case (M).

receiving). As discussed earlier, the probability of binding toa receiver after diffusion is reasonably high in (H), and thus(H) produces significant noise even for larger L. On the otherhand, (D) and (M) experience little noise after receiving theinformation molecule. This implies that a single informationmolecule can easily diffuse away from the receiver if there arefew microtubules that lead to the receiver.

V. CONCLUSION

Biological systems use various propagation techniques (e.g.diffusion or molecular motors) to perform the molecularcommunication system described in figure 1. In this paper,we compared three propagation methods (diffusion-only (D),molecular motor (M), and hybrid (H)) to determine the impactof propagation on uni-cast transmission of information. Wecompared the propagation techniques by designing an infor-mation rate model and by measuring signal and noise in acomputer simulation. The information rates were (M) (H)(D) for sender to receiver distances of 1 μm and 64 μm. Also,in terms of capability to communicate at longer distances, theorder (M) (H) (D) applied. Thus, it may be productive toimprove the rate of information transmission by identifyingtechniques to directionally transport information molecules toreceivers.

From figures 6, 7, and 8, it is possible to optimize informa-tion rate with respect to interval L. Transmitting at too shortof an interval does not provide sufficient time for informationmolecules to propagate to the receiver. Transmitting at a longerinterval causes the information rate to decrease since the rate isinversely proportional to L. Thus, as long as some informationmolecules can reach the receiver, there exists some optimalvalue of L which maximizes information rate. Also, in termsof design, a single nanomachine is unlikely to communicateany information at longer distances. Thus, it is likely thatadditional information molecules and/or nanomachines are

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necessary to support the transmission of information in alarger-scale molecular communication system.

Design of molecular communication systems remains chal-lenging, for example designing nanomachines with reliableproduction of molecules or the capability to communicate witha specific receiver(s). The current simulation and modeling islimited in that it does not consider transmission of multipleinformation molecules and assumes a one-way transmissionof information. In future work we may consider designinga communication system with feedback from the receiveror error correction. Also, from the communication systemperspective, there are other parameters to consider such asencoding techniques to improve information rates, handlenoise, and handle interference from other molecular commu-nications. Through such research we hope to engineer morereliable molecular communication and thus enable engineeringof coordinated nanomachine systems.

ACKNOWLEDGMENT

This research is supported by the NICT (the NationalInstitute of Communication Technology, Japan), by the NSFthrough grants ANI-0083074, ANI-9903427, ANI-0508506and OISE-0741742, by DARPA through grant MDA972-99-1-0007, by AFOSR through grant MURI F49620-00-1-0330,and by grants from the California MICRO and CoRe programs,Hitachi, Hitachi America, Hitachi CRL, Hitachi SDL, DENSOIT Laboratory, DENSO International America LA Laborato-ries, NTT Docomo and Novell.

The authors also thank and Tadashi Nakano from UCIand researchers from NICT in Japan (Atsushi Kayasuga,Hiroaki Kojima, Hitoshi Sakakibara) for refining experimentsnecessary to model the molecular motor system and for theircontributions towards discussion, writing, and modeling ofmolecular communications.

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