Molecular Communication through Biological Pattern Formation Tadashi Nakano1 , Tatsuya Suda2 , and Michael John Moore3 1
Graduate School of Frontier Biosciences, Osaka University, Japan 2 University Netgroup Inc., CA, USA 3 University of California, San Diego, CA, USA Email:
[email protected],
[email protected],
[email protected]
Abstract—This paper proposes to use spatio-temporal patterns that the concentration of propagating information molecules form in the molecular communication environment and develops a new modulation technique for molecular communication between bionanomachines. In molecular communication considered in this paper, information molecules transmitted from a group of sender bio-nanomachines propagate in the environment, chemically react with the molecules in the environment, change their concentration, and form an oscillating and propagating pattern. The rates at which sender bio-nanomachines transmit information molecules determines the frequency, amplitude and phase characteristics of the pattern, and the sender bio-nanomachines modify the transmission rates in order to modulate information on to frequency, amplitude and phase characteristics of the pattern. A group of receiver bio-nanomachines detects these characteristics to collectively decode information. This paper develops a new model of molecular communication through pattern formation. Using the model developed in this paper and numerical examples, this paper demonstrates the advantages of the proposed modulation technique, namely, higher information capacity and longer communication distances.
I. I NTRODUCTION Molecular communication is an emerging communication paradigm that uses molecules for communication among bionanomachines [1], [2], [3]. In molecular communication, information is encoded onto and decoded from molecules (referred to as information molecules in this paper). An information source generates information to encode onto information molecules and triggers a group of sender bionanomachines to transmit information-encoded information molecules. Information molecules transmitted from the sender bio-nanomachines propagate in the molecular communication environment (referred to as the environment in this paper) and are detected by a group of receiver bio-nanomachines. Receiver bio-nanomachines may forward information molecules that they receive to next-hop bio-nanomachines or may pass them to an information destination for decoding information. Existing studies in molecular communication develop various techniques for sender bio-nanomachines to modulate properties of information molecules to represent information to transmit [3]. In one modulation technique, sender bionanomachines select one type of information molecules to transmit from a set of distinguishable types of molecules, each molecule type representing given information (i.e., Molecule Shift Keying or MoSK) [4], [5], [6], [7]. In another modulation
technique, sender bio-nanomachines modify the manner of transmitting information molecules by either changing the number of information molecules to transmit (i.e., Amplitude Shift Keying or ASK) [8], [9], [10] or changing the time interval to transmit information molecules (i.e., Frequency Shift Keying or FSK) [11]. In all existing modulation techniques, once the information molecules are transmitted from the sender bio-nanomachines, they propagate through the environment, decaying in its concentration as they propagate. As a result, the receiver bio-nanomachines need to be located within a short distance from the sender bio-nanomachines. In this paper, we explore spatio-temporal patterns that propagating information molecules form in the environment and develop a new modulation technique for molecular communication. In molecular communication considered in this paper, information molecules transmitted from a group of sender bio-nanomachines propagate in the environment, chemically react with the molecules in the environment, change their concentration, and form an oscillating and propagating pattern. (In the rest of this paper, we refer to this phenomena as “reaction-diffusion of information molecules.”) The rates at which senders transmit information molecules determine the amplitude, frequency and phase characteristics of the pattern, and the sender bio-nanomachines modify their transmission rates in order to modulate information on to frequency, amplitude and phase characteristics of the pattern. A group of receiver bio-nanomachines detects these characteristics to collectively demodulate information. Unlike the existing modulation techniques (e.g., MoSK, ASK and FSK), which solely rely on information molecules propagating and decaying in their concentration in the environment, the proposed modulation technique explores reactiondiffusion of information molecules, i.e., information molecules propagating and chemically reacting with the molecules in the environment. The chemical reactions between information molecules and molecules in the environment may generate additional information molecules and form an oscillating and propagating pattern of the concentration of information molecules. This may help the information molecules propagate over longer distances than the existing modulation techniques, which solely rely on diffusion of information molecules. The chemical reactions in the environment also help increase the complexity of spatial-temporal patterns that the concentration
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of information molecules forms, thereby potentially making the information capacity of the proposed modulation technique higher than that of the existing modulation techniques. In addition, as reaction-diffusion of molecules is often observed in biological systems in nature (such as Ca2+ oscillating in their concentration and propagating between cells [12] and cAMP oscillating and propagating in a similar manner between cells [13]), the proposed modulation technique may be friendly to biological systems in nature and may take an advantage of biological systems in its implementation [14], [15]. In this paper, in order to verify the advantages of the proposed modulation technique, we first develop a model of molecular communication and a pattern that information molecules form through reaction-diffusion in the environment (in Section II). We also define the proposed modulation technique and apply the concept of mutual information to the model to characterize the proposed modulation technique for molecular communication (in Section III). We then illustrate, through numerical examples, the information capacity of the proposed modulation technique using a Ca2+ signaling system (in Section IV). We also examine, through numerical examples, communication distances that the proposed modulation technique may achieve using the same Ca2+ signaling system (in Section IV). Finally, we provide a summary of the work presented in this paper (in Section V). II. PATTERN F ORMATION IN B IOLOGY Pattern formation in biological systems is well known in biology [16], [17], [18], [19]. A basic model of biological patten formation involves two types of molecules, U (often referred to as activator molecules due to their role of activating chemical reactions) and V (often referred to as inhibitor molecules due to their role of inhibiting chemical reactions); it is known as the reaction-diffusion model and written as ∂u = f (u, v) + DU Δu, (1) ∂t ∂v = g(u, v) + DV Δv, (2) ∂t where u and v are the concentrations of U and V, functions f and g are reaction terms for U and V, DU and DV are diffusion ∂2 ∂2 coefficients of U and V, and Δ is the Laplacian (e.g., ∂x 2 + ∂y 2 for a two dimensional Euclidean coordinate). In each equation, the reaction term defines how the two types of molecules U and V interact with each other or interact with molecules in the environment, and the diffusion term (the second term in the right hand side of the equation) defines how quickly U and V diffuse in the environment. The reaction-diffusion model produces oscillatory patterns that propagate in space, such as periodic traveling waves and rotating spiral waves, under certain conditions [13], [20], [21]. For example, in the activator (U) and inhibitor (V) system, where U stimulates the production of both U and V, and V inhibits the production of both U and V, oscillatory patterns of concentration of U appear and propagate in space under the condition that only U, not V, diffuses. The reaction-diffusion
model also produces non-uniform stationary patterns, namely, Turing patterns such as stripes, spots and spirals, from an initially homogeneous environment where molecules U and V are uniformly distributed. For example, Turing patterns emerge when V diffuses faster than U. III. T HE M ODEL In this section, we explore spatio-temporal patterns that information molecules form in the environment and develop a new modulation technique for molecular communication. A. Information Source, Information Destination and Information Transmission We consider molecular communication where a single information source communicates information with a single information destination. In our model, an information source and an information destination may be a person, a microscale device [22], a bio-nanomachine, or a group of bio-nanomachines [3]. Information in this model is a concept or statement that is understood by the information source and information destination. In our model, information is represented in a message. An information source passes a message to a group of sender bio-nanomachines (simply referred to as senders), which in turn modulate the message on to an oscillating and propagating pattern that it generates. A group of receiver bio-nanomachines (simply referred to as receivers) detects characteristics of the information modulated pattern generated by a group of senders and passes the message to the information destination. In the following, information generated by the information source is denoted as X and that received by the information destination is denoted as Y . In ideal communication, the information that the information destination receives (Y ) is identical to the information that the information source generates (X). B. Information Transmission A group of N senders, are spatially distributed in the environment, and their locations are given as a set S ∈ {s1 , s2 , · · · , sN }, where si is the location of sender i ∈ [1, N ]. Each of these senders is capable of transmitting information molecules at two different rates x0 and x1 ; xi ∈ {x0 , x1 } refers to the rate at which sender i transmits information molecules. Under certain conditions, information molecules transmitted from the senders generate oscillating and propagating pattern of the concentration of information molecules in the environment, and the rates (x1 , x2 , · · · , xN ) at which N senders transmit information molecules determine the amplitude, frequency and phase of the oscillating and propagating pattern. In transmitting information X, an information source determines, for each sender i ∈ [1, N ], rate xi at which sender i ∈ [1, N ] transmits information molecules. In other words, an information source generates an N -bit sequence of rates, x = (x1 , x2 , · · · , xN ), for given information X.1 1 In this paper, x is a binary bit representing two possible transmission i rates of sender i without loss of generality. It is straightforward to expand xi to represent more than three transmission rates.
C. Information Reception Similarly to the senders, a group of M receivers, are distributed in the environment, and their locations are given as a set R ∈ {r1 , r2 , · · · , rM }, where rj is the location of receiver j∈ [1, M ]. Each of these receivers takes one of two states y 0 and y 1 ; yi ∈ {y 0 , y 1 } refers to the state of receiver j. Further, each of these receivers is sensitive to a change in a characteristic φ (either amplitude, frequency or phase) of the pattern that the concentration c(r) of the information molecule forms in the environment and changes its state to y 0 when a value of φ is smaller than a predetermined threshold θ, or y 1 otherwise. For example, a receiver may be sensitive to a frequency of an oscillating pattern; this “frequency” detecting receiver changes its state based on the frequency of an oscillating pattern it observes and the threshold θ. In our model, all receivers are assumed to be of the same type detecting the same characteristic φ. In retrieving information Y , an information destination collects the state information yj from each and every receiver j ∈ [1, M ]. In other words, an information destination receives an M -bit sequence of receiver states, y = (y1 , y2 , · · · , yM ), from the group of receivers.2 D. Mutual Information In this paper, we are interested in information capacity of molecular communication where the proposed modulation technique is applied in transmitting messages from an information source to an information destination. Information capacity is measured through mutual information between information X that is transmitted by a group of senders and information Y that is received by a group of receivers. Information capacity of molecular communication relates to how many of the patterns that the group of senders (or equivalently by an information source) collectively generates using the proposed modulation technique are collectively recognized as distinct by the group of receivers (or equivalently by an information destination). In order to illustrate how many patterns are recognized as distinct at the group of receivers, see the example in Table I. This table assumes 2 senders (N = 2) and 3 receivers (M = 3). In this example, an information source produces a 2-bit sequence x = (x1 , x2 ) and gives each bit to each of the two senders, each of which in turn transmits information molecules at the rate specified by the given bit. The information destination receives a 3bit sequence y = (y1 , y2 , y3 ) from a group of three receivers, where each bit indicates whether the value of characteristic φ of the pattern that the receiver detects is either above or below the threshold. In this example, for simplicity of explanation, we assume that mapping from x to y is 1-to-1, namely, for each of the four possible distinct 2-bit sequences that a group of senders receives from an information source generates, the receivers collectively detect the “frequency” characteristic this paper, yj is a binary bit representing two possible states of receiver j without loss of generality. It is straightforward to expand yj to represent more than three states. 2 In
TABLE I I NFORMATION TRANSMISSION : AN EXAMPLE (x1 (x0 (x0 (x1 (x1
x
x2 ) x0 ) x1 ) x0 ) x1 )
(y1 (y 0 (y 0 (y 1 (y 1
y y2 y0 y0 y0 y0
y3 ) y1 ) y0 ) y0 ) y0 )
of a pattern that the group of senders generates such that they collectively construct a unique 3-bit sequence from the detected “frequency” characteristic. Namely, in this table, neither errors at the receivers nor noise in the environment are considered in any phases of molecular communication. We further assume that no other combinations of y , except for those shown in the table, are constructed by the receivers. In the example shown in Table I, the three receivers collectively construct three distinct patterns (y 0 , y 0 , y 1 ), (y 0 , y 0 , y 0 ) and (y 1 , y 0 , y 0 ), and therefore, the three distinct patterns are transmitted from the senders to the receivers using the proposed modulation technique, if the senders choose to do so. Note that, when errors occur at the receivers in detecting characteristic φ of the incoming pattern, or when noise is introduced in the environment and distorts characteristic φ of the pattern that information molecules form, the number of patterns that the receivers collectively distinguish becomes smaller than three patterns depending on the degree of errors and the level of noise. As defined in Section III A, X represents information that an information source generates or information that a group of senders transmit, and Y represents information that an information destination receives or information that a group of receivers receive. We assume that each of X and Y is represented by a vector of random variables, where X is defined over a set X = {x0 , x1 }N and Y is defined over a set Y = {y 0 , y 1 }M . Using information theory [23], mutual information between X and Y is given as I(X; Y ) =
pXY (x, y ) log
x∈X y ∈Y
pXY (x, y ) , pX (x)pY (y )
(3)
where pXY (x, y ) = Pr[X = x, Y = y ], pX (x) = Pr[X = x] and pY (y ) = Pr[Y = y ]. The information capacity C of molecular communication is then given as the maximum value of mutual information: C = max {I(X; Y )}, pX ( x)
(4)
where the maximum value is taken over all possible probabilities pX (x). The maximum number of patterns that can be transmitted through the proposed modulation technique is thus 2C . E. Information Propagation In the proposed modulation technique, sender i transmits information molecules at a constant rate of xi ∈ {x0 , x1 }. The influx J of information molecules to the environment,
due to a group of senders transmitting information molecules, is obtained by aggregating the rate at which each sender transmits the information molecules over all senders and is given by the following.
J=
N
xi δ(r − si ),
(5)
i=1
where r is the location and δ(·) is the Dirac delta function. In the modulation technique proposed in this paper, only one type of molecule (i.e., information molecules) propagates and the other type of molecule (i.e., environmental molecules) does not propagate, unlike a general reaction-diffusion model in Section II, where two types of molecule, U and V, propagate. Note that, even when only one type of molecules propagate, an oscillating and propagating pattern is formed [24]. Assuming that U is the information molecules that propagate and that V is the environmental molecules that do not propagate in (1) and (2), and knowing that DV Δv (the rate of diffusion of V) is zero, we rewrite (1) and (2) as ∂u = f (u, v) + DU Δu + J, (6) ∂t ∂v = g(u, v). (7) ∂t The above set of equations dictates the characteristics of oscillating and propagating pattern that a group of senders generate in the environment through transmitting information molecules. IV. N UMERICAL E XPERIMENTS In the numerical experiments described in this section, we use the Ca2+ signaling system to generate oscillating and propagating patterns for molecular communication [15], [25], [26] and examine the information capacity of molecular communication where the proposed modulation technique is applied. A. Configurations for Numerical Experiments We assume a group of 201×201 cells arranged in a 2dimensional grid configuration as the environment of molecular communication (see Fig. 1). Each cell takes a rectangular shape with each edge length of 1 (unit distance). The location of each cell is denoted by the grid coordinate of cell’s center, (i, j), with the origin of the coordinate (0, 0) at the center of the grid. We also assume that there are either one or two (N = 1 or 2) senders (sender cells) and four or less (M ≤ 4) receivers (receiver cells) in the environment. When there is only one sender, it is located at s1 = (0, 0) (i.e., at the center of the grid). When there are two senders, the second sender is added at s2 = (0, 20). Locations of four possible receivers are at r1 = (0, 0), r2 = (5, 0), r3 = (15, 0), r4 = (20, 0), respectively. Note that sender i = 1 and receiver j = 1 are collocated at (0, 0). Each cell in the environment is capable of receiving Ca2+ from its neighboring cells and releasing Ca2+ from its internal Ca2+ store in response to Ca2+ from its neighboring cells,
Fig. 1. Molecular communication environment assumed in numerical experiments.
resulting in oscillating Ca2+ concentration in its cytosol. Each cell is also capable of transmitting Ca2+ to its neighboring cells. Here we assume Ca2+ in the cytosol of each cell as information molecules and Ca2+ in its store as environmental molecules. Using the model of Ca2+ oscillation and propagation in [27], [28], we write the rates of change in the Ca2+ concentration c(i, j) (concentration of information molecules) in cell at (i, j) and the Ca2+ concentration in the store cs (i, j) (concentration of environmental molecules) in cell at (i, j) as follows: dc(i, j) dt
dcs (i, j) dt
= v0 − v2 + v3 + kf cs (i, j) − kc c(i, j) + P {c(i + 1, j) + c(i − 1, j) + c(i, j + 1) + c(i, j − 1) − 4c(i, j))} + J, = v2 − v3 − kf cs (i, j),
(8) (9)
where v0 is the rate of Ca2+ influx from the extracellular environment to the cytosol, v2 is the rate of Ca2+ uptake in to the Ca2+ store in cell (i, j), v3 is the rate of Ca2+ release from the Ca2+ store in cell (i, j), kf cs (i, j) is the rate of Ca2+ leak from the Ca2+ store to the cytosol in cell (i, j), kc c(i, j) is the pumping rate of Ca2+ to remove Ca2+ from the cytosol in cell (i, j) to the extracellular environment, P is the degree of cell-to-cell coupling, and J is the Ca2+ influx due to the release of Ca2+ from a sender (i.e., J = x0 or x1 if a sender is at (i, j); otherwise, J = 0). Note that (8) and (9) are discretized representations of (6) and (7) over space, as cells in our numerical examples are discrete units in space. Note also that (8) and (9) are obtained from (6) and (7) by considering Ca2+ propagating from cell to cell as the information molecules and Ca2+ stored in cell’s cytosol as environmental molecules; the first five terms in the right hand side of (8) correspond to the reaction term f in (6), the next term corresponds to the diffusion term in (6), and the last term corresponds to J in (8); the three terms in the right hand side of (9) correspond to the reaction term g in (7).
B. Calculation of Mutual Information In numerical experiments, we compute the mutual information based on (3) under the following assumptions: • The sender (when there is only one sender) or each sender (when there are two senders) transmits Ca2+ (i.e., information molecules) at the rate of either x0 or x1 with equal probability. • Each receiver is sensitive to the frequency of oscillation of the pattern that the Ca2+ concentration forms in its cytosol. Receiver j sets its state yj with the probability of 1−e where e is the error probability; i.e., if the frequency is below (above) threshold θ = 1.8, receiver j correctly sets its state to yj = y 0 (y 1 ) with probability 1 − e and incorrectly sets its state to yj = y 1 (y 0 ) with probability e. Note that the error represents environmental noise that disturbs the frequency at each receiver location. In numerical experiments, a sender or senders start transmitting Ca2+ at time t = 0 and continuously transmit Ca2+ over a given period of time T . We then compute c(i, j) over this time period T . We also count the number n of spikes observed at each cell in the environment over the time period T and determine the frequency of oscillation at each receiver’s location as Tn . At time t = T , each receiver determines its state y ∈ {y 0 , y 1 } based on the frequency and threshold θ = 1.8. In our numerical experiments, we arbitrary chose the time period as T = 20 units of time. To compute mutual information between X and Y given in (3), we numerically integrate (8) and (9) for given x = (x1 , x2 ), obtain frequencies at all receiver locations, and determine y = (y1 , y2 , y3 , y4 ). C. Numerical Results: Oscillating and Propagating Patterns of Ca2+ Concentration In Fig. 2, there is only one sender at (0, 0), transmitting Ca2+ at the rate of x0 = 0.1 (μM/s) or x1 = 0.2 (μM/s).
Fig. 2.
Calcium concentration c at receiver location r1 .
Based on the model of Ca2+ oscillation [27], we write v1 and v2 in (8) and (9) as follows c(i, j)2 , (10) v2 = V M 2 2 K2 + c(i, j)2 cp (i, j)2 c(i, j)4 v3 = V M 3 2 , (11) 4 2 KR + cp (i, j) KA + c(i, j)4 where VM 1 , VM 2 , K1 , KR and KA are parameters. The following parameter values are from [27] and used in our numerical experiments: v0 = 1 (μM/s), kf = 1 (1/s), VM 2 = 65 (μM/s), VM 3 = 500 (μM/s), K2 = 1 (μM), KR = 2 (μM), and KA = 0.9 (μM). kc = 3.55 (1/s), a different value of kz from [27], is used in our numerical experiments to produce an oscillating and propagating pattern. The parameters we introduced in our model are x0 , x1 and P , and their values are chosen to produce an oscillating and propagating pattern: x0 = 0.1 (μM/s), x1 = 0.2 (μM/s), P = 0.5 (1/s). Initial conditions are arbitrarily chosen and are c(i, j) = 1.6 (μM) and cp (i, j) = 0.2 (μM) at time t = 0 (s).
Fig. 3.
Calcium concentration c at receiver locations r1 through r4 .
Fig. 2 shows how the Ca2+ concentration c at cell (0, 0) (y-axis) oscillates over time (x-axis). Namely, this figure shows the oscillating pattern of c at the sender that may propagate through the environment. As shown in the figure, the oscillation frequency of the Ca2+ concentration c observed at cell (0, 0) in the case of x0 is smaller than that in the case of x1 , verifying that the rate of Ca2+ transmission at a sender impacts the characteristic of a pattern generated. Fig. 3 shows how the Ca2+ concentration c changes over time at each of the four receivers located at r1 , r2 , r3 , r4 , when there is only one sender at (0, 0), transmitting Ca2+ at the rate of x0 . This figure shows that Ca2+ concentration oscillates at each receiver and that this oscillating pattern, starting as the pattern shown in Fig. 2, propagates from a receiver to another receiver (from receivers 1 to 2, 3 and to 4). This figure also shows that receivers at different locations may experience different oscillation frequencies, as the number of spikes per unit time is different at different receivers. D. Numerical Results: Mutual Information 1) Single Sender Case: Fig. 4 shows the mutual information obtained in (3) as a function of error probability e for different number M of receivers. Fig. 4 assumes that there is only one sender at s1 (i.e., at (0, 0)) and that the
Fig. 4.
Mutual information I vs. error probability e (single sender case).
information source uses the single sender to generate a 1bit of information, x = (x1 ). This figure shows that, when M = 1 (when there is only one receiver at r1 (i.e., at (0, 0))), mutual information becomes 0 (i.e., no information is transmitted from the sender to the receiver). This is because each of the two rates at which the sender transmitted Ca2+ (i.e., x0 = 0.1 and x1 = 0.2) generated a pattern whose frequency is above the receiver’s threshold, and, therefore, the receiver was not able to distinguish the two patterns generated by x0 and x1 . This figure also shows that, as M increases from 1 (one receiver at r1 ) to 4 (four receivers at r1 , r2 , r3 , r4 ), the mutual information increases for a given value of error probability e. Further, this figure shows that the mutual information decreases for a given value of M , as the error probability e increases. 2) Two Sender Case: Fig. 5 shows the mutual information as a function of error probability e for different number M of receivers. Fig. 5 assumes that there are two senders at s1 (i.e., at (0, 0)) and s2 (i.e., at (0, 20)) and that the information source uses them to generate 2-bits of information, x = (x1 , x2 ). Similarly to Fig. 4, Fig. 5 shows that no information is transmitted from the senders to the receiver when M = 1. This is because each of the four possible rate combinations at the sender, (x1 , x2 ) ∈ {(0.1, 0.1), (0.1, 0.2), (0.2, 0.1), (0.2, 0.2)}, generated a pattern whose frequency is above the receiver’s threshold, and therefore, the receiver was not able to distinguish these four cases. It also shows that the mutual information increases as M increases for a given value of error probability e and that it decreases for a given value of M , as the error probability e increases. Fig. 5 shows the mutual information is higher than that shown in Fig. 4, for a given value of error probability e and M . This means that the two sender case generates more patterns that are distinguishable by the receivers than the single sender case.
Fig. 5.
cytosol of a cell forms. Figs. 6 and 7 show the frequency and amplitude, respectively, at each receiver as a function of distance (measured in the number of cells) from the sender. These figures show results for both the proposed modulation technique where Ca2+ diffuse and react in the environment and an existing technique where Ca2+ only diffuse in the environment. Results for an existing technique in these figures are obtained using (8) without v2 and v3 (i.e., without the reaction terms responsible for generating oscillating patterns). Figs. 6 and 7 show that an oscillating and propagating pattern that the proposed modulation technique generates propagates over a distance longer than 100 cells with decay in its frequency (as shown in Fig. 6) and without decay in its amplitude (as shown in Fig. 7). On the contrary, an existing modulation technique does not generate an oscillating pattern (as shown in Fig. 6) and decays significantly in its amplitude (concentration) as it propagates in the environment (as shown in Fig. 7). Fig. 7 shows that the Ca2+ concentration quickly disperses completely after propagating 10 cells and reaches the base amplitude, i.e., the Ca2+ concentration formed in cytosol of a cell when the sender does not transmit Ca2+ . By comparing the results for the proposed modulation technique and those for an existing technique in Figs. 6 and 7, we may conclude the following. •
•
E. Numerical Results: Comparison with Existing Techniques Figs. 6 and 7 assume that there is a single sender at s1 (i.e., at (0, 0)), transmitting Ca2+ at the rate of x1 = 0.1, and that, unlike the previous figures where the maximum of 4 receivers are assumed, each cell is a receiver and detects, at its location, the frequency and amplitude characteristics of an oscillating and propagating pattern that the concentration of Ca2+ in
Mutual information I vs. error probability e (two sender case).
•
The proposed modulation technique enables longer communication distance than an existing modulation technique. Frequency detecting receivers may be able to detect patterns generated by the proposed modulate technique but may not be able to detect patterns generated by an existing modulation technique; the proposed modulate technique achieves higher information capacity than an existing modulation technique, when information is modulated using the frequency characteristic of an oscillating and propagating pattern. Amplitude detecting receivers for the proposed modulation technique do not need to be as sensitive as those for an existing modulation technique, because the proposed modulation technique achieves higher amplitude of Ca2+ concentration.
Fig. 6.
Frequency as a function of distance
Fig. 7.
Amplitude as a function of distance
V. C ONCLUSION This paper proposed a new modulation technique that uses spatio-temporal patterns that the concentration of propagating information molecules form in the molecular communication environment. Future research issues include developing coding and encoding mechanisms, refining modulation and demodulation techniques, developing techniques for transmitting a sequence of messages, and identifying the impact of noise on the information capacity of molecular communication through pattern formation. ACKNOWLEDGMENT This work was supported in part by the Japan Society for the Promotion of Science (JSPS) through the Grant-in-Aid for Scientific Research (No. 25240011). R EFERENCES [1] T. Suda, M. Moore, T. Nakano, R. Egashira, and A. Enomoto, “Exploratory research on molecular communication between nanomachines,” in Genetic and Evolutionary Computation Conference 2005 (GECCO 2005), 2005. [2] T. Nakano, A. Eckford, and T. Haraguchi, Molecular Communication. Cambridge University Press, 2013. [3] T. Nakano, T. Suda, Y. Okaie, M. J. Moore, and A. V. Vasilakos, “Molecular communication among biological nanomachines: A layered architecture and research issues,” IEEE Transactions on Nanobioscience, 2014. [4] A. W. Eckford, “Achievable information rates for molecular communication with distinct molecules,” in Proc. Workshop on Computing and Communications from Biological Systems: Theory and Applications, 2007, pp. 313–315.
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