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1
Externally Controllable Molecular Communication
Tadashi Nakano∗,Member, IEEE, Shouhei Kobayashi, Tatsuya Suda, Fellow, IEEE,
Yutaka Okaie, Member, IEEE, Yasushi Hiraoka, and Tokuko Haraguchi
Abstract—In molecular communication, a group of biological
nanomachines communicates through exchanging molecules and
collectively performs application dependent tasks. An open re-
search issue in molecular communication is to establish interfaces
to interconnect the molecular communication environment (e.g.,
inside the human body) and its external environment (e.g., outside
the human body). Such interfaces allow conventional devices in
the external environment to control the location and timing of
molecular communication processes in the molecular commu-
nication environment and expand the capability of molecular
communication.
In this paper, we first describe an architecture of exter-
nally controllable molecular communication and introduce two
types of interfaces for biological nanomachines; bio-nanomachine
to bio-nanomachine interfaces (BNIs) for bio-nanomachines to
interact with other biological nanomachines in the molecular
communication environment, and inmessaging and outmessaging
interfaces (IMIs and OMIs) for bio-nanomachines to interact with
devices in the external environment. We then describe a proof-
of-concept design and wet laboratory implementation of the IMI
and OMI, using biological cells. We further demonstrate, through
mathematical modeling and numerical experiments, how an
architecture of externally controllable molecular communication
with BNIs and IMIs/OMIs may apply to pattern formation, a
promising nanomedical application of molecular communication.
Index Terms—Molecular communication, bio-nanomachine,
interface design, external control, pattern formation
I. INTRODUCTION
In molecular communication, a group of biological nanoma-
chines communicates through exchanging molecules and col-
lectively performs application dependent tasks [1], [2], [3], [4],
[5]. Biological nanomachines, referred to as bio-nanomachines
in the rest of the paper, are nano-to-micro scale devices
composed of biological materials and capable of interacting
with biological molecules. Examples of bio-nanomachines in-
clude nanoscale molecular complexes such as DNA molecules
designed to perform logical operations [6] and motor proteins
reconstructed to transport molecules in an engineered environ-
ment [7]. Examples of bio-nanomachines also include micro-
Manuscript received November 15, 2013. 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). Asterisk indicates
corresponding author.
T. Nakano and Y. Hiraoka are with the Graduate School of Frontier
Biosciences, Osaka University, 1-3 Yamadaoka, Suita 565-0871, Japan (email:
{tadasi.nakano, hiraoka}@fbs.osaka-u.ac.jp).
S. Kobayashi and T. Haraguchi are with the Advanced ICT Research Insti-
tute, National Institute of Information and Communications Technology, 588-
2 Iwaoka, Iwaoka-cho, Nishi-ku, Kobe 651-2492, Japan (email: {skobayashi,
tokuko}@nict.go.jp).
T. Suda is with the University Netgroup Inc., P.O.Box 1288, Fallbrook, CA
92088, USA (email: tatsuyasuda@gmail.com).
Y. Okaie is with the Graduate School of Information Science and Tech-
nology, Osaka University, 1-5 Yamadaoka, Suita 565-0871, Japan (email:
okaie.yutaka@ist.osaka-u.ac.jp).
scale, genetically engineered cells that are capable of simple
tasks such as sensing conditions of the environment [8].
An open research issue in molecular communication is to
establish interfaces to interconnect the molecular commu-
nication environment (typically, a nano-to-micro scale and
aqueous environment such as inside the human body) and the
environment external to the molecular communication envi-
ronment (typically, a macro-to-larger scale and non-aqueous
environment such as on or outside the human body) [9].
Such interfaces allow conventional devices in the external
environment to control the location and timing of molecular
communication processes in the molecular communication
environment and expand the capability of molecular communi-
cation. Establishing such interfaces is also a first step toward
developing fully autonomous molecular communication that
does not require external control [6], [10].
An application that may benefit from such interfaces is
nanomedicine [11]; a human physician (i.e., an external entity)
may use the interfaces to control bio-nanomahcines to release
molecules at a desired location and timing. For instance, if
externally controllable molecular communication is applied
to tissue regeneration [12], [13], an external device may
allow a human physician to control a series of molecular
communication processes that are required to occur in a certain
sequence for desired tissue formation to occur [14].
Another application that may benefit from such interfaces
is the dermal display, an envisioned nanotechnology appli-
cation enabled from a population of bio-nanomachines [11]
(Fig. 1). In this application, a large number of display bio-
nanomachines (e.g., three billion display bio-nanomachines)
are embedded 200 – 300 µm below the human skin surface to
provide a small-size (e.g., 6 cm ×5 cm) interactive display.
These display bio-nanomachines respond to the tapping of
a finger (an external and mechanical signal), communicate
with sensor bio-nanomachines embedded in the human body
gathering information about the molecular communication en-
vironment, and emit visible photons to display the information
over the human skin.
The remainder of this paper is organized as follows. Sec-
tion II describes an architecture of externally controllable
molecular communication. Section III describes our initial
design and wet laboratory experiments of the architecture of
externally controllable molecular communication. Section IV
describes mathematical modeling and numerical experiments
to demonstrate how an architecture of externally controllable
molecular communication may apply to pattern formation.
Finally, Section V summarizes future directions and concludes
this paper.
2
Fig$2$
External$device$
Bio3nanomachine$
(Sender)$
Bio3nanomachine$
(Receiver)$
Molecular$communica<on$environment$
Inmessaging$
interface$(IMI)$
Outmessaging$
interface$(OMI)$
External$environment$
Bio3nanomachine$to$$
bio3nanomachine$interface$
(BNI)$
Molecules
Molecular$communica<on$
Fig. 2. An architecture of externally controllable molecular communication
Fig. 1. Dermal display, an envisioned nanotechnology application [11].
c
2005 Gina Miller (www.nanogirl.com), animation, and Robert A. Freitas
Jr. (www.rfreitas.com), design. All Rights Reserved.
II. ANARCHITECTURE OF EX TE RNA LLY CONTROL LA BL E
MOL EC UL AR COMMUNICATION
An architecture of externally controllable molecular com-
munication consists of groups of bio-nanomachines in an
aqueous environment, referred to as a molecular communi-
cation environment, and an external device located outside
the molecular communication environment, referred to as an
external environment. Bio-nanomachines may implement two
types of interfaces: bio-nanomachine to bio-nanomachine in-
terfaces (BNIs) and inmessaging and outmessaging interfaces
(IMIs and OMIs), as shown in Fig. 2. Bio-nanomachines use
BNIs to interact with each other in the molecular communica-
tion environment. They also use IMIs to receive inmessages,
messages generated by the external device, and OMIs to
generate outmessages, messages for an external device to
receive. Note that not all bio-nanomachines in the molecular
communication environment implement IMIs and OMIs. The
following describes key architectural components.
A. External Devices
An external device is a microscale or larger scale conven-
tional device that exists in an environment external to the
molecular communication environment. It may be orders of
magnitude larger than bio-nanomachines.
An external device may be made from materials that are not
compatible with the molecular communication environment
and also relies on traditional means of communication (such
as electrical and optical signals) that is not directly compatible
with molecular communication.1An external device is capable
of generating inmessages to and receiving outmessages from
bio-nanomachines that reside in the molecular communication
environment.
B. Bio-nanomachines
A bio-nanomachine is defined based on three criteria:
material, size and functionality [4], [5], [16]. First, a bio-
nanomachine is composed of biological materials (e.g., pro-
teins, nucleic acids, lipids, biological cells) with or without
non-biological materials (e.g., magnetic particles and gold
nanorods). Second, the size of a bio-nanomachine ranges
from the size of a macromolecule to that of a biological
cell. Note that our definition of bio-nanomachines include
biological cells, entities much larger than what the term “nano”
typically refers to (i.e., dimensions of 1–100 nm).2Third, a
1Note that an “external” device is a device that operates in an environ-
ment external to the molecular communication environment and includes a
device that is placed in an environment that can be used as the molecular
communication environment such as “inside” the human body. For instance,
implantable medical devices [15] rely on traditional means of communication
and are considered external devices in this paper.
2We consider biological cells as bio-nanomachines, because they are much
smaller than typical external devices [17] and rely on means of communication
that is directly compatible with molecular communication, namely molecules
used by bio-nanomachines.
3
bio-nanomachine implements a set of simple functionalities
to manipulate molecules, such as detecting, modifying and
releasing molecules.
Examples of bio-nanomachines include:
•DNA sequences capable of detecting a complementary or
partially complementary DNA sequence in the environ-
ment and cutting and releasing a segment of the DNA
sequence using enzymes [6],
•Protein motors capable of binding to a specific type of
molecules, moving along protein filaments carrying the
molecules, and unbinding the molecules [7],
•Liposomes capable of storing and releasing certain types
of molecules [18],
•Single celled organisms and genetically engineered cells
capable of actively moving in the environment [19] or
detecting a range of concentration of a certain type of
molecules [20], and
•Biological cells surface-coated with non-biological mate-
rials (e.g., magnetic particles and gold nanorods) to per-
form non-cell-native functions (e.g., absorbing mercury)
[21].
C. Bio-nanomachine to Bio-nanomachine Interfaces (BNIs)
A bio-nanomachine implements a BNI to exchange
molecules and communicate with other bio-nanomachines
in the molecular communication environment. A bio-
nanomachine with a BNI may act as a sender of molecular
communication and transmits molecules through the BNI
directly into another bio-nanomachine or into the molecular
communication environment. A bio-nanomachine with a BNI
may also act as a receiver of molecular communication; it ei-
ther receives molecules directly from another bio-nanomachine
through the BNI or captures molecules in the environment
through the BNI and biochemically reacts to the captured
molecules.
Materials and mechanisms found in biological systems
may be useful in developing BNIs for bio-nanomachines. For
instance,
•Exocytosis and endocytosis through which biological
cells direct its internal molecules into the extracellular
space and uptake molecules outside the cells through cell
membranes,
•Receptor-ligand pairs where one type of biological cells
releases ligands, and another type of biological cells binds
to the ligands using its receptors [22], [23],
•Gap junction channels that directly interconnect the cy-
tosolic environments of two biological cells, allowing
small molecules to diffuse between the two cells [24],
and
•Vesicles budding from one organelle and fusing with
another organelle, transporting molecules between the
two organelles within a biological cell [25], [26].
Note that in the above examples, biological cells in the first
three examples and organelles in the last example may be
considered bio-nanomachines.
D. Inmessaging and Outmessaging Interfaces (IMIs and
OMIs)
A bio-nanomachine implements an IMI and an OMI to
interact with an external device. A bio-nanomachine may
receive inmessages from the external device through the IMI.
A bio-nanomachine may transmit outmessages to the external
device through the OMI.
An external device is a conventional device that relies on
traditional means of communication (such as electrical and
optical signals) that are not directly compatible with means
of communication used in molecular communication, namely
molecules (or chemical signals) used by bio-nanomachines.
The IMI must convert conventional signals used by external
devices into chemical signals that bio-nanomachines biochem-
ically react to, while the OMI must convert chemical signals
generated by bio-nanomachines to externally detectable (con-
ventional) signals.
These functionalities of the IMI and OMI may be im-
plemented using either naturally occurring biomaterials or
artificially synthesized bio and non-biomaterials and integrated
into bio-nanomachines. Examples of such materials include the
following.
•Photosensitive materials as IMIs to convert optical sig-
nals from external devices to chemical signals for bio-
nanomachines: In response to light at a specific wave-
length emitted from an external laser source, for instance,
photoactivatable proteins become active (or inactive)
through conformational changes to control biochemical
processes in the environment they exist [27], caged-
compounds release encapsulated molecules through bond
breaking [28], and gold nanorods generate heat to initiate
temperature sensitive biochemical processes in their sur-
roundings [29]. Bio-nanomachines integrated with these
materials may thus respond to optical signals from an
external device.
•Temperature-sensitive materials as IMIs to convert ther-
mal signals from external devices to chemical signals
for bio-nanomachines: In response to an increased tem-
perature caused by an external heat source, for in-
stance, temperature-sensitive liposomes [30], [31] and
dendrimers [32] change their conformation and re-
lease molecules they store inside their structures. Bio-
nanomachines integrated with these materials may bio-
chemically react to the released molecules and thus
respond to thermal signals from an external device.
•Magnetic materials as IMIs to convert magnetic sig-
nals from external devices to chemical signals for bio-
nanomachines: In response to a radio-frequency (RF)
magnetic field generated by an external RF signal gen-
erator, for instance, gold nanocrystals attached to DNA
molecules [33] induce hybridization (or dehybridiza-
tion) process of the DNA molecules, generating double-
stranded (or single-stranded) DNA molecules. Bio-
nanomachines integrated with these materials may re-
act to the generated double-stranded (or single-stranded)
DNA molecules and thus respond to magnetic signals
from an external device.
4
•Luminescent materials as OMIs to convert chemical
signals from bio-nanomachines to optical signals for
external devices: In response to chemical signals from
bio-nanomachines, bioluminescent molecules such as lu-
ciferases catalyze chemical reactions that consume chem-
ical energy (e.g., ATP) and emit light photons [34],
which in turn are detected by an external device. Also,
fluorescent molecules such as rhodmamine derivatives
emit fluorescence at a specific wavelength under cer-
tain biochemical conditions when excited to a higher
energy level (for instance, in response to excitation light
from an external device). Chemical signals from bio-
nanomachines may change the biochemical conditions to
cause fluorescent molecules to emit fluorescence in re-
sponse to excitation light, which in turn is detected by an
external device (e.g., through fluorescence microscopy).
Bio-nanomachines integrated with these materials thus
convert chemical signals that they use to optical signals
detectable by an external device.
III. ENGINEERING INT ER FACE S FO R BIOLOGICAL CEL LS
Biological cells are promising materials for engineering
bio-nanomachines. Biological cells reside in a nano-to-micro
scale and aqueous environment such as the cellular environ-
ment in a human body and are highly compatible with the
molecular communication environment. Biological cells may
be deployed in the molecular communication environment
with little concern regarding safety in key molecular commu-
nication applications such as nanomedical applications (e.g.,
drug delivery and tissue regeneration) [19]. Biological cells are
autonomous entities with built-in functionalities such as ac-
quiring and expending energy to perform their functionalities,
moving around in the environment, and storing and processing
molecules in the environment. Biological cells may provide
means to control biochemical conditions in the molecular
communication environment (e.g., concentration of a given
type of molecules) for a wide variety of applications.
In this section, we focus on biological cells as bio-
nanomachines and present how inmessaging and outmessaging
interfaces (IMIs and OMIs) may be implemented on biological
cells. (Biological cells are hereafter simply referred to as cells.)
We first discuss previous efforts based on genetic engineering
to implement bio-nanomachine to bio-nanomachine interfaces
(BNIs), inmessaging interfaces (IMIs) and outmessaging in-
terfaces (OMIs) on cells. We then present our approach of
embedding artificially synthesized materials (ARTs) in cells
and the wet laboratory experiments to implement IMIs and
OMIs on cells. Although our wet laboratory experiments are
yet to allow an external device to control molecular communi-
cation processes through IMIs and OMIs, our efforts present an
important first step towards fully implementing the architecture
of externally controllable molecular communication described
in Section II.
A. Genetic Engineering Approaches
Existing studies demonstrate that genetic engineering ap-
plies to engineering of cells with BNIs [24], [35], [36] and
also cells with IMIs [37] and OMIs [34].
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Fig. 3. A genetic engineering approach to implement gap junction-based
BNIs. (A) A schematic showing formation of gap junction channels between
two adjacent cells. (B) Green Fluorescence Protein (GFP)-labeled connexins
localized at the boundary of two adjacent cells as indicated by arrows. (C)
Propagation of molecules over time between two adjacent cells (1 and 2)
through gap junction channels. Fluorescent molecules were introduced prior to
experiments and found in both cells 1 and 2 (at 0 min). Cell 2 was then photo-
bleached, causing cell 2 to lose the fluorescent molecules (in 1 min). Cell 2
gradually recovered fluorescence (at 10 min), indicating that the fluorescent
molecules diffuse from cell 1 to cell 2. (B) and (C) are obtained from wet
laboratory experiments. Scale bar, 20 µm.
As discussed in Section II-C, a cell may implement a BNI,
for instance, using gap junction channels. A cell may release
and capture molecules directly from another cell through a
direct connection (gap junction channels) with another cell,
as shown in Fig. 3 (A). Gap junction channels directly inter-
connect the cytosols of two biological cells and allow small
molecules to diffuse between the two cells [24]. To implement
such BNIs on cells, DNA sequences encoding channel-forming
proteins (i.e., connexins [38]) may be inserted into cells
[24]. Cells then synthesize connexins through gene expression,
assemble them into hemichannels, and transport the hemichan-
nels to their plasma membranes. Two hemichannels from two
adjacent cells, by docking at their plasma membranes, form
protein channels called gap junction channels, interconnecting
the cytosols of the two adjacent cells. Fig. 3 (B) shows
connexins localized at the boundary of two adjacent cells,
and Fig. 3 (C) shows that gap junctionally connected cells
act as senders and receivers of molecular communication
and propagate molecules through gap junction channels; gap
junction channels implement BNIs between adjacent cells.
As also discussed in Section II-C, a cell may implement
a BNI, for instance, using ligand-receptor pairs. A cell re-
leases molecules of a specific structure (e.g., ligands) into the
environment, and another cell may capture such molecules
in the environment through using receptors that bind to the
molecules. To implement such BNIs on cells, DNA sequences
encoding molecules that are membrane permeable and dif-
fusive (e.g., N-acyl homoserine lactones or AHL molecules)
5
may be inserted into cells [35], [36]. Cells then synthesize the
molecules that DNA sequences encode, directs the synthesized
molecules out of the cell membrane and into the extra-
cellular environment, and synthesized molecules propagate
in the environment. Cells thus act as senders of molecular
communication. Similarly, DNA sequences encoding receptor
proteins may be inserted into cells. Cells then synthesize
receptors, and synthesized receptors bind to molecules of a
specific structure in the environment. Cells thus function as
receivers of molecular communication.
Furthermore, genetic engineering applies to engineering of
cells with IMIs and OMIs using some materials discussed in
Section II-D. For instance, cells may be genetically engineered
to synthesize photoactivatable GTPases to implement an IMI
[37]. The photoactivatable GTPases synthesized in a cell
become active in response to light from an external light
source, regulate cytoskeltal behaviors of the cell and control
the direction of cell movement. Cells may also be genetically
engineered to synthesize florescent molecules to implement an
OMI [34]. The florescent molecules synthesized in cells emit
fluorescence depending on conditions of the cells in response
to excitation light, functioning as an OMI.
B. The ART-based Approach
In genetic engineering, DNA sequences encoding biomate-
rials (e.g., proteins) are inserted into a cell, and the cell synthe-
sizes encoded biomaterials through gene expression and uses
them as interfaces. As an alternative to genetic engineering,
our approach embeds materials artificially synthesized outside
a cell, i.e., artificially synthesized materials (ARTs), into the
cytosol of a cell and uses the embedded ARTs as interfaces.
The ART-based approach has the following key features.
•ARTs are composed of materials artificially synthesized
outside of a cell, and thus, choice of materials to
compose ARTs is wide. Materials for composing ARTs
are diverse and include artificially synthesized materi-
als such as photosensitive materials (e.g., photosensi-
tive caged-compounds and gold nanorods), temperature-
sensitive materials (e.g., temperature-sensitive liposomes
and dentrimers), magnetic materials (e.g., gold nanocrys-
tals), and luminescent materials (e.g., rhodmamine deriva-
tives). The ART-based approach may thus provide a wide
range of options to implement different types of interfaces
to support conventional signals used by an external device
(e.g., electrical, optical and magnetic signals). As genetic
engineering is limited in types of biomaterials for creating
interfaces only to those that can be encoded onto and
decoded from DNA sequences, supporting different types
of conventional signals is more complex with genetic
engineering.
•IMIs and OMIs implemented with ARTs are more pre-
dictable in responding to inmessages and in generating
outmessages, compared to IMIs and OMIs implemented
with genetic engineering. This is because gene expres-
sion levels of genetically engineered cells and, therefore,
functionalities of synthesized biomaterials to respond to
inmessages and to generate outmessages are often not
predictable.
•ARTs may remain in cells temporarily. ART-embedded
cells divide as the original cells (i.e., cells before ARTs
are embedded) do. When an ART-embedded cell divides,
a daughter cell retains the characteristics of the original
cell, while it may no longer contain an ART. This tempo-
rary nature of ART-embedded cells may be advantageous
in some applications. In tissue regeneration, for instance,
cells may be embedded with ARTs to allow an external
device to control the formation of a certain structural
pattern (see Section IV). Cells then may undergo cell
division, resulting in a desired structural pattern of origi-
nal cells with no ARTs. This temporary nature of cells is
not likely with genetic engineering, as the effect becomes
permanent once a DNA sequence is integrated into the
genome of a cell.
C. Wet Laboratory Experiments
Wet laboratory experiments in this paper focus on the first
step toward the engineering of cells with IMIs and OMIs using
the ART-based approach; namely, they focus on introducing
ARTs into the cytosols of living cells and examining, through
fluorescence microscopy, the feasibility of using ARTs as IMIs
and OMIs.
Fig. 4 (A) shows a schematic of an ART used in the
wet laboratory experiments. The ART consists of a body and
effectors. The body is to implement an IMI, and the effectors
are to collectively implement an OMI.3In the wet laboratory
experiments, an ART is composed of a polystyrene bead and
pHrodo molecules. A polystyrene bead, a sphere of a few
micrometers in diameter (i.e., a non-biological material), is
used as the body of an ART. The body plays no functional
role in the wet laboratory experiments discussed in this paper;
it is reserved for implementing an IMI (e.g., functionalities
such as releasing molecules or absorbing molecules in re-
sponse to inmessages) in future wet laboratory experiments.
The pHrodo molecules are attached to the body and used
as the effectors that collectively function as an OMI. The
pHrodo molecules are fluorogenic dyes that are almost non-
fluorescent under neutral pH conditions and only become
highly fluorescent under lower pH conditions. The pHrodo
molecules function as pH indicators, allowing an external
device to detect acidification or neutralization in cells by
measuring the intensity of fluorescence (i.e., an outmessage)
emitted by the pHrodo molecules upon illumination on the
pHrodo molecules at a specific wavelength (560 nm). Further,
to promote internalization of ARTs through endocytosis in
cells, the ART is coated with lipid molecules.
The ART-based approach exploits endocytosis and its asso-
ciated endocytic membrane transport pathway [39] to deliver
ARTs in a cell. Fig. 4 (B) illustrates the process of delivering
an ART into a cell. A cell first absorbs an ART through the
plasma membrane via endocytosis. Once the ART is attached
to a cell, it activates the endocytic membrane transport path-
way; the absorbed ART is entrapped in an acidic endosome,
3This functional division of the ART body for an IMI and the ART effectors
for an OMI is based on our current interface designs. We acknowledge that
this functional division is yet to be proven effective in interface designs.
6
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Fig. 4. The ART-based approach to implement IMIs and OMIs. Delivery of ARTs into the cytosols of living cells: (A) design of an ART, (B) delivery of an
ART into the cytosol of a living cell, (C) ARTs within living cells (cell membranes are indicated by dotted circles), and (D) time-lapse images of a single
ART indicated by an arrow in (C). The numbers on the top of each image in (D) show the time in minutes. In (C) and (D), red signals indicate that ARTs
are localized in acidic endosomes, and green signals indicate that ARTs are in autophagosomes. Scale bar, 20 µm.
the endosome then breaks, and an autophagosome is formed.
The ART absorbed into a cell is located in the autophagosome.
In the wet laboratory experiments, a body of relatively large
size was used. This is because a body of large size presents
potential to implement complex functionalities such as storing
a large number of molecules inside the body and absorbing a
large number of cytosolic molecules into or on the surface
of the body. The wet laboratory experiments successfully
delivered a polystyrene bead of up to 3 µm (in diameter)
into a cell of approximately 20 µm (in length). Other details
of the wet laboratory experiments such as types of cells,
treatment of cells, cell culture techniques, preparation of beads,
methods to confirm delivery of ARTs into a cell, live cell
imaging techniques, and microscopy used in the wet laboratory
experiments are described in [40].
Wet laboratory experiments demonstrated that the ARTs
are delivered into living cells via endocytosis. The processes
described in Fig. 4 (B) were successfully observed through
fluorescence microscopy. Figs. 4 (C) and (D) show images ob-
tained from fluorescence microscopy. Fig. 4 (C) shows that an
ART was successfully incorporated into a living cell through
endocytosis and entrapped in acidic endosomes (indicated by
the red markers in Fig. 4 (C)). A series of images in Fig. 4 (D)
shows that the red markers at 2.5 minutes turned to no markers
at 5 minutes, i.e., endosomes containing ARTs indicated by the
red markers (at 2.5 minutes) broke to expose the ART to the
cytosol (at 5 minutes). Fig. 4 (D) also shows green markers at
12.5, 15 and 17.5 minutes, i.e., autophagosomes indicated by
the green markers were formed around the ART at 12 minutes
and continued to exist at least up to 17.5 minutes.
D. Discussions
The wet laboratory experiments described in Section III-C
verified that an ART of relatively large size are introduced
into a cell through endocytosis and that the ART introduced
into a cell emits fluorescence that is detected by an external
device, demonstrating feasibility of the ART-based approach
in implementing IMIs and OMIs on cells.
The web laboratory experiments conducted in this paper
represent the state-of-the-art experiments at the time of writing
this paper. They are, however, limited in a number of aspects.
For instance,
•Material limitation: Materials of the body and effectors
of the ART used in the wet laboratory experiments
were limited to polystyrene beads and pHrodo molecules.
Future wet laboratory experiments should examine ARTs
composed of other materials.
•Functionality limitation: The body of the ART used
in the wet laboratory experiments served no functional
purposes. The effectors communicated with an external
device only through fluorescence. Future wet laboratory
experiments should examine ARTs that support other
types of optical signals and non-optical signals (e.g.,
electric and magnetic signals).
•No IMI: As the ART and the cell used in the wet
laboratory experiments did not communicate, the IMI was
not examined through the wet laboratory experiments.
Future wet laboratory experiments should examine IMIs.
•Channel capacity limitation: The effectors of the ART
used in the wet laboratory experiments communicated 1
bit of information (i.e., fluorescence on or off per mea-
surement of fluorescence intensity) to the external device;
they did not communicate multiple bit information (i.e.,
different levels of fluorescence intensity). The effectors
7
communicated with the external device using only green
fluorescence, i.e., using only one communication chan-
nel; they did not use fluorescence of different colors,
i.e., using multiple communication channels). Future wet
laboratory experiments should examine interfaces that are
capable of communicating multiple bit information using
multiple communication channels.
•No noise: As there were only one type of ARTs and one
external device used in the wet laboratory experiments,
there were no noise (no interfering fluorescence from
other cells; no interfering excitation light from other ex-
ternal devices). Future wet laboratory experiments should
examine impact of noise on the IMI and OMI.
Addressing each limitation explained above requires major
research efforts in theoretical modeling and analysis, design
of ARTs and interfaces, and wet laboratory experiments.
Required research efforts include the following.
•Identifying suitable materials for ARTs for various com-
binations of signals that an external device uses (e.g.,
electrical, optical, magnetic signals) and chemical signals
that a bio-nanomachine uses,
•Developing methods for engineering ARTs using various
materials,
•Establishing techniques to deliver ARTs into living cells
and also to target sites within cells, while ensuring
that ARTs delivered into cells do not cause unintended
reactions (e.g., cell death),
•Establishing methodology to design an IMI and an OMI
using a given ART, and
•Establish a theoretical framework to examine the channel
capacity between a cell (i.e., bio-nanomachine) and an
external device through an IMI and an OMI.
IV. APP LI CATION OF EXTER NA LLY CON TROLLAB LE
MOL EC UL AR COMMUNICATION TO PATTE RN FO RM ATIO N
In this section, we show, through mathematical modeling
and analysis, how the architecture of externally controllable
molecular communication and the ART-based interfaces may
apply to pattern formation. In externally controllable molecular
communication, a group of ART-embedded cells exchange
molecules and form a concentration pattern of the molecules
over the group of cells. Such patterns may be useful in appli-
cations such as tissue regeneration to control the formation of
a certain structural pattern of cells.
In this section, we first consider a single ART-embedded
cell and examine concentration of molecules released from the
ART within the cell (Section IV-A). We then consider a group
of cells and introduce an ART-embedded cell in the group
of cells. We examine concentration patterns of the molecules
released from the ART-embedded cell formed over the group
of cells (Section IV-B). We further consider three types of
molecular communication systems: a gene expression system,
a Ca2+ oscillation system and an enzymatic reaction system,
each system consisting of a group of ART-embedded cells.
We show in each system that varieties of spatial and temporal
patterns of molecule concentration are formed, demonstrating
potential application of ART-embedded cells to controlled
pattern formation (Section IV-C).
Cell$
ART$
O$
FigS4.A$
r0$ r1$
r$
Fig. 5. Model of an ART in the cytosol enclosed by the plasma membrane
of a cell.
A. Concentration of Molecules in an ART-embedded Cell
In this section, we assume that an ART is embedded within
a cell and that the ART releases molecules of a single type
either at a constant rate or at a variable rate through its surface
into the cytosol of the cell. Under these assumptions, we derive
mathematical expressions for the steady-state concentration of
molecules in an ART-embedded cell and numerically analyze
the obtained mathematical expressions.
A1. Mathematical Modeling
Fig. 5 shows a simple model of an ART in a three-
dimensional environment. In this model, the ART is a sphere of
radius r0and contains molecules of a single type in a sufficient
amount within the spherical structure. The environment is
also a sphere of radius r1and represents the cytosolic space
enclosed by the plasma membrane of the ART-embedded cell.
To simplify the analysis, we assume that the environment
is spherically symmetric at the center of the sphere and that
the centers of the ART and the environment are both at the
same location as shown in Fig. 5. We further assume that
the molecules released by the ART diffuse in the environment
with diffusion coefficient D, the molecules are not produced
in the environment (i.e., the ART in a cell is the only source
of molecules), and the molecules decay in the environment as
a first order reaction with decay rate constant k. With these
assumptions, the rate of change in the cytosolic concentration
uof molecules is then described using a spherical coordinate
system with distance rfrom the origin (r0≤r≤r1)and
time t:
∂u(r, t)
∂t =D1
r2
∂
∂r r2∂u(r, t)
∂r −ku(r, t).(1)
(1) assumes that the centers of the two spheres (i.e., the ART
and the environment) are placed both on the origin of the
spherical coordinate system. Note that the environment where
the molecules diffuse is between the ART surface (r=r0)
and the plasma membrane of the cell (r=r1).
The boundary condition to (1) due to the ART surface (r=
r0) describes a process of ART releasing molecules from its
surface. ART may release molecules from its surface either at
a constant rate (CR) or at a variable rate (VR), and thus, we
8
consider the following two models, CR and VR models [41],
in deriving the boundary conditions:
•In the constant rate model (CR model), the ART releases
molecules from its surface at a constant flux w. The CR
model describes how certain cells secrete molecules (e.g.,
how 1N8A cells secrete growth factor molecules). The
CR model may be implemented by using biomaterials
and mechanisms found in cells that secrete molecules at
a constant rate.
•In the variable rate model (VR model), the ART releases
the molecules at a variable rate, while maintaining the
concentration of the molecules at its surface at a given
constant, u0.4The VR model describes how certain
drug carriers release drug molecules (e.g., how polymer
microspheres release proteins). The VR model may be
implemented by using molecules that diffuse faster within
the ART than in the environment.
For the CR and VR models, the boundary condition due to
the ART surface (r=r0) is given as
−D∂u(r, t)
∂r r=r0
=w(CR model),(2)
u(r0, t) = u0(VR model),(3)
where w(flux) and u0(concentration) are constants.
The boundary condition to (1) due to the plasma membrane
of the cell (r=r1) describes the permeability of the molecules
to the plasma membrane of the cell. Assuming that the
molecules are membrane impermeable, and thus do not diffuse
across the plasma membrane of the cell into the extracellular
environment, the boundary condition is given below for both
the CR and VR models:
∂u(r, t)
∂r r=r1
= 0 (CR and VR models).(4)
At the steady state (where no concentration changes occur),
∂u(r,t)
∂t = 0, and thus, the left hand side of (1) becomes 0. The
steady state concentration of the molecules at distance rfrom
the center of the sphere, denoted as ¯u(r), is then derived by
solving the ordinary differential equation (ODE) below.
D1
r2
d
dr r2d¯u(r)
dr −k¯u(r)=0 (5)
The solution to (5) is derived with boundary conditions that
are equivalent to (2) and (4) for the CR model, and (3) and
(4) for the VR model, resulting in
¯u(r) = ¯u(r0)v(r) = (ˆu0v(r) (CR model)
u0v(r) (VR model),(6)
where
4The number of molecules at the ART surface depends on the number
of molecules that diffuse away from the ART surface and the number of
molecules that decay at the ART surface. Thus, in order to maintain the
concentration of molecules constant at the ART surface, an ART needs to
release molecules at a variable rate.
v(r) = r0
r
r1βcosh (β(r1−r)) −sinh (β(r1−r))
r1βcosh (β(r1−r0)) −sinh (β(r1−r0)).(7)
For ˆu0in (6), see (8)5. Note that the square root of the k
(decay rate) to D(diffusion coefficient) ratio, β(= pk/D),
is used to simplify the expressions in (7) and (8).
Note that, when the decay rate constant is 0(i.e., k= 0),
molecules released from the ART do not decay within the cell.
Since the boundary condition at r=r1is that molecules do
not diffuse across the plasma membrane of the cell, the con-
centration of the molecules that the ART releases approaches
infinity as time progresses, i.e., ¯u(r) = ∞, for the CR model.
For the VR model, the concentration of the molecules released
from the ART approaches the concentration at the surface of
the ART in the steady state; i.e., (5) with k= 0 results in
¯u(r) = u0.
A2. Results
Fig. 6 shows normalized concentration u(r, t)/¯u(r0)as a
function of time tand the relative distance r/r1from the origin
of the spherical coordinate system. Parameter values assumed
in this figure are r0= 1 (µm), r1= 20 (µm), and β= 0.1
(1/µm). Values of the normalized concentration are obtained
by numerically solving (1) with boundary conditions (2) and
(4) for the CR model, with boundary conditions (3) and (4)
for the VR model, and with an initial condition u(r, 0) = 0 for
both models. Fig. 6 shows that the normalized concentration
takes the maximum value of 1at r=r0for both models,
and the concentration decreases as the distance from the ART
increases. As shown in Fig. 6, the VR model approaches the
steady state in a shorter period of time than the CR model.
Note that the normalized concentrations u(r, t)/¯u(r0)for the
CR and VR models reach the same steady-state concentration
v(r)(see (6)).
Fig. 7 shows the impact of β(= pk/D)and r0/r1on the
average concentration vavg of the molecules at the steady state
in the environment. vavg is computed as the average of v(r)
(r0< r < r1) with respect to distance rin the spherically
symmetric coordinate system: i.e.,
vavg =1
VZr1
r0
4πr2v(r)dr (9)
where Vis the volume of the environment and given by
V=4
3π(r3
1−r3
0). Fig. 7 shows that the normalized con-
centration of the molecules in the environment drops quickly
from 1to 0, when the square root of the k(decay rate) to
D(diffusion coefficient) ratio β(= pk/D)increases from
0. Fig. 7 also shows that the normalized concentration of the
molecules increases almost linearly when the size of the ART
(i.e., r0) increases (for a fixed cell size r1.)
B. Concentration of Molecules over a Group of Cells
Cells are often coupled together to form a group of cells
through internal pathways such as gap junction channels
and propagate intracellular messenger molecules (e.g., inositol
5See (8) on the top of next page.
9
ˆu0=wr0
D
r1βcosh (β(r1−r0)) −sinh (β(r1−r0))
(r1−r0)βcosh (β(r1−r0)) −(1 −β2r0r1) sinh (β(r1−r0)) (8)
!"#$%&'()*+
,"-,)-.#%/"-++
01#2.3401#53+
6)&%/7)+
*'8.%-,)+#4#9+
:'$)+.+
9;5+
5;<+
5+
<5+
955+
5;=+
5;9+
5;9<+
5;5<+
>6+
?6+
@'ABCDE=+
Fig. 6. Normalized concentration u(r, t)/¯u(r0)as a function of relative
distance r/r1and time tfor the VR model and for the CR model. The
parameter values assumed in this figure are r0=1(µm), r1= 20 (µm), and
β= 0.1(1/µm).
β" r0/r1"
FigS4,A3"
0"
0.5"
1"
0" 0.5" 1"
Averaged"concentra9on"vavg"
β"or"r0/r1"
β"
r0/r1"
Fig. 7. Impact of βand r0/r1on the average concentration vavg . The
parameter values assumed in this figure are r0=1(µm), r1= 20 (µm),
β= 0.1(1/µm).
trisphosphate and Ca2+) and small metabolites among cells.
Cells are also often coupled together to form a group of cells
through external pathways and propagate paracrine signals
(e.g., adenosine triphosphate, cyclic adenosine monophos-
phate, Ca2+) among cells. In such groups of coupled cells,
a change in the cytosolic concentration of molecules in one
cell may propagate to other cells in the group. Thus, by
placing an ART embedded cell in a group of coupled cells
and by controlling the concentration of molecules in the ART-
embedded cell, it may be possible to control the concentrations
of molecules in other cells in the group. In the following, we
derive the steady state concentrations of the molecules over a
group of coupled cells containing an ART-embedded cell.
B1. Mathematical Modeling
Consider a set Nof cells containing a set Aof ART-
embedded cells. (A set N \ A is a set of non ART-embedded
cells.) The concentration of molecules in a cell is denoted as
Ui(t)for cell i∈ N at time t. To simplify the analysis, we
assume that molecules are uniformly distributed within a cell
(either an ART-embedded cell or a non ART-embedded cell).
We further assume that the concentration of molecules in an
ART-embedded cell is either at the steady state (and thus, no
change occurs in concentration) or maintained by the ART at
a constant, Us: i.e., Ui(t) = Us(i∈ A).
The rate of change in Ui(t)for a non ART-embedded cell
i∈ N \ A is then described as a set of ordinarily differential
equations below:
dUi(t)
dt =−kUi(t) + pX
j∈Ni
(Uj(t)−Ui(t)) (i∈ N \ A),(10)
where parameter prepresents the degree of coupling among
adjacent cells, and Nirepresents the set of cells that are
directly connected to cell i(for instance, through gap junction
channels). pis assumed to be constant and independent of
which cells are coupled together. The first term on the right
hand side of (10) describes the decay of the molecules as in
(1), and the second term describes the diffusion of molecules
among coupled cells.
When an ART-embedded cell in a group of coupled cells
releases molecules, the concentration of the molecules in cell
i,Ui(t), reaches its steady state value ¯
Uiin time. At the steady
state (where no concentration changes occur), dUi(t)
dt = 0,
and thus, the left hand side of (10) becomes 0. The steady
state concentration ¯
Uiof molecules in cell iis then derived
analytically by solving the simultaneous equations below, with
the condition of ¯
Ui=Us(i∈ A),
0 = −γ¯
Ui+X
j∈Ni¯
Uj−¯
Ui(i∈ N \ A),(11)
where γ(= k/p)is the ratio of the decay rate kto the degree
of coupling p.
B2. Results
Fig. 8 shows the concentration ¯
Ui(steady state concentra-
tion of molecules in cell i∈ N ) for a 21 cells ×21 cells two-
dimensional array containing an ART-embedded cell at the
center. A two-dimensional array assumed in this subsection
(and in the next subsection) interconnects each cell with its
adjacent cells on the array. The number of neighboring cells
is therefore two for the cells on the four corners of the array,
three for the cells on the four edges of the array, and four for
other cells on the array. Fig. 8 plots the concentration of a
10
!"
!#$"
%"
!" $" %!"
&'()*(+,-.'("/0"
102+-()*"3(456*,"'7")*8829"
:;%"
:;!#%"
:;!#!%"
:;!#!!%"
<0=>?@A"
Fig. 8. Steady state concentration Uiof molecules in cell ias a function of
cell i’s distance from the ART-embedded cell at the center in an array of 21
cells ×21 cells. Us= 1.
cell as a function of the distance from the ART-embedded cell
(measured in the number of cells), starting with 0for the ART-
embedded cell at the center and ending at 10 for the cell at the
corner of the array or at an edge of the array, for various values
of γ(= k/p). The value of Us(i.e., concentration of molecules
in an ATR-embedded cell) is assumed to be 1(Us= 1) in Fig.
8. Fig. 8 shows that the concentration of molecules depends
on the value of γand on the distance to the cell from the ART-
embedded cell, indicating that it may be possible to control
concentrations of molecules in cells on the array by adjusting
k(decay rate) and p(degree of coupling).
C. Pattern Formation in Molecular Communication
The previous subsection IV-B shows that the cytosolic con-
centration of molecules in a group of cells may be controlled
by introducing ART-embedded cells into the group of cells.
In this section, we introduce ART-embedded cells into three
types of cell-based molecular communication systems to show
that complex patterns of molecule concentrations are formed
in each system.
C1. Mathematical Modeling
The three types of molecular communication systems con-
sidered in this subsection are (1) a gene expression system,
(2) a Ca2+ oscillation system and (3) an enzymatic reaction
system. As described below, each type of molecular commu-
nication systems consists of ART-embedded cells that release
molecules.
•The gene expression system [20] consists of a group of
(bacterial) cells that are genetically engineered to form
spatial patterns of gene expression. In this system, cells
acting as senders release N-acyl homoserine lactones
(AHL) molecules, the released AHL molecules propagate
in the environment from cell to cell, and cells acting
as the receivers of the AHL molecules express green
fluorescence proteins (GFPs) when the AHL molecules is
in the medium concentration. (Cells do not express GFPs
when the AHL is either in a high or low concentration.)
In this section, we consider a gene expression sys-
tem implemented using the architecture of externally
controllable molecular communication, where cells are
embedded with ARTs and externally controlled to release
AHL molecules from their ARTs and to emit fluorescence
through the interface implemented using ARTs.
•The Ca2+ oscillation system [42] consists of a group
of cells, each containing a set of molecules to oscillate
the Ca2+ concentration in the cell. The Ca2+ oscillation
system propagates Ca2+ cell-to-cell to form complex
temporal patterns of Ca2+ concentrations (see Section
IV-D) over a group of cells.
In this section, we consider a Ca2+ oscillation sys-
tem implemented using the architecture of externally
controllable molecular communication, where cells are
embedded with ARTs and externally controlled to release
Ca2+ mobilizing molecules to trigger the release of Ca2+
from Ca2+ stores in the cells. Note that in this system
Ca2+ propagate among the group of cells, while Ca2+
mobilizing molecules released from ARTs do not.
•The enzymatic reaction system [43] consists of a group
of cells, each containing a set of molecules to induce
enzymatic reactions. Enzymatic reactions occur within a
cell and consume substrate molecules to yield product
molecules. Both substrate and product molecules prop-
agate from cell to cell in a group of cells, leading to
the formation of complex spatial patterns (e.g., Turing
patterns, see Section IV-D) of concentration of these
molecules over the group of cells.
In this section, we consider an enzymatic reaction
system implemented using the architecture of externally
controllable molecular communication, where cells are
embedded with ARTs and externally controlled to release
a type of molecules that accelerate the formation of
product molecules. Note that in this system substrate and
product molecules propagate among the group of cells,
while the molecules released from ARTs do not.
Table I shows, for each of the three types of molecular
communication systems, how it is modeled mathematically.
Expressions listed under “Model equations” describe how the
concentration of molecules changes in cells to form a pattern
for each system. They are obtained from existing work listed in
“Reference for model equations” with modifications explained
in the table. In each system, Uidescribes the concentration
of the molecules (at cell i) that form a pattern. Further,
a two-dimensional array of cells is assumed in numerically
calculating the values of Uifrom the equations in Table I, as in
Subsection IV-B. The two-dimensional array of cells assumed
determines the set of cells Nithat are directly connected to a
cell i.
C2. Results
The model equations in Table I are solved numerically
to demonstrate formation of various concentration patterns
of molecules. Figs. 9, 10 and 11 use the parameter values
described in the corresponding figure captions and show
examples of patterns that are formed in each system. Note that,
in these figures, ART-embedded cells at locations indicated by
red squares release molecules from their ARTs; other cells do
not release molecules from their ARTs.
Fig. 9 shows spatiotemporal patterns of molecule concen-
tration that are formed on the gene expression system. In Fig.
11
TABLE I
MODELS FOR MOLECULAR COMMUNICATION SYSTEMS
System Model equations Original equations and modifications made
Gene
expression
system
˙
Gi=αG
1+(Li/βL)2−γGGi,˙
Li=αL1
1+(Ci/βC)2+αL2Ri
θR+Ri−γLLi
˙
Ci=αCRi
θR+Ri−γCCi,˙
Ri=ρR[LuxR]2U2
i−γRRi
˙
Ui=−k Ui+pPj∈Ni(Uj(t)−Ui(t))
(1) – (4) in [20]. Uiis incorporated in ˙
Rito describe the
effect of AHL molecules released from ARTs (replacing A
in [20].)
Ca2+
oscillation
system
˙
Zi=v0+v1Ui−v2+v3+kfYi−kzZi+PPj∈Ni(Zj−Zi)
˙
Yi=v2−v3−kfYi
v2=VM2Z2
i
K2
2+Z2
i
,v3=VM3Y2
i
K2
R+Y2
i
Z4
i
K4
A+Z4
i
(1) and (2) in [42]. The propagation term for Ca2+ is
added to ˙
Ziusing the degree of coupling P.Uiis added
to ˙
Zito describe the effect of Ca2+ mobilizing molecules
released from ARTs (replacing βin [42].)
Enzymatic
reaction
system
˙xi=φ−χ1vi+PxPj∈Ni(xj−xi)
˙yi=χ2vi−yi
1+ωyi+PyPj∈Ni(yj−yi) + ηUi
vi=xi(α+βyi)
1+xi+γyi+xiyi
(18) and (19) in [43]. The propagation terms for substrate
and product molecules are added to ˙xiand ˙yiusing degrees
of coupling Pxand Py.ηUiis added to ˙yito describe the
effect of molecules released from ARTs.
FigS4C'BD*
(A)*
(B)*
t*=*0* t*=*1* t*=*2* t*=*3* t*=*4*
t*=*10* t*=*11* t*=*12* t*=*13* t*=*14*
t*=*5*
t*=*15*
Fig. 9. Patterns formed on the gene expression system. An array of 201 cells ×201 cells is assumed. Us= 1,p= 1,k= 0.01,η= 1. Other parameter
values are obtained from [20]: αG= 2,αL1=αL2=αC= 1,βL= 0.8,βC= 0.008,γG=γC= 0.0692,γL=γR= 0.0231,θR= 0.001,
ρR= 0.5, and [LuxR] = 0.5. (Units are arbitrary.) (A) One cell at the center indicated by the red square release AHL molecules to form a circular pattern.
(B) After a circular pattern is formed in (A), the cell at the center stops releasing AHL, and the two cells indicated by the red squares (10 cells from the
center to each direction) start releasing molecules to form an oval pattern. The concentration of molecules (Gi) is shown in the figure: low concentration in
black and high concentration in white.
9 (A), the cell at the center releases AHL molecules from
its ART, showing how a basic pattern of a circle is formed
as time progresses. When sufficient amount of time passes,
the concentration of AHL molecules in each cell reaches the
steady state, and the stable circular pattern appears. At time
t= 10, we externally control the center cell to stop releasing
AHL molecules and two new cells to start releasing AHL
molecules from their ARTs. These two new cells are located
away from the center with an equal distance in an opposite
direction (10 cells away from the center to each direction).
Fig. 9 (B) shows how a circular pattern transforms into an
oval pattern as time progresses. Note that patterns at t= 5
and 10 are stable while the center cell (in Fig. 9 (A)) and two
new cells (in Fig. 9 (B)) continue to release AHL molecules
from its/their ART(s) and that the patterns dissapear when
these cells stop releasing AHL molecules. Figs. 9 (A) and
(B) show that external control triggers formation of a pattern,
adjusts the formed pattern and terminates the formed pattern.
Fig. 10 shows spatiotemporal patterns of molecules that are
formed on the Ca2+ oscillation system. The two cells located
away from the center with an equal distance from the center in
an opposite direction (20 cells from the center) release Ca2+
mobilizing molecules from their ARTs. These cells release
the molecules in different amounts to break the symmetry
of the system to generate highly complex spatiotemporal
patterns. These patterns disappear when external control is
exercised and the two cells stop releasing molecules from their
ARTs (data not shown). Thus, external control can trigger and
terminate formation of these patterns.
Fig 11 shows spatiotemporal patterns of molecules that are
formed on the enzymatic reaction system. In Fig. 11 (A), the
four cells at the four corners release molecules from their
ARTs to form complex patterns. In Fig. 11 (B), all cells release
molecules from their ARTs at a rate dependent on the distance
from the center; the rate of releasing molecules increases as
the distance from the center increases. The pattern formed at
t= 5 in Fig. 11 (A) and the pattern at t= 5 in Fig. 11 (B) are
stable (i.e. Turing patterns) and do not change even after cells
12
FigS4C'Ca)
t)=)0) t)=)1) t)=)2) t)=)3) t)=)4) t)=)5)
t)=)8) t)=)10) t)=)12) t)=)14) t)=)16) t)=)18)
t)=)20) t)=)30) t)=)40) t)=)50) t)=)60) t)=)70)
Fig. 10. Patterns formed on the Ca2+ oscillation system. An array of 201 cells ×201 cells is assumed. Us= 0.25 or 0.5and p= 0.06. Other parameter
values are obtained from the original model [42]: v0= 1,kf= 1,v1= 7.3,VM2= 65,VM3= 500,K2= 1,KR= 2, and KA= 0.9except for
kz= 3.55. Initial conditions are Zi= 1.6and Yi= 0.2at time t= 0. (Units are arbitrary.) The two cells indicated by the red squares (20 cells from the
center in an opposite direction) release Ca2+ mobilizing molecules at the different rates: Us= 0.25 for the cell on the top-left, and Us= 0.5for the cell
on the bottom-right. The concentration of Ca2+ (Zi) is shown in the figure: low concentration in black and high concentration in white.
FigS4C'Meta,
(A),
(B),
t,=,0, t,=,1, t,=,2, t,=,3, t,=,4,
t,=,0, t,=,1, t,=,2, t,=,3, t,=,4,
t,=,5,
t,=,5,
Fig. 11. Patterns formed on the enzymatic reaction system. An array of 201 cells ×201 cells is assumed. Us= 1,p= 0 in (A)(B) and 10 in (C), k= 0.1,
η= 1. Other parameter values are obtained from [43]: φ= 1,χ1= 3.5,χ2= 0.5,α= 0.5,β= 4,γ= 0.5,ω= 5,Px= 20,Py= 0.01. Initial
conditions are xi= 0.17 and yi= 0.5at time t= 0. (Units are arbitrary.) (A) The four cells on the four corners indicated by the red squires release
molecules. (B) All cells on the array release molecules at a rate dependent on the distance from the center. The concentration of the product molecule (yi)
is shown in the figure: low concentration in black and high concentration in white.
(i.e., 4 corner cells in Fig. 11 (A) and all cells in Fig. 11 (B))
stop releasing molecules from their ARTs. In order to modify
the stable patterns in Figs. 11 (A) and (B), significant changes
are required in the location and timing of releasing molecules
and the amount of molecules to release, and external control
may not be able to introduce such significant changes with
the limited functionality of the ARTs in cells. Thus, external
control may be limited to only triggering formation of these
patterns.
D. Discussion
Section IV-C assumes that external control is available to
determine the location and timing of releasing molecules and
the amount of molecules to release and shows that various
patterns of concentrations of molecules are formed in space
and time (i.e., Figs. 9, 10 and 11). Such patterns may be
useful for tissue formation in regenerative medicine, promising
applications of molecular communication.
Modeling and analysis presented in Section IV-C are based
on existing work on pattern formation. The mathematical
basis for pattern formation has been provided by Alan Turing
13
in 1952 [44] and later studied extensively [45], [46], [47]
followed by experimental verifications [48]. A basic model
consists of two types of morphogen (signaling molecules used
in tissue development), Uand V, and is known as the reaction-
diffusion model. It is described as
∂u
∂t =Du∆u+f(u, v)(12)
∂v
∂t =Dv∆v+g(u, v)(13)
where uand vare the concentrations of Uand V,Duand
Dvare diffusion coefficients of Uand V, functions fand g
describe reaction terms for Uand V, and ∆is the Laplacian
(e.g., ∂2
∂x2+∂2
∂y2for a two dimensional Euclidean coordinate).
The reaction-diffusion model is able to produce oscillatory
patterns that propagate in space, such as periodic traveling
waves and rotating spiral waves [49], [50], [51]. For exam-
ple, in the activator (U) and inhibitor (V) system, where U
stimulates the production of both Uand Vand Vinhibits the
production of both Uand V, oscillatory patterns appear and
propagate in space when only U, not V, diffuses. The Ca2+
oscillation system described in Section IV-C is a variation of
this model and produces patterns such as those shown in Fig.
10.
The reaction-diffusion model also produces non-uniform
stationary patterns – Turing patterns such as stripes, spots and
spirals – from an initially uniform environment. For example,
in the activator and inhibitor system described above, Turing
patterns emerge when Vdiffuses faster than U(i.e., Dv/Duis
greater than some threshold). The enzymatic reaction system
described in Section IV-C is a variation of this model and
produces Turing patterns such as those shown in Fig. 11.
Our modeling and analysis presented in Section IV-C are
built upon the existing work on pattern formation, and our
contributions include the following.
•We extended mathematical expressions in existing work
to incorporate assumptions of externally controllable
molecular communication.
•We investigated how concentration patterns emerge in
various applications of externally controllable molecular
communication.
•We examined the role of external control in pattern
formation, namely, how external control dynamically
alters a pattern being formed when it is applied during a
formation of a concentration pattern and whether formed
patterns are stable or unstable.
Future efforts are required to understand how patterns are
formed and modified with external control. External control
applied in Section IV-C is simple; it is applied once to
determine the location and timing of releasing molecules and
the amount of molecules to release. A series of external control
may guide the formation of different patterns. Future efforts
also include inducing local rules or parameters to achieve
desired global patterns [52] and controlling the formation of
patterns in three dimensional space when external control is
available.
V. CONCLUSIONS
In this paper, we examined a key research issue in molecular
communication, namely, an issue of establishing interfaces that
interconnect a molecular communication environment and an
environment external to the molecular communication envi-
ronment. Such interfaces expand capability and functionality
of molecular communication and facilitate creation of novel
applications of molecular communication such as externally
controllable drug delivery systems, externally controllable
tissue regeneration systems and dermal displays.
Discussions and results presented in this paper provide
a starting point for further research, including refining the
architecture of externally controllable molecular communi-
cation, implementing externally controllable molecular com-
munication and its interfaces, and designing and demonstrat-
ing potential applications of externally controllable molecular
communication.
ACRONYMS
AHL N-acyl homoserine lactones
ART Artificially synthesized material
ATP Adenosine Triphosphate
BNI Bio-nanomachine to Bio-nanomachine Interface
DNA Deoxyribonucleic Acid
GFP Green Fluorescent Protein
IMI Inmessaging Interface
OMI Outmessaging Interface
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