SUGISAKAMASANORI

Journal of Advances in Artificial Life Robotics
Vol. 1(2); September (2020), pp. 56–59
ON LINE ISSN 2435-8061; ISSN-L 2435-8061
https://alife-robotics.org/jallr.html

Research Article

Modeling and Simulation of Molecular Artificial Intelligence with
DNA computing by using Abstract Rewriting System on
Multisets
Yasuhiro Suzuki

Department Complex Systems Science, Graduate School of Informatics, Nagoya University, Furocho, Chikusa, Nagoya City, 464-8601, Japan

ARTICLE INFO
Article History
Received 25 November 2019
Accepted 19 July 2020
Keywords
Molecular artificial intelligence
DNA computing
Bio-chemical logic gate

ABSTRACT

We have bio-chemically realized Artificial Intelligence by using DNA reactions, which iscomposed of a well-known as oscillating DNA reactions, the seesaw gate reaction. Throughbiochemical experiments, we confirm that mismatched interact-able DNA sequences can adapt toperturbations of environmental change, which is caused by making point mutation in an input
sequence. Based on this result, we model this reaction by using abstract chemistry and confirm
that the model exhibits the same behavior as biochemical experiments. Through computational
simulations show that this DNA reaction can compose the logic gate bio-chemically.

© 2022 The Author. Published by Sugisaka Masanori at ALife Robotics Corporation Ltd.
This is an open access article distributed under the CC BY-NC 4.0 license(http://creativecommons.org/licenses/by-nc/4.0/).

The seesaw gate reaction

which integrates the discrete and continuous
mathematical model.
1.1 Self-sustained Chemical Reaction Networks,
CRN

1. Introduction
Research on DNA computing has evolved into researchon Molecular Robots[1]. Recent vast advances incomputing power, artificial intelligence, AI researches
are progressing and expanding rapidly. Shortly, AI
research will develop into molecular AI and merge withmolecular robots. From various challenges in AI
researches, we aim to compose an adaptive system. An
adaptive system is a system, which can change behaviors
in response to the change of environment; adaptivenesshas been an essential subject Robotics in general [2].
In this paper, we model an adaptive system by using
the Toehold Strand Displacement Reaction, which has
commonly used in DNA computing [3]; simulate themodel by using the Abstract Rewriting System on
Multisets, ARMS [4],[5],[7],[8]. ARMS is aphysiochemically strict hybrid computational model,

In this research, we use a simple self-sustaining ChemicalReaction Network, CRN [6];A + B → C + D,
(1)
C + E → A + F.
(2)
CRN and its dynamics have studied in Chemistry andPhysics since innovation of the low of mass action6. In
this CRN, we assume that the concentrations of B and E
are sufficient and D and E flow out immediately, so theconcentration of A to be sustained.
This CRN describes the seesaw gate reaction by using
Toehold mediated Strand Displacement Reaction, TMSD,
which has commonly used in DNA computing.

Corresponding author’s E-mail: ysuzuki@nagoya-u.jp URL: www.ysuzuki.info

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1.2. Seesaw gate reaction by Toehold mediatedStrand Displacement Reaction, TMSD

duplication (multiplicity) the element as M(a), a ∈ A.
For example, M (a) and M (b) of {a, a, b, b} are 2, and M(c) = 0. In this paper we describe a multiset explicitly ora vector w = (M (a1), M (a2) . . . M (an)). The union of twomultisets M1, M2 is the addition of vectors w1 and w2; theinclusion of M1, M2 is M1(ai) ≤ M2(ai) for all ai ∈ A. We
denote A# as a set of all combinations of multisets overA including an empty multiset.
A reaction rule l → r, l, r ∈ A# is a pair of a multiset
and a reaction vector wr = -l + r. A reaction (rewriting)calculation is defined as wi+1 = r + wi, where i denotes
the step time of the multiset. For example, an ARMS witha reaction rule a, b → a, c; since l = (1, 1, 0) and r = (1,0, 1), wr = −(1, 1, 0) + (1, 0, 1) = (0, −1, 1) and in casewi = (1,1,1), wi+1 = (1,1,1) + (0, -1, 1) = (1, 0, 2); which
denote the reaction calculation of from {a, b, c} to {a, c,c} by a, b → a, c.

Fig. 1. Seesaw Gate Reaction; from the Journal of the Royal
Society Interface, 2011[3] (distributed under the terms of theCreative Commons Attribution License)

2. ModelToehold mediated Strand Displacement Reaction, TMSD
is a reaction between a double-strand DNA and singlestrand DNA (Fig.1), in which a strand in a doublestranded DNA is replaced with the same or nearly
identical single-strand DNA. DNA strand displacement
reaction is composed of the three single strands namedthe ‘invader’,‘incumbent’ and the ‘substrate’; thisreaction is a swapping reaction between the invader andthe incumbent strands on the substrate strand. The
invader corresponds to an input signal, while theincumbent corresponds to an output signal. Toehold
Exchange Reaction TER, which is known as a class ofstrand displacements, since this reaction allows
sequence-dependent control, it is peculiarly useful. InTMSD, the shorter incumbent forms a partial duplex withthe more extended, complementary substrate; then, theinvader hybridizes with the toehold, which is theunbound region of the partially duplexed complement.

In the seesaw gate reaction, first, TMSD occurs between
the single-strand DNA named 'input', and the doublestrand DNA named 'gate:output' then single-strand DNA
named the 'output' strand and the double-strand DNA
named "input:gate" are produced. In the CRN, it isdescribed as A + B → C + D, where A stands for input,B, gate:output, C, input:gate and D, output. Since
input:gate reveals a scaﬀold (T) for interaction with thesingle-stranded DNA named 'fuel ', SDR occurs next
between fuel and input:gate, then the input and gate:fuelare produced, it is described as C + E → A + F ; whereC stands for input:gate, E, fuel strand, and F, gate:fuel. In
this reaction these two reactions occur like a seesaw,
while input strand consumed in the first reaction andsupplied in the second reaction.
2.1. Environment Change by giving a point
mutation in the input strand

1.3. Multiset Rewriting System on Multisets,
ARMS

To change the environment of CRN, we give a point
mutation in the input strand; input’ stands for mutatedinput strand. We confirmed that even if a point mutation
occurred in input strand, several mutated input strands
can bind and form mismatched pair with gate:output
through biochemical experiments [9]. The self-sustaining
CRN with non-mutated input strand is described as;
input + gate:output ↔ input:gate + output (1),input:gate + fuel ↔ input + gate:fuel(2).

We have proposed a CRN, based on Abstract Rewriting
Systems, ARS; the ARS is a theoretical model ofcomputation; we expand ARS on the multiset as Abstract
Rewriting system on Multisets. A multiset is defined as asimple set and a map, which returns the duplication of anelement. A denotes for the set of alphabets, and every
element of ARMS is an element of A. We denote57

While, the CRN with the mutated input strand, input’:
input’ + gate:output ↔ input’:gate + output(3),
input’:gate + fuel ↔ input’ + gate:fuel(4).
Since the binding force of mismatch strands pair isweaker than non-mismatch one; we express it bychanging reaction speed to the reaction speed of themismatched pair is slower than non-mismatched one.

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2003. Method
In the CRN, the rate constants for the forward and reverse
reactions are the same; the rate constant for the mutatedinput strand is 100 times slower than the non-mutatedinput strand.

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Fig.3. (Top) Time change of the number of the input and input'strands. When the same amount of the input and input' strand,
the input' strand does not react. (Bottom) When the number ofthe input' strand is significant if the amount the input' strand is
100 times larger, the reaction system will use the input' strand.

Fig. 2. Time change of the number of input strands. The
horizontal axis of the graph is the number of steps (one reaction
is one step), and the vertical axis is the number of input strands;
because of the structure of reaction rule is the same, the timechange of the amount of input’s strands are equivalent.

When there is either input or input' strand, the reaction
reaches an equilibrium state (Fig.2). In the case when
input and input' strands coexist, if both concentrations are
the same since the reaction speed of the input strand is
100 times faster than the input' strand, the input' strand
rarely to react. In the case when the concentration of theinput' strand is 100 times larger than the input strand, theinput' strand mainly to react. These results of simulations
show the CRN can adapt to environmental change; if theconcentration of non-mutated strand is smaller than themuted one, the reaction system selects it and can sustain
reactions (Fig.3).
5.

Fig. 4. The bit shift operation by adding the strands. by adding
the 30 of the input strands [i] or input' strand the equilibrium
state shifts from around 50 to 80.

adding input or input’ strands. By using thischaracteristic, we can express a basic unit of information,a bit. We set the value of a bit to 0 when the number ofthe input or input strand is approximately 50, which is anequilibrium state. By adding input strands into the system,
the equilibrium state shifts; in this simulation, we add 30strands, then the equilibrium state shifts from 50 toaround 80 (Fig.4). We define the value of a bit as 1 forthis shifted equilibrium state. In the case when the bit of
input is 1, if we remove 30 strands of input strands thenDiscussion

The simulation results show that when the amount ofinput strands is half to the number of input’ strands, theconcentrations of both become the same in theequilibrium state, and the equilibrium state shifts by58

Fig. 5. 2-bit register using the CRN. The value of the bit is 0 when the number of the strand is around 50, while 1 for approximately 80.
[i], [i] stands for the number of input, input’ strand respectively.

the equilibrium state shift from 80 to 50 and the value ofthe bit return from 1 to 0; this operation of bit is the same
when input’ strands are used (Fig.4).
We confirmed that by adding or removing 30 strands,
a two-bit register can realize by using this CRN (Fig.5).
For Biochemical implementation, removing strands will
be able to realize by adding double-strand DNA, whichis named as ‘threshold’[3] (Fig.6).

2.

3.
4.
5.

6.
7.

Fig. 6. The threshold; from the Journal of the Royal SocietyInterface, 20113 (distributed under the terms of the Creative
Commons Attribution License)

8.

Biochemical implementation of DNA circuits by using
this two-bit register is our future work. The speed ofcomputation of DNA logic circuits [5] often need hours
to compute and complicated reactions, through ourbiochemical experiments of this model, transient time toequilibrium state is around half-hour [6] and reactions are
simple compared with other models e.g. [6].
Since this his two-bit register holds information as
dynamic equilibrium states, is suitable for constructing
artificial intelligence of molecular robots because brain
activities such as attention can be regarded as a dynamic
equilibrium state9.

9.

its shape in response to signal molecules.” ScienceRobotics 2 (2017).
Ziemke, T., & Sharkey, N. E. (2001). A stroll through theworlds of robots and animals: Applying Jakob von
Uexkülls theory of meaning to adaptive robots andartificial life, Semiotica, 2001(134), 701-746.
L. Qian, E. Winfree, A simple DNA gate motif forsynthesizing large-scale circuits, Journal of the Royal
Society Interface, Vol. 8, 2011.
M. Umeki and Y. Suzuki, A Simple Membrane Computing
Method for Simulating Bio-Chemical Reactions,
Computer and Informatics, 27, 529-550, 2008.
Wegscheider, R. (1901) Über simultane Gleichgewichte
und die Beziehungen zwischen Thermodynamik undReactionskinetik homogener Systeme, Monatshefte fürChemie / Chemical Monthly 32(8), 849--906.
Y. Suzuki, Emergence of Adaptive behavior insimulations by using Abstract Rewriting System on
Multisets, ICAROB, 2020.
Song T, Eshra A, Shah S, et al. Fast and compact DNA
logic circuits based on single-stranded gates using stranddisplacing
polymerase.
NatNanotechnol.
2019;14(11):1075-1081. doi:10.1038/s41565-019-0544-5
Y. Suzuki and R. Taniguchi, Toward Artificial
Intelligence by using DNA molecules, Journal of
Networking and Artificial Life, 5(2), pp128-130, 2018,Atlantis Press
Lajoie Y, Teasdale N, Bard C, Fleury M. Attentional
demands for static and dynamic equilibrium. Exp Brain
Res. 1993;97(1):139-144. doi:10.1007/BF00228824

Authors Introduction
Dr. Yasuhiro Suzuki

References
1. S. Yusuke, Y. Hiratsuka, I. Kawamata, S. Murata and S.
M. Nomura. “Micrometer-sized molecular robot changes

59

He is an Associate Professor of
Graduate School of Informatics,Nagoya
University Japan.
graduated from Japan Advanced
InstituteofScienceandTechnology in 1995, receivedDoctor degree of Informatics from
Kyoto University in 2001.

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