Slime mould electronic oscillators
Andrew Adamatzky
arXiv:1403.7350v1 [cs.ET] 28 Mar 2014
University of the West of England, Bristol, BS 16 1QY, United Kingdom;
Email:andrew.adamatzky@uwe.ac.uk
Abstract
We construct electronic oscillator from acellular slime mould Physarum polycephalum. The slime mould oscillator is made of two electrodes connected by a
protoplasmic tube of the living slime mould. A protoplasmic tube has an average
resistance of 3 MOhm. The tube’s resistance is changing over time due to peristaltic
contractile activity of the tube. The resistance of the protoplasmic tube oscillates
with average period of 73 sec and average amplitude of 0.6 MOhm. We present
experimental laboratory results on dynamics of Physarum oscillator under direct
current voltage up to 15 V and speculate that slime mould P. polycephalum can be
employed as a living electrical oscillator in biological and hybrid circuits.
Keywords: oscillator, slime mould, bioelectronics
1
Introduction
“A device without an oscillator either doesn’t do anything or expects to be
driven by something else (which probably contains an oscillator).”
Horowitz and Hill, The Art of Electronics, 1980.
The plasmodium of Physarum polycephalum (Order Physarales, class Myxomecetes, subclass Myxogastromycetidae) is a single cell, visible with the naked eye,
with many diploid nuclei. The plasmodium feeds on bacteria and microscopic
food particles by endocytosis. When placed in an environment with distributed
sources of nutrients the plasmodium forms a network of protoplasmic tubes
connecting the food sources. The topology of the plasmodium’s protoplasmic
network optimises the plasmodium’s harvesting of nutrient resource from the
scattered sources of nutrients and makes more efficient the transport of intracellular components [23]. In [3] we have shown how to construct specialised and
general purpose massively-parallel amorphous computers from the plasmodium (slime mould) of P. polycephalum that are capable of solving problems of
Preprint submitted to Elsevier
31 March 2014
computational geometry, graph-theory and logic. Plasmodium’s foraging behaviour can be interpreted as a computation [23,24,25]: data are represented by
spatial of attractants and repellents, and results are represented by structure
of protoplasmic network [3]. Plasmodium can solve computational problems
with natural parallelism, e.g. related to shortest path [24] and hierarchies of
planar proximity graphs [1], computation of plane tessellations [26], execution
of logical computing schemes [30,2], and natural implementation of spatial
logic and process algebra [28].
In the framework of our “Physarum Chip” EU project [4] we aim to experimentally implement a working prototype of a Physarum based general purpose computer. This computer will combine self-growing computing circuits
made of a living slime mould with conventional electronic components. Data
and control inputs to the Physarum Chip will be implemented via chemical, mechanical and optical means. Aiming to develop a component base of
future Physarum computers we designed Physarum tactile sensor [5] and undertook foundational studies towards fabrication of slime mould chemical sensors (Physarum nose) [9,32], Physarum memristive devices [11] and insulated
Physarum wires [7].
A future Physarum Chip will be a hybrid living-electronic computing device.
Being a bio-electronic device the chip will need components to generate waveforms and a clock, the source of regularly spaced pulses, implemented as oscillators. We experimentally demonstrate that it is possible to implement an
electronic oscillator — a device which converts direct current to alternating
current signal — with living slime P. polycephalum. Experimental setup is outlined in Sect. 2. Section 3 presents experimental results on Physarum resistance
oscillations, input to output potential transfer function and current dynamics in Physarum oscillators. Advantages and limitations of living Physarum
oscillators are discussed in Sect. 4.
2
Materials and Methods
A scheme of experimental setup is shown in Fig. 1. Two blobs of agar 2 ml
each (Fig. 1b) were placed on electrodes (Fig. 1c) stuck to a bottom of a plastic Petri dish (9 cm). Distance between proximal sites of electrodes is 10 mm
in all experiments. Physarum was inoculated on one agar blob. We waited till
Physarum colonised the first blob, where it was inoculated, and propagated
towards and colonised the second blob. When second blob is colonised, two
blobs of agar, both colonised by Physarum (Fig. 1a), became connected by a
single protoplasmic tube (Fig. 1d). In each experiment a resistance, potential
and current were measured during 10 min with four wires using Fluke 8846A
precision voltmeter, test current 1±0.0013 µA. Direct current potential was
2
applied using Gw Instek GPS-1850D laboratory DC power supply. Dynamics
of resistance of the blobs connected by a single protoplasmic tube was measured in 22 experiments; dynamics of electrical potential difference between
blobs and current for direct current potential applied in a range of 2 V to 15 V
was measured in 6 experiments for each value of potential difference applied.
3
Results
Resistance of two agar blobs colonised by Physarum and connected with each
other by a silver wire exhibits quasi-chaotic oscillations (Fig. 2a) with a wide
range of dominating frequencies (Fig. 3a). When a Physarum propagates from
one agar blob to another blob it connects two blobs with a single protoplasmic
tube (Fig. 1b). Average resistance of a 10 mm protoplasmic tube is 3 MOhm,
standard deviation 0.715 MOhm. Resistance of the protoplasmic tube exhibits
oscillatory behaviour (Fig. 2bc) with highly pronounced dominating frequency
(Fig. 3bc). Average dominating frequency is 0.0137606 Hz, median dominating frequency is 0.0126953 Hz, standard deviation is 0.0033492429 Hz. The
resistance oscillations have average amplitude 0.59 MOhm, standard deviation 0.256 MOhm; minimum amplitude of resistance oscillations observed was
0.11 MOhm and maximum amplitude 1 MOhm. Oscillation in resistance observed are due to peristaltic contractions of the protoplasmic tube [29], see
details in Sect. 4.
When we apply a potential to a protoplasmic tube oscillations of the tube’s
resistance result in oscillation of the output potential as shown in Fig. 4.
Values of average output potential; and frequencies, periods and amplitudes
of potential oscillations are given in Tab. 1.
Average output potential and average amplitude of output potential oscillations grow linearly with increase of an input potential (Fig. 5ab). Frequency of
oscillations remains almost constant (Fig. 5c), Physarum oscillator produces
the same frequency oscillations at 2 V and 15 V applied potential. A ratio of
average amplitude of output potential oscillations to average output potential
decreases by a power low with increase of input potential (Fig. 5d).
Examples of oscillations of output current for for 5, 10 and 14 V input potential
applied as shown in Fig. 6 and values of current are given in Tab. 2.
3
4
Discussions
Stability, accuracy, adjustability and ability to produce accurate waveforms
are amongst key desirable features of an ideal electronic oscillator [14].
To test Physarum oscillators’ stability we recorded output behaviour of oscillators for 30 min, examples are shown in Fig. 7. In such long runs oscillations
of an output potential persisted and frequency of oscillations was stable. We
observed drifts of the output potential baseline and, sometimes sudden yet
short-living, changes in amplitude of oscillations, e.g. between 300th and 500th
seconds in example Fig. 7a, 1100th and 1500th seconds in example Fig. 7b,
and 1100th and 1500th seconds in example Fig. 7c. Frequency of oscillations
is stable during over 70% time of Physarum oscillator functioning.
A drift of the electrical potential baseline occurs more likely due to unequal growth of Physarum on agar blobs. Dynamically changing difference
in Physarum body mass on reference and recording electrodes leads to a corresponding changes in resistance of the system and subsequent drift of the
background potential. This drift is often in a range exceeding the electrical
potential oscillation amplitude and therefore must be dealt with. Immediate
solution would be to involve auxiliary components to independently measure
background resistance or potential, calculate and adjust the baseline potential [19]. Further studies will concern how to control growth of Physarum mass
on the electrodes. This could possibly be done by illuminating blobs with a
strong light every time increase of mass is detected. Physarum exhibits photoavoidance and therefore its grows will be limited in the illuminated areas.
Protoplasmic tubes of the slime mould exhibit periodic propagations of calcium wave along the tubes. A calcium ion flux through membrane triggers
oscillators responsible for dynamic of contractile activity [21,10]. The calcium
waves are reflected in oscillations of external membrane potential of Physarum
and periodic reversing of cytoplasmic flow in the tubes [16,17,18,21]. Average
dominating frequency of resistance oscillation is 0.0137606 Hz, i.e. period of
oscillations is c. 73 sec. This is consistent with our previous findings on periods of electrical potential oscillation and reversing of cytoplasmic flow. Thus,
average period of electrical potential oscillation recorded in our experiments
is 67 sec [5], 97 sec [6], 103 sec [20], and 115 sec [32]; average 95 sec over
four above sets of data [5,6,20,32]. Cytoplasmic flow in tubes reverses with
period 54 sec [8]. Further experiments might deal with establishing an exact
link between oscillations of a protoplasmic tube’s resistance and peristaltic
oscillations of the tube [29].
Frequency of electrical potential oscillations of Physarum can be modified by
tactile [5] and chemical [32] stimuli, by coloured illumination of a protoplasmic
4
tube [6], and by loading Physarum with functional nano-particles [32]. The
correlation between resistance frequency and frequency of electrical potential
oscillations allows to speculate that frequency of resistance oscillation can be
also tuned by chemical, optical and tactile control inputs. Thus, we believe
the Physarum electrical oscillator is adjustable.
Applicability of Physarum oscillators in conventional electronic circuits is
limited to none. Physarum oscillators produce a very low frequency waveforms and therefore can only be used in computing devices where speed of
information processing is not critical. Thus a potential application domain
of Physarum oscillators is in self-growing biological computing devices and
hybrid bio-silicon devices, and amorphous bio-inspired robots [22]. Another
promising application would be in disposable bio-sensors and bio-circuits: living Physarum oscillator can produce stable waveforms for up to 5-7 days;
such time frame is sufficient to make reliable measurements and to perform
non-time consuming computations.
5
Conclusions
A single protoplasmic tube of an acellular slime mould P. polycephalum can be
employed as a living electronic oscillator which produces stable, accurate, and,
in principle, adjustable waveforms. This is because the tube exhibits periodic
peristaltic contractions which lead to oscillations of the tube’s resistance.
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sensor: Mapping chemical inputs onto electrical potential dynamics of Physarum
Polycephalum. Sensors and Actuators B: Chemical (2013), in press.
7
2
ADAMATZKY
b
b
a
d
a
c
c
Figure 1. Top: A scheme of experimental setup. (a) Physarum, (b) agar
Fig.
1. Top:
scheme of experimental
setup.tube.
(a) Physarum,
agar blobs,shown
(c) elecblobs,
(c)Aelectrodes,
(d) protoplasmic
All parts (b)
of Physarum
trodes,
(d)grey
protoplasmic
tube.
All Bottom:
parts of Physarum
in blobs
dark grey
form a
in dark
form a single
cell.
A snapshotshown
of agar
occupied
single
cell.
Bottom:
A
snapshot
of
agar
blobs
occupied
by
Physarum
and
connected
by Physarum and connected by a protoplasmic tube.
by a protoplasmic tube.
of plane tessellations [26], execution of logical computing schemes [30, 2], and natural
implementation of spatial logic and process algebra [28].
Table
1
In the
framework
of our “Physarum Chip” EU project [4] we aim to experimentally
Data on
Physarumprototype
oscillator. of a Physarum based general purpose computer. This
implement
a working
computer
willpotential,
combineVself-growing
computing
circuits
a living slime
mould
with
Input
Av. freq., Hz
Av. period,
sec made
Av. of
amplitude,
V Av.
output
potential, V
conventional electronic components. Data and control inputs to the Physarum Chip
2
0.01465
68.26
0.035
1.192
will be implemented via chemical, mechanical and optical means. Aiming to develop a
3 of future Physarum
0.01318 computers
75.87
0.06
component base
we designed Physarum
tactile sensor1.32
[5]
and undertook foundational studies towards fabrication of slime mould chemical sensors
4
0.01074
93.11
0.115
2.59
(Physarum nose) [9, 32], Physarum memristive devices [11] and insulated Physarum
6
0.014
71.43
0.2
3.43
wires [7].
A future Physarum
Chip will
be a hybrid living-electronic
computing
device. Being
a
7
0.01074
93.11
0.26
5.72
bio-electronic device the chip will need components to generate waveforms and a clock,
8
0.01269
78.80
0.31 We experimentally
6.87
the source of regularly
spaced
pulses, implemented
as oscillators.
demonstrate that
to implement75.87
an electronic oscillator
— a device which
9 it is possible
0.01318
0.37
7.74
converts direct current to alternating current signal — with living slime P. polycephalum.
0.01562
64.02 3 presents0.45
Experimental 10
setup is outlined
in Sect. 2. Section
experimental results8.42
on
Physarum resistance
oscillations,
input
to
output
potential
transfer
function
and
cur11
0.01172
85.32
0.46
9.32
rent dynamics in Physarum oscillators. Advantages and limitations of living Physarum
12
0.01513
66.09
0.475
9.13
oscillators are discussed in Sect. 4.
14
15
0.0166
60.24
2.
Materials and
0.01465
68.26Methods
0.64
11.61
0.71
12.07
A scheme of experimental setup is shown in Fig. 1. Two blobs of agar 2 ml each
(Fig. 1b) were placed on electrodes (Fig. 1c) stuck to a bottom of a plastic Petri dish
8
4
ADAMATZKY
MOhm
0.150
0.145
0.140
0
50
100
150
200
250
300
350
400
450
500
550
600
650
300 350
sec
400
450
500
550
600
650
400
450
500
550
600
650
Sec
(a)
MOhm
3.0
2.5
2.0
0
50
100
150
200
250
(b)
2.1
MOhm
2.0
1.9
1.8
0
50
100
150
200
250
300 350
sec
(c)
Fig. 2. Resistance of (a) of agar blobs, colonised by Physarum, blobs are connected
Figure
2. Resistance of (a) of agar blobs, colonised by Physarum, blobs
with each other by a silver wire, (bc) agar blobs, occupied by Physarum, blobs are
are connected
connected
eachbyother
by a silver
(bc) agar
blobs,during
occupied
withwith
each other
a protoplasmic
tube.wire,
The resistance
is recorded
10 min. Verticalblobs
axis is are
resistance
in MOhm,
and horizontal
axis is
sec.
by Physarum,
connected
with
each other
bytime
a in
protoplasmic
tube. The resistance is recorded during 10 min. Vertical axis is resistance
9
in MOhm, and horizontal axis is time in sec.
SLIME MOULD OSCILLATORS
5
8×10−4
6
4
2
0
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.25
0.30
MHz
0.35
0.40
0.45
0.50
0.55
0.35
0.40
0.45
0.50
0.55
Hz
(a)
0.25
0.20
0.15
0.10
0.05
0
0
0.05
0.10
0.15
0.20
(b)
0.10
0.05
0
0
0.05
0.10
0.15
0.20
0.25
0.30
MHz
(c)
Fig. 3. Spectra of resistance dynamics of (a) of agar blobs, colonised by Physarum,
Figure
3. Spectra of resistance dynamics of (a) of agar blobs, colonised
blobs are connected with each other by a silver wire, (bc) agar blobs, occupied by
by Physarum,
blobs
are connected
with
other tube.
by The
a silver
Physarum, blobs
are connected
with each other
by aeach
protoplasmic
spectra wire,
are calculated
recordings of
Fig. 2.are connected with each
(bc) agar
blobs,onoccupied
byresistance
Physarum,
blobs
10shown in
other by a protoplasmic tube. The spectra are calculated on recordings
of resistance shown in Fig. 2.
6
ADAMATZKY
1.30
V
1.25
1.20
1.15
0
50
100
150
200
250
300 350
sec
400
450
500
550
600
650
400
450
500
550
600
650
400
450
500
550
600
650
400
450
500
550
600
650
(a) 2V applied
2.6
V
2.5
2.4
2.3
2.2
0
50
100
150
200
250
300 350
sec
(b) 4V applied
V
5.0
4.5
4.0
0
50
100
150
200
250
300 350
sec
(c) 10V applied
V
12.5
12.0
11.5
0
50
100
150
200
250
300 350
sec
(d) 15V applied
4. Examples
output dynamics
potential for
dynamics
various
values input,
of
Fig. Figure
4. Examples
of output of
potential
various for
values
of applied,
applied,
input,
potential.
Vertical
axis
is
potential
in
V,
and
horizontal
potential. Vertical axis is potential in V, and horizontal axis is time in sec.
axis is time in sec.
11
Average potential recorded, V
SLIME MOULD OSCILLATORS
7
10
5
0
1
2
3
4
5
6
7
8
9
10
Potential applied, V
11
12
13
14
15
16
11
12
13
14
15
16
11
12
13
14
15
16
11
12
13
14
15
16
(a)
Amplitude of oscillations, V
0.8
0.6
0.4
0.2
0
1
2
3
4
5
6
7
8
9
10
Potential applied, V
(b)
Frequency of oscillations, Hz
0.016
0.014
0.012
0.010
1
2
3
4
5
6
7
8
9
10
Potential applied, V
Amplitude to potential recorded ratio
(c)
0.010
0.005
0
1
2
3
4
5
6
7
8
9
10
Potential applied, V
(d)
Fig. 5.Figure
Graphs of
values of an (a)
average
potential,
(b) average
5. experimental
Graphs of experimental
values
of anoutput
(a) average
output
potential,
(b) average
amplitude
of output
potential
oscillations,
(c) average
amplitude
of output
potential
oscillations,
(c) average
frequency
of output
potential
frequency
output
(d) ratio
of average
ampli- to
oscillations,
and of(d)
ratio potential
of averageoscillations,
amplitude and
of output
potential
oscillations
12 to average output potential for input
tude
of output
potential
oscillations
average
output
potential
for input
potential
2 V to 15 V applied. Trend lines are
2 V power
to 15 V
linear potential
in (abc) and
lowapplied.
in (d). Trend lines are linear in (abc) and power
low in (d).
SLIME MOULD OSCILLATORS
9
A
5×10−6
4
3×10−6
0
50
100
150
200
250
300
350
400
450
500
550
600
650
400
450
500
550
600
650
400
450
500
550
600
650
sec
(a) 5V applied
12×10−6
A
10
8
6×10−6
0
50
100
150
200
250
300 350
sec
(b) 10V applied
A
1.6×10−5
1.4
1.2×10−5
0
50
100
150
200
250
300 350
sec
(c) 14V applied
Fig. 6. Current oscillations in Physarum protoplasmic tubes at (a) 5 V, (b) 10 V
Figure
oscillations
in Physarum
protoplasmic
tubes at
and (c) 6.
14 VCurrent
input potential
applied. Vertical
axis is current
in A, and horizontal
is time
(a) axis
5 V,
(b) in10sec.V and (c) 14 V input potential applied. Vertical axis
is current in A, and horizontal axis is time in sec.
13
with our previous findings on periods of electrical potential oscillation and reversing of
cytoplasmic flow. Thus, average period of electrical potential oscillation recorded in our
Table 2
Values of current in µA obtained in experiments.
Potential applied, V
Av. current
St. dev.
Av. current amplitude
St. dev
5
4.06
0.53
1.23
0.29
10
9.04
1.5
2.22
0.22
14
11.2
0.72
3.49
0.24
14
10
ADAMATZKY
3.0
V
2.8
2.6
2.4
0
200
400
600
800
1000
sec
1200
1400
1600
1800
2000
1400
1600
1800
2000
1400
1600
1800
2000
(a) 4V applied, 30 min
8.5
V
8.0
7.5
7.0
6.5
0
200
400
600
800
1000
sec
1200
(b) 10V applied, 30 min
13
V
12
11
10
0
200
400
600
800
1000
sec
1200
(c) 15V applied, 30 min
Fig. 7. Dynamics of output potential of Physarum oscillator during 30 min applica-
Figure
Dynamics
ofVertical
Physarum
oscillator
during
tion of 7.
input
potential ofof
(a)output
4 V, (b) potential
10 V, (c) 5 V.
axis is potential
in V,
30 min
application
input
potential of (a) 4 V, (b) 10 V, (c) 5 V. Vertical
and horizontal
axis of
is time
in sec.
axis is potential in V, and horizontal axis is time in sec.
15
Frequency of electrical potential oscillations of Physarum can be modified by tactile [5] and chemical [32] stimuli, by coloured illumination of a protoplasmic tube [6],