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Slime Mould Memristors
Article in BioNanoScience · November 2014
DOI: 10.1007/s12668-014-0156-3 · Source: arXiv
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ARE SLIME MOULDS LIVING MEMRISTORS?
ELLA GALE, ANDREW ADAMATZKY, AND BEN DE LACY COSTELLO
arXiv:1306.3414v1 [cs.ET] 14 Jun 2013
A BSTRACT. In laboratory experiments we demonstrate that protoplasmic tubes of acellular slime
mould Physarum polycephalum show current versus voltage profiles consistent with memristive
systems. This result complements previous findings on memristive properties of other living
systems (human skin and blood and leaves) and contributes to development of self-growing bioelectronic circuits.
Keywords: memristor, slime mould, bioelectronics
1. I NTRODUCTION
Memristors [7] have revolutionised the material basis of computation [24, 27] and neuromorphic architectures [22, 13, 20, 9]. Since the announcement of the first documented two-terminal
memristor [24] researchers have been eager to experiment with memristors, but they are difficult
to synthesize and not yet commercially available. Few looked beyond silicon but those who did
uncovered a promising behaviour of living systems. Thus, Johnsen et al [14] found that conductance properties of sweat ducts in human skin are well approximated by memristive model [14],
and experimental evidence that blood [15] and leaves [16] exhibits memristive properties was
provided by Kosta et al.
In 2008 Pershin et al [19] described an adaptive behaviour [21] of slime mould Physarum
polycephalum in terms of a memristor model. The plasmodium of Physarum polycephalum
(Order Physarales, class Myxomecetes, subclass Myxogastromycetidae) is a single cell, visible
with an unaided eye. The plasmodium behaves and moves as a giant amoeba. It feeds on bacteria, spores and other microbial creatures and micro-particles [23]. In an environment with
distributed sources of nutrients the plasmodium forms a network of protoplasmic tubes connecting the food source. The network of protoplasmic tubes developed by Physarum shows some
signs of optimality in terms of shortest path [18] and proximity graphs [1]. In [2] we have used
slime mould to make prototypes of massively-parallel amorphous computers — Physarum machines — capable of solving problems of computational geometry, graph-theory and logic. The
Physarum machines implement morphological computation: given a problem represented by a
spatial configuration of attractants and repellents the slime mould gives a solution by patterns of
its protoplasmic network. This limits application domain of slime mould processors to computational tasks with natural parallelism. If we were able to make electronic devices from living
slime we would need to be able to construct the full spectrum of computing devices achievable with a conventional architecture. To make a set of ‘all possible computing devices’ it is
enough to make a material implication gate: memristors naturally implement material implication logic [25]. Thus answering the question ‘Is Physarum a memristor?’ is a task of upmost
priority.
1
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GALE, ADAMATZKY, AND DE LACY COSTELLO
b
b
a
d
a
c
c
F IGURE 1. A scheme of experimental setup: (a) Physarum, (b) agar blobs,
(c) electrodes, (d) protoplasmic tube. All parts of Physarum shown in dark grey
form a single cell.
Physarum’s growth can be directed with chemo-attractants and repellants [4] and it chooses
efficient paths between food sources. Thus, Physarum could be used to ‘design’ efficient circuits. Previous preliminary work [17] has shown that Physarum can take-up iron-based magnetic
particles, so it could be used to lay down efficient circuits and, if the magnetic effects were detrimental to the Physarum, we might expect it to lay down circuits with a good electromagnetic
profile. Because Physarum can internalise magnetic particles, we also investigated the electrical
properties of the Physarum tubes with and without these particles.
Structurally Physarum is a semi-rigid gel which is put down by the living cytosol within it
(and this gel is covered with a protective ‘slime’ which gives rise to the plasmodium’s colloquial name ‘Slime mould’). This living cytosol undergoes shuttle-transport, switching direction
approximately every 50 seconds. Thus, when measuring electrical properties of Physarum, we
must take care to separate the effects of the living cytosol and ‘dead’ exteriour gel and slime
layers and remember that the cytosol is a moving and living system.
2. M ETHODS
Plasmodium of Physarum polycephalum was cultivated in ventilated plastic lunch boxes on
wet kitchen towels and fed with oat flakes. Culture was periodically replanted to a fresh substrate. The experimental scheme is shown in Fig. 1. Two blobs of agar 2ml each (Fig. 1b)
were placed on one of the electrodes (Fig. 1c) attached to the bottom of a plastic Petri dish
(≈9cm). Distance between proximal sites of electrodes was always ≈10mm. We waited while
the Physarum colonised the first blob, where it was inoculated, and propagated towards the second blob. When the second blob is colonised, the two blobs of agar and electrodes are both
colonised by Physarum (Fig. 1a), became connected by a single protoplasmic tube (Fig. 1d).
Note that the physarum tube is rarely straight as in the diagram and is usually much more serpentine. At this point we measured memristive properties of Physarum, using the set-up as shown
in Fig. 1. This setup has already been proved to be sufficient for the recording and analysing
of electrical activity of Physarum [5] and studies of electrical response of Physarum to tactile
stimulation [6]. The properties were measured on a Keithley 617 programmable electrometer
which allowed the measurement of currents from pA-3.5mA. As memristance is a frequency
and voltage range dependent effect, several different measurement values were tested to discover which ranges were best for the measurement. All presented I-V curves were performed
with a descretized voltage waveform of 160 points equivalent to an a.c. frequency of 19.186mHz
(period of 327.5s) unless otherwise stated. Devices were tested over a range of 19-341 mHz (the
strange numbers result from the use of rational numbers of seconds to set the average measurement time). Measurements were performed with a voltage range from ± 50mV (sample 1-13) to
ARE SLIME MOULDS LIVING MEMRISTORS?
3
100mV or higher (samples 15-22). Because Physarum is a living system we needed to compare
first and second runs across different dishes, so the tests were divided into two batches: batch 1
was measured under different frequencies and a voltage range of ±50mV and ±100mV; batch 2
was measured only with the 19mHz frequency voltage waveform and a voltage amplitude range
of ±100-±250mV.
Three different electrode set-ups were tested: thick 2mm aluminium wire, thin 0.5mm silver
wire and thin aluminium mesh. Physarum was also tested for the electrical effect of the uptake
of magnetic particles (FluidMAG-nano-particles, ChemCell GmbH, Berlin, Germany, are ferrofluids consisting of an aqueous dispersion of magnetic iron oxides with a diameter of 200 nm)
by inoculating the starting or ending oat flakes with the particles. As Physarum is sensitive to
light, the electrical tests were run in the dark and controls were run under strong fluorescent light
to test if this effected the electrical properties. The effect of light was also tested by running I −t
responses where the Physarum was kept in the dark under constant current and then exposed to
light at a set point.
3. R ESULTS
3.1. Memristive Effects. 23 samples were made, in 1 sample the Physarum did not form a tube
across the electrodes, in 1 sample the Physarum grew, formed and abandoned the tube before
it could be measured, this sample (no. 10) was used as a control for the gel and slime part of
the tube structure. The remaining 21 samples were measured and these comprised of 2 samples
with magnetic nanoparticles on the inoculation electrode (no. 1,4), 2 samples with magnetic
nanoparticles on the target electrode (no. 5,6), the rest were normal non-inoculated Physarum.
3 samples (numbers 3,8 and 14) were electrically unconnected (usually due to the tube being
mechanically broken).
Of those measured in batch 1, although memristance was observed at 0.05V, the lowest frequency (19mHz) worked better. Of the 11 samples in batch 1, 2 exhibited good memristance
curves, the other 9 exhibited open curves (as shown in Fig. 3. These open curves are interesting
as they are similar to those which when seen in TiO2 sol-gel memristors over the ±0.5V range
were found to be indicative of memristive curves in the ±3V range [10].
Batch 2 which were measured at a larger voltage range (between ±100mV and ±250) and
8 out of 8 samples showed good memristive curves as shown in Fig. 2. This shows that slime
mould can act as a living memristor. These results show that relatively large voltages are needed
for the measurement of memristance in Physarum.
Comparison between the memristance curves shown in Fig. 2 and the results for an abandoned
tube shown in Fig. 5 shows that the memristance is due to the living Physarum (specifically
the cytosol). Similarly to inorganic memristors, this could be due to voltage driven charge
transport. Shuttle transport reverses direction around every 50s and this could give rise to a
measurable hysteresis, however because these data were measured at an average 2s apart for 160
steps the period is 327.5s which is over 3 times the period of the shuttle transport and, as such,
it is unlikely to be the cause of the measured effect. A voltage-mediated change in material
properties of the cytosol which has a relaxation time could lead to a memristive hysteresis.
Note, that the memristive Lissajous curves do not always cross the axes at the origin as they
should [7], we suspect that this is due to the living nature of slime mould in that it possesses an
internal battery (in electronic terms) and applies a small potential difference to the system. As
the electrometer works by sourcing voltage and measuring current, it may not pick up a small
4
GALE, ADAMATZKY, AND DE LACY COSTELLO
(a)
(b)
(c)
(d)
F IGURE 2. Typical current versus voltage profiles recorded in laboratory experiments with slime mould P. polycephalum, these pinched hysteresis loops
are indicative of memristance.
voltage drop generated by the living plasmodium’s metabolic actions. This does, technically,
make Physarum an active memristor [12] because it is alive and generating power.
No electrical effect of using different electrode types was seen beyond the mechanical difficulties: the thicker aluminium electrodes put strain on the tube which lead to breakages or
short-circuits. No discernible electrical effect was seen from the presence of magnetic nanoparticles. The Physarum picked them up and internalised them into the tube, but the measured
resistance curves were the qualitatively the same as those without the particles and within the
same range.
3.2. Repeatability and the effect of frequency. Physarum did not ‘like’ the testing process.
Successive applications of voltage caused the Physarum to abandon the tube and seek food
elsewhere as observed by a thinning and lightening of the tube (for this reason the Physarum
were photographed before and after each test to check the cytosol was still present). Figure 4
ARE SLIME MOULDS LIVING MEMRISTORS?
5
F IGURE 3. Different frequencies were tried to see if they affected the memristance curve. They didn’t. Successive runs caused an increase in resistance,
perhaps due to hardening of the gel or increased levels of gel.
(a)
(b)
F IGURE 4. An example from on the experiment inoculated with nanoparticles.
After measurements, the tube has thinned, unnecessary parts have been ‘burnt
off’, colour is a lighter hue.
slows the set-up before and after measurement, note that unnecessary parts have been completely
abandoned and the main tube is much lighter in colour, indicating a movement of living cytosol
to explore another part of the environment. This result was also seen on the non-inoculated
Physarum samples.
As frequency can effect the size of memristor hysteresis (due to natural response speed of the
system) the voltage waveform frequency was altered. As increasing the natural voltage range
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GALE, ADAMATZKY, AND DE LACY COSTELLO
F IGURE 5. Repeated I-V runs performed on an abandoned tube. No memristance or increasing resistance effect is seen.
may turn the ‘open-loop’ type of memristor into a pinched hysteresis loop, the lack of pinched
hysteresis on the open-loop memristor responses could be due to the chosen voltage range. The
effect of frequency is tested in Fig. 3, where three repeats of the same ±V range is tried at the
standard and twice the frequency and one larger ±V range is tried at the standard frequency.
The shape is qualitatively similar over this voltage range and unaffected by frequency over this
voltage range. Figure 3 shows that repeated applications of voltage causes the the resistance of
the tube to increase (similar results were observed on the two repeats with other samples). As
Fig. 5 shows no repeated resistance change and Fig. 4 shows the cytosol leaving the tube, we
suggest that this result it due to the cytosol moving elsewhere (the gel part of the tube has a high
resistance) and rather than a chemical or physical change in the structure of the outer parts of
the tube.
F IGURE 6. In no light, black, the physarum oscillations adapts to the voltage.
In light (red) turned on at 400 s. Complete loss of oscillations after 1200 seconds, but no real strong evidence for light effect.
ARE SLIME MOULDS LIVING MEMRISTORS?
(a)
7
(b)
(c)
F IGURE 7. Vague indication of possible light effect. (a) Current spike response
to voltage followed by visible oscillations, (b) Further oscillations against a
background shift, (c) Cover is removed at ≈ 200s, light moved over about half
a minute afterwards.
3.3. Effect of light on electronic measurements. Physarum moves away from bright lights,
therefore we decided to investigate whether there was an electronically measurable response to
this behaviour. Figure 6 shows the response of a slime mould to light: the black curve shows an
oscillation that persists for about 400 seconds and then changes to a longer wavelength oscillation with the shorter oscillation superimposed between 1200 and 1600 seconds. The red curve
shows a what happens when the test is run again with light applied at 400s, the oscillations disappear, there is still the long wavelength oscillation but there are no short-wavelength oscillatory
features from 1200-1600s. The disappearance of the short-wavelength oscillation is due to the
Physarum responding to the applied voltage, not the light, however the lack of short-wavelength
oscillations at 1200-1600s may be due to the applied light.
This test was repeated with another sample, as shown in Fig. 7. Here we see a drop in resistance due to voltage (consistent with results reported above) and then the short term oscillations.
8
GALE, ADAMATZKY, AND DE LACY COSTELLO
When the cover is removed and light applied, the ‘character’ of these oscillations changes from
smooth regular short-wavelength oscillations on a background of longer wavelength oscillations
to more spiky, less oscillatory decay. We suspect that the electronic oscillations are to do with
differing shuttle-movement patterns as a result of exposure to light. However, because this is a
living system, it is changing all the time and the qualitative ‘character’ of the electronic measurement needs to be compared.
Finally, an I-V curve was run for a different sample in the dark and then in the light this
showed no change other than the increase in resistance, which was seen in repeated runs performed in the dark. Thus, it seems, the presence or absence of light does not show up in the
memristive I-V curves and is irrelevant for the measurement of memristance (or rather the application of voltage is far more relevant). Nonetheless, Figs. 6 and 7 suggest that the ‘character’
of the Physarum’s natural electrical responses do change slightly in response to light.
4. D ISCUSSION
The results clearly show hysteresis and memristive effects in living Physarum. The frequency
and voltage range effected the measured effects, we found that a timestep of δt = 2s and a ±
of over 200mV gave the best results. It was expected that such a large voltage range would
damage the Physarum and the plasmodium did move away from the testing site, although the
Physarum did not dry up or die as a result of testing. At low voltages, an open-curve shape was
measured instead, which we think is the memristive response (or the process that gives rise to
it) when measured at the wrong frequency. As the memristance disappeared when the Physarum
moved elsewhere, and an abandoned tube showed a high linear resistance, we suggest that the
memristive response is due to the living cytosol.
Current versus voltage profiles measured for protoplasmic tubes of P. polycephalum exhibit
great variability in the magnitude of hysteresis and the location of pitch points. This is to be
expected given the fact that slime mould is an ever-changing living entity and although attempts
were made to standardise the experimental set up such as the measurement of single protoplasmic tubes across a known electrode gap it proved difficult to control precisely the morphology
of the tubes. For example even though the electrode distance can be controlled this does not
ensure standardisation of the protoplasmic tubes length or, indeed more importantly, the width.
It also proves difficult to control the position and numbers of small sub-branches which may
arise during experimental measurements. Although these do not usually contact the electrode
except for sub branching at the terminal ends this alteration in morphology is likely to affect the
conductivity. Thus future research would focus on stabilisation of protoplasmic tubes.
Stabilisation could be achieved by employing the slime mould’s potential of internalisation
and re-distribution of conductive and magnetic particles [17] or at least constraining the growing
with some kind of scaffolding [26]. There is also the potential that the slime mould could
construct an internal scaffold or that this could be induced by appropriately applied external
fields, in fact morphological control could be accomplished by application of appropriate fields
per se [8]. Despite the complications of live electronics we demonstrated that it is feasible to
implement living memristive devices from slime moulds P. polycephalum.
We believe that future electronic designs will incorporate growing slime mould networks capable of forming a skeleton of conductive information processing elements as part of integrated
computing circuits. The slime mould circuits will allow for a high density of computing elements
and very low power consumption. To date the useful lifetime of a slime mould memristor is 3-5
ARE SLIME MOULDS LIVING MEMRISTORS?
9
days. However, future studies on loading and coating of the tubes with functional materials with
a dual role of structural re-enforcement such as nano-metallic, nano-magnetic or nano-structured
semiconducting particles, conducting polymers etc. should enable us to increase the life span
substantially whilst also imparting a diverse range of tunable electronic characteristics.
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(Gale) U NIVERSITY OF THE W EST OF E NGLAND , B RISTOL , U NITED K INGDOM
(Adamatzky) U NIVERSITY OF THE W EST OF E NGLAND , B RISTOL , U NITED K INGDOM
(De Lacy Costello) U NIVERSITY OF THE W EST OF E NGLAND , B RISTOL , U NITED K INGDOM
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