This article was downloaded by: [Richard Mayne] On: 14 January 2015, At: 08:07 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Click for updates International Journal of General Systems Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/ggen20 Slime mould foraging behaviour as optically coupled logical operations R. Mayne a & A. Adamatzky a a Unconventional Computing Group, Faculty of the Environment and Technology, University of the West of England, Bristol, UK. Published online: 12 Jan 2015. To cite this article: R. Mayne & A. Adamatzky (2015): Slime mould foraging behaviour as optically coupled logical operations, International Journal of General Systems, DOI: 10.1080/03081079.2014.997528 To link to this article: http://dx.doi.org/10.1080/03081079.2014.997528 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &
Transcript
This article was downloaded by: [Richard Mayne]On: 14 January 2015, At: 08:07Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Click for updates
International Journal of GeneralSystemsPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/ggen20
a Unconventional Computing Group, Faculty of the Environmentand Technology, University of the West of England, Bristol, UK.Published online: 12 Jan 2015.
To cite this article: R. Mayne & A. Adamatzky (2015): Slime mould foraging behaviouras optically coupled logical operations, International Journal of General Systems, DOI:10.1080/03081079.2014.997528
To link to this article: http://dx.doi.org/10.1080/03081079.2014.997528
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &
International Journal of General Systems, 2015http://dx.doi.org/10.1080/03081079.2014.997528
Slime mould foraging behaviour as optically coupled logical operations
R. Mayne∗ and A. Adamatzky
Unconventional Computing Group, Faculty of the Environment and Technology, University of the West ofEngland, Bristol, UK
(Received 11 October 2014; accepted 27 November 2014)
Physarum polycephalum is a macroscopic plasmodial slime mould whose apparently ‘intelli-gent’behaviour patterns may be interpreted as computation. We employ plasmodial phototacticresponses to construct laboratory prototypes of NOT and NAND logical gates with electricalinputs/outputs and optical coupling in which the slime mould plays dual roles of computingdevice and electrical conductor. Slime mould logical gates are fault tolerant and resettable.The results presented here demonstrate the malleability and resilience of biological systemsand highlight how the innate behaviour patterns of living substrates may be used to implementuseful computation.
Is a living organism (or a component of the organism) a computing device? Such questions aredivisive and an unhelpful way of comparing the seemingly incalculable complexity of life to aneasily quantifiable man-made system. But, it is nevertheless clear that certain living systems areable to perform computation. For example, in his seminal article, Adleman (1994) outlined howDNA may be used to implement solutions to NP-complete problems such as the Hamiltonian PathProblem, which has now been realized experimentally by a number of authors (Lee et al. 2004;Liu et al. 2000). Similarly, the human brain is able to concurrently compute responses to a vastnumber of parallel problems from a combination of incoming sensory input and internal feedbackmechanisms: to claim that the brain is a massively parallel computing substrate in a peer-revieweddocument, however, would attract derision, as the fundamental architecture of the brain is toodivergent from that of a conventional computer to allow for a meaningful comparison. Despitethis, both varieties of architecture have significant crossover in the types of ‘useful’ computationthey may perform, such as arithmetic and logic.
Biological systems which are able to carry out computation are typically low energy consump-tion (per unit of processing power), although this is difficult to quantify amorphous and displayemergent behaviour – i.e. complex behaviours emerge from the system which cannot be describedin terms of its relatively ‘simple’ inputs. The multi-disciplinary field of unconventional computing(UC) looks to natural systems for inspiration in order to devise novel computing architecturesthat exploit these properties.
The myxomycete slime mould Physarum polycephalum’s plasmodium (vegetative life cyclestage, pl. plasmodia) is a macroscopic acellular organism formed from an interlinking network of
Figure 1. Plasmodium of P. polycephalum cultivating on an agar-filled Petri dish, feeding on porridge oats.Note the morphology of the plasmodial tubes (arrow), which meet at the ‘fan-shaped’ advancing anteriormargin (arrowhead).
protoplasmic ‘tubes’ (Figure 1). The organism’s topology constantly de- and reform as it moves,typically creating a network of tubes which link spatially distributed nutrient sources. Behavingas an excitable or reaction-diffusion system encapsulated in an elastic membrane (Adamatzky2007), slime mould is capable of simultaneous processing of inputs (light, chemical gradients,temperature, etc.), concurrent decision-making and distributed actuation. The behaviour patternswhich ensue – which are essentially genetically encoded (innate) foraging behaviours – may beinterpreted as forms of computation. Typical laboratory prototypes of slime mould-integrateddevices engineered to demonstrate ‘useful’ computation exploit the organism’s chemotaxis –positive, towards chemoattractants or negative, away from repellents – and/or photoavoidance: asthe plasmoidum is capable of movement via the contraction of muscle proteins invoking rhythmicshuttle streaming of its hydrodynamic core (Adamatzky 2012a; Ishikawa et al. 1991), the outcomeof such experiments usually involve manually analysing migratory patterns. For example, slimemould may approximate the shortest path between any number of spatially distributed points bygrowing into a highly optimized tube network (Adamatzky and Jones 2010), or navigate its wayout of a labyrinth (Adamatzky 2012b; Nakagaki 2001); these may be considered as expressionsof network optimization, computational geometry, decision-making and logic.
In this study, we explore the use of light as a programmable input (as a repellent) into the plas-modium, and use the results to implement a basic, yet functional device. Slime mould computingdevices are typically ‘programmed’with spatially distributed nutrient sources (Adamatzky 2010a,2012a; Nakagaki 2001), but such systems are undynamic and impossible to ‘reprogram’ (i.e. alterthe input configuration). Indeed, viable logic gates have been designed and produced by a numberof authors using different variations of chemical attractant and repellent models (Adamatzky2010b; Jones and Adamatzky 2010; Tsuda, Aono, and Gunji 2004), but all suffer from theaforementioned restrictions. These limitations may be overcome by utilizing light as an input, orrather as a coupling medium between the circuitry of logical gates.
In this investigation, we demonstrate a basic experiment to assess the phototactic responses ofthe plasmodium to different colours of light and follow using the most repellent colour to createtwo logic gates: the NOT gate (inverter), chosen for being the simplest logic operation, and theNAND gate, for being a universal gate. We demonstrate the functionality of each gate and finishby discussing the implications of using light as a reprogrammable input into a living system.
2. Phototaxis experiments
A range of experiments were performed to determine which colour of LED-generated lightproduced the strongest repellent effect in P. polycephalum plasmodia. Plasmodium samples ofapproximately 2 cm2 were inoculated on to 2.5 cm2 squares of 2% non-nutrient agar in the centreof 9 cm Petri dishes. Similar squares of agar loaded with chemoattractants (oat flakes) weresituated at the 3 and 9 o’clock poles of the dishes and were each illuminated by two lid-mountedLEDs (Figure 2(a)). Four colours of diffused lens LED were used – blue (466 nm, 50 mcd), green(568 nm, 40 mcd), yellow (585 nm, 36 mcd) and red (626 nm, 25 mcd) – and each pole had adifferent colour assigned to it in each experiment. Each combination of colours was used andeach was replicated three times. The peripheral regions of the dish were separated from the centreby two strips of thick card glued to the dish lid, with a 0.5 mm gap underneath: this preventedmost of the light from reaching the inoculation point, but allowed the plasmodium to migratethrough the gap underneath. The experiments were carried out in an otherwise lightless box andwere checked periodically.
Test plasmodia were, therefore, given three basic choices in each experiment: migrate towardscolourA, migrate towards colour B or do neither (and hence, stay in the centre/sclerotinize/attemptto colonise the card/escape the dish, etc.). The choices each plasmodium made were compiledinto an order of preference for each colour; the experiment was repeated if the neither colour waschosen. The colour which was avoided most was chosen for use in subsequent logic gate designs.
A completed phototaxis experiment is shown in Figure 2(b). Experiments typically took 3–5days to complete. It should be noted that on no occasion did the plasmodium chose to stay on thecentral agar square and sclerotinize, although on two occasions it migrated up the card barrier andbegun to consume the glue securing it to the lid of the Petri dish.
Figure 2. Phototaxis experiments. (a) A scheme of experimental set-up for phototaxis experiments. Greysquares represent agar cubes: the slime mould is inoculated on the central cube (pentagon) and is left toproliferate. Black rectangles represent card barriers with a 0.5 mm gap underneath, which the plasmodiumis able to migrate underneath to access the peripheral agar cubes, which are loaded with chemoattractantsand illuminated by 2 × LEDs (circles). (b) Photograph of a completed phototaxis experiment: note how theplasmodium has migrated towards the left ‘blue’ side (arrowed).
Dow
nloa
ded
by [
Ric
hard
May
ne]
at 0
8:07
14
Janu
ary
2015
4 R. Mayne and A. Adamatzky
P. polycephalum’s preference to each colour of LED is summarized below, arranged in orderof most avoided → least avoided:
Green → Red → Yellow → Blue
Thus, green LEDs were used in further experiments.
3. NOT gate
The design for the Physarum-NOT gate (PNOT) is shown in Figure 3(a). Two aluminium tapeelectrodes (X and Y ) were stuck to the base of a 9 mm plastic Petri dish, separated by a central10 mm gap. 2 ml blobs of 2% non-nutrient agar were placed on top of each electrode, one of whichwas loaded with plasmodium (X ) and the other a chemoattractanct (an oat flake) (Y ). The gate’s‘input’ consisted of a 9 V power supply connected to a lid-mounted LED overlying electrode Y .When the input is live, i.e. logic 1, the LED is active and prevents the plasmodium from migratingfrom X to Y . When the input is not live, logic 0, the LED is inactive and therefore the plasmodium isfree to migrate to electrode Y , forming a continuous tube of plasmodium between both electrodes.
Both electrodes are connected to a separate ‘output’ circuit consisting of a separate powersupply, set at 9 V, 0.1A. The plasmodium, when spanning the electrodes, acts as a physicalconductor of electricity and hence completes the output circuit. As such, the device’s functionalityis identical a conventional NOT gate, i.e. if the input is live, the output is not and vice versa.
Figure 3. Physarum NOT logic gate. (a) Schematic diagram of a PNOT logic gate.Aplasmodium (pentagon)is placed on agar (grey squares) overlying electrode X and chemoattractants are placed on Y . If the input[A] to the LEDs (circles) is at logic 0, the LED does not switch on and a plasmodial tube is formed betweenelectrodes X and Y , and vice versa. The electrodes are wired into an independently powered output circuit [O].(bc) Photographs of a functional PNOT gate. (b) Experimental set-up with input at logic 1; the plasmodiumdid not migrate to Y and the output was left at logic 0. (c) With input at logic 0, the plasmodium has migratedacross the gap and created a ‘wire’ which was electrically conductive, leaving the output at logic 1.
Dow
nloa
ded
by [
Ric
hard
May
ne]
at 0
8:07
14
Janu
ary
2015
International Journal of General Systems 5
Photographs of a functional PNOT gate are shown in Figure 3. The time it took for theplasmodium to complete its logic function was extremely variable, ranging from 1 to 3 days. Thefailure rate was approximately 25%.
4. NAND gate
Physarum-NAND (PNAND) gates were constructed based upon the same principles of the PNOTgate, but with a second electrode and LED added to the device (Figure 4(a)). LEDs A and Bwere linked to separate power sources and represent independent inputs. Plasmodial samplesinoculated onto electrode X were given the added option of migrating towards electrode Z aswell as Y . If both inputs are at logic 0, the plasmodium can migrate towards either Y or Z atrandom, completing the output circuit. If input A is 1 but B is 0, the plasmodium at electrode X isstill free to complete the circuit by migrating to electrode Z , and vice versa. If both A and B are 1,the plasmodium will not migrate towards either electrode, preventing a circuit from forming andhence leaving the output at 0. Electrodes X and Y were physically separated by a barrier similar
Figure 4. Physarum NAND gate. (a) Schematic diagram of a PNAND gate. Slime mould (pentagon) isplaced on agar (grey squares) overlying electrode X and attractants are placed on Y and Z . A card barrierseparates electrodes Y and Z to prevent light contamination. If inputs A or B are at logic 1, their LEDs(circles) are live, preventing slime mould growth to the corresponding electrode. If both A and B are live,no circuit forms, resulting in no output. When vice versa is true, the slime mould is free to migrate to eitherelectrode and hence complete the circuit. If only one LED array is live, the slime mould is free to migrate tothe non-illuminated electrode. As with the PNOT gate, when a circuit is created between two electrodes, theoutput is live. (bcd) Photographs of a functional PNAND gate. (b) T = 6 h; the left electrode is illuminated.(cd) T = 12 − 24 h; the plasmodium migrates to the unilluminated electrode.
Dow
nloa
ded
by [
Ric
hard
May
ne]
at 0
8:07
14
Janu
ary
2015
6 R. Mayne and A. Adamatzky
to those described in Section 2 to prevent light contamination from opposing LEDs. Experimentalphotos of PNAND gate are shown in Figure 4(b)–(d).
5. Resettability and fault tolerance
Attempts were made to reset and reprogram both varieties of Physarum logic gate. This wasachieved by carrying out a logical operation and subsequently changing the input configuration.Gate resetting was found to be very reproducible, with all experiments resulting in the withdrawalof plasmodium from an illuminated electrode (n = 10 for each gate). This process typically took2–6 h: this comparative rapidity was attributed to cytoplasmic translocation down the existingtube spanning the electrodes, as opposed to forming a new tube.
Gate reprogramming was less successful. PNOT gates were not successfully reprogrammed,likely due to the phenomenon of slime mould chemical ‘memory’, wherein the plasmodium avoidsareas it has already visited, which it senses through chemical reception of effluvia trails left inthe wake of its migration (Reid et al. 2012). PNAND gates were successfully reprogrammed,however, as shown in Figure 5: switching the input configuration resulted in the plasmodiumretreating and forming a new tube to the other electrode. This was a fairly reproducible result(70%, n = 10). Repeated reprogramming was unsuccessful.
Figure 5. Resetting and reprogramming a PNAND gate. (a) T = 36 h. Completed logical operation forinput configuration (0,1 [left, right]) immediately prior to inverting the inputs to (1,0). (b) T = 38 h. Withina few hours, the slime mould has begun to withdraw to its inoculation point away from the light. (c) T = 42 h.The slime mould begins to migrate towards the unilluminated electrode. The tube linking the central andleft electrodes diminished shortly after this.
The fault tolerance of both varieties of Physarum gate was also investigated by altering physicalvariables in the test environment, including:
(1) Increasing the luminosity of the LEDs by replacing them with brighter clear lens variantsof the same colour (each increased by approximately 50 mcd).
(2) Increasing the potential difference between electrodes to 24 V.
Whilst adjusting these variables is of little practical use in the design of these specific devices,they were chosen to measure P. polycephlaum’s resilience to conditions such as overvoltageoutside normal operational parameters, and hence, the fault resilience of slime mould devices.
Increasing the luminosity of the LEDs appeared to have no effect on device operation.Failure rates and propagation delay were not significantly different to those of the standard gates.P. polycephalum also appeared to be tolerant of high voltages. This was likely due to the highresistance of the plasmodium and agar blobs (Mayne and Adamatzky 2014) limiting current flowthrough it. The morphology of plasmodia exposed to high voltages was nevertheless markedlydivergent, tending to form complex tube networks between the two electrodes, as opposed to asingle tube (data not included).
6. Conclusions
The principle finding of this study was that it is possible to ‘program’ the P. polycephalumplasmodium to carry out basic logic functions through the use of optical inputs. Whilst theprototype devices presented here have significant limitations which remove any possibility oftheir practical utilization, they demonstrate the malleability and resilience of biological systemsfor the fabrication of UC devices.
The P. polycephalum plasmodium may be easily manipulated by using green LEDs as arepellent. That it is more phobic of green light than any other colour is somewhat surprising, asother authors have noted that blue light provokes the strongest plasmodial photophobic responses(Sauer 1982), although the stark differences in experimental set-up – e.g. use of LEDs rather thanconventional bulbs – are likely the source of this discrepancy.
The most significant limitation of these prototypes was the vast multi-day propagation delays.This effectively negates the possibility of constructing viable combinational or sequential logiccircuits. The prototype gates produced here therefore hold no specific practical value other thandemonstrating that the normal foraging behaviour of slime mould may be manipulated to performcomputer logic operations. The concepts presented here may be used in the fabrication of a secondgeneration of optically coupled slime mould logic devices, however. Aside from optimizing theexperimental environment (reducing the effects of desiccation, changing the size of the gapsbetween electrodes, etc.), the most viable research direction for producing gates of practical valuewould appear to be minimizing the role of physical movement. Adamatzky and Jones (2011)demonstrated that P. polycephalum responds to a range of environmental stimuli with predictablepatterns of electrical activity. If the electrical responses of the plasmodium to light are similarlypredictable – and indeed, there must necessarily be some form of electrical response to lightirradiation, as plasmodial membrane potential alters during movement due to Ca2+ ion influx todrive muscle protein contraction – then culturing the plasmodium on a large array of electrodeswould, therefore, allow the researcher to track plasmodial responses electrically, which couldvastly reduce propagation delays and hence allow for gate cascading.
It is also prudent to remark, albeit parenthetically, that cyberneticists may find special interestin this topic, as the assignment of ‘purpose’ to a teleonomical phenomenon (i.e. slime mouldforaging behaviour) has been a topic of intense historical interest, dating back to Rosenbleuth,Wiener, and Bigelow (1943).
Were the propagation delay issue may be remedied, a fundamental restriction imposed onslime mould computing devices is the physical size of the organism. Although the size of thePetri dish environment may be scaled down, the organism is still macro scale. There shouldbe an emphasis on further studies, therefore, to implement multiple operations in a singleplasmodium – possibly with multiple input types – rather than scaling up the number of plasmodiaused.
After discussing the limitations of these devices, it is also pertinent to mention their redeemingfeatures. The devices produced here were all cheap and easy to fabricate, using low-cost, low-power consumption components. Indeed, LEDs were chosen as the main input due to theiravailability and efficiency. They are also reusable and produce no hazardous waste. Further-more, the apparent robustness of slime mould devices to adverse conditions such as overvoltagehighlights how Physarum-based computing may be adapted to roles to which standard computingarchitectures are not suited, e.g. in harsh conditions applications and research. These meritsexemplify the characteristics of biological UC devices and augur well for the possibility ofutilizing other cell types to implement computation: indeed, slime mould computing may beregarded as an intermediate stage towards the final goal of implementing neural computing for arange of biomedical uses.
FundingThe authors gratefully acknowledge the EU Commission seventh Framework Program. The authors declareno conflict of interest.
Notes on contributors
R. Mayne is a PhD researcher at the University of the West of England, Bristol, UK.Originally a biomedical scientist specialising in histopathology, Richard now studiesunconventional computing. His active research areas include unconventional, biologicaland emergent computing, protistology (esp. slime mould biology), nanotechnology andexotic/high resolution microscopy.
A. Adamatzky is Professor in the Department of Computer Science and Director ofthe Unconventional Computing Centre, University of the West of England, Bristol, UK.He is expert in reaction-diffusion computing, cellular automata, physarum computing,massive parallel computation, applied mathematics, collective intelligence and robotics,bionics, computational psychology, non-linear science, novel hardware, and future andemergent computation.
ReferencesAdamatzky, A. 2007. “Physarum Machines: Encapsulating Reaction–diffusion to Compute Spanning Tree.”
Die Naturwissenschaften 94 (12): 975–980.Adamatzky, A. 2010a. Physarum Machines: Computers from Slime Mould. London: World Scientific.Adamatzky, A. 2010b. Slime Mould Logical Gates: Exploring Ballistic Approach. Amsterdam, The
Adamatzky, A. 2012a. “Routing Physarum with Repellents.” European Physics Journal E, Soft Matter 4:403–410.
Adamatzky, A. 2012b. “Slime Mould Solves Maze in One Pass, Assisted by Gradient of Chemo-attractants.”IEEE Transations on NanoBioscience 11 (2): 131–134.
Adamatzky, A., and J. Jones. 2010. “Road Planning with Slime Mould: If Physarum Built Motorways itWould Route M6/M74 through Newcastle.” International Journal of Bifurcation and Chaos 20 (10):3065-3084.
Adamatzky, A., and J. Jones. 2011. “On Electrical Correlates of Physarum Spatial Activity: Can We SeePhysarum Machine in the Dark?” Biophysical Reviews and Letters 6 (1–2): 29–57.
Adleman, L. 1994. “Molecular Computation of Solutions to Combinatorial Problems.” Science 266 (5187):1021–1023.
Ishikawa, R., T. Okagaki, S. Higashi-Fujime, and K. Kohama. 1991. “Simulation of the Interaction betweenActin and Myosin by Physarum Caldesmon-like Protein and Smooth Muscle Caldesmon.” Journal ofBiological Chemistry 266 (32): 21784-21790.
Jones, J., and A. Adamatzky. 2010. “Towards Physarum Binary Adders.” Biosystems 101 (1): 51–58.Lee, J., S. Shin, T. Park, and B. Zhang. 2004. “Solving Travelling Salesman Problems with DNA Molecules
Encoding Numerical Values.” Biosystems 78 (1–3): 39–47.Liu, Q., L. Wang, A. Frutos, A. Condon, R. Corn, and L. Smith. 2000. “DNA Computing on Surfaces.”
LIFE 4 (1450007).Nakagaki, T. 2001. “Smart Behavior of True Slime Mold in a Labyrinth.” Research in Microbiology 152
(9): 767–770.Reid, C., T. Latty, A. Dussutour, and M. Beekman. 2012. “Slime Mold Uses and Externalized Spatial
“Memory” to Navigate in Complex Environments.” PNAS 109 (43): 17490-17494.Rosenbleuth,A., N. Wiener, and J. Bigelow. 1943. “Behavior, Purpose and Teleology.” Philosophy of Science
10: 18–24.Sauer, H. 1982. Developmental Biology of Physarum. Cambridge: Cambridge University Press.Tsuda, S., M. Aono, and Y. Gunji. 2004. “Robust and Emergent Physarum Logical-computing.” Biosystems
