A Would-Be Nervous System Made from a Slime Mold

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A Would-Be Nervous System Andrew Adamatzky** Made from a Slime Mold University of the West of England

Keywords Slime mold, nervous system, unconventional computing Abstract The slime mold Physarum polycephalum is a huge single cell that has proved to be a fruitful material for designing novel computing architectures. The slime mold is capable of sensing tactile, chemical, and optical stimuli and converting them to characteristic patterns of its electrical potential oscillations. The electrical responses to stimuli may propagate along protoplasmic tubes for distances exceeding tens of centimeters, as impulses in neural pathways do. A slime mold makes decisions about its propagation direction based on information fusion from thousands of spatially extended protoplasmic loci, similarly to a neuron collecting information from its dendritic tree. The analogy is distant yet inspiring. We speculate on whether alternative—would-be—nervous systems can be developed and practically implemented from the slime mold. We uncover analogies between the slime mold and neurons, and demonstrate that the slime mold can play the roles of primitive mechanoreceptors, photoreceptors, and chemoreceptors; we also show how the Physarum neural pathways develop. The results constituted the first step towards experimental laboratory studies of nervous system implementation in slime molds.

1 Introduction

The plasmodium of Physarum polycephalum (order Physarales, class Myxomecetes, subclass Myxo- gastromycetidae) is a single cell, visible with the naked eye, with many diploid nuclei [63]. 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 (Figure 1a). The topology of the plasmodiumʼs protoplasmic network optimizes the plasmodiumʼs harvesting resource from the scattered sources of nutrients and makes more efficient the transport of intracellular components [49]. In [6] we have shown how to construct specialized and general-purpose massively parallel amorphous computers from the plasmodium (slime mold) of P. polycephalum that are capable of solving problems of computational geometry, graph theory, and logic. The plasmodiumʼsforagingbehaviorcanbeinter- preted as a computation [49, 51]: data are represented by the spatial distribution of attractants and repellents, and results are represented by the structure of the protoplasmic network [6]. The plasmodium can solve computational problems with natural parallelism, such as finding shortest paths [50] and hierarchies of planar proximity graphs [5], plane tessellations [56, 6], and planar

** University of the West of England, Bristol BS16 1QY, United Kingdom. E-mail: [email protected]

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Figure 1. Plasmodium of P. polycephalum. (a) Oat flakes colonized by the slime mold are black irregular blobs. (b) A hypothetical neural network made of P. polycephalum. Every Physarum blob (oat flake colonized by Physarum) is a neuron, shown by a black disc. Protoplasmic tubes connecting the blobs are analogues of synaptic connections; they are shown by lines ending with small grey disks.

shapes [12]; execution of logical computing schemes [66, 3]; and natural implementation of spatial logic and process algebra [58], unconventional hybrid wetware and hardware [11], and prototypes of microfluidic logic gates [16]. Nowadays Physarum has become a dominant popular substrate for designing future and emergent computing architectures. This is because the slime mold is easy to culture and handle, most experiments do not require sophisticated equipment, technical difficulties are minimal, and costs of prototyping are very low. The plasmodium of P. polycephalum is a simple-to-maintain substrate that requires minimal equipment to experiment with. In [6] we developed a concept and designed a series of experimental laboratory prototypes of computing devices—Physarum machines [6]—based on P. polycephalum.APhysarum machine is a programmable amorphous biological computing device experimentally implemented in plasmodium of P. polycephalum.APhysarum machine is programmed by configurations of repelling and attracting gradients. The mechanics of Physarum machines is based on the following unique features of P. polycephalum [6]:

• Physarum is a living, dynamical reaction-diffusion pattern formation mechanism. • Physarum may be considered as equivalent to a membrane-bound subexcitable system (excitation stimuli provided by chemoattractants and chemorepellents).

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• Physarum may be regarded as a highly efficient and living micromanipulation and microfluidic transport device. • The induction of the pattern type is determined partly by the environment—specifically, nutrient quality and substrate hardness, dryness, and the like. • Physarum is sensitive to illumination and electric fields and therefore allows for parallel and nondestructive input of information. • Physarum represents results of computation by the configuration of its body.

Physarum is thus a computational material based on modification of protoplasm transport by the presence of external stimuli. The range of laboratory prototypes of living slime mold devices is impressive: robot controllers [67], microfluidic logic gates [16], computational geometry processors [12, 6], and electronic elements [17], to name but a few. We decided to go a bit further and to answer a question borrowed from the field of living technologies [18, 19]: “Can we make an artificial living neural system from the slime mold?” Rephrasing Bedau et al. [18], we can say that a nervous system made from Physarum is artificial in that it is created by our intentional activities, yet is natural in that it grows, responds to environmen- tal stimuli, and adapts according to its own biological laws. A model nervous system would be a spatial configuration of the Physarum neurons (slime mold blobs, such as sources of food colonized by Physarum; the blobs are interconnected with each other by Physarum neuron terminals), protoplasmic tubes, and imitating axons and dendrites (Figure 1b). In this article we highlight some analogies between the slime mold and neurons, and demonstrate that the slime mold can play the roles of primitive exteroceptors such as touch (mechanoreceptors), and teleceptors such as sight (photoreceptors) and smell and taste (chemoreceptors). The article is structured as follows. We introduce methods of culturing and experimenting with the slime mold in Section 2. We discuss neuronlike features of Physarum electrical behavior in Section 3. Section 4 shows what types of mechanical, chemical, and optical receptive organs can be made from Physarum. In Section 5 we investigate the growth of Physarum neural pathways.

2 Methods

The following experimental conditions were employed and equipment used in the experiments discussed. Plasmodium of Physarum polycephalum wascultivatedinplasticlunchboxes(withafew holes punched in their lids for ventilation) on wet kitchen towels and fed with oat flakes. The culture was periodically replanted to fresh substrate. In all recordings mentioned we used planar aluminum foil electrodes (width 5 mm, thickness 0.04 mm, sheet resistance 0.008 V/cm2). In experiments on sensorial properties two blobs of 2% non-nutrient agar (Select Agar, Sigma-Aldrich), 2 ml each, were placed on electrodes stuck to the bottom of a plastic petri dish (9 cm). The distance between proximal sites of electrodes was 10 mm in all experiments. Physarum was inoculated on one agar blob. We waited till the Physarum colonized the first blob, where it was inoculated, and propagated towards and colonized the second blob. When the second blob was colonized, the two colonized blobs of agar became connected by a single protoplasmic tube (Figure 2a). Electrical activity of plasmodium wasrecordedwithADC-24HighResolutionData Logger (Pico Technology, UK). The data logger ADC-24 employs differential inputs, galvanic isolation, and software-selectable sample rates, all contributing to superior noise-free resolution; its 24-bit A/D converter maintains a gain error of 0.1%. When necessary, a resistance was measured with four wires using a Fluke 8846A precision voltmeter, test current 1.0000 ± 0.0013 lA. InoneoftheillustrativeexampleswestimulatedPhysarum with regular waveforms using a bench Tenma function generator.

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3 Physarum Neurons

We represent a Physarum neuron by a physically localized and almost everywhere isolated locus of Physarum, such as the blobs of agar colonized by Physarum in Figure 2a. There is no difference between axons and dendrites in the Physarum analogue models of a neural network, so we use a general term “connection” or “pathway.” A connection is a protoplasmic tube linking two Physarum neurons. An example is shown in Figure 2a, and the key elements are enhanced in the drawing in

Figure 2. (a) Experimental setup for recording oscillation of Physarum electrical potential. (b) Drawing of the setup (a) with key elements enhanced: Physarum is black, agar blobs are gray, and the protoplasmic tube connecting the blobs is shown by an arrow. (b) Scheme of measurements taken.

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Figure 3. Stimulation of Physarum neuron with triangular waveforms. The stimulating waveforms on the graph look distorted due to the low frequency of sampling during recording.

Figure 2b. The protoplasmic tube is conductive [9], propagating patterns of calcium waves, electrical potential, and peristaltic waves from one neuron to another. An undisturbed Physarum exhibits periodic changes, or oscillations, of its surface electrical potential; see the example in Figure 2b and further below. A typical normal oscillation of a surface potential has amplitude of 0.1 to 5 mV (sometimes less, depending on the location of the electrodes) and period 1–4 min [39, 41, 43]. The exact pattern of electric potential oscillations depends on the physiological state and age of the Physarum culture and the details of the experimental setup [1]. In 1939 Heilbrunn and Daugherty discovered that the peristaltic activity of protoplasmic tubes is governed by oscillations of electrical potential propagating along the tubes [35]. The exact nature of the correlation between electrical and contractile oscillation of plasmodium is still unclear; there is a view that these two oscillations are governed by the same mechanism but may occur independently of each other [59]. The oscillations can be tuned by external electrical stimulation. In the example shown in Figure 3 we stimulated Physarum with triangular waveforms, frequency 0.009 Hz. Physarum oscillations were irregular before stimulation with average amplitude 0.42 mV. After ≈18 min of stimulation with the waveforms, Physarumʼs oscillatory activity regularized and its average amplitude almost doubled, increasing to 0.74 mV (Figure 3). The oscillatory pattern of a single Physarum neuron is stable, apart from some possible drifts in the baseline potential due to mass transfer of the propagating Physarum. Physarum neurons linked electrically may exhibit high-amplitude spikes. An example of such very low-frequency irregular high-amplitude spikes is shown in Figure 4. Three petri dishes (a single dish is shown in Figure 2a) were connected with electrodes in series, and the potential difference was measured between the two most distant electrodes. This Physarum neural network shows a low amplitude of electrical potential oscillations, about 1 mV. High-amplitude spikes were observed at ≈1800 s (13.2 mV), ≈5500 s (16.9 mV), ≈11,500 s (16.7 mV), ≈1200 s (17.6 mV), ≈13,300 s (36.3 mV), ≈14,100 s (44.6 mV), and ≈17,200 s (27.2 mV). Physarum neural networks do not have synapses represented as discrete structural elements. Synaptic-like morphological contacts could not be formed: When two pieces of Physarum are inoculated at a distance from each other, they start exploring the space around them and form branching networks of protoplasmic tubes. When two networks grown from different sites of inoculation come into contact, they usually fuse, forming a single united network. However, there is a functional analogue of synapses that is an intrinsic feature of Physarum protoplasmic tubes and makes any locus of a Physarum network a synapse. This is the memristive property. A memristor is a resistor with a memory, whose resistance depends on how much current has flowed through the device. Postulated theoretically by Chua in 1971 [25] and implemented practically

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Figure 4. Large-amplitude spiking activity in three pairs of Physarum blobs (Figure 2a) connected in series. Zoomed are domains of normal oscillatory activity.

by Strukov et al. [64], memristors have influenced the recent development of computing circuits [64, 70, 30] and neuromorphic architectures [60, 40, 52, 37, 27, 28]. In laboratory experiments [29] we demonstrated that protoplasmic tubes of acellular slime mold P. polycephalum show current-versus-voltage profiles consistent with memristive systems. Experi- mental laboratory studies show pronounced hysteresis and memristive effects exhibited by the slime mold. The memristor is an analogue of a synaptic connection [52, 23], and in fact is capable of direct emulation of the temporal dynamics of real-life synapses [38]. As a living memristor, each protoplasmic tube of Physarum is a synaptic element with memory, whose state is modified depending on its presynaptic and postsynaptic activities. As with memristors, several protoplasmic tubes in a Physarum network can form an associative memory network [52]. The synapses shown in Figure 1 correspond to protoplasmic tubes with memristive properties.

4 Sensor Organs Made from Slime Mold

4.1 Mechanoreceptors In [13] we demonstrated touch sensitivity of the slime mold by applying loads (made from glass capillary tubes) to Physarum colonizing an agar blob on the recording electrode (Figure 2). A typical response of Physarum to application of a load is shown in Figure 5. Physarum exhibits more or less

Figure 5. Physarumʼs response to application of 0.05-g load. Vertical axis is electrical potential in millivolts; horizontal axis is time in seconds. Glass capillary weighing 0.05 g is applied across protoplasmic tube at 2400 s from beginning of recording. We can observe the following patterns: oscillation before stimulation, immediate response to stimulation, prolonged response to stimulation, return to normal oscillatory activity. See details in [13].

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classical oscillations before stimulation (Figure 5); the shape of the oscillatory waves is a bit distorted, possibly due to minor branches of the tube connecting the blobs and electrodes. A segment of a glass capillary was placed across the protoplasmic tube at approximately the 2400th second from the beginning of recording. Physarum demonstrates two types of responses to application of this load: an immediate response with a high-amplitude impulse (Figure 5) and a prolonged response with changes in oscillation pattern (Figure 5). The immediate response is a high-amplitude spike: Its amplitude is 12.33 mV, and its duration is 150 s. The prolonged response is an envelope of increasing- amplitude oscillations. An average amplitude of the oscillations before stimulation, in the example shown in Figure 5, was 2.3 mV, and the duration of each wave was 120 s. The amplitude of the waves in the prolonged response became 5.29 mV, and the duration of a wave slightly increased to 124 s. We found [13] that the slime mold of P. polycephalum reacts to application and removal of a load with a high-amplitude impulse and with a temporary change of its oscillatory activity pattern. There are two possible types of response: an immediate response in the form of a high-amplitude impulse, and a prolonged response in the form of changes in oscillation frequency and amplitude. We did not find a rigorous correlation between weight of object applied and amplitude of the response impulse or amplitude and frequency of oscillations. For the time being, we can definitely claim that slime mold P. polycephalum can be used at least as an on-off tactile sensor. The experimental results above describe Physarum receptors that can detect touch and pressure. Most animals also have receptors in hair follicles, including hairs on skin and hair cells in the cochlea. The receptive terminals typically react to their stretching when a hair is deflected. To make tactile hair with Physarum we used the setup shown in Figure 2 but with a hair rooted in the agar blob on the recording electrode [15]. With regard to composition of the hairs, we tried human hairs and synthetic (nylon) hairs; the Physarum colonizes natural and artificial hairs equally well and does not show any preferences. Typically, in 1–3 days after inoculation of Physarum to an agar blob on a reference electrode, it propagates to and colonizes an agar blob on a recording electrode. A slime mold analogue of a neuron terminal connecting two blobs of Physarum is formed. Physarum propagates onto the hair and occupies a third to a half of the hairʼs length (Figure 6a). In many cases a subnetwork of protoplasmic tubes is formed around the base of the whisker. A typical response of Physarum to stimulation is shown in Figure 6b. The response is composed of an immediate response—a high-amplitude impulse—and a prolonged response. The high-amplitude impulse is always pronounced; the prolonged response oscillations can sometimes be distorted by other factors, for example, growing branches of a protoplasmic tube or additional strands of plasmodium propagating between the agar blobs. The responses are repeatable not only in different experiments, but also during several rounds of stimulation in the same experiment [15].

4.2 Chemical Sensors The slime mold P. polycephalum has been proved to be very sensitive to volatile aromatic substances [4, 8]. Not only is plasmodium strongly attracted to herbal somniferous tablets, but the Physarum can differentiate between various types of plants with sedative properties. To select the principal chemo- attractant in the tablets we undertook laboratory experiments on the plasmodiumʼs binary choice between samples of dried plants: Valeriana officinalis, Humulus lupulus, Passiflora incarnate, Lactuca virosa, Gentiana lutea, Verbena officinalis. Valerian root dominates in the hierarchy of chemoattractive forces and of Physarum preferences [4, 8]. Possible molecular mechanisms linking the sedative activity of valerian and its chemoattraction via relaxation of contractile activities of slime mold are outlined in [10]. The contractile activity of plasmodium is closely associated with its electrical activity. We believe that in the future it will be possible to build a mapping between all types of aromatic substances and patterns of electrical activity exhibited by the slime mold. The experiments described in [4, 8] laid the foundation for the laboratory prototyping of a Physarum-based chemical sensor [69]. Based on previous extensive testing of Physarum binary preferences with respect to various volatile chemicals [26], Whiting et al. [69] derived an experimental

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Figure 6. Slime mold tactile hair. (a) Photograph of experimental setup: Hair is partly colonized by slime mold. (b) Typical responses of Physarum to deflection of hair. Vertical axis is electrical potential value in millivolts; horizontal axis is time in seconds. Physarum responds with a high-amplitude impulse and envelope of four to five waves. Moment of hair deflection is shown by arrow. See details in [15].

mapping between sets of chemoattractants and chemorepellents: farnesene, tridecane, s-(−)-limonene, cis-3-hexenyl acetate, geraniol, benzyl alcohol, linalool, nonanal (Figure 7). The slime moldʼsreaction to the strongest (as demonstrated in binary choice experiments) attractants—farnesene, tridecane, s-(−)-limonene, and cis-3-hexenyl acetate—is manifested in the increase of frequency of electrical potential oscillations. Repellents—linalool, benzyl alcohol, nonanal—were indicated by a decrease of oscillation frequency and, for cases of linalool and benzyl alcohol, substantial increase of the oscillation amplitude. Thus, Whiting et al. [69] have shown that P. polycephalum can identify indi- vidual chemicals by the change in relative amplitude and frequency after exposure; the detection of chemicals can occur at 4 cm, without diffusion through a growth medium such as agar. It is

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possible that this setup could be employed as a chemical sensor, allowing the contactless detection of volatile organic compounds as well as potentially other chemicals.

4.3 Optical Sensors Plasmodium of P. polycephalum shows a substantial degree of photosensitivity. A plasmodium moves away from light when it can, or it switches to another phase of its life cycle or undergoes fragmentation when it cannot escape from light. If a plasmodium, especially a starving one [34], is subjected to a high intensity of light, the plasmodium enters a sporulation phase [53]. Phytochromes are involved in the light-induced sporulation [62], and a sporulation morphogen is transferred by protoplasmic streams to all parts of the plasmodium [36]. Photomovement is a less (than sporulation or fragmentation) drastic response to illumination. Pioneer articles on photomovement of Physarum reported that plasmodium exhibits the most pronounced negative phototaxis to blue and white light [20, 54]. The illumination increase causes changes in the plasmodiumʼs oscillatory activity; the degree of change is inversely proportional to the distance from the light source [71, 21]. The exact mechanism of the response to light is as yet unknown. A few relevant phenomena have, however, been uncovered in experiments. The first is the presence of phytochrome-like pigments [42], which might be primary receptors of illumination. The light response of the pigments triggers a chain of biochemical processes [54]. These processes include increase in activity of isomerase enzymes [61], changes in mitochondrial respiration [44], and spatially distributed oscillations in ATP concentrations [68]. Nakagaki et al. [48, 51] undertook the first ever experiments on shaping plasmodium behavior with illumination. They discovered that protoplasm streaming oscillations of plasmodium can be tuned by, or approximately synchronized with, periodic illumination [48]. They also demonstrated that plasmodium optimizes its protoplasmic network structure in a field with heterogeneous illumination [51]: The thicknesses of protoplasmic tubes in illuminated areas are less than those in shaded areas [51]. In laboratory experiments, described in detail in [14], we studied Physarumʼsreactiontolight of different colors. The Physarum-based recording electrode was illuminated from above using a white LED (1400 lx) with a set of color lenses: red (635 nm), green (560 nm), and blue (450 nm). We also illuminated Physarum with white light through a transparent lens. The amount of light on the blob was 80–120 lx for each color. In each experiment we recorded the electrical activity

Figure 7. Physarum chemical sensor reacts by changes in amplitude and frequency of oscillations to exposure to volatile chemicals. Modified from [15].

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Figure 8. Patterns of oscillation of Physarum surface electrical potential before, during, and after illumination. See details in [14].

of Physarum in darkness (10 min), under illumination (10 min), and after illumination was removed (10 min); see Figure 8. We say that the slime mold recognizes a color c if it reacts to illumination with the color c by unique changes in the amplitudes and periods of oscillatory activity. Let w be the value of a param- eter (average amplitude, average period, standard deviation of amplitude or period) of the oscillations before the stimulus is applied or removed, and w* its value after stimulus applied or removed. D ¼ w − Then we define w w 1. We found that Physarum recognizes when red and blue light are switched on and when red light is switched off [14]. Red and blue illuminations decrease the frequency of oscillations, that is, increase the period. Red light increases amplitude of oscillations, but blue light decreases the amplitude. Physarum does not differentiate between green and white light. Switching off any light but red affects both amplitude and frequency of oscillations. Switching off red light leads to increase in periods and decrease in amplitudes of oscillations. Diversity of oscillations, calculated as the standard deviation of amplitudes or periods, is another useful characteristic of Physarumʼs response to illumination. In this regard, Physarum recognizes when white and green colors are switched on. Physarum recognizes that illumination is switched off (its oscillating behavior becomes uniform) but does not recognize what exact color is switched off. Switching off all types of illumination decreases the diversity of amplitudes and periods. Increase in the diversity of oscillation might be explained by the formation of additional micro- oscillators in Physarum protoplasmic networks. Different phases and frequencies of oscillations and different positions of micro-oscillators relative to each other lead to the emergence of waveforms with different amplitudes and periods, as recorded in experiments. Switching off illumination may extinguish some of the micro-oscillators, so that Physarum reacts to switching off the illumination by producing rather uniform patterns of oscillation [14].

5 Growth of Information Pathways

Physarum propagates using active growing zones (Figure 9). These zones bear a striking resemblance to neuronal growth cones [31]. The Physarum growth cone, similarly to the neuronal growth cone, actively optimizes its trajectory in gradients of chemoattractants and repellents [7]. We explored the analogy between the behavior of neuron growth cones and Physarum active growing zones: To test if Physarum can develop information pathways, we conducted several experiments on 1 : 1 scale models of the human brain and skull. We used real scale models for the following reasons: first, to show that information pathways made of protoplasmic tubes can be tens of centimeters in length and thus match the lengths of neural pathways; second, to demonstrate that—when propagating inside a human skull model—the plasmodium follows general anatomical trajectories of ocular and olfactory nerves.

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In the experiment illustrated in Figure 10 we imitated the formation of information pathways on the surface of a 3D model of a human brain. We attached two aluminum electrodes (10-mm width, 100-mm total length) to the parietal lobe and prefrontal areas of the cortex, and placed agar blobs (each ≈2 ml of 2% agar) on the electrodes. We inoculated the Physarum on the blob in the parietal lobe and placed several oat flakes, meant to act as sources of chemoattractants, on the blob in the prefrontal area. The model was kept in a closed camera with 80% humidity, in darkness, and at room temperature. In 5–8 days Physarum propagated from its original site of inoculation to the agar blob with chemoattractants. A protoplasmic tube connecting two blobs was formed. This tube exemplifies an information pathway between the parietal lobe and prefrontal areas of the cortex established by Physarum (Figure 10a). The information about the humidity, concentration of nutrients, and illumination around each blob of the slime mold was communicated via cytoplasmic flow, frequencies and amplitudes of calcium waves, electrical potential differences, and contractile waves to another blob. The easiest way to check the functionality of the connection is to record the dynamics of the electrical potential difference between two Physarum blobs, as demonstrated below. In the experiments illustrated in Figure 10, the electrode positioned in the parietal lobe was a reference electrode, and the electrode in the prefrontal lobe was a recording electrode. We found that the protoplasmic tubes connecting two Physarum blobs on the electrodes remain functional and support communication between parts of the Physarum for up 15 days. An example of electrical activity is shown in Figure 10b. This is a classical pattern of oscillation of the Physarum extracellular membrane potential with dominating frequency 0.0049 Hz (which is about one cycle per 200 s). Formation of olfactory and ocular pathways was imitated and their functionality was tested with Physarum growing inside a life-size 3D model of a human skull (Figures 11 and 12). Four aluminum electrodes (10-mm width, 100-mm total length) were attached inside the skull on the greater wings of the spheroid bone (Figure 11a). Two electrodes were attached to maxilla on the inside bottom of the nasal cavity, and two electrodes at the bottom parts of the eye sockets on the dorsal part of zygomatic bone inside the sockets. Agar blobs were placed on the electrodes. Oat flakes colonized by Physarum were placed on the agar blobs situated on the electrodes inside the cranium. Fertile oat flakes, to act as sources of chemoattractants, were positioned on the agar blobs in the eye sockets and nasal cavity. The skull inoculated with Physarum was kept in a dark humid chamber and sprayed

Figure 9. Physarum growth cones. (a) Active growing zone formed around an oat flake. (b) Branching of Physarum is guided by two active zones.

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Figure 10. Slime mold information pathways. (a) A protoplasmic tube grown between two loci of Physarum on a rubber model of a brain. (b) Electrical activity reflecting information exchange between the loci; external electrical potential difference recorded between the electrodes. (c) Power spectrum of the potential dynamics.

with distilled water daily. In seven of the twelve experiments conducted, the Physarum propagated from its inoculation sites to the target sites with chemoattractants. In the other five experiments, the Physarum either ceased to propagate or exhibited rather explorative growth without reaching the target sites. Below we describe instances of successful experiments.

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Figure 11. Olfactory Physarum pathways. (a) Intracranial part. In the photograph we see two electrodes fixed on the greater wing of the spheroid bone. A blob of agar is on top of each electrode. The agar blobs are colonized by Physarum. (b) Slime mold enters left nasal cavity and colonizes agar blob and oat flakes on the reference electrode.

Figure 12. Ocular Physarum neural pathways. Protoplasmic tube originating at Physarum locus inhabiting the cranium base, shown by arrow in (a), enters eye socket via optical canal in (b).

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Figure 13. Functionality test of the Physarum ocular pathway. (a) Physarum colonizing reference electrode in right eye socket is illuminated with 1400-lx white light spot. (b) Electrical activity of Physarum recorded on electrode based inside cranium, as shown in Figure 12a. Light was switched on after 600 s of recording.

Typically, the Physarum inoculated on the spheroid bones (Figure 11a) propagated into the nasal cavity and reached the target electrode in 3–4 days (Figure 11b). Functionality of the imitated olfactory pathway was checked by recording oscillations of the electrical potential between the reference electrode, positioned in the nasal cavity, and the recording electrode, positioned inside the cranium. Results of experiments on formation of ocular pathways with Physarum were equally impressive. From its inoculation site on the greater wing of the spheroid bone (Figure 12a), Physarum propagated via the optical canal into the eye socket, grew along the frontal and spheroid bones, and reached the target agar blob on the zygomatic bone (Figure 12b). Being light sensitive [71, 21, 2], Physarum could play the role of a primitive eyelike organ. To test this possibility we undertook a series of experiments, one of which is described below.

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After an ocular pathway was formed by Physarum and the slime mold reached and established itself in an eye socket, we illuminated the eye socket with a 1400-lx LED white spot light (Figure 13a). We assigned the electrode positioned inside the cranium on the greater wings of the spheroid bone (Figure 11a) as the recording electrode, and the electrode at the bottom of the eye socket as the reference. The electrical activity of the unilluminated Physarum with respect to its illuminated part located inside the eye socket is shown in Figure 13b. The Physarum in the eye socket responded to the illumination with high-amplitude and large-period oscillations. When the light was turned off at the 600th second of the experiment, the Physarum oscillations became low amplitude and less regular (Figure 13b). The power spectrum of the electrical potential dynamics is shown in Figure 14: We see that in darkness the Physarumʼs potential oscillates with two dominating frequencies, 0.0078 and 0.0156 Hz, that is, approximately with periods 128 and 64 s (Figure 14a). Oscillations of the electrical potential of illuminated Physarum show dominating frequencies of 0.0049 and 0.0063 Hz, that is, approximately 204 and 159 s (Figure 14b). Thus the parts of the Physarum residing inside the cranium receive information about illumination—via changes in parameters of electrical activity—from the parts residing inside an eye socket and exposed to illumination. To imitate sensorial innervation of the front scalp, we inoculated Physarum on the frontal bone 50 mm above the glabella and placed a few oat flakes on the parietal bone as shown in Figure 15. In twodaysthePhysarum developed an extensively branching tree of protoplasmic tubes. The tree spanned a substantial part of the frontal lobe, even covering its lateral parts, crossed the coronal suture, and developed actively branching growing zones moving towards the target site on the parietal bone (Figure 15).

Figure 14. Power spectrum of electrical potential dynamics in Figure 13b. (a) Illumination is off. First two dominating frequencies are 0.0078 and 0.0156 Hz. (b) Illumination is on. First two dominating frequencies are 0.0049 and 0.0063 Hz.

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Figure 15. Physarum network growing on the life-size model of a human skull.

6 Discussion

Based on morphological and behavioral similarities between plasmodium of acellular slime mold P. polycephalum and neurons, we have speculated on how functional neural networks might be made from the living slime mold. A Physarum neural network consists of agar blobs colonized by Physarum, the blobs linked one to another via protoplasmic tubes. The blobs represent neurons, and the protoplasmic tubes connecting the blobs are analogues of axons and dendrites. The blobs exhibit sophisticated patterns of electrical potential oscillations, which are analogues of neuron spiking behavior. The oscillations of the electrical potential on the Physarum neurons can be controlled by direct electrical stimulation, and by chemical, optical, and mechanical stimulation. The Physarum neurons change the frequency, and sometimes the amplitude, of their oscillation in response to external stimulation. It is possible, in principle, to derive a one-to-one mapping between exact nature of chemical stimulation, force of tactile stimulation, and color of optical stimulation on one side, and the frequency and amplitude of the electrical stimulations on the other side. Thus, the Physarum can play the roles of chemical, mechanical, and optical receptors in the neural networks made from the slime mold. What are potential applications of the would-be nervous system grown from the slime mold? The Physarum sensors and information pathways presented could make a feasible complement to biohybrid sensors incorporating live cells as parts of transduction systems [65, 24]. Typically, living substrates integrated into biohybrid systems rely on external bandwidth, such as microfabricated vascular networks [55], to receive nutrients and remove metabolites [46]. The slime mold nervous system does not require any auxiliary life support system, and can reside on virtually any surface for days or weeks, depending on the humidity. The Physarum networks are slow: Their speed is on the order of seconds, much slower than mammalian networks and very much slower than silicon computing. However, slime mold circuits are self-growing and self-repairing and can be incorporated in hybrid wetware-hardware devices for sensing and analyzing non-lethal substances, and for detection of molecules or certain types of living cells [26]. Physarum gates, especially their microfluidic implementations [16], could be incorporated into disposable, biocompatible, mechanically controlled devices [45], as embedded fluidic controllers and circuits in bio-inspired robots [47], or as memory arrays [32, 33] embedded into soft-bodied robots. Neural networks process information and learn. We have mostly presented results on morphological features, morphogenesis, and sensorial features of the Physarum neural network. Memristive

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properties of the slime moldʼs protoplasmic tubes [29] indicate that Physarum neural networks are capable of learning. More experimental studies are required for implementing learning by Physarum networks [22, 57] in real-life scenarios.

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