A Method for Growing Bio-memristors from Slime Mold

Today’s computers are built using the three two-terminal fundamental passive circuit elements: the capacitor, the resistor, and the inductor. Passive elements are only capable of dissipating or storing energy, not generating it. These elements were established in the 18^th and 19^th century and are linked through Maxwell’s equations. We define each of these three circuit components in terms of their relationship between two of the four circuit variables namely, current (I), voltage (V), charge (Q), and flux-linkage (φ). The charge is the time integral of the current and Faraday’s law defines the voltage as the time integral of the flux. Thus, a capacitor is defined by a relationship between voltage and charge, a resistor is defined by a relationship between voltage and current, and the inductor is defined by a relationship between flux and current. For well over a century, these elements were a cornerstone of electronics. However, they only represent three of the possible four relationship pairs between the circuit variables, leaving flux-linkage and charge unlinked. In 1971, Leon Chua published a paper¹ where he postulated that there was a missing fourth element that linked the remaining two variables, which he called the memristor. The memristor can be described as a resistor that remembers its history, hence the contraction 'memory resistor.' This element functions by altering its resistance according to the magnitude of the previously applied voltage and its duration. Moreover, the memristor retains its last resistance state once the voltage is no longer applied. Unlike the capacitor, resistor, and inductor, the memristor's behaviour is nonlinear, which is evident in its I-V profile where a pinched hysteresis loop is formed under an AC voltage. This loop takes the form of a Lissajous figure containing two perpendicular oscillations of high and low resistant states. Before Chua’s formalized memristance theory, other researchers had reported on memory resistance effects at certain frequencies when experimenting with materials such as polymers and metal oxides, along with developing electrical devices at the micrometer scale². However, in many cases, these effects were considered undesirable. It took almost forty years for Chua’s formalization to be connected to a physical device and for researchers to begin developing methods of exploiting memristive effects. A team at the HP Laboratories succeeded in fabricating a memristive device in 2008³ that ignited huge interest in the element. 

Computer scientists have a keen interest in the memristor due to it being credited as the first element to combine processing and memory abilities in a single unit. It also displays behaviors that are analogous to certain neurological processes such as Spike-Timing-Dependent Plasticity (STDP)⁴, to name but one. Such behaviors are giving rise to perspectives of building brain-like computing technologies that relinquish the distinction between memory and central processing unit (or CPU)⁵. In contrast to the popular approaches to developing memristors (using TiO₂, for example), our ambition is to develop an organic bio-memristor. Furthermore, we are interested in how this component may provide means of exploring paradigms beyond conventional approaches to engineering computing devices; e.g., creative applications in the field of Computer Music⁶.

Memristance is an effect that researchers have recently found throughout a range of biological systems. For example, memristive properties have been observed in aloe vera plants⁷ and human skin⁸, to cite but two. These discoveries indicate that it may be possible to implement processing and memory devices on biological substrates. Harnessing organic systems within technology may allow us to explore exciting concepts such as self-assembly, self-repair, low environmental impact, and self-powering. Before we can investigate these opportunities however, several challenges need to be addressed. Many of the biological systems that have memristive properties have significant constraints that limit their viability as an actual electronic component. For example, an aloe vera leaf⁷ needs light, has a limited lifespan, and would be difficult to integrate into a circuit. Furthermore, several other in vivo memristive phenomena, such as human sweat ducts⁸, are not currently feasible options for developing systems for use outside of the laboratory and in everyday electronic systems. However, of all the memristive phenomena, there is one potential candidate: P. polycephalum.

The plasmodium of P. polycephalum is an amorphous unicellular system that has been discovered to act as a memristive component^9,10. This organism is an ideal candidate for research in hybrid hardware-wetware electronics for a number of reasons. Firstly, the organism is non-pathogenic, macroscopic, and requires no specialist equipment use, which renders the plasmodium accessible to engineers and non-biologists. Secondly, the cell is amorphous, forms networks of wire-like veins, and will grow on most substrates (Figure 1). These properties allow the cell's morphology to be easily delineated to conform to a conventional electrical scheme. There is also research demonstrating that the plasmodium can live for over four years¹¹, and that its veins can act as self-repairing conductive pathways¹². Several laboratory studies have confirmed the organism's memristive abilities^9,10,13 and now the time is ripe to explore its potential.

The idea of using P. polycephalum memristors is relatively new. As a result, there are no established standards for measuring and observing its electrical properties. Such a lack of uniformity in experimental procedures within the same research group and between groups may be the reason there are inconsistencies amongst published results^9,10. It is likely that such variation is most prominent in sample growth conditions and handling. Thus, we need to establish methods for producing and testing P. polycephalum memristors where factors that might cause errors are better controlled and monitored.  Furthermore, we need to create methods of implementing P. polycephalum memristors that allow for stable and easy integration into electrical systems.

The method presented in this paper provides a platform for exploration of practical applications of P. polycephalum memristors by providing means of incorporating the organism as a component into an electrical schematic. It is likely that these techniques will appeal to engineers looking to explore real-world uses of hybrid hardware-wetware systems. Furthermore, it is accessible to non-experts (e.g., open-source electronic prototyping enthusiasts) who may be interested in experimenting with aspects of unconventional computing but have found it difficult to find prototypes to adapt to their needs. Some potential applications may include implementing probabilistic models harnessing the memristors spiking behavior, developing approaches to performing stateful logic operations, and modelling neurological processes for information storage and processing.