Physicists in the US have modelled a simple electronic circuit that they say is an analogue of how a single-celled organism learns.

The circuit consists of a capacitor, an inductor and a resistor — together with the recently discovered fourth basic circuit element, the “memristor”. The researchers claim it is this element that provides the memory needed for learning, and that the circuit could help in the understanding of primitive intelligence.

Single-celled memory

Earlier this year, Yoshiki Kuramoto of Kyoto University and colleagues showed how the amoeba Physarum polycephalum learns to respond to its environment. They found that when they subjected it to three regularly-spaced dips in temperature and humidity — both of which the organism finds unpleasant — it slowed down with the arrival of each. But they also found that the amoeba continued to oscillate in speed for a while after the last dip, and that in the future just a single dip would set the speed oscillating again. This implied that the amoeba expected a single dip in temperature or humidity to lead to more regular bursts.

Kuramoto’s group argued that the amoeba’s response could be explained by systems of chemicals in which properties fluctuate, known as “chemical oscillators”. The learning, they said, took place when external stimuli, such as the dips in temperature and humidity, synchronize the phase of the different oscillators.

However, Massimiliano Di Ventra, Yuriy Pershin and Steven La Fontaine of the University of California San Diego point out that the many-oscillator model cannot explain how an amoeba responds to a single temperature dip later on. For this, they say, the amoeba requires memory.

Simple circuit

To demonstrate the principle of how this memory could work, Di Ventra and his group linked a resistor, an inductor and a capacitor in series and then placed a memristor across the capacitor. A memristor is a device, predicted in the seventies and realized by scientists in California earlier this year, in which resistance varies according to the amount of charge that has flowed through it.

The result of this property is that when the external voltage is stable or varying non-periodically the memristor exists in a low-resistance state, which dampens the oscillation in voltage across the memristor set up by the inductor-capacitor combination. However, when the external voltage varies periodically — and with a frequency close to the inductor-capacitor resonant frequency — the memristor switches to a high resistance state, and the oscillations are much less damped. This high-resistance state can persist for so long that a single voltage dip in the future can also trigger low-damped oscillations. In other words, after the circuit receives a series of dips at its input it then it “remembers” that, given just a single dip in the future, it should continue to produce a periodic output (arXiv:0810.4179).

Di Ventra’s group points out that an analogue of the memristor exists inside Physarum polycephalum, which is a viscous gel. This gel normally impedes the motion of the organism, but with changing environmental conditions can increase the pressure inside to the point where the gel breaks up, forming low-viscosity channels that alter the organism’s motion. The organism can revert to its initial motion only after a while, which in effect allows it to “remember” how to respond to the new conditions.

According to Di Ventra, the fact that periodic signals trigger the memory mechanism suggests that their circuit could be used to recognize particular inputs, in other words carry out pattern recognition. The three researchers believe that their circuit is in a sense conceptually similar to neurons in the brain, and are currently trying to model multiple memristive circuits to study the complex behaviour that results.