Memristors: Memory elements in potato tubers

Abstract

A memristor is a nonlinear element because its current-voltage characteristic is similar to that of a Lissajous pattern for nonlinear systems. This element was postulated recently and researchers are looking for it in different biosystems. We investigated electrical circuitry of red Irish potato tubers (Solanum tuberosum L.). The goal was to discover if potato tubers might have a new electrical component - a resistor with memory. The analysis was based on a cyclic current-voltage characteristic where the resistor with memory should manifest itself. We found that the electrostimulation by bipolar sinusoidal or triangle periodic waves induces electrical responses in the potato tubers with fingerprints of memristors. Tetraethylammonium chloride, an inhibitor of voltage gated K⁺ channels, transforms a memristor to a resistor in potato tubers. Our results demonstrate that a voltage gated K⁺ channel in the excitable tissue of potato tubers has properties of a memristor. Uncoupler carbonylcyanide-4-trifluoromethoxy-phenyl hydrazone decreases the amplitude of electrical responses at low and high frequencies of bipolar periodic sinusoidal or triangle electrostimulating waves. The discovery of memristors in plants creates a new direction in the understanding of electrical phenomena in plants.

Abbreviations

C

capacitance

CCCP

carbonylcyanide-3-chlorophenylhydrazone

DAQ

data acquisition

FCCP

carbonylcyanide-4-trifluoromethoxyphenyl hydrazone

PXI

PCI eXtensions for Instrumentation

I

electrical current

M

memristor

P

electrical power

q

charge

R

resistance

TEACl

tetraethylammonium chloride

VFG

voltage of an function generator

VP

voltage between electrodes in plants

VR

voltage on resistor R

ϕ

magnetic flux.

Introduction

Electrical signals propagate along sophisticated electrical circuitry of plants consisting of many electrical components developed by nature.^1-4 The standard electrical circuits comprise 3 basic elements: a resistor, a capacitor and an inductor. In addition to these elements, Chua,⁵ postulated the existence of a new element, which has electrical memory (Fig. 1). This is the fourth basic circuit element, a memristor or a resistor with memory. Memristors are memory circuit elements whose properties depend on the history and state of the system. A memristor is a nano-scale memory device, carries huge perspective technical applications; for example they can replace flash memories and DRAMs in electronic appliances.⁶ A memristor is a nonlinear element because its current-voltage characteristic is similar to that of a Lissajous pattern. No combination of nonlinear resistors, capacitors and inductors can reproduce this Lissajous behavior of the memristor. It is a fundamental 2-terminal described by the state dependent Ohm's Law.^6-7 Memristance can be described mathematically by equation:

$${\displaystyle M(q(t))=\frac{d\phi (q)}{dq}=\frac{\left(\frac{d\phi (q)}{dt}\right)}{\frac{dq}{dt}}=\frac{V(t)}{I(t)}}$$ (1)

Figure 1.

Four basic circuit elements.

The power of a memristor is:

$${\displaystyle P\left(t\right)=I^2\left(t\right)M\left(q\left(t\right)\right),}$$ (2)

where ϕ and q denote the flux and charge, respectively.

During the last decade, different memristors were developed as semiconductor devices, enzymatic systems, polymers and electrified interfaces.^8-10 Theoretical analysis shows the existence of memristors in neural networks, voltage gated channels, synapses and in the brain.^11-15 Markin et al.¹⁶ created mathematical model of memristors with capacitors in plants. Adhikaru et al.¹⁷ found that a memristor has 3 characteristic fingerprints: “When driven by a bipolar periodic signal the device must exhibit a pinched hysteresis loop in the voltage-current plane, assuming the response is periodic; starting from some critical frequency, the hysteresis lobe area should decrease monotonically as the excitation frequency increases; the pinched hysteresis loop should shrink to a single-valued function when the frequency tends to infinity.” The pinched hysteresis loop transforms to a non-pinched hysteresis loop in bioelectrochemical systems instead of a single line I = V/R at high frequencies of the applied voltage because the amplitude of electrical current depends also on capacitance, frequency and direction of scanning:^18-21

$${\displaystyle I=C\frac{dV}{dt}}$$ (3)

The pinched hysteresis loop of memory elements, when subject to a periodic stimulus, can be self crossing (type I memristor) or not (type II memristor). Volkov et al.^18-21 found that the electrostimulation of plants by bipolar periodic sinusoidal or triangle waves induces electrical responses with fingerprints of memristors of type I or type II. To elucidate this mechanism, Markin et al.¹⁶ proposed analytical models of a memristor and a memristor with a capacitor connected in parallel.

Electrical circuits in plants operate over large distances.^4,22,23. The activation of these circuits can lead to various physiological and biochemical responses.^24-25 The cells of many biological organs generate electric potentials that can result in the flow of electric currents and propagation of action potentials. The Hodgkin-Huxley axon model describing action potentials is based on voltage gated channels. These channels can be identified as a potassium ion-channel memristor and a sodium ion-channel memristor.^11-12. Since plants and animals have similar voltage gated K⁺ channels, it would be interesting to investigate the possible presence of memristors in the plant kingdom. Biological tissue in many organisms exhibit memristive behaviors. We have found memristors in the electrical circuitry of Venus flytrap, Aloe vera and Mimosa pudica.^16,18-20 Gale et al.²⁶ found memristive properties of protoplasmic tubes of a cellular slime mold Physarum polycephalum. Johnsen et al.²⁷ found that the sweat ducts in the skin are memristors. Hota et al.²⁸ create transparent memristors from natural regenerated silk fibroin protein obtained from cocoons of Bombyx mori silkworm. Plant tissues have different forms of memory such as sensory, short, and long-term memory.^1,3,29

Plants have a biological clock and circadian rhythms, which involve electrical elements of memory.^1,2,3,29 We should expect the finding of biomemristors in many different biological systems in the near future. The main goal of this article is to find out if potato tubers comprise memristors.

Results

Experimental setup is shown in Figure. 2. Bipolar sinusoidal or triangle periodic waves with amplitude V_FG were applied from a function generator. To measure electrical current, we included in the circuit additional 1 kΩ resistor R, so that electrical current was found as I = V_R/R. Potential difference, V_P, between electrodes in plants is equal to V_P = V_FG − V_R (Fig. 2).

Figure 2.

Block diagram of the data acquisition and electrostimulation system.

We recorded the current flowing through the plant, generated by a bipolar sinusoidal wave with amplitude of ±5.5V and frequency of 0.001 Hz (Fig. 3A). Figure. 3A presents a pinched hysteresis loop in the voltage-current plane with one important difference. The plot displays a common pinched point without self-crossing between curves with coordinates I = 0 μA and V_P = 0 V (Fig. 3A). Increasing of a bipolar sinusoidal wave frequency to 1 kHz changes the shape of the line: it is still a loop but without a pinched point. The electrostimulation of the potato tuber by a periodic sinusoidal wave induces electrical responses with fingerprints of a memristor. Similar results were obtained for electrostimulation of a potato tuber by bipolar triangle wave with V_FG amplitude of ±5.5V and frequency of 0.001 Hz (Figure. 4).

Figure 3.

Dependencies of electrical current, I, in the potato tuber on V_P induced by sinusoidal voltage wave V_FG from a function generator; Frequency of voltage V_FG scanning was 0.001 Hz (A) and 1 kHz (B). Position of electrodes in the potato tuber is shown in Figure 2. The simplest equivalent electrical circuits are shown in inserts.

Figure 4.

Cyclic voltammetry in a potato tuber with 0.001 Hz scanning rate of periodic triangle wave. Position of electrodes in the potato tuber is shown in Figure 2.

Voltage gated ion channels regulate generation and transduction of electrical signals. For their analysis there are very efficient tools - blockers of ionic channels.^24,29 It was intriguing to investigate if these blockers would change characteristics or even the presence of memristors in plants. Tetraethylammonium chloride (TEACl) is known as a blocker of a voltage gated K⁺ channel.²⁴ We found that the injection of 200 μL of 0.3 M TEACl in the middle of a potato tuber with the average of 2 mM concentration of TEACl in the potato tuber induces contraction of the amplitude of electrical current and the shrinkage of the hysteresis (Fig. 5). This can be caused by the increasing of resistance in the potato tuber. Injection of 0.2 mL of distilled water in control experiments does not inhibit memristive properties of the potato tuber while an inhibitor of voltage gated K⁺ channels tetraethylammonium chloride transforms a memristor to a resistor. These results demonstrate that a voltage gated K⁺ channel in the potato tuber is an essential component of a memristor.

Figure 5.

Electrical current I versus voltage V_P applied to a potato tuber. Frequency of bipolar sinusoidal (A) or triangle (B) voltage scanning was 0.001 Hz. 200 μL of 0.3 M TEACl were injected by a syringe to the potato tuber 48 hours before measurements.

Figure 6 shows the effect of uncoupler carbonylcyanide-4-trifluoromethoxyphenyl hydrazone (FCCP) on electrical current induced by bipolar triangle electrical waves. The same results were obtained during electrostimulation by bipolar sinusoidal wave. Forty eight hours delay between the FCCP injection to the middle of a potato tuber and electrostimulation experiments was required because of slow diffusion and partition of FCCP to the plant tissue. FCCP decreases the amplitude of electrical responses at low and high frequencies.

Figure 6.

Electrical current I vs. voltage V_P applied to a potato tuber. Frequency of bipolar triangle voltage scanning was 0.001 Hz. 200 μL of 10 μM FCCP were injected by a syringe to the leaf 90 hours before measurement.

Figure 7 shows the effect of uncoupler CCCP on electrical current induced by bipolar sinusoidal electrical wave in a potato tuber. The same results were obtained during electrostimulation of a potato tuber by bipolar triangle electrical wave. As in the previous case, 90 hours delay between the plant treatment and electrostimulation experiments was required because of slow penetration of CCCP to the plant tissue. CCCP decreases the amplitude of electrical responses at low and high frequencies. Similar results were obtained by substitution of CCCP by uncoupler carbonylcyanide-4-trifluoromethoxyphenyl hydrazone (FCCP).

Figure 7.

Electrical current I versus voltage V_P applied to a potato tuber. Frequency of bipolar triangle voltage scanning was 0.001 Hz (A) and 1 kHz (B). 200 μL of 10 μM CCCP were injected by a syringe to the leaf 90 hours before measurement.

The tuber has a vascular system, part of which is concentrated in the area called the vascular ring and part of which is dispersed throughout the tuber. The vascular ring contains cells that transport nutrients from the above growing cells to the medulla. Electrostimulation of the potato tuber by bipolar triangle or sinusoidal waves can induce the propagation of electrical signals along a vascular ring. To check this hypothesis, we applied bipolar triangle and sinusoidal waves to potato tuber (Figs. 8 and 9). Electrostimulation of the potato tuber by function generator connected to platinum electrodes induces small graded potential propagation along potato (Figs. 8 and 9). Amplitude of the electrical response was 100 times less than the amplitude of electrostimulation by bipolar triangle or sinusoidal waves.

Figure 8.

Time dependencies of electrical signals in the potato tuber induced by a bipolar triangle wave from a function generator. The frequency of scanning was 100,000 samples/s with a low pass filter at 50,000 scans/s. The frequency of electrostimulation was 1 Hz. Distance between electrodes was 7 mm.

Figure 9.

Time dependencies of electrical signals in the potato tuber induced by a bipolar sinusoidal wave from a function generator. The frequency of scanning was 100,000 samples/s with a low pass filter at 50,000 scans/s. The frequency of electrostimulation was 1 Hz. Distance between electrodes was 7 mm.

Discussion

Electrical processes play important roles in electrophysiology of plants. The electrical form of energy has no entropy content and 100% of this energy can be used to do work or in information transfer and analysis. These signals propagate along sophisticated electrical circuitry of plants consisting of many electrical components developed by nature. The standard electrical circuits comprise 4 basic elements: a resistor, a capacitor, an inductor, and a memristor. Memristors are memory circuit elements whose properties depend on the history and state of the system.

According to Chua,⁷ a memristor is best defined as any 2-terminal device that exhibits a pinched hysteresis loop in the voltage-current plane when driven by any periodic voltage or current signal that elicits a periodic response of the same frequency. Here we are going to analyze the memristance in the Irish red potato.

We selected for this analysis the potato tubers. In these tubers, we found the presence of resistors with memory. When driven by a bipolar periodic sinusoidal or triangle signal potato tubers exhibit a pinched hysteresis loop in the voltage-current plane (Figs. 3 and 4). Starting from some critical frequency, the hysteresis loop changes shape and a pinched hysteresis loop transforms to a non-pinched hysteresis (Fig. 3) as the excitation frequency increases. Adhikari et al.¹⁷ have shown that there are 2 types of pinched hysteresis loops in memristors: a transversal type where 2 branches of the hysteresis loop are self-crossing and a non-transversal type where 2 branches of the hysteresis loop are tangent at the pinched point. Voltage gated channels can exhibit more than one self-intersection points.¹⁵ The third fingerprint of a memristor discovered by Chua,⁶ and Adhikari et al.¹⁷ “the pinched hysteresis loop should shrink to a single-valued function when the frequency tends to infinity” is correct for ideal memristors. For a plant tissue, the pinched hysteresis loop transforms to a non-pinched hysteresis loop instead of a single line I = V/R at high frequencies of the applied voltage because the amplitude of electrical current hysteresis depends also on capacitance of a plant tissue and electrodes, frequency and direction of scanning (equation 3).

Figure. 3 shows simple equivalent electrical circuits for low frequency measurements with a memristor (Fig. 3A) and for high frequency measurements with a resistor (Fig. 3B).

The memristor driven by the sinusoidal current generates I-V pinched hysteresis loop. The pinched hysteresis loop is a double-valued Lissajous figure of (V(t), I(t)) for all times t, except when it passes through the origin, where the loop is pinched. It was theoretically shown that the voltage gated potassium ion channels in axons are locally active memristors.^7,11,12,15 Plants have the voltage gated potassium ion channels associated with plasma membranes. Figures 3 and 4 show memristive properties of potato tubers. A blocker of the voltage gated potassium ion channels, TEACl inhibits the memristive properties of the potato tuber (Fig. 5). It means that the voltage gated potassium ion channels in the potato tuber can be memristors. However, TEACl is not specific and could block also some non-selective cation channels.

Uncouplers CCCP and FCCP decrease the amplitude of a hysteresis loop (Figs. 6 and 7) by depolarizing of a plasma membrane and by decreasing of a membrane capacitance. Uncouplers, which are soluble in both water and lipid phases, permeate the lipid phase of a membrane by diffusion and transfer protons across the membrane, thus eliminating the proton concentration gradient and/or a membrane potential.^24,30,31 The plant physiology must include memristors as essential model building blocks in electrical networks in plants. This study can be a starting point for understanding mechanisms of memory, circadian rhythms and biological clocks.

Materials and Methods

Plants

Tubers of red Irish potato (Solanum tuberosum L.) were received from Catbird Seat Garden Center (Madison, AL, USA). Mass of a potato tuber was about 28.5 g (Mean 28.52 g, Median 28.00 g, Std. Dev. 5,88 g, Std. Err. 0.86 g, n = 47). The humidity averaged 45–50%. Temperature was 22°C. All experiments were performed on healthy specimens.

Chemicals

Tetraethylammonium chloride (TEACl), carbonylcyanide-3-chlorophenylhydrazone (CCCP) and carbonylcyanide-4-trifluoromethoxyphenyl hydrazone (FCCP) were obtained from Fluka (New York).

Electrodes for extracellular measurements

Ag/AgCl electrodes were prepared in the dark from Teflon coated silver wires (A-M Systems, Inc.., Sequim, WA, USA) with a diameter of 0.2 mm by electrolysis of 5 mm long silver wire tip without Teflon coating in a 0.1 M KCl aqueous solution. The response time of Ag/AgCl electrodes was less than 0.1 μs. We also used platinum electrodes instead of Ag/AgCl electrodes and acquired the same results. Platinum electrodes were prepared from Teflon coated platinum wires (A-M Systems, Inc..) with diameter of 0.076 mm. In all experiments we used identical Ag/AgCl) electrodes as a measuring and as reference (Ref) electrodes. Platinum electrodes were used for electrostimulation of red Irish potato tubers by bipolar sinusoidal or triangle periodic waves.

Data acquisition

All measurements were conducted in the laboratory at constant room temperature of 22°C inside a Faraday cage, which was mounted on a vibration-stabilized table (Fig. 2). High speed data acquisition of low-pass filtered signals was performed using microcomputer NI-PXI-1042Q (National Instruments) with simultaneous multifunction I/O plug-in data acquisition board NI-PXI-6115 (National Instruments) interfaced through a NI SCB-68 shielded connector block to electrodes (Jovanov and Volkov, 2012). The system integrates standard low-pass anti-aliasing filters at one half of the sampling frequency. The multifunction NI-PXI-6115 data acquisition board provides high resolution and a wide gain range. Any single channel can be sampled at any gain at up to 10 MSamples/s.

Plant electrostimulation

The function generator FG300 (Yokagawa, Japan) was interfaced to NI-PXI-1042Q microcomputer and used for electrostimulation of plants. We selected a resistor R = 1 kΩ for measuring of voltage, V_R, and for estimation of electrical current I.

Statistics

All experimental results were reproduced at least 14 times. Software SigmaPlot 12 (Systat Software, Inc..) was used for statistical analysis of experimental data.

Disclosure of Potential Conflicts of Interest

No potential conflicts of interest were disclosed.

Funding

This article is based upon work supported by the Henry C. McBay (UNCF) Research Fellowship.