Memristors in plants

Abstract

We investigated electrical circuitry of the Venus flytrap, Mimosa pudica and Aloe vera. The goal was to discover if these plants might have a new electrical component—a resistor with memory. This element has attracted great interest recently and the researchers were looking for its presence in different systems. The analysis was based on cyclic current-voltage characteristic where the resistor with memory should manifest itself. We found that the electrostimulation of plants by bipolar sinusoidal or triangle periodic waves induces electrical responses in the Venus flytrap, Mimosa pudica and Aloe vera with fingerprints of memristors. Tetraethylammonium chloride, an inhibitor of voltage gated K⁺ channels, transforms a memristor to a resistor in plant tissue. Our results demonstrate that a voltage gated K⁺ channel in the excitable tissue of plants has properties of a memristor. This study can be a starting point for understanding mechanisms of memory, learning, circadian rhythms, and biological clocks.

Keywords: :

• Aloe vera
• Mimosa pudica
• Venus flytrap
• electrophysiology
• memristor
• signal transduction

Introduction

Electrical signals play important roles in electrophysiology of plants. These signals propagate along sophisticated electrical circuitry of plants consisting of many electrical components developed by nature. The standard electrical circuits comprise three basic elements: a resistor, a capacitor and an inductor. In addition to these elements, Chua¹ postulated the existence of a new element, which has electrical memory. This is the fourth basic circuit element, a memristor or a resistor with memory. In spite of initial skeptical attitude to this idea, the first solid-state memristor was built already in 2008.² Memristors are memory circuit elements whose properties depend on the history and state of the system. Since then, researchers have been looking for the presence of memristors in different systems.^3-12 They found a number of examples but up to now nobody was able to detect it in plants. Here we are going to demonstrate the existence of memristors in plants.

A memristor is a nano-scale memory device, which carries huge perspective technical applications. For example, they can replace flash memories and DRAMs in electronic appliances.¹³ 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. Mathematically it can be described by an equation:

(1) $$M=R(q)=\frac{d\phi (q)}{dq}$$(1)

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

Electrical circuits in plants operate over large distances.^14-18 The activation of these circuits can lead to various physiological and biochemical responses.^19-25 The cells of many biological organs generate electric potentials that can result in the flow of electric currents^14,26,27 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.^3,4 Since plants and animals have similar voltage gated K⁺ channels, it would be interesting to investigate the possible presence of memristors in plants. Chua et al.^3,4 and Adhikari et al.²⁸ found that a memristor has three 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 of memory elements, when subject to a periodic stimulus, can be self crossing (type I memristor) or not (type II memristor).

Plant tissues have different forms of memory such as sensory, short, and long-term memory.¹⁵ Plants have a biological clock and circadian rhythms, which involve electrical elements of memory.^21,24,29,30 We selected for this analysis the Venus flytrap and the Mimosa pudica as dicots, and the Aloe vera as a monocot and CAM plant. Aloe vera (L.) is a member of the Asphodelaceae (Liliaceae) family with crassulacean acid metabolism (CAM). In Aloe vera, stomata are open at night and closed during the day. CO₂ acquired by Aloe vera at night is temporarily stored as malic and other organic acids, and is decarboxylated the following day to provide CO₂ for fixation in the Benson-Calvin cycle behind closed stomata. The main goal of this article is to find out if plants comprise memristors.

Results

Experimental setup is shown in Figure 1. 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 47 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. 1).

Figure 1. Block diagram of the data acquisition and electrostimulation system.

The Venus flytrap is a carnivorous plant. The trap can be closed by mechanical stimulation of trigger hairs or by an electrical pulse between the midrib and a lobe of the upper leaf.¹⁹

We recorded the current flowing through the plant and generated by a bipolar triangle wave with frequency of 0.001 Hz (Fig. 2) for closed trap (panel A) and for an open trap (panel B). In both cases we obtained a pinched hysteresis loop in the voltage-current plane with one important difference. If the trap is closed, the plot displays a common pinched point with self-crossing between curves when I = 0 μA and V_P = 0 V (Fig. 2A). If the trap is open, the plot also displays a common pinched point but without self-crossing between curves with coordinates I = 1.5 μA and V_P = 0.16 V (Fig. 2B). At the first glance it might be not obvious that the curves in Figure 2A self-cross. So, to avoid the confusion we added the arrows to this panel. If one just follows these arrows, the crossing of the curves becomes immediately clear.

Figure 2. Dependencies of electrical current, I, in the Venus flytrap on V_P induced by triangle voltage wave V_FG from a function generator (A,B,C); Frequency of triangle voltage V_FG scanning was 0.001 Hz (A,B) and 10 Hz (c); R = 47 kΩ. Position of Ag/AgCl electrodes in the Venus flytrap is shown. The trap was open in (B,C) or closed in (A). These results were reproduced 16 times.

The behavior in Figure 2B can be described as “kiss-and-go”: the two branches touch each other but do not cross. The deviation of coordinates V_P and I from zero value can be caused by the action potential propagation in the trap, which has amplitude of 0.16 V.^20,31 Increasing of a triangle wave frequency to 1 kHz changes the shape of the line: it is still a loop but without a pinched point for both open (Fig. 2C) and closed traps. The branches of the loop go parallel to each other. So, the electrostimulation of the Venus flytrap by a periodic wave induces electrical responses in the Venus flytrap with fingerprints of a memristor.

Voltage gated ionic channels regulate generation and transduction of electrical signals. For their analysis there are very efficient tools - blockers of ionic channels.^29,30 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.³⁰ We found that deposition of 20 μL of 10 mM TEACl on the midrib of the Venus flytrap decreased the amplitude of electrical current and the hysteresis shrank (Fig. 3A). This can be caused by the increasing of resistance in the plant tissue. An inhibitor of voltage gated K⁺ channels tetraethylammonium chloride transforms a memristor to a simple resistor in plant tissue. Increasing of a triangle wave frequency to 10 Hz changes the shape of the line: it is still a loop but without a pinched point (Fig. 3B). These results demonstrate that a voltage gated K⁺ channel in the excitable tissue of the Venus flytrap is an essential component of plant memristor.

Figure 3. Effects of voltage gated channel inhibitor TEACl deposited on the midrib of the Venus flytrap 5 h before electrical measurements. Frequency of triangle voltage V_FG scanning was 0.001 Hz (A) and 10 Hz (B); R = 47 kΩ. Position of Ag/AgCl electrodes in the Venus flytrap is shown. The trap was open. These results were reproduced 16 times.

The Mimosa pudica is a nyctinastic plant that closes its’ leaves in the evening. The leaves open in the morning due to a circadian rhythm, which is regulated by a biological clock with a cycle of about 24 h. Leaf movement in the Mimosa pudica appear to be regulated by electrical signal transduction. Mechanics of these movements are hidden in the specialized organ - the pulvinus.^17,25 We have found that the movements of the petiole, or pinnules, connected to pulvinus are accompanied by a change of the pulvinus morphing structures. This structure has rather peculiar electrical properties similar to the electrical synapse in the animal nerves.²⁵ Therefore, it was interesting to investigate electrical circuitry of this organ. Figure 4 shows dependencies of electrical current induced by bipolar sinusoidal wave with amplitude of ± 3.5V (a) or ± 4.5V (b) and frequency of 0.001 Hz, where platinum electrodes are inserted along the pulvinus of Mimosa pudica.

Figure 4. Dependencies of electrical current, I, on voltage V_P applied along a pulvinus. Frequency of sinusoidal voltage scanning was 0.001 Hz. R = 47 kΩ. Position of Pt electrodes in the pulvinus of the Mimosa pudica is shown. Amplitude of applied voltage V_FG from a function generator varies from -3.5 V to + 3.5 V (A) and from -4.5 V to + 4.5 V (B). These results were reproduced 27 times.

There is a pinched point in hysteresis loop at low frequency of sinusoidal wave in the voltage-current plane when I = 0 μA and V_P = 0 V, which is a typical sign of a memristor. Figure 4A shows that there is a self-crossing between curves when amplitude of the applied sinusoidal voltage is between ± 3.5V. Increase of the amplitude of the sinusoidal voltage to 4.5 V changes the curve (Fig. 4B): the plot displays a common pinched point without self-crossing. Increasing of a sinusoidal wave frequency to 1 kHz changes the shape of a hysteresis loop and a pinched point disappears. Similar dependencies of electrical current on voltage were observed in a stem of the Mimosa pudica. There is a pinched point but without self-crossing between curves when I = 0 μA and V_P = 0 V.

The Aloe vera (L.) is a member of the Asphodelaceae (Liliaceae) family with crassulacean acid metabolism (CAM). Figure 5 shows cyclic voltammetry in the leaf of Aloe vera. At a low frequency of scanning, there is a pinched point with self-crossing between curves when I = 0 μA and V_P = 0 V, which is a typical fingerprint of a memristor (Fig. 5A). There is also an additional pinched point at the potential of 2 V. Increasing the speed of scanning from 2 mV/s (2x10⁻⁴ Hz) to 500 mV/s (0.05 Hz) leads to the disappearance of pinched points in the hysteresis loop (Fig. 5B). The simple possible equivalent electrical circuits are shown in inserts.

Figure 5. Cyclic voltammetry in a leaf of Aloe vera with a scanning rate of periodic triangle wave of 2 mV/s (A) and 500 mV/s (B). Position of Pt electrodes in the Aloe vera is shown. The simplest equivalent electrical circuits are shown in inserts. Electrodes were located along the leaf on the distance of 1 cm. These results were reproduced 16 times.

Discussion

In the Venus flytrap, Mimosa pudica, and Aloe vera plants we found the presence of resistors with memory. It is truly fascinating that even plants exhibit memristor fingerprints. When driven by a bipolar periodic sinusoidal or triangle signal plants exhibit a pinched hysteresis loop in the voltage-current plane (Figs. 2,4,5). Starting from some critical frequency, the hysteresis loop changes shape and a pinched hysteresis loop transforms to a non-pinched hysteresis (Figs. 2C, 5B) as the excitation frequency increases. Adhikari et al.²⁸ have shown that there are two types of pinched hysteresis loops in memristors: a transversal type where two branches of the hysteresis loop are self-crossing and a non-transversal or tangential type where two branches of the hysteresis loop are tangent at the pinched point. Voltage gated channels can exhibit more than one self-intersection points.⁵ The third fingerprint of a memristor discovered by Chua¹³ and Adhikari et al.⁵: “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.

Figure 5 shows simple equivalent electrical circuits for low frequency measurements with a memristor (Fig. 5A) and for high frequency measurements with a resistor (Fig. 5B). The goal of this work is not to offer an exact memristor model of the plants, which would be subject of future research, but to point out for the first time, that even plants exhibit memristive characteristics. The physiology of plants must include memristors as essential model building blocks in electrical networks in plants. The memristor is an “ideal” circuit element and no real-world biodevices can be exactly mimicked by an ideal circuit model. There are different models of increasing accuracy that can be developed at the cost of increasing complexity.

Materials and Methods

Plants

The Dionaea muscipula Ellis (Venus flytrap) plants were purchased from Fly-Trap Farm Supply (North Carolina, USA) and grown in well drained peat moss in plastic pots at 22 °C with 12:12h light: dark photoperiod. The soil was treated with distilled water.

Fifty Aloe vera L plants were grown in clay pots. Aloe vera plants had 25 – 35 cm leaves.

The seeds of Mimosa pudica L. were soaked in warm water (30 °C) for 48 h. They were then grown in well drained peat moss at 21 °C with a 12:12 h light:dark photoperiod. After growing for two weeks, the seedlings were transplanted into pots and placed inside a plant growing chamber. The plants were watered every day. Two-three month old plants were used for the experiments.

Irradiance was 700–800 μmol photons m⁻²s⁻¹. The humidity averaged 45 – 50%. All experiments were performed on healthy adult specimens.

Chemicals

Tetraethylammonium chloride (TEACl) was 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 (Pt or Ag/AgCl) electrodes as a measuring and as reference (Ref) electrodes.

Data acquisition

All measurements were conducted in the laboratory at constant room temperature of 22 ^oС inside a Faraday cage which was mounted on a vibration-stabilized table (Fig. 1). 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.

Plant electrostimulation

The function generator FG300 (Yokagawa, Japan) was interfaced to NI-PXI-1042Q microcomputer and used for electrostimulation of plants. Resistance between electrodes in plants in all our experiments was between 1.1 MΩ and 1.5 MΩ. We selected a resistor R = 47 kΩ for measuring of voltage, V_R, for estimation of electrical current I.

Cyclic voltammetry

The SI1287 Advanced Electrochemical Interface (Solartron, Hampshire, England)) was connected via the GPIB to PC and used in two terminal configuration for cyclic voltammetry.

Statistics

All experimental results were reproduced 25 times on different plants. Software SigmaPlot 12 (Systat Software, Inc.) was used for statistical analysis of experimental data.

Abbreviations:
C	=	capacitance
DAQ	=	data acquisition
PXI	=	PCI eXtensions for Instrumentation
I	=	electrical current
V	=	voltage between electrodes in plants, VFG, voltage of an function generator VR,voltage on resistor R
Vp	=	voltage between electrodes in plants

Disclosure of Potential Conflicts of Interest

No potential conflicts of interest were disclosed.

Acknowledgments

This work was supported in part by the National Science Foundation (grant no. CBET-1064160) and in part by the U. S. Army Research Office (contract/grant no W911NF-11-1-0132).   L. Chua's  research is supported  by  AFOSR  grant  number  FA9550-13-1-0136.