Memristors in the electrical network of Aloe vera L.

Abstract

A memristor is a resistor with memory, which is a non-linear passive two-terminal electrical element relating magnetic flux linkage and electrical charge. Here we found that memristors exist in vivo. The electrostimulation of the Aloe vera by bipolar sinusoidal or triangle periodic waves induce electrical responses with fingerprints of memristors. Uncouplers carbonylcyanide-3-chlorophenylhydrazone and carbonylcyanide-4-trifluoromethoxy-phenyl hydrazone decrease the amplitude of electrical responses at low and high frequencies of bipolar periodic sinusoidal or triangle electrostimulating waves. Memristive behavior of an electrical network in the Aloe vera is linked to the properties of voltage gated ion channels: the K⁺ channel blocker TEACl reduces the electric response to a conventional resistor. Our results demonstrate that a voltage gated K⁺ channel in the excitable tissue of plants has properties of a memristor. The discovery of memristors in plants creates a new direction in the modeling and understanding of electrical phenomena in plants.

Introduction

Aloe vera (L.) is a member of the Asphodelaceae (Liliaceae) family with crassulacean acid metabolism (CAM). In the 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. Aloe vera is a model for the study of plant electrophysiology with crassulacean acid metabolism. The natural habitats of Aloe vera are the subtropical parts of the world. Aloe vera is considered to be intolerant of low temperatures. Its succulent leaves contain substances used for numerous medical and cosmetic applications. Recently, we analyzed anisotropy and nonlinear properties of electrochemical circuits in the leaves of Aloevera.^1,2 The newly developed DC charge stimulating method^3,4 permits direct in vivo evaluation of the simplest electrical circuits in a cluster of cells or in a single cell. Using this method, we discovered strong electrical anisotropy of the Aloe vera leaf.¹ Along the conductive bundles, the behavior of the Aloe vera leaf is strongly nonlinear. Electrostimulation by voltages with amplitude higher than 2 V is applied to the plant, a drastic change in the leaf: the initial input resistance drops. These changes occur in the conducting bundles and are probably due to the opening of voltage gated ion channels in the Aloe vera leaf.

Chua⁵ postulated in 1971 the existence of the fourth basic electrical circuit element, memristor, a resistor with memory, which is a nonlinear passive 2-terminal electrical element relating magnetic flux linkage and electrical charge (Fig. 1). Memristor has the ability to recall the resistance of a previous current when turned off, and will remember that resistance when the current flow resumes. During the last decade different memristors were developed as solid state semiconductor devices, polymers, and modified electrodes.^6-11 Analysis of the Hodgkin-Huxley axon model shows that voltage gated channels can be identified as a potassium ion-channel memristor and a sodium ion-channel memristor.^12-16 Since plants have voltage gated K⁺ channels, it would be interesting to investigate the possible presence of memristors in plants. 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. Mathematically memristance can be described by equation:

Figure 1. Relationships between a voltage, current, charge, and flux.

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

The power of a memristor is

P(t) = I²(t)M(q(t)) (2)

where ϕ and q denote the flux and charge, respectively (Fig. 1).

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).¹⁷ We found earlier 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 of type I or type II.¹⁸ The main goal of this article is to study memristive properties of the Aloe vera plant in vivo. Due to large size and thickness of Aloe vera leaf, it is possible to do electrostimulation in 3 dimensions – along the leaf, perpendicular, and from top to bottom directions.

Results

Electrostimulation of the Aloe vera by bipolar periodic waves from a function generator

Experimental setup is shown in Figure 2. Two methods were used for Aloe vera electrostimulation: function generator FG300 and potentiostat SI1287. 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 10 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

Figure 2. Two methods of cyclic voltammetry: (Method A) Block diagram of the data acquisition and electrostimulation system; (Method B) The SI1287 Advanced Electrochemical Interface was connected via the GPIB to PC and used in 2 terminal configuration for cyclic voltammetry.

V_P = V_FG – V_R (3)

V_P is always less than V_FG because of a voltage drop on a resistor R (Fig. 2).

Figure 3 shows how electrical current depends on the voltage V_p induced by bipolar sinusoidal wave from a function generator with frequency of 0.001 Hz, when platinum electrodes are inserted along the vascular bundles in a leaf of Aloe vera. There is a self-crossing between curves and 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 of a first kind (Fig. 3A). In some experiments 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 without a self-crossing between curves, which is a typical sign of a memristor of a second kind (Fig. 3B). Increasing of a sinusoidal wave frequency to 1000 Hz leads to the disappearing of a pinched point in the complete agreement with characteristics of memristors, which had a small “parasitic” capacitor connected across the memristor. This capacitance can be a function of membrane, electrodes, and plant tissue capacitances. We found that a self-crossing between curves exists in 71% of experiments (Mean 71.43%, Std. Dec. 46.88%, Std. Err. 12.53%, n = 14). The amplitude of electrical current increases if the applied voltage amplitude to the leaf of Aloe vera increases. The simple possible equivalent electrical circuits are shown in inserts.

Figure 3. Electrical current I vs. voltage V_P applied to a leaf of Aloe vera. Frequency of sinusoidal voltage scanning was 0.001 Hz (A) and 1000 Hz (B). Position of Pt electrodes in a leaf of Aloe vera is shown. These results were reproduced 14 times. The simplest equivalent electrical circuits are shown in inserts.

The power consumption characteristic can be estimated from Figure 3 using equation:

P(t) = I(t)V(t). (4)

At low frequencies of a bipolar periodic sinusoidal wave from a function generator, the power consumption is positive (Fig. 4A). Memristance has positive values for passive devices at all values of electrical charge. Figure 4B shows the power consumption at high frequencies, which has high positive and small negative values during electrostimulation of Aloe vera by a bipolar sinusoidal wave from a function generator. Capacitive currents cause this effect during charging and discharging processes (Fig. 4).

Figure 4. Electrical power P vs. time t estimated from Figure 3. Frequency of sinusoidal voltage scanning was 0.001 Hz (A) and 1000 Hz (B). Position of Pt electrodes in a leaf of Aloe vera is shown.

Figure 5 shows electrical responses induced by bipolar sinusoidal wave from a function generator with frequency of 0.001 Hz (A) and 1000 Hz (B), when platinum electrodes are inserted on top and on bottom of the leaf of Aloe vera. 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, without a self-crossing between curves (Fig. 5A). This is a typical sign of a memristor of a second kind. There is low amplitude of the loop at positive voltages and level of signal to noise ratio is low. The pinched hysteresis disappears at high frequencies (Fig. 5B). 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 depends also on capacitance of a plant tissue and electrodes, frequency, and direction of scanning:

Figure 5. Electrical current I vs. voltage V_P applied to a leaf of Aloe vera. Frequency of sinusoidal voltage scanning was 0.001 Hz (A) and 1000 Hz (B). Position of Pt electrodes in a leaf of Aloe vera is shown. These results were reproduced 14 times.

$$I=C\frac{dV}{dt}$$ (5)

Electrostimulation of the Aloe vera by linear sweep cyclic voltammetry

The cyclic voltammetry shows also memristive properties of Aloe vera (Figs. 6A, B, and 7A). At low frequencies of scanning at 10⁻⁴ Hz (Fig. 6A) and 10⁻³ Hz (Fig. 6B), 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. 6A, B). Increasing the speed of scanning, from 20 mV/s (10⁻³ Hz) to 1 V/s (5x10⁻² Hz), leads to the disappearance of pinched points in the hysteresis loop (Fig. 6C, D).

Figure 6. Cyclic voltammetry in a leaf of Aloe vera with a scanning rate of periodic triangle wave of 2 mV/s (A), 20 mV/s (B), 200 mV/s (C), and 1000 mV/s (D). Position of Pt electrodes in the Aloe vera is shown. These results were reproduced 14 times.

Figure 7. Electrical current I vs. voltage V_P applied to a leaf of Aloe vera. Frequency of sinusoidal voltage scanning was 0.001 Hz (A) and 1000 Hz (B). 200 μL of 10 mM TEACl were injected by a syringe to the leaf 25 h before measurement. Position of Pt electrodes in a leaf of Aloe vera is shown. These results were reproduced 14 times.

Effect of inhibitors and uncouplers on memristive responses

According to theoretical calculations, voltage gated K⁺ ion channels are memristors.^6,12-14 To confirm this hypothesis, we used tetraethylammonium chloride (TEACl) as a chemical compound, which is known to block voltage gated K⁺ ion channels in plant and animal electrophysiology. Figure 7 shows the effect of tetraethylammonium chloride (TEACl) on electrical current induced by periodic bipolar sinusoidal wave when platinum electrodes are inserted along the pulvinus of Aloe vera. A 0.2 mL aliquot of 10 mM TEACl was injected in the Aloe vera leaf 25 h before electrical measurements. A 25 h delay was required because of the slow distribution of TEACl in the plant tissue. The pinched hysteresis loop (Fig. 7) disappears and the memristive system transforms to a resistance. Frequency of sinusoidal voltage scanning was 0.001 Hz. (A) in Figure 7 is a response to a bipolar periodic sinusoidal electrostimulating wave with frequency of 10⁻³ Hz and panels B shows the response to a bipolar periodic sinusoidal wave with frequency of 1000 Hz.

TEACl decreases the amplitude of electrical current between electrodes in the pulvinus of the Aloe vera. TEACl is known as a blocker of voltage gated potassium channels. TEACl, an inhibitor of voltage gated K⁺ channels, transforms a memristor to a conventional resistor in plant tissue at low and high frequencies of a bipolar periodic sinusoidal wave. Injection of 0.2 mL of distilled water or 10 mM CaCl₂ solution in control experiments does not inhibit memristive properties of the Aloe vera leaf. Our results demonstrate that a voltage gated K⁺ channel in the excitable tissue of plants has properties of a memristor.

Figure 8 shows the effect of uncoupler carbonylcyanide-4-trifluoromethoxyphenyl hydrazone (FCCP) on electrical current induced by bipolar sinusoidal electrical waves at different frequencies when electrodes are inserted along the leaf of Aloe vera. The same results were obtained during electrostimulation by bipolar triangle wave. As in the previous case, 25 h delay between the plant treatment and electrostimulation experiments was required because of slow diffusion of FCCP to the plant tissue. FCCP decreases the amplitude of electrical responses at low and high frequencies. Similar results were obtained by substitution of FCCP by uncoupler CCCP (Fig. 9).

Figure 8. Electrical current I vs. voltage V_P applied to a leaf of Aloe vera. Frequency of sinusoidal voltage scanning was 0.001 Hz (A) and 1000 Hz (B). Two-hundred μL of 10 μM FCCP were injected by a syringe to the leaf 25 h before measurement. Position of Pt electrodes in a leaf of Aloe vera is shown. These results were reproduced 14 times.

Figure 9. Electrical current I vs. voltage V_P applied to a leaf of Aloe vera. 200 μL of 10 μM CCCP were injected by a syringe to the leaf 25 h before measurement. Frequency of sinusoidal voltage scanning was 0.001 Hz (A) and 1000 Hz (B). Position of Pt electrodes in a leaf of Aloe vera is shown. These results were reproduced 14 times.

Discussion

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.^12-15 Plants have the voltage gated potassium ion channels associated with plasma membranes. Figures 3, 5, and 6 show memristive properties of 2 types in the Aloe vera leaf. Figures 3 and 6 shows that plant tissue has properties of memristor type I and Figure 5 illustrates electrical characteristics of a memristor type II. A blocker of the voltage gated potassium ion channels, TEACl inhibits the memristive properties of the Aloe vera leaf. It means that the voltage gated potassium ion channels in the Aloe vera leaf are memristors. Figure 4 shows the power characteristics of the Aloe vera memristors at different frequencies of applied periodic bipolar sinusoidal wave.

Uncouplers FCCP and CCCP decreases the amplitude of a hysteresis loop 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. Most protonophoric uncouplers widely used in photosynthesis research are oxidized by the manganese cluster of the Photosystem II O₂-evolving complex in chloroplasts and inhibit photosynthetic water oxidation. The membrane pool of plastoquinone can reduce oxidized uncouplers, leading to formation of an artificial cyclic electron transfer chain around Photosystem II involving uncouplers as redox carriers. Uncouplers promote auto oxidation of the high-potential form of cytochrome b559 and partially convert it to lower potential forms. Protonophores uncouple electron transport, accelerate the deactivation of the S-2 and S-3 states on the donor side, and facilitate the oxidation of cytochrome b559 on the acceptor side of Photosystem II.

By applying the periodic bipolar sinusoidal or linear periodic bipolar waves to the Aloe vera leaves, we found memristors of types I and 2 in vivo. Voltage gated potassium channels play a role of bio-memristors in plants. This study can be a starting point for understanding mechanisms of memory,²⁰ learning,¹⁹ circadian rhythms,³ and biological clocks.

Biological tissue in many organisms exhibit memristive behaviors. We found bio-memristors in different plants such as the Aloe vera, Venus flytrap,¹⁸ and Mimosa pudica.¹⁸ Gale et al. ²¹ found memristive properties of protoplasmic tubes of acellular slime mold Physarum polycephalum. Johnsen et al. ²² found that the sweat ducts in the skin are memristors. Hota et al.²³ create transparent memristors from natural regenerated silk fibroin protein obtained from cocoons of Bombyx mori silkworm. We should expect the finding of bio-memristors in many different biological systems in the near future.

Materials and Methods

Plants

Aloe vera L. plants were grown in clay pots. Fifty plants were exposed to a 12:12 h light/dark photoperiod at 21 °C (Environmental Corporation, USA). Volume of soil was 2.0 L. Aloe vera plants had 25–35 cm leaves. The average humidity was 40%. Irradiance was 700–800 μmol photons m⁻²s⁻¹. All experiments were performed on healthy adult specimens.

Chemicals

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

Data acquisition

All measurements were conducted in the laboratory at constant room temperature of 22 °С inside a Faraday cage, which was mounted on a vibration-stabilized table. In order to estimate possible high frequency content of the responses evoked, a high performance National Instruments data acquisition system was used. 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. 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.

Cyclic voltammetry

The SI1287 Advanced Electrochemical Interface (Solartron, Hampshire, England) was connected via the GPIB to PC and used in 2 terminal configuration for cyclic voltammetry.

Images

A photo camera Nikon D3X (Nikon USA Inc, Melville, NY USA) with AF-S Micro Nikkor 105 mm 1:2.8 G ED VR lens (Nikon USA) was used for the photography.

Statistics

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

Glossary

Abbreviations:

C

capacitance

CAM

crassulacean acid metabolism

CCCP

carbonylcyanide-3-chlorophenylhydrazone

DAQ

data acquisition

FCCP

carbonylcyanide-4-trifluoromethoxyphenyl hydrazone

I

electrical current

M

memristor

P

power

PXI

PCI eXtensions for Instrumentation

R

resistance

TEACl

tetraethylammonium chloride

q

charge

V

voltage

V_FG

voltage of an function generator

V_P

voltage between electrodes in a plant

V_R

voltage on resistor R

ϕ

magnetic flux