Sensors and Materials, Vol. 26, No. 7 (2014) 471–482
MYU Tokyo
S & M 1014

Analysis of Plant Bioelectric Potential Response
to Illumination by Curve Fitting
Ki Ando*, Yuki Hasegawa1, Hidekazu Uchida1 and Akinori Kanasugi
Tokyo Denki University, 5 Senju-Asahi-cho, Adachi-ku, Tokyo 120-8551, Japan
Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama-shi, Saitama 338-8570, Japan

1(Received January 27, 2014; accepted May 14, 2014)
Key words: bioelectric potential of plant, photosynthesis, photochemical reaction, carbonfixation reaction, plant factory, curve fitting

Measurement of plant bioelectric potential is one of the promising methods forevaluating plant activities. For example, the photosynthetic rate can be evaluated using
the amplitude of the potential response to illumination. In our previous work, we foundthat this potential response consisted of two potential variations due to photochemical
and carbon-fixation reactions. These reactions are important parts of the photosynthetic
reaction. However, these potential variations may overlap each other. In this case, awaveform of the potential response differed variously, and it was difficult to evaluate
the photosynthetic rate using its amplitude. Therefore, we performed curve fitting for
estimating and separating these overlapped potential variations. First, we defined f1 andf2 as functions to represent the potential variations due to the photochemical and carbonfixation reactions, respectively. Additionally, we modelled the potential response toillumination as F = f1 + f2 and we fit F to the original data of the potential response. As
a result of curve fitting, F fit to the original data of the potential response very well. The
amplitude of f2 strongly correlated with the photosynthetic rate. This result suggested
that information on the photosynthetic rate was recovered by curve fitting. We consider
that this method can be applied to a more accurate evaluation of the photosynthetic
activity using the bioelectric potential of the plant.

Corresponding author: e-mail: kiando@mail.dendai.ac.jp

*

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Sensors and Materials, Vol. 26, No. 7 (2014)

Introduction

Recently, safe farm products have attracted considerable interest among customers.
The plant factory has been developed for satisfying the demand of customers.(1) The
plant factory controls the cultivation environment and grows farm products under aclosed indoor condition.(2) This cultivation process is not affected by toxic chemicals
and the weather from outside and can realize the effective cultivation of safe crops.
However, the costs of equipment and controlling the environment are greater than thoseof conventional outdoor cultivation at the present stage.(3) Therefore, evaluating plant
activities and feeding their information back to the environment control are necessary toincrease cultivation efficiency. However, there is no suitable method for practical use in
the actual cultivation site. Therefore, in most cases, the plant activities are evaluated on
the basis of experience and feeling of expert farmers.
For this purpose, we focused on the bioelectric potential of the plant and its application.(4)The bioelectric potential of the plant is generated by internal ions of plant cells. It has
been reported that the potential varies with the change of the cultivation environment andreflects various physiological activities of the plant.(5) Therefore, it is expected that thephysiological activities of the plant will be evaluated and monitored by measuring thebioelectric potential. For example, when the plant is illuminated, a potential response
is observed. Many studies have reported that the amplitude of this potential response
correlates with the photosynthetic rate of the plant.(6,7)
However, in our latest research, we reported that the amplitude of the potential
response did not correlate with the photosynthetic rate depending on the conditions of
the experiment such as the illumination condition. The potential response of the plantconsists of multiple potential variations reflecting each physiological activity. We
considered that the waveform of the potential response became different depending on
the overlapping of each potential variation. In the worst case of their overlap, significant
information about the potential response was lost, and we were not able to evaluate
the plant activities using the amplitude of the potential response, which was one of theconventional methods.(8)Otherwise, the integration value and frequency characteristic of the bioelectric
potential are often used for the detailed analysis of the potential response.(9,10) Thesemethods are effective for evaluating the resting potential and periodic response.
However, the potential response to illumination, which we focused on, is a type of action
potential and is observed only once for each illumination. We considered that the lost
information of the overlapped potential was difficult to recover by these methods.
In this paper, we propose an analysis method that can be used to evaluate thephotosynthetic rate even in this case. For this purpose, we separated the overlapped
multiple potential variations and estimated each variation component by the curve
fitting to the response. In particular, we prepared a composite function for modeling theoverlapped multiple potential variations, and carried out the curve fitting of this function
to time-series data of the bioelectric potential response. In addition, we investigated therelationship between the photosynthetic rate and the potential variation estimated by thismethod.

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Sensors and Materials, Vol. 26, No. 7 (2014)2.

Measurement of Plant Bioelectric Potential

2.1

Measurement system of plant bioelectric potential

In this experiment, we used a foliage plant called golden pothos (Epipremnun
aureum) as a measuring object of the bioelectric potential. Golden pothos is tolerant
to environmental changes and allows long-term stable measurement. Figure 1 shows
schematically the measurement system of the plant bioelectric potential. The potential
was measured using a pair of electroencephalographic disc electrodes (NE-155A, Nihon
Kohden Corp.) attached to the plant surface with a conductive paste (Z-401CE, thesame manufacturer). To detect the potential response induced by the photosynthetic
reactions, we attached an electrode on the leaf stem as a reference electrode, andobserved the potential difference using another electrode attached to the leaf surface
where the photosynthesis takes place actively. The potential was measured with adigital multimeter (DMM, R6552A, ADC Corp.) and was recorded using a PC with 1 s
sampling intervals.
The plant was placed in an airtight vessel with a volume of 22.4 L, and the change
in CO2 concentration was obtained with an NDIR-type CO2 sensor (LI-840, Meiwafosis
Co., Ltd.) for evaluating the photosynthetic and respiration rates of the plant. When theplant is placed in the dark, the CO2 concentration increases owing to the respiration of
the plant. We defined this CO2 variation in the airtight vessel as the respiration rate (mg/h). On the other hand, the CO2 concentration decreases owing to photosynthesis underillumination. However, the measured decrease in CO2 concentration consists of CO2
absorption due to photosynthesis and CO2 emission due to respiration. Therefore, we
defined the sum of the respiration and measured CO2 decrease rates during illumination
as the photosynthetic rate (mg/h). To accurately determine the photosynthetic rate, weused the respiration rate that was measured just before starting the illumination.
The experiment of measuring the bioelectric potential was performed in a dark room
at a temperature of 25 to 35 °C and a humidity of 60 to 70%. The light source consisted

LED panel

Control
unit
DMM

+

Dark room

Closedvessel－PC

Disc electrodeCO2
sensorPothosFig. 1. (Color online) Measurement system of plant bioelectric potential.

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Sensors and Materials, Vol. 26, No. 7 (2014)of blue (470 nm), green (525 nm), red (660 nm), and infrared (735 nm) LEDs (ISL305X302-RFGB, CCS), and illumination patterns were controlled with a controller (ISC101-4). In this study, the photosynthetic photon flux density (PPFD, μmol/m2∙s) wasused as an index of illumination intensity and the PPFD was measured at the leaf surface.
The PPFD was adjusted to 15, 30, 60, and 90 μmol/m2∙s to control the photosynthetic
rate. The PPFD ratio of LEDs was blue:green:red = 1:1:2 and the color with this PPFD
ratio appeared white to the eye. The PPFD was evaluated by a quantum sensor (QMSS
type, Apogee). However, infrared is outside of the measurement range of the quantum
sensor because infrared hardly contributes to photosynthesis. Therefore, we set thevoltage of the infrared LED line to the same value as the red LED line. To inhibit theeffects of attaching the electrodes and placement in the dark room, the plant was kept
in total darkness for about 60 min prior to illuminating the LED light and recording thepotential.

2.2

Plant bioelectric potential response to illumination

Figure 2 shows an example of the plant bioelectric potential response to starting andstopping illumination. When the illumination was started, the potential rose, dropped,
and then recovered to the resting potential. The photosynthesis process of the plant canbe divided into two stages. The first stage is photochemical reaction, which generates
high-energy molecules by receiving light energy. The second stage is carbon-fixation
reaction, which fixes carbon to phosphoric acid using the high-energy molecules. As aresult of these reactions, carbohydrate was synthesized in the plant. It has been reported
that the potential rise to illumination is related to the photochemical reaction and thefollowing potential drop is related to the carbon-fixation reaction.(6,8,11) In addition, manystudies also reported that the photosynthetic rate is related to the amplitudes of thesepotential rise and drop as well as the amplitude of the whole response Von.(6,7)
On the other hand, when the illumination was stopped, the potential dropped
sharply, and then recovered to the resting potential. We have reported that the intensity

Illumination start

Illumination stop

Potential (V)

Von

Voff

Time (s)Fig. 2. (Color online) Example of plant bioelectric potential response to illumination start and
stop.

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Sensors and Materials, Vol. 26, No. 7 (2014)of illuminating light correlated with the amplitude Voff, and have considered that
Voff indicates the intensity of the photochemical reaction, which occurred until theillumination was stopped.(8) The amplitudes of these responses to illumination generally
range from 10 to 20 mV under sufficient light intensity.

3.

Overlap of Potential Variations

On the basis of our results described above, we performed further experiments. As
shown in Figs. 3 and 4, we found that the potential response to illumination may takedifferent waveforms from the response shown in Fig. 2.(8) In the case of Fig. 3, theamplitude of the potential response was not observed clearly, and in the case of Fig.
4, the order of the potential rise and drop was inverted. This waveform difference
was observed in the experiment not only among different individuals but also with thesame leaf. This tendency was obtained among three individuals and two leaves in eachindividual. In the case of the same leaf, the waveform differed depending on the dark
period before starting illumination. We considered that the waveform was affected by

Illumination start

Illumination stop

Potential (V)

Von

Voff

Time (s)Fig. 3. (Color online) Example of unclear potential response to illumination start.

Von

10 minIllumination start

Von

10 mv

10 mv

Illumination start

10 minFig. 4. (Color online) Various waveforms of potential response at illumination start.

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the carbon-fixation reaction, because the carbon-fixation reaction is deactivated slowly
during a dark period.(8)On the other hand, we found that two common peaks of the potential rise and drop
can be seen in Figs. 2–4. In addition, it was considered that the waveform strongly
depended on the peak time of the potential rise and drop. The peak times of these
responses, as well as their amplitudes, also differ from those of the photosynthetic
activities. However, when these peak times were close to each other, the potential riseand drop overlapped and information on the amplitude was lost.
When the potential responses took various waveforms and overlapped significantly,
we were not able to evaluate the photosynthetic rate using their amplitudes directly.
Figure 5 shows the relationship between the photosynthetic rate and the amplitude Von.
In this experiment, the potential was measured from the same individual and the sameleaf. The dark period before illumination start was 30 or 60 min and the illumination
intensity differed in each measurement. We obtained Von by subtracting the value justbefore starting illumination from the peak value of the potential rise. The potential
responses took various waveforms, as shown in Figs. 2–4, depending on the dark period.
As a result, Von showed no correlation with the photosynthetic rate. From this result, it
was considered that the photosynthetic rate may be difficult to evaluate by simply using
the amplitude of the potential response.

4.

Analyzing Potential Response by Curve Fitting

4.1

Definition of fitting function

As described above, two potential variations, the potential rise and drop, were mainly
observed in the potential response to illumination. Additionally, it was considered thatthese potential variations were due to the photochemical and carbon-fixation reactions in
the photosynthetic process, respectively. We expected that if these potential rise and drop

Photosynthetic rate (mg/h)

Correlation coefficient = −0.02

Von (mV)

Fig. 5. Relationship between amplitude Von obtained from the responses of various waveforms
and photosynthetic rate.

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were separated from the overlapped potential response, any waveform of the response
could be used for evaluating the photosynthetic activities. Therefore, we performed
curve fitting to estimate the potential rise and drop.
First, we defined f1 and f2 as functions to represent the potential rise and drop,
respectively. f1 and f2 were functions of time t determined by modifying the Gumbel
distribution. The original Gumbel distribution is a type of probability density function
shown asf (x) =

1
x− µ
x− µ
exp −exp −
−
η
η
η

.

(1)

The Gumbel distribution is a left-right asymmetry function, and the slope of the rightside is gentler than that of the left side under η > 0. In addition, μ is related to theposition of the peak and η is related to the peak value of the function. We thought that
this characteristic is similar to the behavior of the bioelectric potential. However, theGumbel distribution has no independent coefficient related to the degrees of the slopes.
Therefore, we modified the Gumbel distribution as shown in eq. (2) and used thisfunction for curve fitting.
f (t) = p1 exp −exp −t − p3t − p5
−
+1
p4
p2

(2)

The number of coefficients was increased to 5. Each coefficient is mainly related tothe characteristics of the function as follows. p1 and p5 are related to the peak valueof the function. p2 and p4 are related to the degrees of the slopes before and after thepeak, respectively. p3 is related to the peak time of the function. This formula can betransformed more simply. However, we used this expression because the contribution ofeach coefficient could easily be understood.
Then, we defined F as F = f1 + f2. F was the modelization of the whole potential
response induced by illumination. We obtained the coefficients p1 to p5 of f1 and f2 to fit
F to the original time-series data of the plant bioelectric potential. This calculation was
carried out using a solver of Microsoft Excel by the least-squares approach.
In addition, we made two corrections to the time-series data before performing curve
fitting to obtain a better fitting result. First, the bioelectric potential often has a gentle
slope, as shown in Figs. 2 and 3. It has been reported that this slope is related to thetime of day and watering condition.(12) However, this slope was not considered in thisstudy, and the modelling function F did not have a member corresponding to the slope.
Therefore, we corrected the slope of the potential response to become a horizontal slope
as a whole. Second, the data obtained before starting and after stopping the illumination
were not modelled in F, and these parts interfered with obtaining a fine fitting result.
Therefore, we used the time-series data between the beginning of illumination and therecovery to the resting potential.

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The Gumbel distribution used in this study is an example of functions for the curve
fitting to the potential response. We think that there may be a more suitable function forthis purpose.

4.2

Estimation of overlapped potential variations

Figure 6 shows an example of performing the curve fitting to the potential response
to illumination shown in Fig. 2. In Fig. 6, the solid line shows the original data of thepotential response, and the broken line shows the result of the curve fitting F. The
broken line represents almost the same waveform as the solid line. This finding suggeststhat the result of the curve fitting is good. f1 and f2, which constitute F, are represented
by the gray solid and dotted lines in Fig. 6, respectively. We defined the amplitudes of f1
and f2 as Vf1 and Vf2, respectively.
Figure 7 shows the result of the curve fitting to the response shown in Fig. 3. In
contrast to Fig. 2, it seemed that the potential rise and drop of the target response
overlapped deeply, and their amplitudes were small and unclear. However, thewaveform of F fit the original data very well, and f1 and f2 obtained using the curve fitting
represented a similar waveform to the result shown in Fig. 6. Moreover, Vf1 and Vf2 werelarger than the amplitude of the original data.
In addition to these results, we performed the curve fitting to various waveforms of
the potential response such as those shown in Figs. 4(a) and 4(b). In most results ofthe curve fitting, the waveform of F was able to fit to the original data of the potential
response. We considered that the actual potential rise f1 and actual potential drop f2 were
estimated and separated from the potential response to illumination by curve fitting.
Investigation of the relationship between this estimation result and the photosynthetic
rate was explained in § 5.

Potential (V)Potential (V)

Vf1

Vf2
Original data

Vf1

Vf2

F
f1
f2

Time (s)Fig. 6 (left). Result of curve fitting to the response with clear amplitude.
Fig. 7 (right). Result of curve fitting to the response with unclear amplitude.

Original data

F
f1
f2

Time (s)479

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4.3

Restriction condition to curve fitting

In the case of some potential response, even though the waveform of F fit to theoriginal data, f1 and f2 may take multiple combinations. Figure 8 shows an example
of a different combination of f1 and f2 obtained from the same original data. In thecomparison of (a) and (b), the result of the curve fitting F and the residual sum obtainedby the least-squares approach were almost the same. However, the amplitudes of f1 andf2 differed significantly between (a) and (b). We considered that this problem was caused
by a very wide range of coefficients that f1 and f2 could take.
To avoid this problem, we appended a restriction to the curve fitting, which was Vf1≈ Voff. Voff indicated the amplitude of the potential response at stopping illumination, as
shown in Figs. 2 and 3. The basis of this restriction is shown as follows.
First, Fig. 9 shows the potential response induced by illumination under the N2 gas
condition, which we reported previously.(8,11) In N2 gas, the carbon-fixation reaction
is inhibited owing to the CO2-free condition. In addition, both amplitudes, Von-N2 andVoff-N2, correlated with the intensity of illumination. Therefore, we considered thatthese responses were commonly due to the photochemical reaction. In particular, theamplitude Von-N2 usually indicated a similar value to Voff-N2 without depending on theexperimental condition and their correlation coefficient was 0.97.(11)On the other hand, as described in §§ 2.2 and 4.1, the potential rise at illumination (f1)and the potential response at stopping illumination were also related to the photochemical
reaction. Therefore, we assumed that Vf1 indicated the same amplitude as Voff as well as
the relationship between Von-N2 and Voff-N2 in N2 gas. In the experiment, we obtained Voffby subtracting the peak value of the potential drop from the value just before stopping
illumination. This value was used for the restriction condition of the curve fitting.

Original data

F

f1

f2

Illumination start

Illumination stop

Potential (V)Potential (V)Potential (V)

Von-N2

Voff-N2Time (s)Time (s)Time (s)Fig. 8 (left). Different results of curve fitting obtained from the same original data.
Fig. 9 (right). (Color online) Bioelectric potential response to illumination in N2 gas for inhibiting
carbon-fixation reaction.(11)480

Sensors and Materials, Vol. 26, No. 7 (2014)

5.

Relationship between Estimation Result and Photosynthetic Rate

5.1

Amplitude of potential drop Vf2 and photosynthetic rate

5.2

Restriction condition Voff and photosynthetic rate

In this section, we investigated the relationship between the estimated amplitudeof the actual potential drop Vf2 and the photosynthetic rate. As described in Fig. 3, it
is considered that the potential drop response to illumination is due to the carbon-fixation
reaction.(6,8,11) Therefore, we predicted that if the potential drop f2 were estimatedcorrectly by curve fitting, its amplitude Vf2 would strongly correlate with the intensity of
the carbon-fixation reaction, namely, the photosynthetic rate.
Figure 10 shows the relationship between the estimated amplitude of the potential
drop Vf2 and the photosynthetic rate. The original data for the curve fitting is completely
the same as the data used in Fig. 5. Although Vf2 had a certain variance with eachphotosynthetic rate range, it was approximately proportional to the photosynthetic rate.
The correlation coefficient was about 0.85. In comparison with the result shown in Fig. 5
using unprocessed data, the variance of the amplitude became smaller, and a proportional
relationship was observed.
From this result, we considered that the information lost by overlapping thepotential rise and drop could be estimated and recovered by curve fitting, and that thephotosynthetic rate could be evaluated using the estimated amplitude Vf2.

Photosynthetic rate (mg/h)

In the previous section, the amplitude Vf2 correlated with the photosynthetic rate.
However, this Vf2 was obtained under the restriction condition Vf1 = Voff in the curve
fitting, as described in § 4.3. We considered that the result shown in Fig. 10 could
possibly indicate the relationship between Voff and the photosynthetic rate. Therefore,
we also investigated this relationship and showed the result in Fig. 11. The amplitude
Voff was obtained from the same original data shown in Figs. 5 and 10. The correlation
coefficient was 0.67, and the photosynthetic rate was observed to be proportionally

Correlation coefficient = 0.85

Vf2 (mV)

Fig. 10. Relationship between estimated amplitude Vf2 and photosynthetic rate.

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Photosynthetic rate (mg/h)

Correlation Coefficient = 0.67

Voff (mV)Fig. 11. Relationship between amplitude Voff used for restriction condition and photosynthetic rate.

related to Voff. However, the correlation coefficient of Vf2 (Fig. 10) was greater than thatof Voff (Fig. 11).
Therefore, Vf2 was considered to be more strongly related to the carbon-fixation
reaction than Voff. In other words, the correlation with the photosynthetic rate was
improved by estimating Vf2 using Voff. In comparison with the result obtained using raw
amplitude data (Fig. 5), the result in Fig. 10 suggested a significant recovery of the lost
information on the carbon-fixation reaction. We considered that this curve fitting can beapplied to a more accurate evaluation of the photosynthetic rate.

6.

Conclusions

The plant bioelectric potential response induced by illumination consisted of thepotential rise due to the photochemical reaction and the potential drop due to the carbonfixation reaction. When these potential variations overlapped deeply, the informationon the potential amplitude related to the photosynthetic activities was lost. In this case,we could not evaluate the photosynthetic rate using the potential amplitude. Therefore,
we performed the curve fitting to the potential response to estimate and separate theseoverlapped potential variations.
For this purpose, we defined the potential rise and drop as two Gumbel distributionfunctions, and modelled the whole potential response to illumination using the sum of
two Gumbel distribution functions. The Gumbel distribution used in this study is an
example of functions for the curve fitting to the plant bioelectric potential response.
We think that there may be a more suitable function for this purpose. Additionally, weappended the restriction condition to the curve fitting for obtaining better results.
As a result of the curve fitting, the waveform of the modelled function fit the original
data very well, and the potential rise and drop were estimated and separated. The
estimated potential drop correlated with the photosynthetic rate strongly. This result

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suggested that the lost information on the carbon-fixation reaction was recovered. We
considered that this curve fitting can be applied to a more accurate evaluation of thephotosynthetic rate.

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