The Effect Mechanism and Model Optimization of Pulsed Light Dark Duration on Lettuce

Background: Despite its rapid development, the costs of crop artificial light source technology are still high. In addition, both the luminous efficiency and photosynthetic light supplement efficiency of the light source require further improvement. This study aims to improve the photosynthetic light supplement efficiency by altering the luminescence mode of the light source, transforming the conventional continuous supplementary light source into a pulse light source, and exploring how to further reduce energy consumption and improve the light supplement efficiency without influencing the light supplement effect of Lettuce. Results: For this purpose, Lettuce ( Lactuca sativa L.) was selected as the experimental material to investigate the effects of varying the duty ratio, frequency and dark duration on the Pn (net photosynthetic rate) of leaves. The results revealed that Pn values under each duty ratio treatment increased with frequency and gradually stabilized to a level similar to that of continuous light. At higher duty ratios, the lettuce leaf Pn under pulse light reached a stable state at a lower frequency, with Pn leveling showing an overall upward trend with the decreasing dark period duration and a large increase in the early stage. For dark period durations lower than a certain value (0.000683594 s), variations in Pn among treatments were minimal, with a gradual increasing trend until no significant differences are observed with continuous light (CK); Under the D 3 (weak light) condition, plants were easy to spindling ( excessive growth)and exhibited narrow and slender leaves. Plants under the D 2 condition (The duration period duration was 0.000465468s) presented the strongest roots and stems, with wide leaves and a compact growth. The following trend in Pn was observed across all duty ratios D 2 >D 1 (0.000046547s)>CK>D 3 ( 0.004654685s ) . Conclusions: The dominant influencing factor of the plant net photosynthetic rate was determined as the ratio of the frequency and duty ratio (i.e., dark period duration). Compared with continuous light, pulsed light is more beneficial to plant growth and utilization. able to the Pn of different pulse Verification tests critical using of and and gradually stabilizes to a level similar to that of continuous light. At higher duty ratios, the lettuce leaf Pn under pulse light reaches a stable state at a lower frequency. This indicates that the determining factor of the net photosynthetic rate may not be frequency and duty ratio, but rather their ratio, namely, the dark period duration. Compared with continuous light, pulsed light is more beneficial to plant growth and utilization. In this study, the response relationship between the pulse light parameters (duty ratio and frequency) and Pn was used to elicit the dark period duration. The experiment was designed and the response model between the dark period duration and Pn of lettuce leaves was constructed based on the test results. Finally, the model was verified. Through the derivation of the model, the fitting equation between the best dark period duration and duty ratio was established, which provided the basis for exploring the best pulse light suitable for lettuce growth. This allows plant factories and facilities to select high efficiency and energy saving artificial light sources.

light [16]. As early as 1905, Brown and Escombe used a rotating disk to reduce the light intensity by 25% without changing the light quality, with no reductions in the photosynthetic rate [17]. Ki-ho Son demonstrated that a 75% duty ratio and low frequency pulsed LED did not results in any significant inhibitory effects on plant growth. This indicates the potential of pulsed LED irradiation technology in saving energy during plant production [18]. Other studies have revealed improvements in the photochemical efficiency of photosystemⅡand the electron transport efficiency of tomato plants under pulsed light [19]. Thus, pulsed light be superior to continuous light in terms of plant growth.
Previous research has demonstrated that an adequately set pulsed light frequency (or duty ratio) that matches the photosynthetic reaction time of plants cannot only reduce light energy consumption and improve the utilization efficiency of light energy, but can also effectively avoid photoinhibition [20][21][22]. Weller and Franck (1941) observed that the Pn saturation values depend upon the number of flashes，i.e., the dark period duration [23]. Yoneda and Mori (2004) used pulsed light to measure the photosynthetic activity and fresh weight of lettuce plants and revealed an improvement in the photosynthetic capacity and fresh weight of lettuce leaves via a frequency flash treatment and an appropriate duty ratio combination (50% and 10 KHz). Furthermore, the authors demonstrated that the employment of more and higher pulsed light frequencies facilitates research on the effects of pulsed light frequency on plant growth [24]. Jao and Fang (2004) proposed that the influence of high frequency (>1000 Hz) LEDs on plant growth should be further studied in subsequent experiments [25]. Thus, observing the effects of pulsed light parameters on Pn can aid in revealing the complex dynamic laws of photosynthesis.
In the current study, an LED system was employed to provide different supplementary light environments for plants through pulse width modulation; and to explore the biological rules between the frequency, duty ratio and dark period duration of pulsed light and the Pn of plants. In addition, a relatively simple response model was built between the pulse light dark period length and the Pn of leaves based on a mathematical method and experimental data. The proposed model is able to predict the Pn of leaves under different pulse lights. Verification tests were designed based on the results. The critical value of the optimal dark duration under any duty ratio was subsequently obtained using the model. The aims of the study were to: i) improve the photosynthetic light supplement efficiency by transforming the conventional continuous supplementary light source into a pulse light source, and ii) explore how to further reduce energy consumption and improve the light supplement efficiency without influencing the light supplement effect of Lettuce. Our work facilitates the selection of a highly efficient and energy saving artificial light source for plant factories and related facilities.

Materials and treatments
Experiments were conducted at the laboratories of the Agrobiology and Environmental Engineering Faculties, College of Horticulture, Northwest A&F University, US from May 2018 to May 2021. The lettuce (Lactuca sativa L.) variety ' Hong Kong glass ' (which was originally sourced from the Qingxian Qingfeng Seed Industry Co. LTD) was selected as the teste subject. Prior to transplanting, the seedling management was consistent. Following the acceleration of the lettuce seed buds, they were sown in a tray with 72 seedling holes and placed in an overhead LED light incubator for routine seedling management. Seedlings of an uneven growth were removed with a single leaf. When four leaves were in one mind (i.e., the fourth true leaf is fully unfolded), strong plants with a uniform growth were selected, and the plants in the nursery hole were transplanted into a 6 cm × 6 cm plastic cultivation tank. The day and night temperature, humidity and photoperiod in the overhead LED light incubator were set to (23±1)℃/ (20±1)℃, 55%-60%, and 14 h/10 h, respectively. The light intensity of the LED lamp board was set to 180 μmol•m -2 • s -1 , with a 20 cm × 30 cm lamp board. The plants were evenly placed under the lamp board.  Five duty ratio levels and 14 frequency levels were initially set to explore the effects of pulsed light forms on the Pn of blades (Table 1). Based on the results, we selected four minimum combinations of the duty ratio and frequency that did not exhibit any significant differences from continuous light (20%+512 Hz; 40% + 512 Hz; 60% + 256 Hz; 80%+128 Hz). The dark period duration (0.001367188 s) was determined via Formula 1 and was set as the experimental parameter. The combination of five dark period durations and four duty ratios was set as the central value and continuous light was used as the control for a total of 21 treatments ( Table 2). The results were then used to select the dark period duration value, which was taken as the experimental parameter of the long-term light treatment of LED plants. With this as the central value, three dark period durations were determined to further explore the effects of different dark period durations on the growth and photosynthetic characteristics of lettuce (Table 3).

Data Analysis
The data analysis and parameter estimations were performed using DPS (Data Processing System) 7.5, while IBM SPSS Statistics 22.0 was used to calculate the mean data values and determine significant differences using analysis of variance. Origin 2017 (origin lab) and Microsoft Excel 2010 (Microsoft Corporation) were employed to create the graphs and tables, respectively.

Analysis of the Pn effect on lettuce leaves
Leaf Pn under different duty ratios and frequencies    and 60% duty ratios, the dark period duration is 0.000683594 s, and no significant differences are observed between the lettuce Pn and that under continuous light. At the 80% duty ratio, the dark period duration is 0.001367188 s. Although there is no significant difference between Pn and that of continuous light, it is significantly lower than that of 0.000341797 s; while when the dark period duration is 0.000683594s, there is no significant difference between Pn and that of 0.000341797 s. Therefore, 0.000683594 s is the optimal dark period duration amongst those tested, indicating that there is no significant difference between plant Pn and the continuous light treatment at this value. At high duty ratios and frequencies, the power consumption of the light source will increase, that is, the shorter the dark period, the more unfavorable the energy saving effect of the pulse light. Therefore, in order to further reduce the energy consumption and accurately calculate the specific value of the optimal dark period duration, we perform further analysis of the test data.

Model construction
Based on the Pn and dark period duration in Fig. 3, we selected the Unary nonlinear equation, with a similar change rule, in order to perform regression statistics on the photosynthetic data of leaves under varying duty ratios (20%, 40%, 60% and 80%) with different nonlinear equations of one variable (i.e., the relationship between dependent variables and independent variables is not linear). A total of 11 models with a high fitting degree were selected (Table 5). Pn is observed to exhibit the same variation trend as the dark period duration across different duty ratios. In order to further verify the prediction performance of the Pn prediction model for unknown data, we selected the four most accurate models in terms of fitting degree. The actual and predicted Pn values were calculated with the Peal-Reed, Polynomial Fitting, Yield Density and Logistic models using the test data set (Fig. 4). The fitting result between the predicted and actual value of the Peal-Reed and Polynomial Fitting models is 1, with intercepts of 0.000003 and 0.00006, respectively. In comparison, the fitting degrees of the Yield Density and Logistic models are much lower. reports the model parameters.   We assume that the parameters of the nonlinear models fitted with one variable under different duty ratios exhibit regular changes resulting from the duty ratio. Under this assumption, when the nonlinear equations of each duty ratio are synthesized into the multivariate nonlinear equation, the parameters can be replaced by the fitting equation of the duty ratio. Taking the model parameters in Table 6 as the dependent variable and the duty ratio as the independent variable, appropriate equations were selected for fitting ( 20%, 40%, 60%, 80% and 100% duty ratios were converted into 0.2, 0.4, 0.6, 0.8 and 1, respectively). Table 7 reports the optimal fitting equation. where Y is Pn; X1 is the duty ratio; and X2 is dark period duration.

Analysis of marginal effect
The marginal photosynthetic rate can be used to determine the optimal parameters of each factor, as well as where Y X 1 / 、 2 / are the marginal functions of Pn to the duty ratio and dark period length, respectively. Fig. 6a and 6b plot Y X 1 / and 2 / , respectively. An ordinate greater (less) than zero indicates that the factors (duty ratio and dark period duration) promote (inhibit) the marginal photosynthetic rate. Fig. 6a reveals the marginal function to be constantly always greater than 0, indicating that the marginal net photosynthetic rate will increase with the duty ratio. Fig. 6b is a parabola with an upward opening, showing that as the dark period length increases, the photosynthetic rate is initially promoted, subsequently inhibited and promoted once again. Marginal function Y / x2 is a quadratic with one variable and its original function has two inflection points. At Y / x2=0, the inflection points are equal to the intersection with the X-axis. We calculated the two inflection points U1 and U2 of the dark period length: the marginal photosynthetic rate was enhanced at the dark period length of 0--U1; when the dark period length was between U1 and U2, the marginal photosynthetic rate was inhibited.
Dark period lengths longer than U2 continued to promote the marginal photosynthetic rate. However, the actual measurements in this experiment reveal that for larger dark period lengths (i.e., low frequencies), the net photosynthetic rate of plants decreased with the gradually increasing dark period length. As the dark period duration increases, the marginal photosynthetic rate should initially be promoted and subsequently inhibited, which is not consistent with the final stage of the marginal effect analysis. However, the research purpose of this experiment is to ensure that the Pn of lettuce leaves is not lower than that of the continuous light treatment by using pulse light treatment without affecting the normal growth of lettuce. Following an excessively long dark period duration, low frequencies reduce the Pn of the plants far lower than that of the continuous light treatment, which obviously fails to meet our purpose. Therefore, we emit the final stage analysis and only consider the first two stages in the subsequent sections, namely, the dark period duration in taken as (0，U2.).
Formula 4 is used to determine U1 and U2 under different duty ratios, while the value of U1 for the optimal dark period duration under different duty ratios is obtained from Table 8. After integration, the equation of the optimal dark period duration and duty ratio is as follows: where X1 is the duty ratio; and X2 is dark period duration. In the actual production process, it is only necessary to input the duty ratio based on Formula 5 to obtain the most optimal dark period duration and thus optimize the LED light supplement parameters. This provides a theoretical basis for the development of the most energy-saving and efficient plant growth light source under a combined frequency and duty ratio.  The marginal function of the model reflects the change rule between Pn, the pulsed light duty ratio and dark period length. This is consistent with the measured value (Fig. 2), indicating that the model is highly accurate.

Fig. 7
Interactive effect of the duty ratio and duration of the dark period on the net photosynthetic rate.

Effects of long-term light tests on lettuce growth
We performed a long-term light treatment to validate the proposed model. Light supplement parameters were designed based on the results of the short-term pulsed light treatment. In particular, the plants were placed under a LED light supplement lamp board for a period of 21 days to explore the variations in plant apparent morphology and photosynthesis under different pulsed light conditions. In the later growth period, the plant stems were not able to support the upright growth of plants in all directions, resulting in plant breakage. Under a short dark period duration, the roots and stems of the plants were stronger, the leaves were wider and thicker, the number of leaves was greater, the growth between true leaves was compact, and the overall growth of the plants was better. Compared with the short dark period treatment, no significant difference were observed in the appearance of plants under the D1, D2 and CK treatments. In particular, plants of the short dark period treatment exhibited thicker roots and rhizomes compared to the D3 treatment, and the plants maintained an upright and compact growth (Fig. 8) .

Effects of pulse light under different dark period durations on lettuce growth
An increase in the dark period duration was observed to enhance the leaf length and plant height. Under low light conditions, the leaves appeared to be thinner. In contrast, the leaf width and dry and fresh weight of plants increased significantly during stages D3 to D2 with a reduction in the dark stage length, and subsequently stabilized after reaching critical point D2. Changes in the leaf width and dry and fresh weight were essentially equal under different duty ratio conditions. At the dark period length of D3, the leaf width and dry and fresh weight were at the lowest level and gradually increased as the dark period duration decreased. The leaf width and dry and fresh weight were maximized at dark period length D2 and were slightly larger than those under D1 and CK. Compared with CK, there was no significant difference among D1, D2 and CK, with the exception of the lowest duty ratio level of D3 (Table 9). Furthermore, the stem diameter differences among treatments indicate plant growth to be most robust under D2.

Effects of pulse light under different dark period durations on the photosynthetic characteristics of lettuce
The Pn of glass lettuce gradually increased as the dark period duration decreased until saturation was reached.
No significant differences were observed between the Pn of D1, D2 and the continuous light treatment (CK), while D3 Pn values were significantly lower. In addition, the parameters of D2 were slightly higher than those of the other treatments. The overall performances of the treatments were observed as D2>D1>CK>D3 across all duty ratios. There were no significant differences in intercellular carbon dioxide concentrations among treatments.
Transpiration rate and stomatal conductance showed no significant difference among D1, D2 and CK treatments except that the D2 treatment was significantly higher than the control when the duty ratio was 20%. Furthermore, the plants of D3 presented the lowest transpiration rate under any duty ratio as well as significant differences with other dark ratio treatments (Table 10) .

Discussion
LED light is closely related to photosynthesis and the light absorption, transformation and dissipation of plants [26][27][28]. In order to maximize the utilization of light and avoid the adverse effects of high/low light on plant growth and development, it is necessary to determine how to improve the optimal pulse light parameters in a controlled environment [29,30]. Pulsed light is generally characterized by three parameters: average optical flux density (PPFD), frequency and duty ratio. The increase of Pn with the duty ratio is generally due to the characteristics of the pulsed light itself, in particular, PAR (photosynthetically active radiation) is proportional to the duty ratio. While the response between frequency and Pn is related to the electron transport and energy conversion process in photosynthesis [31,32].  [37]. In addition, Yustinadiar used the optimal light/dark cycle method to determine that the 45:15 min (light: dark) cycle significantly enhanced Nanocloranopsis thaliana yields [38]. Chen (YEAR) revealed intermittent light to be more suitable for plant growth compared to continuous light, and the lower light/dark cycle L/D) may lead to higher biomass prodctivity [39]. Zarmi (YEAR) also proposed that the photon efficiency of algae photosynthesis can be increased by 3 to 10 times compared with continuous light when pulse light is correctly applied. The author also explained how the photonic efficiency enhancement depends on the optical pulse and the photon flux density of time scales. More specifically, the key is through the correct timing of the algae cell light/dark cycle to avoid photosynthetic pathway jams [40]. absorbed and stored in the reaction center, and that pigments used in the dark ages to transport electrons to the lutein cycle were not affected by the lutein cycle. This indicates that the application of efficiently calculated intermittent light can reduce energy consumption [42]. Song (year) also suggested that the implementation of a short-interval pulsed light strategy may reduce the energy requirements of growing crops in artificially lit environments [43]. With green and red skirt as the research object, Cho showed that LED pulse light can improve LUE and save energy more effectively compared with continuous light [44]. In the actual production process, although the combination of high frequency and duty ratio is more conducive to the utilization of crop light energy, the power consumption of a light supplement lamp will also increase to some extent [45]. Therefore, under the condition of high yielding plants (i.e., the Pn of plants under pulse light condition is not lower than continuous light), the effect of low consumption, high efficiency and energy saving can be achieved only by determining the optimal dark period duration.
Finally, it's a bit of a shame though our results reveal that Pn has a strong regularity for different pulse light environmental conditions, the proposed model is established on the basis of fixed environmental conditions (light intensity, temperature, humidity, gas flow rate) and a single plant. Whether the model adapt to different environmental conditions and response rules between the pulse light duty ratio, dark period and Pn of different plants remains to be verified. Future research will focus on the application of pulsed light in plant research, and the dark period will become a new research area of the effects of pulsed light on plant growth and development. More attention should be focused on different facilities (e.g., light intensity, CO2, temperature, humidity, etc.) to continuously optimize the model. "Low consumption, high efficiency" is also a research hotspot in the field of plant factory production, as well as the application of light environments in agriculture facilities.

Conclusion
In the current study, according to Formula 1, any combination of duty ratio and frequency can obtain the corresponding dark period duration value. The lettuce leaf Pn under each duty ratio increases with the frequency