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Article

The Simulation of Stomatal Aperture Size on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves Based on Cellular Automata

by
Xinlong Shi
1,
Yanbo Song
2,
Xiaojing Shi
3,
Penghui Li
1,
Yun Wang
1,
Liyan Jia
1,3,* and
Zhenyu Liu
1,2,*
1
College of Agricultural Engineering, Shanxi Agricultural University, Jinzhong 030801, China
2
College of Life Sciences, Shanxi Agricultural University, Jinzhong 030801, China
3
College of Food Science and Engineering, Shanxi Agricultural University, Jinzhong 030801, China
*
Authors to whom correspondence should be addressed.
Agriculture 2025, 15(8), 878; https://doi.org/10.3390/agriculture15080878
Submission received: 12 March 2025 / Revised: 2 April 2025 / Accepted: 15 April 2025 / Published: 17 April 2025
(This article belongs to the Section Digital Agriculture)
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Abstract

:
Stomata are essential structures in plants for gas exchange, and their opening and closing are influenced by complex external environmental factors. Using Gynura formosana Kitam as the research object, the regulation of stomatal aperture is crucial for ensuring healthy growth. By simulating and predicting the variation in stomatal aperture, it is possible to determine whether the stomatal response is adapted to environmental conditions. Furthermore, predicting environmental factors such as light intensity and electric fields can help adjust stomatal apertures to enhance Gynura formosana Kitam’s adaptability to different conditions. To explore the impact of external factors like light and electric fields on stomatal aperture, this study employs a cellular automaton model, selecting a 24 h period to observe the stomatal variation law. By incorporating the multi-faceted influences of the external environment on the stomatal apertures of both the upper and lower epidermis of Gynura formosana Kitam leaves, a simulation model of stomatal opening and closing based on metacellular automata is proposed. Based on the physiological characteristics and opening and closing laws of stomata, the rule changes of stomatal opening and closing under different environmental conditions were defined, and the stomatal development area was divided into several two-dimensional and three-dimensional cellular spatial structures. The grid of cells in the structure with stomatal “open” and “closed” states was regarded as an intelligent agent. For different environments under the law of change and simulation of the law of change for simulation research, the simulation results and the actual results match, and the law is consistent. In order to ensure the accuracy of the simulation model, 100 training fits were carried out and the results were statistically analyzed, and the average error was kept within 0.05. This model effectively predicts the variations in stomatal apertures on the upper and lower epidermis of Gynura formosana Kitam leaves, providing a theoretical basis for implementing precise control and improving the economic benefits of Gynura formosana Kitam cultivation.

1. Introduction

The stomata play a critical role in plant growth, particularly in the exchange of gases between the plant and the external environment. Through the regulation of stomatal opening and closing, they effectively control the absorption of carbon dioxide, providing the essential materials for photosynthesis and supporting plant growth and development. In this process, the patterns of stomatal opening and closing directly impact the plant’s adaptability and physiological functions. Gynura formosana Kitam, also known as “white-backed ginseng”, is a perennial herb of chrysanthemum, Panax notoginseng in the composite family [1]. Often referred to as the “best health medicine diet vegetable” [2], it is highly nutritious and delicious, possesses anti-inflammatory [3] and anticancer properties, and is commonly used to treat conditions such as hypertension and fever [4]. With the gradual enhancement of people’s awareness of health care, Gynura formosana Kitam has gained widespread attention from related industries. The stomata on the leaves of Gynura formosana Kitam mainly regulate its gas, moisture, and temperature through the external environment [5,6,7]. Stomata exhibit a high sensitivity to changes in the growth environment, with their size, shape, and density varying according to environmental factors such as temperature, light, and CO2 concentration [8,9,10,11]. Consequently, stomatal parameters are commonly used to assess Gynura formosana Kitam’s response to environmental changes. The size and density of stomatal apertures directly influence the gas exchange between Gynura formosana Kitam and its external environment, thereby affecting its photosynthesis, respiration, and transpiration processes. Under conditions of drought stress or viral infection, Gynura formosana Kitam effectively regulates stomatal openings to minimize water loss and pathogen entry, thereby enhancing its survival and stress tolerance [12,13]. This defense mechanism not only improves Gynura formosana Kitam’s ability to withstand stress during growth, but also contributes to the stability of its growth and reproduction. The stomata on the leaves of Gynura formosana Kitam are randomly distributed. If the prediction model of stomatal opening and closing on leaves can be built to accurately and efficiently predict the opening and closing of stomata under the influence of external environmental conditions, we can predict whether the growth environment of Gynura formosana Kitam is suitable for its healthy growth. Consequently, timely and effective measures could be taken to regulate stomatal openings, providing the most stable and optimal environment for Gynura formosana Kitam. Traditional predictive methods rely heavily on human experience and experimental predictions. These methods are not only cumbersome but also suffer from low accuracy and efficiency in their predictions. In the field of computer science, cellular automata have been widely applied in traffic rule simulations related to vehicles [14], disaster modeling [15], emergency evacuations [16], and crowd movement simulations [17], demonstrating the stability of cellular automata in dynamic simulation processes.
In recent years, some studies have focused on simulating habitat conditions to explore methods for creating plant community habitats. Researchers have constructed various types of habitats, such as dense forests, grasslands, and wetlands, to simulate plant communities in natural states [18]. Another part of the research focuses on exploring how wetland plant landscapes can be created under different water conditions and lighting conditions [19]. Moreover, by simulating the natural environment in the field, the plant community structure in the rural environment is deeply studied, which aims to provide a strong basis for the design of country parks [20]. Existing methods can effectively analyze stomata on leaves and detect the number and opening of stomata, such as those used by Takahashi [21], Peel [22], Sumathi [23] and other researchers who use manual counting to determine the number of stomata on the plant leaf epidermis. Haus et al. studied the upper epidermis of plants using Optical Topometry (OT), a method based on confocal microscopy imaging technology that can generate nanoscale images of the plant leaf surface. However, the imaging system is relatively complex [24,25]. Laga et al. employed a template matching method to detect stomata in the wheat leaf epidermis and used local analysis to measure relevant parameters of the stomatal pores [6]. Other researchers have conducted precise classification and recognition analysis on the size of stomatal apertures [26]. However, simulating the opening and closing variations of stomata remains a challenge. The simulation of stomatal opening and closing is crucial for understanding plant adaptability to environmental changes and photosynthetic efficiency. To address this issue, some studies have focused on cellular automata-based simulations to explore the effects of light and electric field conditions on the stomatal variations in the leaves of Gynura formosana Kitam. Through comparative simulation and analysis of stomata, these studies can help to understand and predict the evolution of stomatal phenomena by using spatial and temporal discretization, flexible hypothesis testing, and handling uncertainties.
This study innovatively proposes a CA model method for the opening and closing of stomata on the upper and lower epidermis of Gynura formosana Kitam leaves. Compared with traditional model methods, this model distinguishes the opening and closing of stomata in the cellular state and defines their variation ranges within a two-dimensional and three-dimensional space. The main purpose of this model is to simulate the changes in stomatal opening and closing on the upper and lower epidermis of Gynura formosana Kitam leaves under the influence of external environmental conditions. The aim is to ensure that stomatal opening and closing on the leaves of Gynura formosana Kitam can adapt to the dynamic changes in the environment when facing complex external environmental conditions, thereby balancing the physiological needs of Gynura formosana Kitam for photosynthesis, transpiration, and water retention. It explores the influence of the environment on stomatal opening and closing in different parts of the leaves and promotes in-depth research on the efficacy of Gynura formosana Kitam.

2. A Framework for Evaluating the Stomatal Opening Size of the Upper and Lower Epidermis of Gynura formosana Kitam Leaves Based on Cellular Automata

2.1. Cellular Automaton Model

The cellular automaton (CA) model is a dynamic system that discretizes time, space, and state. It involves defining cells and finite motion states on a grid, and their states will change over time according to the rules of interaction between them. The cellular automaton model is an abstract definition of a system state [27,28] that enables complex systems to simulate evolutionary processes. The cellular automaton model mainly consists of four parts: cells, domains, rules, and boundary conditions. The model uses multiple cells to simulate complex ecological environments. In the simulation process, adjacent cells in the system are connected using relative rules. Based on the corresponding change rules formulated in the model, the change rules will be updated, which simplifies the process. The simulation effect can also be well expressed, with good robustness and reliability [29].
In this study, metacellular automata were used to simulate the dynamic change process of leaf stomata. In the simulation model, the state variable of each metacell represents the stomatal opening and closing state, which is updated in discretized iterations with a time step of 5 min. During each iteration, each metacell interacts with the domain metacells based on the preset local rules, and at the same time integrates the effects of light and electric field environmental factors to realize the dynamic update of its own state through the state function. The model accurately simulates the temporal characteristics of stomatal opening and closing changes by controlling the number of iterations, thus realizing the simulation of the regulation mechanism of stomatal movement by external environmental factors.
The operation rule of the cellular automata model: The state of a cell at time (t + 1) is jointly determined by the state of the cell at time (t) and the states of adjacent cells. The formula is:
S t + 1 = f ( R t , N t )
In Equation (1), S t + 1 is the cellular state at time (t + 1); R t is the cellular state at time t; N t is the case of cell proximity at time t; f( ) is a conversion rule function.

2.2. Basic Composition of Stomatal Opening Size on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves Based on Cellular Automata

2.2.1. The Expression Form of Stomatal Opening and Closing in Gynura formosana Kitam Leaves

The variation in turgor pressure of the guard cells is the direct cause of stomatal opening and closing in Gynura formosana Kitam leaves. This process is represented by the parameters G, Q, N, and f, as detailed below:
G = { c ( x c , y c , z c ) | c ∈ R 3 , 0 ≤ x c ≤ M , 0 ≤ y c ≤ N , 0 ≤ z c ≤ B }
In Equation (2), R 3 represents the three-dimensional space, G represents the cellular space of the stomatal opening and closing size of the Gynura formosana Kitam leaves in the cellular automaton, and M, N, and B are the length, width, and height numbers of the space R 3 ; x c , y c , z c are selected as natural numbers;
Q is the change rule of the cell (stomatal opening and closing size) at time t, which is a variable in a specific time period;
N is the domain of the central cell c ( x c , y c , z c ) , and the law of stomatal opening and closing on its leaves is defined as molar type;
f represents the rule of variation of Q t → Q t + 1 ; Q is the total size of leaf stomatal opening and closing in the simulation space, according to the total amount of stomatal opening and closing of metacells at the moment t and the total amount of stomatal opening and closing between metacells at the moment t + 1 by the presence or absence of light to determine the total amount of metacells’ “stomatal openings and closings” at the moment t + 1.

2.2.2. The Size of Stomatal Openings on the Upper and Lower Epidermis of the Leaves of the Gynura formosana Kitam, and the Cellular Automata and Their Cellular Space

The stomatal aperture of Gynura formosana Kitam leaves, which regulates gas exchange and transpiration under the influence of external environmental conditions, requires a clear definition of cellular space and neighborhood scope before model operation. The size of the cells in the model must accurately reflect the stomatal aperture and its response to environmental factors. Additionally, the cellular size influences both the spatial range of the neighborhood and the overall system stability. The cell size must effectively capture the environmental impact on stomatal aperture size while ensuring the accuracy of the stomatal data and maintaining computational efficiency during model operation.
The stomatal aperture size on Gynura formosana Kitam leaves is classified based on the structure of the epidermis. The size of the stomatal opening is redistributed by the influence of light and electric field stimulation on the number of stomatal openings. The opening and closing of stomata play a crucial role in the physiological processes of Gynura formosana Kitam, particularly in response to environmental stress. In conditions such as drought or pathogen attacks, Gynura formosana Kitam effectively regulates stomatal aperture size to minimize water loss and prevent pathogen entry, thus ensuring its healthy growth.
The CA model is defined in a two-dimensional Euclidean space, with each cell shaped as a regular square grid. As shown in Figure 1, during the simulation process, the actual position of the modeled cellular space is achieved by adding neighboring cells, ensuring that adjacent cells can undergo regular transitions. This setup also facilitates the validation of the model. To prevent the stomata within the simulated leaf from remaining in an open or closed state for an extended period, and to ensure that the actual stomatal opening and closing changes are accurately reflected, the evolution of the stomata is updated according to a set rule at each simulation time step.

3. Materials and Methods

3.1. Materials

Data Source

In order to achieve the double guarantee of data quality and representativeness, this study selected Gynura formosana Kitam as the test object for the experiment, whose leaf blade is elliptic, 8–15 cm long, and covered with short tomentum on both sides. It has undulating small cusp teeth on the edge and the tip of the leaf blade is slightly obtuse. Select data from the mature stage of about 3–4 months were collected, with a specific time span from 7 July 2023 to 10 August 2023. During the data collection process, experiments were conducted at three time periods throughout the day—morning, afternoon, and evening—to ensure that the simulation of changes in the stomatal opening of Gynura formosana Kitam leaves was more representative. In order to accurately simulate the influence of leaf stomatal opening under light conditions, as shown in Figure 2, data were collected from the leaf epidermis of Gynura formosana Kitam at three locations: the leaf base, leaf center, and leaf tip. Stomatal images were collected vertically at a 90° angle downwards using an upright fluorescence microscope (DM6B, Leica, Weizla, Germany).

3.2. Methods

3.2.1. Intelligent Adaptive Environmental Model Construction of Stomatal Opening Size on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves

The size of the stomatal opening on the upper and lower epidermis of Gynura formosana Kitam leaves is a key growth characteristic for intelligent adaptation to the environment, involving a complex physiological regulatory system. In this system, the control of stomatal opening mainly relies on the guard cells of the leaf epidermis. In order to predict the changes in stomatal opening of the upper and lower epidermis of Gynura formosana Kitam leaves under different external environmental conditions, we set each individual agent to a different stomatal opening state. The metameric space consists of several independent metameric cells, in which external environmental factors such as light and electric field are introduced and the corresponding change rules are set, so as to intuitively simulate the change rule of stomatal opening and predict the intelligent law of stomatal opening evolution with time. During the experiment, external environmental factors had an important influence on the change rules of stomata. Under light conditions, the stomatal opening gradually increased as a result of increasing temperature to promote photosynthesis. On the contrary, the stomatal opening decreased until it was closed. In contrast, under electric field stimulation, stomatal opening was promoted earlier and the opening time was prolonged.
Considering the high density of stomata in the leaves and the random distribution used in the model, in order to reduce the impact of errors, we set the number of stomata on the upper and lower epidermis of the leaves of Gynura formosana Kitam to 500 and 300, respectively. On the basis of the set change rules, the evolution of stomatal openings follows the domain evolution as shown in Figure 3.

3.2.2. Changes in Domain Rules

According to the principles of cellular automata, the domain in the simulation process influences the update of the cellular state at time t + 1, thereby affecting a set of other cells. The update rule for the cells is determined by the conditions of the agents and the integration of behaviors, which leads to regular changes. During these regular changes, the selection and shape of the domain range directly affect the complexity and behavior patterns of the cellular automaton. A well-suited domain range can accurately simulate system behavior, enhancing the model’s interpretability and generalizability.

3.2.3. Model Pre-Configuration

During the pre-configuration of the model, all stomatal aperture conditions are distributed within each individual cell. The stomatal aperture on the Gynura formosana Kitam leaves changes in response to external environmental influences, and the changes in stomatal aperture follow specific updating rules. Under the growth conditions with or without light or electric field stimulation, the size of the stomatal aperture can occupy a cell space. The remaining cell space will generate new intelligent cell spaces following a specific rule.

3.2.4. Formulation of Rule Changes

Based on the actual variation in stomatal aperture, the rule changes in the model are defined probabilistically. Therefore, probability parameters, such as the probability of color variations, are used to simulate the stomatal aperture size in Gynura formosana Kitam leaf tissue. The system’s states during the simulation process are presented in Table 1. The specific rules governing the evolution of the cellular state based on stomatal aperture changes are as follows: when the sum of the number of stomata is 0, the metacell is empty; when the sum of the number of stomata is non-zero, the size of the stomatal openings generates the corresponding intelligences with random probability.

4. Case Simulation and Comparative Analysis

4.1. Selection of Stomatal Regions on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves

Considering the variation in stomatal density across different regions of the Gynura formosana Kitam leaf, specific areas on the upper and lower epidermis of the leaf were selected for the simulation process. As shown in Figure 4, the variation in stomatal aperture sizes can be clearly observed on the leaf surface. To ensure the representativeness and consistency of the stomatal characteristics, fully mature leaves were chosen as experimental samples. The stomatal opening and closing behaviors are influenced differently under various light and electric field conditions. Therefore, multiple regions on the lower epidermis of the leaf were selected for further analysis.

4.2. Comparative Analysis of Stomatal Aperture Changes on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves

The experiment was conducted to simulate the development trend of stomatal opening in the upper and lower epidermis of the leaves of Gynura formosana Kitam. The purpose was to study the development trend of stomatal opening under the influence of external environmental stimuli. Regular photographs were taken and collected through a microscope. During the experiment, it was found that the stomata were initially closed under dark conditions. Under the influence of light stimulation, stomata initially begin to open and gradually reach their maximum opening. After a period of exposure to light, the stomata begin to further close, and ultimately, in a sustained dark environment, all stomata completely closed. In the presence of an electric field, stomata opened earlier than under light conditions and their opening lasted longer. The partial development process is shown in Figure 5.

4.3. Simulation and Analysis

The simulation experiment was completed on the basis of the Python language, and the number of cell iterations was set to once every five minutes. The core configuration is shown in Table 2. The structure of the cellular automaton program was compiled to simulate the change in stomatal opening of the upper and lower epidermis of the leaf under the influence of light and electric field conditions.
Through further research on the growth of Gynura formosana Kitam, the opening and closing patterns and spatial configuration of leaf stomata, which play a key role in its growth, were determined with and without the influence of light and electric field conditions, in order to ensure the healthy growth of Gynura formosana Kitam. By comparing 2D and 3D simulations, the trend of stomatal opening and closing on the upper and lower epidermis of Gynura formosana Kitam leaves was analyzed, thereby providing guarantees for achieving the expected growth status of Gynura formosana Kitam. The cellular automaton model reproduces the complex pattern on the entire leaf by simulating the size of the local leaf epidermis. By modifying the initial state of the defined cellular stomata, it can simulate the effects of changes in spatial patterns of different plant types in the presence or absence of light and electric field conditions. That is, the density and size of different types of cellular stomata affect the opening and closing of cellular stomata, leading to the invasion of factors such as high temperature and high concentration pollution during the growth process of Gynura formosana Kitam.

4.3.1. Two-Dimensional Simulation of Stomatal Opening Changes in the Upper and Lower Epidermis of Gynura formosana Kitam Leaves

During the experimental process, a 2D simulation was conducted to model the variation in stomatal apertures on the upper and lower epidermis of Gynura formosana Kitam leaves. The simulation was divided into three distinct time periods: early, mid, and late stages, with iterations performed every five minutes. The aim was to strictly adhere to the actual stomatal dynamics, ensuring that the simulation accurately reflects the real-time changes and dynamic characteristics of stomatal behavior. This approach guarantees a high level of consistency between the simulation results and real-world observations across different time scales.
Under different light conditions, as shown in Figure 6 and Figure 7, the growth of Gynura formosana Kitam exhibits a distinct diurnal rhythm, with stomatal opening and closing patterns closely linked to variations in light intensity. Initially, during the night, the stomata are completely closed. As the light intensity and temperature gradually increase in the morning, the stomata begin to open. With further increases in light intensity and temperature, the stomata reach a fully open state. At midday, when the temperature peaks, partial stomatal closure occurs, resulting in a noticeable reduction in apertures. In the afternoon, both light intensity and temperature begin to decline, leading to a partial reopening of the stomata. By evening, as light intensity continues to decrease, the stomata gradually close again. Finally, as night sets in, the stomata are fully closed once more.
The stimulation of an electric field significantly influences the stomatal opening and closing behavior on the upper and lower epidermis of Gynura formosana Kitam leaves. During the simulation process, when compared with the effects of light conditions, a noticeable change in the stomatal dynamics was observed. As shown in Figure 8 and Figure 9, in the initial phase, Gynura formosana Kitam is still in the nighttime, and its stomata remain fully closed. As the stomata gradually begin to open, their timing precedes the effects of light exposure. Under the combined stimulation of light and temperature, the stomata become fully open. At midday, some stomata begin to close, accompanied by a reduction in stomatal aperture. In the afternoon, some stomata visibly reopen. Finally, during the night, most of the stomata close again.

4.3.2. Three-Dimensional Simulation of Changes in Stomatal Opening on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves

Building upon the 2D simulation, this study further conducted a 3D simulation analysis of the stomatal aperture changes on the upper and lower epidermis of Gynura formosana Kitam leaves to validate the accuracy of the observed stomatal dynamics. A comparison was made between the stomatal aperture changes in 2D and 3D models, revealing consistent trends in both cases. However, the 3D results exhibited more pronounced changes compared to the 2D simulation. The results are presented in Figure 10 and Figure 11.

4.4. Simulation Analysis of Changes in Stomatal Opening on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves

In order to observe the detailed changes in realistic stomatal openings from the simulation results, the changes in stomatal openings in the 2D and 3D simulation models under the influence of different external factors were further analyzed. Combined with the experimental data in Table 3 and Table 4, the results show that the stomatal changes under the effect of an electric field are earlier than those in the light condition. Therefore, electric field stimulation can promote the opening of leaf stomata, and the opening time is also prolonged. To verify the accuracy of the model, this study conducted 100 training fits with an average error of 0.05. By comparing the changes in stomatal opening of Gynura formosana Kitam leaves in 2D and 3D simulations, it can be clearly observed that the simulation results are highly consistent with the actual development trend, as shown in Figure 12.
Therefore, when the Gynura formosana Kitam is in a low-light or dark environment, the defense cell photosynthesis stops, the cell is prone to water loss, and the stomata close to prevent water loss. Under light conditions, light causes chloroplasts inside guard cells to undergo photosynthesis, using carbon dioxide to increase the pH value inside the cells, triggering a series of physiological reactions that cause guard cells to absorb water, expand, and open stomata. The stimulation of an electric field can significantly affect the opening and closing behavior of stomata on the leaves of Gynura formosana Kitam. Appropriate electric field stimulation can promote the opening of stomata and enhance the carbon dioxide absorption capacity of Gynura formosana Kitam, thereby improving the efficiency of photosynthesis and promoting the growth and yield of Gynura formosana Kitam.

5. Discussion

Stomata are critical for plant photosynthesis and transpiration, especially in the process of plant adaptation to environmental changes. Therefore, the study of stomatal opening changes in response to the environment is the key to exploring the dynamic changes in energy and water on the vegetation surface and to understand the stomatal behavior.
In the process of the stomatal opening change in Gynura formosana Kitam leaves, this study used a metacellular automata model to simulate the dynamic change in opening and closing of stomata in the upper and lower epidermis of Gynura formosana Kitam leaves. Compared with the Ball-Berry model [13], which is a traditional kinetic model based on differential equations, the CA model is able to simulate the spatial heterogeneity of the stomatal openings in the external environmental conditions and has high computational efficiency, which makes it suitable for long-time-scale simulation. In this study, the effects of external factors (e.g., light and electric field stimulation) on stomatal behavior were thoroughly investigated, and the simulation time was set at 24 h. The simulation results show that the role of external environmental factors in regulating stomatal opening and closing has obvious spatial and temporal specificity, and the interaction of different external stimuli shows diverse responses to stomatal opening and closing.
Firstly, light, as one of the key regulatory factors for stomatal opening and closing in Gynura formosana Kitam leaves, had a significant effect on the dynamic changes in leaf stomata. In the morning, as light intensity gradually increases, the stomata begin to open, facilitating photosynthesis and the absorption of carbon dioxide. At midday, when light intensity reaches its peak, the stomatal apertures remain maximally open to absorb more carbon dioxide to support the demands of photosynthesis. In the evening, as light intensity decreases, the stomata gradually close, eventually fully closing at night to reduce water evaporation and prevent moisture loss during the night. Overall, the diurnal variation in light significantly regulates stomatal behavior, exhibiting clear circadian rhythms and adaptive responses. Although the model is valid under current environmental influences, there are still shortcomings in its spatial heterogeneity. Metacellular automata usually assume that each cell is spatially homogeneous, whereas in reality, the distribution of stomata may be affected by leaf surface texture, microclimate, and other factors, and metacellular automata usually fail to capture these subtle spatial differences.
Electric field stimulation, as an external regulatory factor, also plays a role in modulating stomatal opening and closing. The simulation results of this study indicate that under an appropriate electric field strength, the stomata remain open for an extended period, enhancing carbon dioxide absorption and increasing the rate of water evaporation. However, with prolonged electric field exposure, the stomata gradually tend to close. This regular change is consistent with the adaptive mechanism of Gynura formosana Kitam to environmental stress, reflecting the complex response of Gynura formosana Kitam under multiple stress conditions. However, metacellular automata models tend to rely on simple rules and grid structures, which potentially makes the models too simplified to fully reflect complex biological processes when dealing with real biological systems.
To date, significant breakthroughs have been made in simulating stomatal conductance using artificial neural network models [30]. Ye Zipiao [31] and others proposed a more mechanistic stomatal model. However, research combining changes in stomatal opening and closing with CA models is still very scarce. Therefore, in this study, a metacellular automata-based simulation method of stomatal openings in the upper and lower epidermis of Gynura formosana Kitam leaves was proposed to provide new theoretical references for its further development.
In conclusion, the cellular automaton model used in this study provides valuable insights into the stomatal opening and closing mechanisms of Gynura formosana Kitam leaves, particularly under the influence of external environmental factors such as light and electric fields. The opening and closing process of stomata exhibit highly dynamic variations and complex interactions in response to these factors. The model results emphasize the complexity of stomatal regulation, highlighting that the opening and closing processes are influenced by multiple intertwined factors. This underscores the need to consider the combined effects of various environmental factors in practical applications. Future research can further explore more detailed stomatal regulation mechanisms, especially the responses of stomata under extreme environmental conditions, and provide a theoretical basis for the growth regulation of Gynura formosana Kitam.

6. Conclusions

Stomata are important channels for the exchange of matter and energy between Gynura formosana Kitam and its environment. This study combines intelligent agents and cellular automata to simulate the changes in stomatal opening on the upper and lower epidermis of Gynura formosana Kitam. Through experimental data and theoretical analysis, this study further explored the role of light and electric fields in stomatal regulation, and demonstrated a certain synergistic effect.
(1) The distribution of stomata in Gynura formosana Kitam leaves is random, and the probability of changes in stomatal intelligent agents in Gynura formosana Kitam leaves is different. The model reflects the authenticity of the stomatal changes in Gynura formosana Kitam leaves and sets the development rules of stomatal intelligent agents in Gynura formosana Kitam leaves that change over time. The influence of light and electric fields on the stomatal changes of Gynura formosana Kitam leaves is crucial and cannot be ignored in the simulation process. The influence rules of light and electric fields on the stomatal development of Gynura formosana Kitam leaves should be further incorporated.
(2) The simulation of stomatal changes in Gynura formosana Kitam leaves was conducted, and an intelligent agent model was established to intelligently simulate the stomatal changes and behavior patterns of adjacent cells in Gynura formosana Kitam leaves. The simulation results were in good agreement with the actual results, with no change in trend and an error rate of less than 5%. This indicates that the constructed intelligent agent model accurately reflects the trend of stomatal changes in Gynura formosana Kitam leaves, verifying the rationality of the simulation model. This provides a theoretical basis for predicting the changes in stomata of Gynura formosana Kitam leaves under external influences and the selection of an environment suitable for the growth of Gynura formosana Kitam to ensure its healthy growth.
The variation trend of stomata on Gynura formosana Kitam leaves was analyzed, and a predictive model for stomatal changes was developed based on the agent-based model. This model can accurately forecast future stomatal variations on Gynura formosana Kitam leaves, although some issues and limitations remain that require further investigation.
Due to the constraints of the experimental conditions, the long-term effects of light, electric fields, and their combined influence on stomatal behavior were not fully revealed. Further research should incorporate additional environmental factors and time dimensions to explore in greater depth the mechanisms by which light and electric fields regulate stomatal behavior. This would provide a more robust foundation for Gynura formosana Kitam physiological studies and environmental management strategies for its growth.

Author Contributions

X.S. (Xinlong Shi): Conceptualization, Methodology, Software, Formal analysis Investigation Writing—original draft, Visualization; Y.S.: Validation, Investigation, Data curation; X.S. (Xiaojing Shi): Formal analysis, Project administration; P.L.: Data curation, Visualization, Supervision; Y.W.: Visualization, Project administration; L.J.: Investigation, Resources, Supervision; Z.L.: Methodology, Resources, Writing—review and editing, Supervision. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Research Project Supported by ShanxiScholarship Council of China [grant number: 2023-092]. Shanxi Agricultural University’s “Introduction of Talents Research Initiation Project”, grant number: 2021BQ113.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

The data used in this study were self-collected and the dataset is being further improved. Thus, the dataset is unavailable at present.

Acknowledgments

The authors thank the editor and anonymous reviewers for providing helpful suggestions for improving the quality of this manuscript.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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Figure 1. Schematic diagram of cellular unit.
Figure 1. Schematic diagram of cellular unit.
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Figure 2. Data acquisition.
Figure 2. Data acquisition.
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Figure 3. Evolutionary rules.
Figure 3. Evolutionary rules.
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Figure 4. Selection of stomatal region.
Figure 4. Selection of stomatal region.
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Figure 5. Changes in stomatal opening of Gynura formosana Kitam leaves.
Figure 5. Changes in stomatal opening of Gynura formosana Kitam leaves.
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Figure 6. Simulation of changes in stomatal opening of the lower epidermis of Gynura formosana Kitam leaves under illumination conditions.
Figure 6. Simulation of changes in stomatal opening of the lower epidermis of Gynura formosana Kitam leaves under illumination conditions.
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Figure 7. Simulation of changes in stomatal openings in the upper epidermis of Gynura formosana Kitam leaves under light conditions.
Figure 7. Simulation of changes in stomatal openings in the upper epidermis of Gynura formosana Kitam leaves under light conditions.
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Figure 8. Simulation of changes in stomatal opening on the upper epidermis of Gynura formosana Kitam leaves under electric field conditions.
Figure 8. Simulation of changes in stomatal opening on the upper epidermis of Gynura formosana Kitam leaves under electric field conditions.
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Figure 9. Simulation of stomatal opening changes in the lower epidermis of Gynura formosana Kitam leaves under electric field conditions.
Figure 9. Simulation of stomatal opening changes in the lower epidermis of Gynura formosana Kitam leaves under electric field conditions.
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Figure 10. Simulation of changes in stomatal opening on the upper and lower epidermis of Gynura formosana Kitam leaves under illumination conditions.
Figure 10. Simulation of changes in stomatal opening on the upper and lower epidermis of Gynura formosana Kitam leaves under illumination conditions.
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Figure 11. Simulation of stomatal opening changes in the upper and lower epidermis of Gynura formosana Kitam leaves under electric field conditions.
Figure 11. Simulation of stomatal opening changes in the upper and lower epidermis of Gynura formosana Kitam leaves under electric field conditions.
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Figure 12. Comparison of real and simulated trends in stomatal openings: (a) light conditions; (b) light conditions + electric field conditions.
Figure 12. Comparison of real and simulated trends in stomatal openings: (a) light conditions; (b) light conditions + electric field conditions.
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Table 1. Running rules for stomatal opening variation.
Table 1. Running rules for stomatal opening variation.
Intelligent Agent IntegrationStomatal Sum
Total number of stomatasum
stomatal closuresum1
Stomatal opening (small)Sum2
Stomatal opening (middle)Sum3
Stomatal opening (large)Sum4
(1) Total number of stomata: sum as the total number of stomata during the change in stomatal opening law. (2) Stomatal closure: sum1 is the total number of stomatal closures. (3) Stomatal opening: sum2, sum3, and sum4 represent the total number of stomatal opening degrees.
Table 2. Experiment configuration.
Table 2. Experiment configuration.
SoftwareHardware
Python 3.11.4CPU: I7-14650HX
Matplotlib 3.7.1GPU: RTX4060
Numpy 1.24.3Operating system: Windows 11
Table 3. Numerical simulation of stomatal development on the upper and lower epidermis of Gynura formosana Kitam leaves (under light).
Table 3. Numerical simulation of stomatal development on the upper and lower epidermis of Gynura formosana Kitam leaves (under light).
SimulateTime PeriodNumber of Iterations (Every 5 min)Simulated Stomatal Opening Rate (%)True Stomatal Opening Rate (%)Error Rate (%)Number of Training SessionsSimulated Stomatal Opening Rate (%)True Stomatal Opening Rate (%)Error Rate (%)
2D20:00–6:001200.000.000.001000.050.000.05
6:00–10:001680.350.320.030.280.320.04
10:00–12:001920.880.900.020.870.900.03
12:00–14:002160.850.890.040.880.890.01
14:00–18:002640.750.720.030.760.720.04
18:00–20:002880.180.200.020.160.200.04
3D20:00–6:001200.000.000.000.020.000.02
6:00–10:001680.280.320.040.290.320.03
10:00–12:001920.880.900.020.850.900.05
12:00–14:002160.860.890.030.860.890.03
14:00–18:002640.700.720.020.680.720.04
18:00–20:002880.220.200.020.150.200.05
Table 4. Numerical simulation of stomatal development on the upper and lower epidermis of Gynura formosana Kitam leaves (light + electric field).
Table 4. Numerical simulation of stomatal development on the upper and lower epidermis of Gynura formosana Kitam leaves (light + electric field).
SimulateTime PeriodNumber of Iterations (Every 5 min)Simulated Stomatal Opening Rate (%)True Stomatal Opening Rate (%)Error Rate (%)Number of Training SessionsSimulated Stomatal Opening Rate (%)True Stomatal Opening Rate (%)Error Rate (%)
2D20:00–5:001080.000.000.001000.020.000.02
5:00–9:301620.370.350.020.300.350.05
9:30–12:301980.780.800.020.810.800.01
12:30–15:002280.850.890.040.840.890.05
15:00–18:002640.700.720.020.750.720.03
18:00–20:002880.180.200.020.220.200.02
3D20:00–5:001080.000.000.000.020.000.02
5:00–9:301620.390.350.030.370.350.02
9:30–12:301980.810.800.010.840.800.04
12:30–15:002280.860.890.030.840.890.05
15:00–18:002640.740.720.020.690.720.03
18:00–20:002880.250.200.050.220.200.02
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MDPI and ACS Style

Shi, X.; Song, Y.; Shi, X.; Li, P.; Wang, Y.; Jia, L.; Liu, Z. The Simulation of Stomatal Aperture Size on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves Based on Cellular Automata. Agriculture 2025, 15, 878. https://doi.org/10.3390/agriculture15080878

AMA Style

Shi X, Song Y, Shi X, Li P, Wang Y, Jia L, Liu Z. The Simulation of Stomatal Aperture Size on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves Based on Cellular Automata. Agriculture. 2025; 15(8):878. https://doi.org/10.3390/agriculture15080878

Chicago/Turabian Style

Shi, Xinlong, Yanbo Song, Xiaojing Shi, Penghui Li, Yun Wang, Liyan Jia, and Zhenyu Liu. 2025. "The Simulation of Stomatal Aperture Size on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves Based on Cellular Automata" Agriculture 15, no. 8: 878. https://doi.org/10.3390/agriculture15080878

APA Style

Shi, X., Song, Y., Shi, X., Li, P., Wang, Y., Jia, L., & Liu, Z. (2025). The Simulation of Stomatal Aperture Size on the Upper and Lower Epidermis of Gynura formosana Kitam Leaves Based on Cellular Automata. Agriculture, 15(8), 878. https://doi.org/10.3390/agriculture15080878

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