To simulate the infection process of nematodes in farmland and to verify the nematicidal effect of TAA diffusing outward from the roots, we used Cellular Automata (CA) to model this process. The following are the specific model design, assumptions, rules, and result.
Assumption
1. Assumption of life cycle: Since the life cycle of nematodes is much longer than the duration of our simulation, natural death, egg-laying, and reproduction of nematodes are not considered during the simulation. This assumption allows the model to focus on the movement and migration behavior of the nematodes.
2. Environmental stability assumption: It is assumed that the external environment remains stable throughout the simulation, and other factors (such as temperature, humidity, soil composition, etc.) that could affect nematode activity are not considered. This simplification facilitates a more focused analysis of the complex ecological variables.
3. Directed movement: It is assumed that nematodes have a tendency to move toward the crop root system.
Rules for cellular automata
Physiological state of nematode and initial condition:
Status update rule:
The egg has a certain probability at each time step to become an adult. The transition probability is the same at each time step.
At each time step, adult nematodes can move toward one of the eight neighboring cells. The specific direction of movement is determined by random selection, but they tend to move closer to the central root system.
When nematodes are located in the peripheral region, they will move towards the center of the root system at a certain speed due to their tendency to root system. When the worm enters the central area, considering that the root density increases, the parasitic probability of nematode increases, we assume that its speed will be reduced to a certain extent.Adults cannot move to cells already occupied by other eggs or adults to avoid crowding.
Figure 1. Flowchart of Nematode Infection Model.
Simulation result
Using the previous rules, we constructed a nematode infection model and simulated it for 3 days. The simulation results are visualized in Figure 2.
Figure 2. Nematode infection simulation.
The image shows that in the absence of TAA, most nematodes migrate to the root zone within three days and establish colonization.
The dose-response curve is a mathematical model used to describe the response of an organism to a certain drug, toxin, or other foreign substances. It reflects the relationship between the dose of a substance and the intensity of the biological response. By using a dose-response curve, we can evaluate the effectiveness, toxicity, or appropriate dosage range of a substance.
In our in-depth study of the lethal effects of TAA on nematodes, we found a significant correlation between TAA concentration and nematode mortality. To more accurately describe this relationship, we chose a two-parameter log-logistic model to fit the data and construct a dose-response curve for TAA.The data on TAA concentration and nematode mortality in Table 1 is from Du in 2017[1]; we have only fitted her data.
Table 1. The relationship between mortality rate and TAA concentration[1]
The two-parameter log-logistic model is a statistical model commonly used in survival analysis and reliability analysis. It efficiently analyzes the impact of treatments or interventions on the survival time of organisms. Here, we use it to quantify the relationship between TAA concentration and nematode lethality.
In the above equation:
Give the result as follows:
The results show that the R² value is 0.988, indicating that our model has a very high degree of fit with the experimental data and a strong correlation. This suggests that our model can accurately quantify the relationship between TAA concentration and nematode lethality.
To dynamically assess the nematode-killing effect of TAA secreted by our engineered bacteria in soil, we combined the TAA diffusion model, nematode infestation model, and the TAA dose-response curve to simulate the actual killing effect of TAA in the field.
We conducted a single-plant simulation within a 2m x 2m x 2m field area, with a simulation duration of three days. The simulation was performed on a cross-section at a soil depth of 10 cm, where is the primary zone where nematodes are active.
By discretizing the farmland space in the same way, we can store the information of TAA concentration and nematode distribution within the discrete grid in two-dimensional matrices of the same dimensions, allowing for their overlay. Additionally, we ensured that the TAA diffusion model and the nematode infestation model are discretized using the same time step size to ensure synchronous updates.
Figure 4. Implementation process of TAA Nematode Killing Simulation.
First, we obtain the TAA concentration matrix at each time step through the TAA diffusion model. Then, using the TAA concentration information stored in the matrix, we convert it into nematode lethality rates via the TAA dose-response curve, thus obtaining the nematode lethality rate matrix.Next, during the simulation of nematode infestation, at each moment, both eggs and adults have a certain probability of death
As a result, the closer to the root center, the higher the TAA concentration, and the higher the probability of nematodes being killed. The final simulation visualization results are as follows:
Figure 5. Nematode killing simulation with TAA.
We can see that although nematodes can survive briefly under low TAA concentrations, there is a good lethal effect around the roots.
[1] Du C, Cao S, Shi X, Nie X, Zheng J, Deng Y, Ruan L, Peng D, Sun M. Genetic and Biochemical Characterization of a Gene Operon for trans-Aconitic Acid, a Novel Nematicide from Bacillus thuringiensis. J Biol Chem. 2017 Feb 24;292(8):3517-3530.