Model

Motivation

Our project is dedicated to the development of a dsRNA-based fungicide designed to prevent and control corn sheath blight, a disease predominantly caused by the pathogen Rhizoctonia solani. Having successfully verified the functionality of dsRNA expressed by prokaryotes under controlled laboratory settings, we recognize the need to address several critical factors to facilitate the successful transition of this fungicide from the lab to real-world agricultural applications.

1. Durability of dsRNA Efficacy

One of the primary concerns is the longevity of the dsRNA’s effectiveness in the field. The natural environment presents a multitude of challenges that can impact the stability and activity of dsRNA. Key factors include:

• Ultraviolet (UV) Radiation: Sunlight, particularly UV rays, can cause photochemical degradation of dsRNA, reducing its half-life and overall effectiveness.
• Hydrolysis Reactions: Exposure to moisture can lead to hydrolytic reactions that break down the dsRNA structure.
• Microbial Activity: Various microorganisms in the soil and on plant surfaces can secrete nucleases, enzymes that degrade dsRNA.

To account for these factors, we will develop a mathematical model that predicts the degradation rate of dsRNA under different environmental conditions. This model will help us estimate the residual activity of the dsRNA and inform strategies to enhance its stability.

2. Production Cost of dsRNA

A second critical factor is the cost of producing dsRNA on a commercial scale. Currently, the production costs for dsRNA are higher than those for traditional chemical fungicides, which presents a significant challenge for market competitiveness. To address this issue, we will:

• Optimize the production process to reduce the cost per unit of dsRNA.
• Explore alternative production methods that may offer economies of scale.
• Investigate the potential for government subsidies or grants to support the development of more sustainable agricultural solutions.

Predictive Modeling for Application Timing

To maximize the control effects of dsRNA and minimize costs, we aim to predict its optimal action time in the field. By developing a predictive model, we can determine the most effective timing for dsRNA application. This model will consider:

• The rate of dsRNA degradation under various environmental conditions.
• The life cycle of Rhizoctonia solani and the susceptibility of different corn growth stages to sheath blight.
• The potential for dsRNA to provide residual protection beyond its immediate application.

By calculating the optimal interval for dsRNA application, we can ensure that it is neither applied too early, leading to unnecessary waste, nor too late, risking reduced efficacy. This approach will also help in strategizing multiple applications throughout the growing season to maintain a protective shield against corn sheath blight.

Methodology

We aim to employ the half-life model to predict the degradation dynamics of dsRNA in the natural environment. This model is based on the radioactive decay principle, adapted here to describe the reduction in dsRNA concentration over time. The fundamental assumption is that dsRNA exhibits an average “half-life,” a period after which half of the initial dsRNA quantity is degraded. This concept allows us to estimate the residual activity and effectiveness of dsRNA under various environmental conditions.

The mathematical formulation of the half-life model for dsRNA degradation is as follows:

Let $N_0$ represent the initial concentration of dsRNA, and $N_t$ denote the concentration of dsRNA at any given time 𝑡. The half-life $T_{1/2}$ is the time required for the dsRNA concentration to decrease to half of its initial value. The relationship between $N_t$ and $N_0$ can be described using the exponential decay formula:

$$N_t = N_0 \times (\frac {1} {2})^{\frac {t} {T_{1/2}}}$$

Where:

• $N_0$ is the amount of dsRNA initially sprayed.
• $N_t$ is the amount of dsRNA remaining in the environment after time t.
• $T_{1/2}$ is the “half-life” of dsRNA, i.e. the time required for its amount to be reduced by half.
• $t$ is the time elapsed since the initial application of dsRNA.

This formula assumes that the rate of dsRNA degradation is constant over time, which is a reasonable approximation for many environmental conditions. However, it’s important to note that in practice, the degradation rate may be influenced by various factors such as temperature, humidity, pH, and the presence of nucleases or other degrading agents.

To refine our model, we can integrate these factors into a more comprehensive degradation rate equation, which could be used to adjust the half-life 𝑇1/2T1/2​ based on specific environmental conditions:

$T_{1/2,adjusted}=T_{1/2,base}⋅f(temperature,humidity,pH,…)$

Where 𝑓 is a function that accounts for the influence of environmental factors on the degradation rate of dsRNA.

By applying this half-life model, we can not only predict the longevity of dsRNA in the field but also optimize the application frequency and dosage to ensure sustained efficacy against Rhizoctonia solani, thereby enhancing the overall performance of our dsRNA-based fungicide.

Results

From the research paper, we know that the half-life of 550 bp dsRNA is about 14 days(Fig. 1)(Chen et al., 2019). Under laboratory conditions, the amount of dsRNA we applied was 50 ng/μL. Substituting these parameters into the formula, we can get the relationship between the remaining amount of dsRNA () and time (t):

$$N_t = 50 \times (\frac {1} {2})^{\frac {t} {14}}$$

It is also found from the literature that the minimum concentration of dsRNA for its effectiveness is 20 ng/μL(Qiao et al., 2021). Substituting =20 into the formula, we can get t=18.51, that is, when we spray 50 ng/μL of dsRNA, dsRNA loses its antibacterial effect after about 18.51 days.