Team:GZHS-United/Model
Modeling
Modeling
Background:
This year our mosquito-killing device contains two main components: the Cry11Aa protein and the recombinant AaeDNV inserted with BmK IT. Due to time constraints, we have not been able to actually test the toxicity of our device to the larvae, so we used the mathematical model to predict the mosquito killing efficiency of our device.
In fact, the toxicity of these two devices to wigglers has been studied separately. However, the synergistic effect of the two has not been studied. We referenced Jazmin A. López-Diaz’s research to obtain the data about Cry11Aa toxicity in Aedes aegypti larvae [1]. And we got the data about recombinant AaeDNV from Jin-Bao Gu’s research [2].
We first used these data to establish a model about their respective efficiency to find their own optimal concentration. Since no studies have shown that there is an interaction between the two components, we assumed that they work individually. And based on this, we have established an efficiency model of the combination of the two, in order to obtain the most efficient and affordable anti-mosquito plan.
R and Excel were used during our modeling.
Modeling
1.According to the research of the Jazmin, we obtained the data about Cry11Aa toxicity in Aedes aegypti larvae (table 1). By regression analysis, we got a function of protein concentration and hemolysis activity:
y = 11.322 ln (x) - 2.9246 (R^2 = 0.9449) (figure 1).
We found that the anti-mosquito activity increased with the increase of protein concentration, but the increasing rate of anti-mosquito activity decreased. When hemolytic toxicity was close to 80%, the increase in protein concentration was very insignificant. Therefore, we believe that the optimal concentration of protein should be 1000~1500ng when used alone.
Figure 1 Cry11Aa toxicity in Aedes aegypti larvae
2. Similarly, we obtained the killing efficiency data of recombinant AaeDNV on wigglers from the study of Jin-Bao Gu (table 2).Using Excel analysis, we found that the recombinant virus was significantly more toxic to wigglers than the wild-type virus (figure 2).
Figure 2. Wild-type and Recombinant AaeDNV toxicity in larvae.
3. Next, we wanted to get the effect model of the effect of the mixture of protein and virus on the wigglers. We assume that the survival rate of the wiggler obtained in the experiment is the probability of wiggler survival under corresponding conditions, and at present, no studies have shown the interaction between the two components, so we assumed that the anti-mosquito effect of the two is independent. Thus, the following formula can be obtained:
P=P1×P2
P: the wiggler survival rate when the two factors work together; P1: wiggler survival rate only with protein; P2: the mosquito larvae survive only with virus.
First, we used the above formula to calculate the survival rate of wigglers under different concentrations of Cry11Aa and wild-type AaeDNV, and obtained the following matrix (table 3).
Similarly, we can obtain the survival matrix of the wigglers under different concentration of Cry11Aa and recombinant AaeDNV (table 4).
Obviously, the survival rate under the recombinant virus was lower than that under the wild type virus. Therefore, we then only analyzed the case of recombinant virus. When we fixed the recombinant AaeDNV’s concentration respectively to 10^10 and 10^11 copies/ml, we can get those survival curves after adding different concentrations of protein (figure 3).The blue point for virus content for 10^10 copies/ml, and orange dots to 10^11 copies/ml. It can be seen that when the virus concentration is fixed, when the protein concentration exceeds 1000ng/ml, the survival rate of the wiggler will not decrease significantly.
Figure 3. Survival Rate under Fixed C (V) and Changing C (P).
Based on the above model, it is not need to continue to increase the protein concentration when it exceeds 1000ng/ml. So we fixed the protein concentration at 1000 and 1500ng/ml, and analyzed the survival rate of wigglers at different concentrations of recombinant AaeDNV, as shown in figure 4. The blue dots represent the case when the protein concentration is 1000ng/ml, and the orange is 1500ng/ml. It can be seen that the recombinant AaeDNV can effectively reduce the survival rate of the wigglers after the protein sterilization of the wigglers reaches the platform stage.
Figure 4. Survival Rate under Fixed C (P) and Changing C (V).
Therefore, it can be concluded that the survival rate of wigglers is lower when the dosage of cry11aa and recombinant AaeDNV is high.
However, considering the cost of practical application, it is obviously uneconomical and unnecessary to make large amounts of protein and recombinant virus. So we artificially define a threshold that we think is acceptable when the survival rate of the wiggler is less than 15%. Therefore, we tried to obtain the minimum amount of protein and virus to achieve our goal. So we performed regression analysis on the data in table 4, then we got the figure 5.
Figure 5. Survival Rate under Changing C (P) and C (V).
We found that these points can be approximated as being on the same surface, and the analytic expression for the surface is below:
Z=-1.934×10^(-4) X - 7.812×10^(-4) Y + 0.9847 Z=wiggler survival (%); X = protein concentration (ng/ml); Y =log virus concentration (copies/ml).
When the survival rate was 15%, the expression of the relationship between protein concentration and virus concentration was:
-1.934×10^(-4) X - 7.812×10^(-4) Y=0.8347
In our opinion, when the protein concentration and virus concentration satisfy the above relationship, it is the minimum amount that can make the survival rate of wiggler lower than 15%. If we can obtain subsequent data related to the cost of cry11aa and recombinant AaeDNV, we can use that expression to find the lowest-cost collocation.
