Our model has two branches – prediction model and statistical model. The aim of both is to help further characterize our system.
We wish our Bio-pesticide project could be brought to the market one day. And when compared to the traditional pesticides, cost is an important competitive factor. So we want to know the real cost of our project under the established experiment design. If it is too much expensive, we would consider to optimize the plan for a lower cost.
DsRNA application dosage model and the cost prediction model are used to answer this question. RNAi efficiency model is to figure out which length of dsRNA is the ideal inhibitor to suppress target gene and the better way to sustain dsRNA under the normal circumstance.
These three models correlate with each other, and finally guided us to optimize our project design in crucial steps.
Our project application depends on a vital factor: the stability and life period of dsRNA in natural surroundings where contains many adverse elements.
Through papers we knew that dsRNA can sustain for more than 2 weeks in soil (Jeffrey G. Scott, et al, 2013), but which is still too short to guarantee enough RNAi efficiency for weeding. We need set up a model of the vital factors that will influence dsRNA stability in order to take steps for prolonging dsRNA lifetime.
Meanwhile, the relationship between dsRNA length and the suppression efficiency is important for our experiments to design optimal dsRNA producing vectors.
We collected a lot of RNAi experiments data from reviews and research articles. Also, Thanks to labs dedicate to RNAi in the school of life science in Lanzhou University, providing us useful data to finish our prediction.
Methodology
1. Set up a model of the vital factors that will influence dsRNA stability.
\[ k=\frac{[n^{dsRNA}]}{[n^e]}+k^{UV}+k^h \]
\[ n^{dsRNA}=M/N_A \]
Where
\( k = \) dsRNA decomposition rate
\( n^{dsRNA} = \) dsRNA concentration(number)
\( n^e = \) dsRNA concentration decreased by the degradation of enzyme
\( N_A = \) Avogadro constant
\( M = \) dsRNA relative molecular weight
\( k^{UV} = \) destruction from light, especially UV
2. Analyze the relationship between the dsRNA length and RNAi efficiency through statistics
3. Fortunately, we found a special material bio-clay, which could storage dsRNA as shelters (more details in project design). We did control experiments to see the protective capacity of bio-clay and according to the experiments data got the conclusion.
Results
1. For a wider application scope, we synthesized RNAi data from different kinds of plants for determining a range of dsRNA length which is suitable for as much as possible species. Because weeds are much more complicated than model organisms like Arabidopsis thaliana and Triticum aestivum. As result shown, 21bp dsRNA is the minimum length to cause gene silence among most species.
Figure 1. dsRNA length affect RNAi efficiency in difference species
2. Based on the formula, a relatively stable curve shows that dsRNA stability change with their length.
Figure 2. dsRNA stability change with their length
At this curve, we took a second derivative to the curve :
\[ f(x)' = 0.0110x^{-0.5} \]
We found that max curvature of f(x)' is appear at 600bp around.
3. DsRNA storage situation in different medium
We dissolved dsRNA in bio-clay solution(particle diameter is 172nm) or in double-distilled water to make dsRNA final concentration 20ng/uL, and we put tubes under the normal condition in different intervals.
Finally we did an agarose gel electrophoresis respectively at the beginning (0 d), 5 days (5 d), 10 days (10 d), 17 days (17 d) and 21 days (21 d) to compare the dsRNA degradation.
Here is the figure put together.
Figure 3. degradation of dsRNA stored in bioclay or dd water
4. Through analysis of gray, the match curve shows the dsRNA degradation trend differs when storage in bio-clay and dd water.
Figure 4: The compreson of dsRNA degradation when storage in bio-clay and dd water.
Results shows that bio-clay(particle diameter is 172nm) can effectively slow down the speed of dsRNA degradation.
Discussion
RNAi differs widely in different plants species, as expectation, the R2 of figure one is too low to give a credible and precise data analysis, but there still a trend could be referred. We found that in almost species when dsRNA length is shorter than 600 base pairs, it can efficiently silence target gene and finally we designed disturbed dsRNA length around 600bp in our experiments.
About bio-clay, the gel picture shows which could slow down the degradation of dsRNA. It gave us a direction in downstream application design.
Reference
[1] Wang L, Zhou J, Yao J, et al. U6 promoter-driven siRNA injection has nonspecific effects in zebrafish[J]. Biochemical and biophysical research communications, 2010, 391(3): 1363-1368.
[2] Huvenne H, Smagghe G. Mechanisms of dsRNA uptake in insects and potential of RNAi for pest control: a review[J]. Journal of insect physiology, 2010, 56(3): 227-235.
[3] Kasai M, Kanazawa A. Induction of RNA-directed DNA methylation and heritable transcriptional gene silencing as a tool to engineer novel traits in plants[J]. Plant Biotechnology, 2013, 30(3): 233-241.
Motivation
We wish our Bio-pesticide project could be brought to the market one day. And for this vision, we need know the actual dosage of dsRNA should be applied in the real crop fileds.
Different fields vary in acreage and weeds amount etc. Based on these variates, we predicted minimum application dosage of dsRNA in areas of China.
Methodology
We used this formula to describe the dsRNA dosage in different areas.
\[ W_{dsRNA} = S_{field}\frac{V_{plant}}{V_{field}} \times P \times \vartheta \]
Where
\( W_{dsRNA} = \) total mass of dsRNA should be used
\( S_{field} = \) area of land
\( V_{plant} = \) water consumption of per plant
\( P = \) the amount of weeds in unit area
\( \vartheta = \) the minimum dosage of dsRNA to kill weed
Thanks to our human practice work, we got many useful data, like the plant water consumption and the total number of weeds per mu (0.0667 hectares)
By the assumption that 133pg/L dsRNA can effectively suppress the expression of target gene confidence interval [2].
Figure 1. Relative water consumption among different crops and different irrigation method.
Meanwhile, water absorption of each plant can be represented by this formula:
\[ V_{plant} = ET_c + C_w \]
Where
\( ET_c = \) Crop transpiration rate
\( C_w = \) Plant water consumption
What known is plant water consumption \( C_w \) is much less than RCE, so we simplify the formula to:
\[ V_{plant} = ET_c \]
Based on the Penman computing method and the data from China Meteorological Observatory (CMO), we use equation set to compute the \( ET_c \) in China.
Plant transpiration, ETc, can be determined by transpiration of reference plant, ET0 and transpiration coefficient, Kc. The method of calculating ETc is following:
\[ ET_c = ET_0 \times K_c \]
We use Penman-Monteith formula to calculate transpiration of reference plant.
\[ ET_0 = \frac{0.408\Delta (R_n-G)+\gamma \frac{37}{T_{day}}u_2(e_s-e_a)}{\Delta + \gamma(1+0.34u_2)} \]
Where
\( ET_0 = \) Transpiration of reference plant in one day
\( R_n = \) Average net radiation in one day
\( G = \) Soil heat flux
\( T_{day} = \) Average temperature in one day
\( u_2 = \) Average wind speed at the height of meters
\( E_s = \) Saturated vapor pressure
\( e_a = \) Actual vapor pressure
\( \Delta = \) Slope of saturation vapour pressure curve at air temperature
\( \gamma = \) Psychrometric constant
In formula, \( T \) and \( u_2 \) can be determined by mesure, \( (e_s-e_a), \gamma, \Delta, G \) can be calculated by parameter. \( G \) , in general, is considered to be 0.5 times \( R_n \) in the evening, 0.1 times \( R_n \) in the day.
\( \gamma \) is related to atmospheric pressure. We can get it by following equation:
\[ \gamma = 0.665 \times 10^{-3} \times 101.3(\frac{293-0.0065z}{293})^{5.26} \]
where \( z \) is Altitude.
Saturated vapor pressure, \( e_s \), can be get by the following equatiin:
\[ e_s = e^0(T_{day})=0.6108exp[\frac{17.27T_{day}}{T_{day}+237.3}] \]
Actual vapor pressure, \( e_a \), can be get by the following equation:
\[ e_a=e^0(T_{day})\frac{RH_{mean}}{100} \]
Where \( H_{mean} \) is average air humidity in one day
Slope of saturation vapour pressure curve at air temperature, \( \Delta \), can be get bu the following equation:
\[ \Delta=\frac{4098[0.6108exp(\frac{17.27T_{day}}{T_{day}+237.3})]}{(T_{day}+237.3)^2} \]
Average net radiation in one day, Rn, is the difference between the incoming net shortwave radiation (\(R_{ns}\)) and the outgoing net longwave radiation (\(R_{nl}\)):
\[ R_n=R_{ns}-R_{nl} \]
Net shortwave radiation, \(R_{ns}\) and net longwave radiation, \(R_{nl}\), can be calculated by the following equation:
\[ R_{ns}=(1-\alpha)R_s \]
\[ R_{nl}=\sigma[\frac{T_{day}^4}{2}](0.34-0.14\sqrt{e_a})(1.35\frac{R_s}{(0.75+2\times 10^{-5})R_a} - 0.35) \]
\[ R_a=\frac{12(60)}{\pi}G_{sc}d_r[(\omega_2-\omega_1)sin(\varphi)sin(\delta)+cos(\varphi)cons(\delta)(sin(\omega_2)-sin(\omega_1))] \]
Where
\(R_a = \) Extraterrestrial radiation
\( G_{sc} = \) Solar constant
\( d_r = \) Inverse relative distance Earth-Sun
\( d = \) Solar declination [rad]
\( j = \) Latitude [rad]
\( \omega_1 = \) Solar time angle at beginning of period [rad]
\( \omega_2 = \) Solar time angle at end of period [rad]
Results
Through modelling, we got the application amount of dsRNA in different areas of China.
Figure 2. dsRNA application dosage in China
Discussion
It could be seen the minimum application dosage of dsRNA in major grain producing areas of China (Northern China Plain, Northeastern China Plain and Yangtze Plain, Middle and Lower) are about 10.16-15.77mg/mu. This model gave us a direction to optimize our dsRNA production experiment. For almost farmers in China, figure 2 can lead them find the special dsRNA dosage of their own field very easily. Then from figure 1 they can easily find relative water consumption of what king of crop they want to plant to confirm dsRNA dosage finally.
Reference
[1] S Tabor, CC Richardson. T7 DNA polymerase 1990
[2] Joga et al. - 2016 - RNAi Efficiency , Systemic Properties , and Novel Delivery Methods for Pest Insect Control What We Know So Far
[3] H huang et al -1957-2012- The reference crop evapotranspiration quantity of space analysis
Motivation
When compared to the traditional pesticides, cost is an important competitive factor if we want to bring our product to the market. For this reason, we want to combined experiment data and the model
Methodology
According to our daily experiments and experience, here are some assumptions:
1) The LB medium is enough and suitable for E.coli to produce dsRNA.
2) The growth curve of E.coli basically conforms to logistic curve.
3) The efficiency of transcription of T7 promoter conforms to the book [1] about per second can .
4) when OD600=0.5, the density of E.coli is 5*107
Based on assumptions above, we use the formula:
Cell density:
\[ \mathrm{d}N = kN(1-\frac{N}{N_m})\,\mathrm{d}t \]
\[ k_i = k_{cell} - k_{T7} \]
dsRNA:
\[ \mathrm{d}c=N(500~700)eM/N_A \]
Where
\( k = \) E.coli escalating rate
\( k_i = \) E.coli escalating rate after induce
\( k_{cell} = \) equilibrium constant of promoter in cell
\( k_{T7} = \) equilibrium constant of T7 promoter
\( N_M = \) maximum density of E.coli
\( N = \) instant density of E.coli
\( \mathrm{d}c = \) the mass of dsRNA produced by E.coli in total
\( e = \) T7 promoter transcription efficiency
\( N_A = \) Avogadro's constant
\( M = \) dsRNA mass
Results
1. We optimized the culture medium by changing the proportion of yeast extract, for controlling cost, we chose 2.0% concentration of yeast extract as the maximum.
We start inducing when OD up to 0.5 (Which is proper time to induce expression of dsRNA), then, the population will increase slowly and at this time the dsRNA production is nearly proportional to the cell density. So it could be deduced that dsRNA increases with inducing time.
Taken together, when yeast extract concentration is 2%, the cost and dsRNA output is the most optimistic scenario.
2. After settling the idealest culture medium, we induced dsRNA expression with iPTG ( make final concentration at 0.5Mmol/L), and we got a range of dsRNA output (between the red line).
Figure3. dsRNA production range
Based on this figure and Gaussian distribution, we got the most possible dsRNA concentration: 0.00204g/L.
Discussion
LB medium price is about $90/Kg in China and producing 1g dsRNA by our project need $439. Related to the result of application dosage model (10.16-15.77mg dsRNA/mu), the real cost of our project is at the range of $23-36/mu, which is slightly higher than the traditional pesticides like glyphosate used by farmers. When it applied in invasive species management, which is more cheaper than any other methods. And we would still working on optimizing our project for lower cost in future work.
Reference
[1] S Tabor,CC Richardson . T7 DNA polymerase 1990
