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<p>In order to assess the real world viability of the BeeT we evaluated the proposed system of application by making a model of the entire system. To do this we used Flux Balance Analysis (FBA) to model the chassis. The
 
<p>In order to assess the real world viability of the BeeT we evaluated the proposed system of application by making a model of the entire system. To do this we used Flux Balance Analysis (FBA) to model the chassis. The
  

Revision as of 12:41, 13 October 2016

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Wageningen UR iGEM 2016

 

Overview

In light of our guiding principles specificity, regulation and biocontainment, we modelled four different aspects of BeeT. The modelling work can inform and improve wet-lab experiments, providing a more robust and well rounded final product. Another facet is to assess the optimal application strategy for our project. We asked ourselves; what critical parts of our system can benefit the most from an interplay between modelling and experimental work? These considerations led us to ask the following questions;

  • How can we assure optimal toxin production using quorum sensing and sub populations?
  • What are important parameters for the killswitch to function optimally?
  • Will BeeT be capable of surviving in sugar water?
  • What is the best application strategy for BeeT?

Quorum Sensing

For the final product, BeeT, we intend to use toxins produced by Bacillus thuringiensis, also called BT toxins. However, these toxins are also harmful to our chassis and would result in a reduction of toxin production. To counteract this effect we envision the use of quorum sensing that activates BT toxin production only when there is a large quantity of BeeT present. Ideally, BeeT is able to produce BT toxin over a long period to improve it's effectiveness against mites. However, if an entire population of BeeT is synchronized, we hypothesize that only a single burst of BT toxin will take place before both the BeeT and mites are killed. Thus, this system will not be maximally effective over long time periods. To accomplish this we need multiple sub populations of BeeT, some producing BeeT while others are recuperating.Synchronization of BT toxin production across the entire population would result in BeeT only producing a single burst of BT toxin before dying to its effects. Ideally, BeeT is able to produce BT toxin over a long period and dramatically improving effectiveness. To accomplish this we need multiple sub populations of BeeT, some producing BeeT while others are recuperating. Therefore we use dynamic modeling that represents the complex system. Tuneable parameters are used, each parameter set can produce dramatically different population dynamics.

Introduction

For the iGEM project a toxin producing system has been made. We created a system where bacteria can produce toxin in waves and thereby create different cell populations. This means only when there are enough bacteria present the system will produce a toxin. The subpopulations are created to have bacteria that do not produce toxin. When the toxin-producing bacteria perish, the subpopulation survives. As the survivors are genetically identical to the rest of the population, they are able to initiate a new growth phase and subsequently new toxin production. With the use of quorum sensing we tried to generate this different populations. In figure 1 you can see how this system looks like.

Figure 1: Schematic of the quorum sensing system. The arrows indicate activation of a part and the flat bars indicate inhibition of a part. The quorum sensing system consists of two parts, LuxR constitutively produces a transcriptional factor that binds to AHL, and LuxI produces an AHL autoinducer that diffuses freely through the cell membrane, from cell to cell.


What is quorum sensing?

Quorum sensing is a cell-cell communication system. The detection of chemical molecules allows the bacteria to distinguish between low and high cell densities. In this way the bacteria control gene expression in response to changes in cell number 1 2. This process is achieved through the production and release of an autoinducer , in our case AHL. An autoinducer is a molecule that can diffuse through the cell membrane. The AHL can travel from one cell to the other. There are many different types of autoinducers in quorum sensing systems. . When sensed, the autoinducer can trigger other cells to produce more autoinducers.

According to the team from Davidson College and Missouri Western State University 2011 3.

negative feedback is present when LuxR protein is present and AHL-3OC6 is absent. They discovered that the BBa_K199052 part promotes "backwards transcription". In this research the importance of a negative feedback in the quorum sensing system, to create different cell populations has been investigated. As you can see in figure() different populations can occur when the production rate of luxR and the complex forming are changed. However when we remove the feedback in the system and change the same parameters, we get similar responses of the system. Shown in

Figure 5: subscription


Which shows that the feedback has a minimal influence on the system to create different cell populations. The figures are simulated with the GFP response obtained from the quorum sensing model using the parameter sets that produce the best response. These sets are obtained from a lognormal distribution a lognormal distribution is a statistical method to describe a probability, in this case the probability of a certain parameter set used to generate a high GFP response. with a parameter estimation based on Raue et al 4. With these confidence intervals Equation for confidence interval used the best parameter sets could be chosen. In the presence and absence of negative feedback in the system different populations can occur. This can happen by changing the following parameters; production rate luxR and the production rate of the complex.

However this system worked to generate different cell populations it was not able to reproduce it in the lab. So we thought of another system that could help us making different populations that is able to be produced in the lab. Since the quorum sensing model do not give us a strong result in subpopulations we extended the model with the subpopulation part.

Why include a subpopulation system?

The subpopulation system consist of two genes; the first encodes for the protein that inhibits the systems expression, the other encodes for the corresponding activation protein of the system. The 434 cl-LVA inactivates the λ-cl directly, or prevents the translation of the λ-cl protein. This subpopulation system is based on the system Bokinsky uses 5

Figure 3: Schematic of the subpopulation system. In this system AraC inhibits the promoter activity of the subpopulation part. The AraC is inhibited by Arabinose, when glucose is added to the system Arabinose is inhibited by glucose. AraC inhibits the constitutive promoter of 434-cl-LVA and lambda-cl where 434-cl-LVA inhibits the promotion of lambda-cl. The production of lambda-cl leads to production of RFP as the reporter protein.


We used the model to predict what will happen when we add glucose in different amounts. Certain data sets can be influenced by glucose. With this sets we can predict what is needed to activate the RFP production. Within the heat map you can see in which ratios the initial amounts ofλ and 434 in the system are needed to get high RFP production.

Figure 4. Heat map of λ and 434 against RFP production

When λ is present in big amounts the RFP response will be high. You need a lot more λ than 434 to get high RFP responses. This can be expected when you look at the subpopulation system, the system is inhibited by 434 which represses the RFP production and λ activates the RFP production. In figure 4 you can see that there is little difference between the 434 and λ amounts that are present for the output of RFP. This means that the initial conditions do not have so much influence on the 434 and λ. With this data we can conclude that the translation rates are more important for the RFP response than the initial conditions. Thomas used a ribosome binding site library in the lab. To predict how this library responded in comparison to the RFP response. I implemented the data from Thomas into my model and got the following results:

Lambda 434-cl-LVA RFP responses
1.94 135.6 7.00
1.94 108.8 8.51
1.94 942.5 1.48
1.94 726 1.77
1.94 628.6 1.962
1.94 577.1 2.09
1.94 529 2.23
1.94 40.3 20.1
1.94 384.9 2.87
1.94 268.5 3.87
1.94 257.8 4.01
1.94 256.7 4.02
1.94 73.2 12.1
1.94 100.9 9.09

Combined system


Figure 4: Schematic of the quorum sensing attached to the subpopulation system. The arrows indicate activation of a part and the flat bars indicate inhibition of a part. The quorum sensing system consists of two parts, LuxR constitutively produces a transcriptional factor that binds to AHL, and LuxI produces an AHL autoinducer that diffuses freely through the cell membrane, from cell to cell. LuxR together with AHL forms a complex that inhibits the subpopulation system, where 434-cl-LVA and λ-cl are under the same promoter. This leads to either Toxin 1 production (in this case GFP) or Toxin 2 production (in this case RFP) depending on the quorum sensing.


We hypothesize the following: the more cells are present in the system, the more AHL-LuxR complex is formed. The complex inhibits the subpopulation promoter. When the promoter is inhibited the production of 434 will be suppressed and the production of λ cl will be activated. At a certain time point the λ-cl takes control over the system, because 434 has a higher turnover rate than λ-cl. In this case more λ-cl results in more RFP.


In later stage to get the desired response the quorum sensing system and the subpopulation system were combined. As shown in Figure 4, you can see how we think to generate different cell populations. With this extended part we try to generate a system which predicts the behaviour of the subpopulations. In figure 4 you can see the increasing RFP with increasing cell population.

Figure 6.

Methods
During the research Matlab version R2016a has been used.
Because there was no data from the wet lab we assumed that all parameters exist within a biological seasonable range numbers between 0 and 1. To determine which of these parameters produce the best system response we used Latin Hypercube Latin hypercube is a statistical method to get random numbers from a box of x by n numbers. For example, if x = 4, where x is the number of divisions within the parameter value range, and n = 2, where n is number of parameters, you will obtain a box with 4 square times 2 square, giving you 24 random numbers. Within each division of the parameter space a single random number is chosen. sampling.

Conclusion

Quorum sensing system

Light Kill Switch

To prevent BeeT from escaping into the environment around the hive and spreading we built a light kill switch. This system consists of a light switch that triggers when blue light hits the organisms. This light switch is coupled to a toxin/anti-toxin system, when the light switch is triggered it inhibits the production of the anti-toxin. With the anti-toxin production inhibited, the constitutive production of toxin kills BeeT. This system was also modeled using dynamic modelling, this was to ensure that the system only kills BeeT in the presence of blue light and it survives when no blue light is present.


Metabolic Modeling

Home Model Lab
comic

In order to assess the real world viability of the BeeT we evaluated the proposed system of application by making a model of the entire system. To do this we used Flux Balance Analysis (FBA) to model the chassis. The chassis The chassis-organism is the framework that is modified for use in synthetic biology experiments. of BeeT is a variant of ​ Escherichia coli, for which it is known that it does not grow overnight in high osmotic pressure environments of 1 mol sucrose / liter or above. 1 Supplementing an Apis mellifera (honey bee) colony with sugar water is a well established practice amongst beekeepers. 4 They usually do this with about 1 kg of table sugar for each liter of table sugar (chemically speaking this is pure sucrose). After heating and stirring this ends up as a concentration of 625 grams of sucrose per liter of water. This concentration can also be defined as 1.82 mol sucrose per liter, which is almost twice the threshold value at which the ​ E. coli would no longer grow. However, in this project we only need the ​ E. coli to survive in the sugar water. This duration need only be as long as the worker bees need to pick the BeeT-cells up and bring them to where the Varroa destructor are. The question we try to answer then is: Does our chassis survive in the sugar water at all, and if so, for how long?

Flux Balance Analysis

Flux balance analysis (FBA) is a mathematical method that can be used for predicting reaction fluxes and optimal growth rates of species using genome-scale reconstructions of their metabolic networks. Though in this case we used it to specifically predict the effect of water efflux on the total amount of ATP the cell has available for maintenance. The model used as a base for this analysis was iJO1366 3from the BIGG database.

Resulting relationships

Figure 1: The relationship between the maximum ATP available for survival for an E. coli in a sugar-water environment and the incrementally increased water efflux.

The relationship between maximum ATP available for survival and water efflux is shown in Figure 1. The results from the metabolic model suggest that there is a linear relationship between ATP availability and water efflux, which implies that if no water is available for ATP used for maintenance outside cell growth, the cell will die. When the model is run without any modification, i.e. in an environment where it is in the exponential growth phase, an ATP Maintenance flux of 3.15 mmol*gram Dry Weight^-1*hour^-1 is given as output by the model.

We do not know the exact amount of ATP needed for survival in sugar water conditions, but because of the results from figure 1 we can start looking at the relationship between survival time and water efflux.

Figure 2: The relationship between the maximum ATP available for survival for an E. coli in a sugar-water environment and the theoretical survival time, given a constant water efflux over this time and a starting volume of 2.8e-13 grams. 2

In Figure 2 we can see not only the relationship of survival time against max ATP available for survival, but also how different thresholds of minimal cell-water tolerance would affect this relationship. The minimal cell-water tolerance threshold gives the value at which percentage of the remaining cell-water reaches a point of no return for the cell. This has a drastic effect on survival time, changing 20 minutes of maximum survival time to a mere ~90 seconds in the worst case scenario.

Up to 90 minutes

Figure 1 shows us that osmotic pressure alone can indeed have an effect on cell regulation and cell death and from Figure 2 it appears that the minimal water allowance threshold has a high impact on range of possible times. Our model is limited in that it predicts an infinite survival time beyond 90 minutes. This suggests that our model may be missing some form of regulation that allows for longer survival times. To understand this effect, we shall conduct an experiment to test this prediction. This experiment can be found here.

What we can say is that if the cells can survive for longer outside of this period, then they must have enough ATP available for basic maintenance, and that if cell death occurs then other processes than pure water-efflux must be the cause of that. This could be due to a combination of lacking nutrients and water-efflux, or over production of osmolytes to keep the balance.

Beehave

Due to regulatory and experimental hurdles it is difficult to test the effectiveness of BeeT in combating Varroa destructor in the field. We would still like to be able to give advice to local beekeepers on the ideal application strategy of BeeT based on several scenarios. To accomplish this, the well-known model BEEHAVE was adapted to include the effect of BeeT on Varroa mite and virus dynamics in simulated colonies. BEEHAVE is an open-source, agent-based model which can be used to examine the multifactorial causes of Colony Collapse Disorder 1 2 . It consists of several modules which controls aspects like foraging, Varroa mite dynamics and colony growth (figure 1) and was extensively tested for robustness and realism 1 .

BeeT can be transported into the hive by adding it to sugar water or bee bread. Each of these sources has its own advantages and disadvantages. In this project we have used Escherichia coli as our model chassis and this can be applied to sugar water [link to Ronald]. Sugar water is supplemented to support a colony during honey harvest and before winter as a substitute for nectar 3 4 . Supplementing Apis mellifera (honey bee) with sugar water is a well established and familiar practice amongst beekeepers 3 . However, reconstructing the same system in Lactobacillus species would allow us to use BeeT in bee bread. Bee bread has certain advantages over sugar water as it is more frequently transported to larvae. It is a combination of pollen, regurgitated nectar and glandular secretions and is inoculated with fermenting bacteria by honeybees 5 . There is mounting evidence that pollen supplementation increases protein content in honey bee hemolymph, likely improving survival of colonies to various stressors 6 7 .

BeeT Module

BEEHAVE is an open-source, GNU licensed agent-based model utilizing NetLogo and consists of several interlocking modules which each model different aspects of the beehive. BEEHAVE has the intended goal of modelling the wide variety of stresses affecting honey bees and is the only model incorporating all these different aspects 1 . As such it is the ideal basis for our investigation into the effects of BeeT on Varroa mites and honey bee dynamics. BEEHAVE has several modules covering inter-colony dynamics, foraging and a Varroa mite model as depicted in Figure 1. Two viruses are also included in the model; deformed wing virus (DMV) and acute paralysis virus (APV) for which Varroa mites are a vector. Our BeeT module, which runs parallel to BEEHAVE, is capable of modeling transport of BeeT into the hive using sugar water or bee bread. It also calculates how much BeeT is transported to larvae based on consumption of respectively honey and pollen stores. Based on the amount of BeeT at larvae the Varroa mite mortality, when Varroa mites emerge from brood cells, is determined. This in turn affects Varroa mite population levels in the hive, reducing virus loads in the hive and allowing colony survival.

Figure 1: The honey bee colony model includes Varroa mite and virus dynamics, agent-based foraging behavior with either pre-defined landscape definitions or a representation of local floral patterns. It is also possible to include weather patterns to more accurately model local conditions. Note; model includes various interdependent mortalities and other parameters which are not included in this figure.

Assumptions

Not everything is known about the BeeT model and as such it was necessary to make certain assumptions. Some of these assumptions are related to BeeT in general, while others are specific to the sugar water or bee bread applications. We will first discuss general limitations of our model and then address each of the applications separately.
General assumptions
Several properties of BeeT and its chassis are currently unknown. This includes the degradation rate of BeeT both inside and outside the hive. With both treatments BeeT encounters different environments while being transported to larvae. For honey, BeeT is exposed to sugar water, the sugar stomach of bees, honey stores and brood cells. While bee bread encounters pollen and brood cells in its travels. We do not know the effects of these different environments on degradation rates of BeeT. For this reason we assumed that degradation rates are stable inside and outside the hive.
Another uncertainty is what the effect of BeeT is on Varroa mite mortality, we modelled this by using a saturating function. We also assumed that the effect of BeeT on Varroa mite mortality is entirely determined by the amount of BeeT at the larvae at the time of capping a brood cell.
Finally, the BEEHAVE model is only able to model a single virus, either DMV or APV. Consequently, we are unable to model the combined effects of both viruses on a bee colony. For all analysis, we used the DWV virus, as it is more harmful to honey bee colony survival than APV 8 .
Sugar water
We know that, based on the experimental results [hyperlink] obtained by Ronald, E. coli is able to survive in sugar water for at least 48 hours. His model additionally predicts that if E. coli is capable of surviving 48 hours, it can likely survive long enough to be transported into the hive [hyperlink]. His results do not predict the degradation rate of E. coli in sugar water, honey or in brood cells.
Additionally, we estimate that in sugar water there are approximately 1 * 10^6 cells*ml-1. This estimate is based on the assumption that we add saturated medium (1 * 10 ^ 8 cells*ml-1) containing BeeT to sugar water and diluted this by a factor of 100. The dilution is performed to avoid rejection of sugar water by bees as it would be too contaminated to consume.
We based the hourly uptake rate of sugar water on a paper by Avni et al. 9 , it is possible that this is not the maximal uptake rate of sugar water. In the measured period all of the sugar water was taken up by the colony, making a higher uptake rate possible.
Bee bread
We assume that the amount of cells in bee bread is roughly equal to the number of CFU*ml-1 in yoghurt 10 . Artificial bee breads can be made using yoghurt and these are readily accepted by bees 10 . Additionally, we assume that the removal rate of artificial bee bread is equal to 22.7 g*day-1 4 . Based on Avni et al. we know that the uptake rate depends on the manner in which bee bread is applied 9 . We chose to base the uptake rate of bee bread on Brodschneider et al. since their experimental setup is similar to Avni et al. 4 10

Key results

The functionality of the BeeT module is primarily based on literature research and as such requires a relatively low amount of parametrization. The main unknown quality is how BeeT will behave, namely degradation and its effectiveness at combating Varroa mites at larvae. We are interested in how BeeT can best be applied given certain assumptions [hyperlink previous section]. As such we are interested in the best period to apply BeeT; either before winter or during spring so we can give recommendations to beekeepers. We also examine the difference in effectiveness between BeeT in sugar water and in bee bread for both periods. This can inform future work on whether it is beneficial to adapt BeeT for functionality in bee bread. There are three additional parameters, related to BeeT, that can be varied and upon which effectiveness relies. These are; degradation of BeeT in the hive, outside the hive and the effect of BeeT on Varroa mite mortality and each is varied across a range of values. Additionally, for every combination we have 5 replicates to reduce the variance in our results. We divided the analyses into 4 treatments, each with the same three parameter ranges and 5 replicates per set of parameters. This can be seen in table 1.

Table 1: Structure of BeeT module analysis.
Period Treatment Range
1st April - 15th June Sugar Water Varroa Mite Mortality, Degradation in-hive and Degradation outside-hive
Bee Bread Varroa Mite Mortality, Degradation in-hive and Degradation outside-hive
1st September - 15 November Sugar Water Varroa Mite Mortality, Degradation in-hive and Degradation outside-hive
Bee Bread Varroa Mite Mortality, Degradation in-hive and Degradation outside-hive


Each combination of period and treatment has the same ranges. We compared the winter period (1 September - 15 November) with the spring period (1ste April - 15 June) for the different ranges and treatments. In each case the spring period was significantly more effective in combating Varroa mites than the winter period. For further analysis we continued with the spring period.

Three scenarios were identified; the colony dies due to virus load, the colony survives at a lower population level or the colony thrives. Every year the BEEHAVE model checks the population after overwintering, if it is below 4000 worker bees the colony is presumed dead. To differentiate between the different scenarios we looked at the mean population of worker bees after overwintering. If this number is below 3000 mean overwintering bees we assume that the colony is dead. If the mean population of overwintering bees is between 3000-5000, the colony is capable of surviving. Above 5000 overwintering worker bees, the colony is thriving and the Varroa mite infestation is under control.Each parameter combination, for sugar water and bee bread, falls within one of these three scenarios. For both treatments, we chose a parameter set which is representative for a certain scenario. From this we have 6 representative parameter sets; three for sugar water (death,survival and thriving) and three for bee bread (death,survival and thriving). As can be seen in table 2, bee bread is significantly more effective than sugar water. Some BeeT is consumed by worker bees instead of deposited at the larvae. This is represented by the fraction of total BeeT moved to the hive that is consumed by larvae and also depicted in table 2.

Table 2: Three parameter sets per treatment representing colony death, survival and thriving. If colonies can survive and thrive with higher degradation of BeeT (in-hive and outside the hive) and a lower effect of BeeT on Varroa mite mortality it indicates a more effective treatment.

In the case of sugar water a far lower fraction of BeeT ends up at larvae and most is consumed by worker bees. This is likely the main reason for the difference in effectiveness for sugar water and bee bread.

Each of the 6 parameter sets was further analysed by examining the population dynamics of worker bees and Varroa mites over time. In figure 2 and figure 3 these are shown, respectively, for a colony barely surviving a Varro mite infestation and thriving regardless of the presence of Varroa mites at the start of the simulations. When the colony is barely surviving we can see that worker bee and Varroa mite populations reach a dynamic equilibrium.

Figure 2: Colony barely survives Varroa mite infestation. Shows Varroa mite in red and worker bee population in blue. Starting population for Varroa mites is low.

When the colony is thriving, the starting Varroa mite population rapidly declines and disappears.

Figure 3: Colony thrives regardless of Varroa mite infestation. Shows Varroa mites in red and worker bee population in blue. Starting population for Varroa mites is low.

This indicates that the treatment is effective for a low population of initial Varroa mites, we further analysed a situation with a higher starting population of Varroa mites which is shown in figure 4.

Figure 4: Colony thrives regardless of Varroa mite infestation. Shows Varroa mites in red and worker bee population in blue. Starting population for Varroa mites is moderately high.

Even with a higher starting population and a high initial virus load, we can see that the treatment is successful in reducing Varroa mite populations and that the colony recovers.

Model analysis

The BEEHAVE model utilizes multiple pseudo-random number generators to calculate mortality amongst Varroa mites and bees. These pseudo-random number generators increase the variance inherent in the model and as such it is advisable to use multiple replicates per parameter set. To determine the error bars we ran a simulation where we varied the Varroa mite mortality and plot the mean worker bee population over 10 years with 10 replicates per value of Varroa mite mortality. This was done for the first version of the BEEHAVE model, which governs year round Varroa mite mortality when they emerge from a brood cell.

Figure 5: Mean worker bee population over 10 years plotted against year round Varroa mite mortality at emergence from brood cell.

With 10 replicates the variance is relatively low, particularly when the mean worker bee population is high.
To analyse the full BeeT module we chose to use 5 replicates, this is a compromise between simulation time (137.100 simulations with 5 replicates running for ~ 8 days) and reduction of variance.

We first separated the results of the analyses of the full BeeT module based on the three scenarios. This resulted in figure 6, this is a 3d graph with the axis degradation in the hive, degradation outside the hive and impact of BeeT on Varroa mite mortality. Additionally, the size of each set of parameters indicates the mean overwintering population of worker bees.

Figure 6: 3d graph with degradation in the hive, degradation outside the hive and impact of BeeT on Varroa mite mortality on its axes. Results are color coded with death of colony in red, survival of colony in yellow and thriving colonies in green. If parameter sets can not be clearly placed within these three scenarios they are black and solid.

Discussion and Conclusions

Currently it is unclear how effective BeeT will be at combating Varroa mites, primarily toxicity is difficult to measure in the lab and deploying BeeT in the field has many regulatory issues. As such we build a BeeT module for the well known BEEHAVE model to assess the minimum effectiveness for certain treatments. We also examined two different periods for administering the BeeT; before winter and during spring. Before winter was chosen to reduce the Varroa mite population before winter and support honey bees during their most fragile period in the year (winter). Additionally, it is normal for current beekeeper practices to supplement with sugar water during this period and this period would provide a minimal amount of disturbance for beekeepers. The advantage of administering BeeT during spring is that this is the period at which most of the Varroa mite population is present at larvae. By administering during this period we can ensure that BeeT is able to affect a large percentage of the Varroa mite population. Beekeepers also visit hives regularly during this period as they harvest honey in spring. Recent papers indicate that feeding of artificial bee bread during this period can have significant positive effects on honey bee health 6 7 . For both sugar water and bee bread the ideal period for administering BeeT is during the spring, due to the large difference in effectiveness between the two periods. In a future application of BeeT this can be given as a recommendation to beekeepers. This is a practice which can be easily adopted since beekeepers already visit hives regularly in the spring period. In particular for supplementation of sugar water, as this is already accepted practice amongst beekeepers.

The main difference between sugar water and bee bread is that a larger fraction of total in-hive BeeT is given to larvae for bee bread. This is not surprising as honey stores are primarily used to support energetic needs of worker bees 1 and as such only a small fraction is transported to larvae. On the other hand, the protein contained in bee bread is crucial for the proper development of larvae and as such is mainly given to larvae to support their growth 1 . Based on our results we expect that BeeT will be effective using sugar water but greater effectiveness can be accomplished by engineering BeeT for compatibility with bee bread.

Modeling methods

In version one of the model the following code was added to BEEHAVE:


This calculates the mortality of Varroa mites when they emerge from the brood cell (mortalityMites). In BEEHAVE the mortality of Varroa mites is encapsulated in the fecundity of female Varroa mites, this means that mortalityNoBeeT is zero. When ScalingVariable is large, the mortalityMites approaches one.
The amount of Varroa mites emerging from a cell is calculated with the variable ‘healthyMitesInSingleCell’, using a random-poisson distribution some of the Varroa mites emerging from the brood cell die. Both versions of the BeeT module only affect the Varroa mite population when Varroa mites emerge from a brood cell. This was done to reduce the chance of introducing bugs into the original BEEHAVE model.

In version 2 of the BeeT module, the mortalityMites was changed to:

So that it is dependent on the concentration of BeeT in the cell at the time of capping. Additionally we included a procedure “BeeTProc which is called daily. It handles BeeT moving from outside to inside the hive at a set rate per hour. It also handles degradation, both hourly degradation outside the hive and daily degradation inside the hive. When Varroa mites invade, the amount of BeeT present at larvae is saved for each invading Varroa mite in the variable BeeTLarvaeInvasion. Whenever a Varroa mite emerges from a cell its mortality is calculated based on BeeTcell which is dependant on BeeTLarvaeInvasion. The total amount of BeeT moving to larvae is based on the amount of sugar water and pollen consumed by larvae. If BeeT is consumed by worker bees it is considered lost and is removed from the BeeT in-hive store.

All variables added to BEEHAVE can be found in table 3, including how they are calculated, if applicable what their initial value is, units, in what procedure they are used and any comments or references.

Table 3: All variables used in BeeT module version 2, including functions used to calculate them (or initial value), units, procedure used and any comments or references.

References

    1. Eri Nasuno, Nobutada Kimura, Masaki J. Fujita, Cindy H. Nakatsu, Yoichi Kamagata, and Satoshi Hanada (2012). Phylogenetically Novel LuxI/LuxR-Type Quorum Sensing Systems Isolated Using a Metagenomic Approach Vol, 78, number 22. ↩

    2.Sergi Abadal Ian F. Akyildiz (2011). Automata modeling of Quorum Sensing for nanocommunication networks, Volume 2, Issue 1, Pages 74–83 ↩

    3.Designed by: Kin Lau Group: iGEM09_MoWestern_Davidson (2009-07-22) ↩

    5. Gregory Bokinsky, Edward E. K. Baidoo, Swetha Akella, Helcio Burd, Daniel Weaver, Jorge Alonso-Gutierrez, Héctor García-Martín, Taek Soon Lee, and Jay D. Keasling(2011).HipA-Triggered Growth Arrest and β-Lactam Tolerance in Escherichia coli Are Mediated by RelA-Dependent ppGpp Synthesis 2013 Jul; 195(14): 3173–3182. ↩

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