Team:Wageningen UR/Model
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.
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 
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
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.
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
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.
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
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?
A model of E. coli survival
In order to make this model a technique called Flux Balance Analysis (FBA) was used to describe the relationship between the metabolism of the E. coli and the osmotic pressure of the sugar water. 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.
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.
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
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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
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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
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Supplementing Apis mellifera (honey bee) with sugar water is a well established and familiar practice amongst beekeepers
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. 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
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There is mounting evidence that pollen supplementation increases protein content in honey bee hemolymph, likely improving survival of colonies to various stressors
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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.
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
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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.
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, 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
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Artificial bee breads can be made using yoghurt and these are readily accepted by bees
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. Additionally, we assume that the removal rate of artificial bee bread is equal to 22.7 g*day-1
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Based on Avni et al. we know that the uptake rate depends on the manner in which bee bread is applied
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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
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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.
| 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 |
