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. 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. This project is ideal for dynamic modelling as it represents a complex system with tune-able parameters, each parameter set can produce dramatically different population dynamics.

Introduction
For the iGEM project a toxin producing system has been made. We wanted to create a system where bacteria can produce toxin in waves and hereby create different cell populations. With the use of quorum sensing and the subpopulation system, as shown in Figure 1, we expect to find different cell populations.

Methods
During the research Matlab version R2016a has been used.
Because there was no data from the wet lab we assumed that all the parameters in the system were random. The parameters are all obtained by latin hypercube Latin hypercube is a statistical method to get random numbers from a box of n by n numbers. For example x = 4 with x is divisions and n = 2 with n is number of samples. You will obtain a box with 4 square times 2 square, give you 24 random numbers. For each parameter one number out of this box is randomly chosen. samples.

Equations

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

The final BeeT product will be applied using sugar water which is transported into the hive by worker bees. This means that our chassis, Escherichia coli is exposed to high osmotic stress. When we started our project it was unclear whether E. coli is capable of surviving in sugar water for long periods of time. If it is unable to do so we need to choose an alternative application method. Additionally, if it can only survive for a limited period of time we can take this into account in our agent-based honey bee model. To accomplish this we made use of Flux Balance Analysis.

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 make model the base chassis. The chassis The chassis is the base organism that is modified of BeeT is a variant of ​ Escherichia coli, for which it is known that it does not grow in sugar water, mainly due to high osmotic pressure. ² The question remained: Does it survive there, and if so, for how long?

What is Flux Balanace Analysis

Flux balance analysis (FBA) is a mathematical method for simulating metabolism in genome-scale reconstructions of metabolic networks.

Key Results

The relationship between maximum ATP available for survival and water efflux is shown in Figure 1, it demonstrates that there is a linear relation. This 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, ie 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 amount needed in sugar water conditions, but because of these results 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 the point of no return for the cell had been reached. Which has a drastic effect on survival time, changing 20 minutes of maximum survival time to a mere ~90 seconds in the worst case scenario.

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 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, mite dynamics and colony growth (figure 1) and was extensively tested for robustness and realism ¹ .

BeeT can be transported into the hive by applying it to sugar water or bee bread, each with its own advantages and disadvantages. Each mode of application requires the use of a different chassis, with the intended chassis of Escherichia coli for sugar water and Lactobacillus species for bee bread. 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 . Bee bread 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 haemolymph, likely improving survival of colonies to various stressors ^{6 7} .

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 bee hive. 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 mite and honey bee dynamics. BEEHAVE has several modules covering inter-colony dynamics, foraging and a mite model as depicted in figure 1. Two viruses are also included in the model; deformed wing virus and acute paralysis virus for which Varroa destructor is 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 mite mortality, when mites emerge from brood cells, is determined. This in turn affects mite population levels in the hive, reducing virus loads in the hive and allowing colony survival.

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. Cheng, Y. L., Hwang, J., & Liu, L. (2011). The Effect of Sucrose-induced Osmotic Stress on the Intracellular Level of cAMP in Escherichia coli using Lac Operon as an Indicator. Journal of Experimental Microbiology and Immunology (JEMI) Vol, 15, 15-21. ↩

3. Neidhardt F.C. Escherichia coli and Salmonella: Cellular and Molecular Biology. Vol 1. pp. 15, ASM Press 1996 ↩

1. M. A. Becher, V. Grimm, P. Thorbek, J. Horn, P. J. Kennedy, and J. L. Osborne, (2014). BEEHAVE: A systems model of honeybee colony dynamics and foraging to explore multifactorial causes of colony failure, Journal of Applied Ecology., vol. 51, no. 2, 470–482. ↩

3. Fasasi, K A (2011) "Cumulative effect of sugar syrup on colony size of honeybees, Apis mellifera adansonii (Hymenoptera : apidae) in artificial beehives " Journal of Natural Sciences, Engineering and Technology ed. 10: 33-43. ↩

4. Robert Brodschneider, Karl Crailsheim (2010) "Nutrition and health in honey bees" Apidologie ed. 41: 278-294 ↩

5. Ellis, Amanda M. Hayes, Jr, G. W. (2009) "An evaluation of fresh versus fermented diets for honey bees (Apis mellifera)." Journal of Apicultural Research 48: 215-216 ↩

� 6. Basualdo, Marina Barragán, Sergio Antúnez, Karina (2014) "Bee bread increases honeybee haemolymph protein and promote better survival despite of causing higher Nosema ceranae abundance in honeybees" Environmental Microbiology Reports 6: 396-400 ↩

7. De Jong, David (2009) "Pollen substitutes increase honey bee haemolymph protein levels as much as or more than does pollen" Journal of Apicultural Research Reports 48: 34-37 ↩