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

Equations for the different systems
Quorum sensing system
ODEs
The ordinary differential equations are constructed the same way as non-linear ODEs in Michaelis Menten kinetics.
LuxI
d[mRNALuxI]dt= α1+k1[LuxR-AHL]1+[LuxR-AHL]-β1[mRNALuxI] (1)
d[LuxI]dt=α2[mRNALuxI]-β2[LuxI] (2)
Where α1 is the production constant of LuxI production and k1 is the production constant of regulation by LuxR-AHL, β1 the degradation mRNA of LuxI and β2 the degradation of LuxI protein.
LuxR
d[LuxR]dt=k2-β4[LuxR]-α3[LuxR][AHL]+β3[LuxR-AHL] (3)
Where k2 is the production constant of LuxR and β4 is the degradation of LuxR. α3 is production constant of regulation by LuxR and AHL and β3 the degradation of the complex LuxR-AHL.
LuxR-AHL complex
d[LuxR-AHL]dt=α3[LuxR][AHL]-β3[LuxR-AHL] (4)
Where α3 is the production constant of regulation by LuxR and AHL, β3 is the degradation of complex LuxR-AHL.
The change in concentration AHL
d[AHL]dt= α4-α3[LuxR][AHL]+β3[LuxR-AHL]-kso[AHL]+ks1[LuxI]-η[AHL]+k3 (5)
Where k3 is the constant external concentration AHL AHL is affected by degradation the AHL synthesis rate of a single cell η=ơA/Vc is the diffusion rate of AHL over the membrane with ơ is the membrane permeability and A is the surface area and Vc is the cell volume. Kso is a degradation parameter and ks1 a production parameter.
GFP
d[GFP]dt=α5[LuxR-AHL]k6+[LuxR-AHL]-β5[GFP] (6)
Where α5 is the production rate of GFP and β5 the degradation of GFP k6 is a production parameter. External AHL concentrations for multiple cells
AHL external
d[AHLExternal]dt=-k4*-[GFP][AHLExternal]+k5*y[AHL]-y[AHLExternal] (7)
With k4 and k5 are production parameters. In the summation y stands for the conditions of the different parameters in all cells.
Subpopulation system
RFP
d[RFP]dt=α10[λ cl]k9+[λ cl]*k10k10+[434 cl-LVA]-β[RFP] (8)
with α10[λ cl]k9+[λ cl] the activation of lambda cl on the RFP. k10k10+[434 cl-LVA] the inhibition of 434 cl-LVA on RFP and β the degradation of RFP
λ cl
d[λ cl]dt=12*kk11k11+[LuxR-AHL]-β[λ cl]
with 12*k11k11+[LuxR-AHL] is the inhibition of the luxR-AHL complex on the subpopulation system β is the degradation of lambda cl.
434 cl-LVA
d[434 cl-LVA]dt= 12*k11k11+[LuxR-AHL]-β[434 cl-LVA] (9)
with α12*k11k11[LuxR-AHL] the inhibition of LuxR-AHL complex on 434 cl-LVA β is the degradation of 434.

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 control gene expression in response to changes in cell number ¹. This process is achieved through the production and release of an autoinducer An autoinducer is a molecule that can diffuse through the cell membrane. In this way they can travel from one cell to the other. There are many different types of autoinducers in quorum sensing systems. . This autoinducer has the ability to trigger other cells in producing more autoinducers, when sensed. Quorum sensing controls the bacterial functions or processes that are unproductive by an individual bacterium and becomes active when multiple bacteria are present. ². In this way the bacteria communicate.

Why subpopulation system

The subpopulation system consist out of two genes; one of two genes encodes for the protein that inhibits the systems expression and the other encodes for the corresponding activation protein of the system. The 434 cl-LVA inactivates the lambda-cl directly or prevent the translation of the lambda-cl protein. This subpopulation system is based on the system G. Bokinsky uses ⁵

How could quorum sensing develop spatial inhomogeneities in the subpopulation system?
When quorum sensing ensures that the toxin is only produced when the density of bacteria is high enough to produce significant amounts of toxin, this ‘standardizes’ the amount of toxin produced by the bacteria. The subpopulation system will be coupled to the quorum sensing system. Together, quorum sensing and forming of non-producing subpopulations by the created system, allow bacteria to produce ‘waves’ of toxin.

The hypothesis of the combined system is 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 lambda cl will be activated. At a certain time point the lambda-cl takes control over the system, because 434 has a higher turnover rate than lambda-cl. In this case more lambda-cl results in more RFP.

Results

Quorum sensing
According to the The team from Davidson College and Missouri Western State University ³. negative feedback is present when LuxR protein is present and AHL-3OC6 is absent. They discovered that this part promotes "backwards transcription". BBa_K199052. In this research there have been looked at the importance of a negative feedback in the quorum sensing system to create different cell populations. 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 () Which shows that the feedback does not have an influence on the system to create different cell populations. The figures are simulated with the GFP response of quorum sensing model best parameter sets. These sets are obtained from a lognormal distribution lognormal distributions 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. With and without 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.

Subpopulation
Thomas got no results from the subpopulation system in the lab by adding glucose to the system. So 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 lambda and 434 are needed to get high RFP production.

When lambda is present in big amounts the RFP response will be high. You need a lot more lambda 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 lambda activates the RFP production. In the Heat Map 1 you can see that there is little difference between the 434 and lambda 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 lambda. With this data we can conclude that the translation rates are more important for the RFP response than the initial conditions.

Combined system

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

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?

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.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. ↩

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. ↩

2. J. Horn, M. A. Becher, P. J. Kennedy, J. L. Osborne, and V. Grimm (2015), “Multiple stressors: Using the honeybee model BEEHAVE to explore how spatial and temporal forage stress affects colony resilience,” Oikos, no. September 2015, 1001–1016. ↩

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 ↩