Line 152: | Line 152: | ||
<h1 id="QS_subpop"> Why include a subpopulation system?</h1> | <h1 id="QS_subpop"> Why include a subpopulation system?</h1> | ||
<p>Since the quorum sensing mechanism could not provide the subpopulations we desired using genetically identical cells, we created a system that could act downstream of quorum signalling | <p>Since the quorum sensing mechanism could not provide the subpopulations we desired using genetically identical cells, we created a system that could act downstream of quorum signalling | ||
− | to provide the response we needed. Population-wide Cry toxin overexpression | + | to provide the response we needed. Population-wide Cry toxin overexpression is likely to kill all E. coli cells in the first moment of toxin expression. Since this would only affect one of the subpopulations, the second subpopulation would be able to initiate a new growth phase after death of the toxin-producing cells. The critical requirement for this is that cells respond at different |
− | + | ||
times to the quorum stimuli despite being genetically identical. A small part of the population that acts differently from the rest of the population is called a subpopulation. The subpopulation system | times to the quorum stimuli despite being genetically identical. A small part of the population that acts differently from the rest of the population is called a subpopulation. 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-cI-LVA inactivates the λ-cI | 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-cI-LVA inactivates the λ-cI | ||
Line 169: | Line 168: | ||
</figure><br/> | </figure><br/> | ||
− | <p>As you can see in Figure 6 | + | <p>As you can see in Figure 6; glucose has a suppressing function on the system, arabinose has an activating function on the system. |
We used the model to predict what will happen when we add glucose in different amounts. The assumptions we made for the subpopulation | We used the model to predict what will happen when we add glucose in different amounts. The assumptions we made for the subpopulation | ||
− | system are the following | + | system are the following: 434-cI-LVA degrades faster than λ-cI, cell division happens when the cell size has doubled, and two cell populations |
exist with one growing differently than another. We tested a number of parameter sets and picked the parameter set that gave the biggest RFP | exist with one growing differently than another. We tested a number of parameter sets and picked the parameter set that gave the biggest RFP | ||
− | response based on the strength of glucose. To see how the model behaved when we changed the ratios of the initial amounts of λ-cI and 434-cI-LVA | + | response based on the strength of glucose. To see how the model behaved when we changed the ratios of the initial amounts of λ-cI and 434-cI-LVA, we investigated the effect of starting conditions on the outcome of the system. The initial conditions were varied between 1 and 10. Within the heatmap you can see in which ratios the initial amounts of λ-cI and 434-cI-LVA in the system are needed to get high RFP production (here glucose and arabinose have a fixed concentration). </p> |
− | + | ||
− | + | ||
<figure> | <figure> | ||
<img src="https://static.igem.org/mediawiki/2016/3/3e/T--Wageningen_UR--heatmap2.jpg"/> | <img src="https://static.igem.org/mediawiki/2016/3/3e/T--Wageningen_UR--heatmap2.jpg"/> | ||
− | <figcaption>Figure 7. Heat map of λ-cI and 434-cI-LVA against RFP production. The right side bar indicates the amount of RFP, | + | <figcaption>Figure 7. Heat map of λ-cI and 434-cI-LVA against RFP production. The right side bar indicates the amount of RFP, where red indicate a high amount and black a low amount. |
− | This | + | This heatmap shows you the amount of RFP produced given the balance between the two genes initial conditions.</figcaption> |
</figure><br/> | </figure><br/> | ||
− | <p> | + | <p> As seen in Figure 7, when λ-cI and 434-cI-LVA are present in similar amounts we have a subpopulation system. But if they are present in different amounts there will be no subpopulations. |
This can be expected when you look at the subpopulation system. The system is inhibited by 434-cI-LVA, which represses the RFP production, and λ-cI activates the RFP production. | This can be expected when you look at the subpopulation system. The system is inhibited by 434-cI-LVA, which represses the RFP production, and λ-cI activates the RFP production. | ||
− | In | + | In Figure 7 you can see the balance between the 434-cI-LVA and λ-cI amounts that are present for the output of RFP. To understand how changing the Ribosomal Binding Site (RBS) impacts RFP responses, we simulated the system for different combinations of transcription rates. From these simulations we found: </p> |
− | + | <figcaption>Table 1: RBS library of the 434-cI-LVA gene with different predicted translation rates.</figurecaption> | |
− | + | ||
− | + | ||
<table> | <table> | ||
<tr> | <tr> | ||
− | <th> | + | <th> λ-cI </th> |
− | <th>434- | + | <th>434-cI-LVA </th> |
<th> RFP responses</th> | <th> RFP responses</th> | ||
</tr> | </tr> | ||
Line 278: | Line 273: | ||
</table> | </table> | ||
− | <p>To confirm that our model represents | + | <p>To confirm that our model represents biological behaviour we analysed the RBS library. |
− | We can conclude | + | We can conclude from these results that the RFP concentration quanlitatively corresponds to the Figure 7. Because as you can see in the table 1. the highest RFP responses are when the λ-cI and 434-cI-LVA are present in the same amount. The lowest responses of RFP when there is a is a big difference between λ-cI and 434-cI-LVA. This is also shown in the heatmap we got form the model. </p> |
<h1 id="QS_combined"> Combined system</h1> | <h1 id="QS_combined"> Combined system</h1> | ||
<figure> | <figure> | ||
<img src="https://static.igem.org/mediawiki/2016/6/62/T--Wageningen_UR--combinedsytem.jpg"/> | <img src="https://static.igem.org/mediawiki/2016/6/62/T--Wageningen_UR--combinedsytem.jpg"/> | ||
− | <figcaption>Figure 8: Schematic of the quorum sensing attached to the subpopulation | + | <figcaption>Figure 8: Schematic of the quorum sensing system attached to the subpopulation network. 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 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 | + | the cell membrane, from cell to cell. LuxR forms a complex with AHL that inhibits the subpopulation system, where 434-cl-LVA and λ-cl are under the same promoter. This leads to either GFP production, |
− | or RFP production depending on the quorum sensing.</figcaption> | + | or RFP production depending on the same strength of quorum sensing.</figcaption> |
</figure><br/> | </figure><br/> | ||
− | <p> Based on the modeling we | + | <p> Based on the modeling we hypothesised the following: when there are more cells present in the system, more AHL-LuxR complex is formed. The complex inhibits the subpopulation promoter. |
− | When the promoter is inhibited production of 434 will be suppressed and production of λ cl will be activated. At a certain time point λ-cl takes control over the system, because 434 has a higher turnover rate than λ-cl. | + | When the promoter is inhibited production of 434-cI-LVA will be suppressed and production of λ-cl will be activated. At a certain time point λ-cl takes control over the system, because 434-cI-LVA has a higher turnover rate than λ-cl. |
In this case more λ-cl results in more RFP. </p><br/> | In this case more λ-cl results in more RFP. </p><br/> | ||
+ | <p>In a later stage, to get the desired response, the quorum sensing system and the subpopulation system were combined. As shown in Figure 8, you can see how we intend to generate different cell populations. | ||
+ | With this extended network we try to generate a model which predicts the behaviour of the subpopulations. In Figure 9 you can see the increasing RFP over time after many cell divisions, indicating an increasing cell population.</p> | ||
+ | |||
+ | <figure> | ||
+ | <img src="https://static.igem.org/mediawiki/2016/7/74/T--Wageningen_UR--oscillations_combined_system4.png"/> | ||
+ | <figcaption>Figure 9. Volume oscillations correspond to the dividing cells. Together they form a growing cell population. On the left y-axis you see the RFP, and on the right y-axis you see the volume. The x-axis is the time.</figcaption> | ||
+ | </figure><br/> | ||
+ | |||
+ | |||
+ | <h1>Methods</h1> <br/> | ||
+ | <p>During the research Matlab version R2016a has been used. <br/> | ||
+ | Because there was no data from the wet lab we assumed that all parameters exist within a biologically reasonable range between 0 and 1. For the analyses we used 100,000 parameter sets, 10 cells, random initial conditions between 0 and 1 and 60 timesteps. Tuneable parameters are used, each parameter set can produce dramatically different population dynamics. To determine which of these parameters produce the best system response we used <a class="tooltip"> Latin Hypercube<span class="tooltiptext" style="width:700px;"> 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. </span> </a> sampling. | ||
+ | </p> | ||
+ | |||
+ | <p>With the Latin Hypercube sampling we made parameter sets that are obtained from a | ||
+ | <a class="tooltip"> lognormal distribution <span class="tooltiptext" style="width:400px;"> | ||
+ | a lognormal distribution assigns probabilities to all positive values. However the distributions is skewed to favour smaller values. Biological reaction rates have been found to follow this distribution | ||
+ | <sup> <a href="#fn8" id="ref8">8</a></sup> </span> </a> with a parameter estimation based on Raue et al<sup> <a href="#fn7" id="ref7">7</a></sup>. In Figure 10 you can see an example. </p> | ||
+ | |||
+ | <figure> | ||
+ | <img src="https://static.igem.org/mediawiki/2016/f/f6/T--Wageningen_UR--lognormal_quorum2.jpg"/> | ||
+ | <figcaption>Figure 8. Here you see the lognormal distribution of the 19 parameters in the quorum sensing system. | ||
+ | The red line indicates the mean of the parameter and on both sides from the mean you could find the left and right border of the confidence interval. </figcaption> | ||
+ | </figure> | ||
+ | <p>With these <a class="tooltip"> confidence intervals <span class="tooltiptext" style="width:300px;"> | ||
+ | Equation for confidence interval used </span> </a> the best parameter sets could be chosen. </p> | ||
<p>In a later stage, to get the desired response, the quorum sensing system and the subpopulation system were combined. As shown in Figure 8, you can see how we think to generate different cell populations. | <p>In a later stage, to get the desired response, the quorum sensing system and the subpopulation system were combined. As shown in Figure 8, 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 9 you can see the increasing RFP over time after many cell divisions, indicating an increasing cell population.</p> | With this extended part we try to generate a system which predicts the behaviour of the subpopulations. In figure 9 you can see the increasing RFP over time after many cell divisions, indicating an increasing cell population.</p> |
Revision as of 11:28, 19 October 2016
Modeling Overview
In light of our guiding principles (specificity, regulation and biocontainment), we modelled four different aspects of BeeT. The modelling work can inform and aid the improvement of wet-lab experiments. Another facet is to assess the optimal application strategy for BeeT in real world applications. We asked ourselves; what 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 subpopulations?
- What are important parameters for the optogenetic killswitch to function optimally?
- Will BeeT be capable of surviving in sugar water?
- What is the best application strategy for BeeT?
Population Dynamics
For the final product, BeeT, we intend to use toxins produced by Bacillus thuringiensis, also called Cry toxins. However, these toxins are also harmful to our chassis, resulting in a reduction of toxin production when it is needed to kill the mites. To counteract this effect we envision the use of quorum sensing that activates Cry toxin production only when there is a large quantity of BeeT present. Ideally, BeeT is able to produce Cry toxin over a long period to improve its effectiveness against mites. However, if an entire population of BeeT is synchronized, we hypothesize that only a single burst of Cry 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 subpopulations of BeeT: some producing BeeT while others are recuperating. To help understand this complex system we use dynamic modelling.
What is Quorum Sensing?
Quorum sensing is a cell-cell communication system. The detection of chemical molecules allows the bacteria to sense the presence of other bacteria. In this way the bacteria control gene expression in response to changes in cell number 1,4. This process is achieved through the production and release of an Acylated Homoserine Lactone (AHL) autoinducer An autoinducer is a molecule that can diffuse through the cell membrane. . The AHL can diffuse 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.
Genetic circuit
The quorum sensing system consists of two proteins: LuxI and LuxR. LuxR is constitutively expressed, together with AHL it forms a complex which activates the transcription of a toxin. In our case we use the detection protein Green Fluorescence Protein (GFP) to follow the behaviour of the system 2. LuxI encodes an AHL synthase. AHL is a molecule that can diffuse freely through the cell membrane, and in this way travels from cell to cell. LuxR encodes for a protein and together they form a complex. In a natural system the LuxR-AHL complex controls transcription of LuxI, forming a positive feedback loop that increases the amount of AHL in the system 3. When there is more AHL in the system, AHL is more likely to bind to the LuxR protein. In Figure 1 you can see a schematic representation of the system.
According to the 2011 team from Davidson College and Missouri Western State University5, LuxR protein represses transcription of the luxR gene in the absence of AHL, establishing a negative feedback. We investigated whether this negative feedback can be used to create different populations. As you can see in Figure 2 different states of GFP responses can occur when the production rate of luxR and rate of complex formation are changed. However, when we remove the feedback in the system and change the same parameters, we get similar responses of the system as shown in Figure 3.
This shows that the feedback has a minimal influence on the system to create different subpopulations. Also when there is no negative feedback in the system, we found more parameter sets that give a high amount of GFP (see Figures 4 and 5).
The figures are simulated with the parameter sets obtained from the quorum sensing model. We are using the parameter sets that give the best response according to the confidence intervals (see Method section). In the presence and absence of negative feedback, the system behaves similarly by assuming the production rate of luxR and the formation rate of the complex are different in each cell. The quorum sensing system can simulate different responses with the same cells and different parameters, if we could control the LuxR production rate. However, we could not envision a method of doing this experimentally. We aim to make cells that are genetically identical but still can respond differently. Therefore, we designed another system that could help us create this response downstream of the quorum sensing mechanism. The two systems were tested in the lab parallel with the modeling.
Why include a subpopulation system?
Since the quorum sensing mechanism could not provide the subpopulations we desired using genetically identical cells, we created a system that could act downstream of quorum signalling to provide the response we needed. Population-wide Cry toxin overexpression is likely to kill all E. coli cells in the first moment of toxin expression. Since this would only affect one of the subpopulations, the second subpopulation would be able to initiate a new growth phase after death of the toxin-producing cells. The critical requirement for this is that cells respond at different times to the quorum stimuli despite being genetically identical. A small part of the population that acts differently from the rest of the population is called a subpopulation. 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-cI-LVA inactivates the λ-cI directly, or prevents the translation of the λ-cI protein. 434-cI-LVA has a higher turnover rate than λ-cI. This subpopulation system is based on a natural system for persister cell formation. 6.
As you can see in Figure 6; glucose has a suppressing function on the system, arabinose has an activating function on the system. We used the model to predict what will happen when we add glucose in different amounts. The assumptions we made for the subpopulation system are the following: 434-cI-LVA degrades faster than λ-cI, cell division happens when the cell size has doubled, and two cell populations exist with one growing differently than another. We tested a number of parameter sets and picked the parameter set that gave the biggest RFP response based on the strength of glucose. To see how the model behaved when we changed the ratios of the initial amounts of λ-cI and 434-cI-LVA, we investigated the effect of starting conditions on the outcome of the system. The initial conditions were varied between 1 and 10. Within the heatmap you can see in which ratios the initial amounts of λ-cI and 434-cI-LVA in the system are needed to get high RFP production (here glucose and arabinose have a fixed concentration).
As seen in Figure 7, when λ-cI and 434-cI-LVA are present in similar amounts we have a subpopulation system. But if they are present in different amounts there will be no subpopulations. This can be expected when you look at the subpopulation system. The system is inhibited by 434-cI-LVA, which represses the RFP production, and λ-cI activates the RFP production. In Figure 7 you can see the balance between the 434-cI-LVA and λ-cI amounts that are present for the output of RFP. To understand how changing the Ribosomal Binding Site (RBS) impacts RFP responses, we simulated the system for different combinations of transcription rates. From these simulations we found:
λ-cI | 434-cI-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 |
To confirm that our model represents biological behaviour we analysed the RBS library. We can conclude from these results that the RFP concentration quanlitatively corresponds to the Figure 7. Because as you can see in the table 1. the highest RFP responses are when the λ-cI and 434-cI-LVA are present in the same amount. The lowest responses of RFP when there is a is a big difference between λ-cI and 434-cI-LVA. This is also shown in the heatmap we got form the model.
Combined system
Based on the modeling we hypothesised the following: when there are more cells present in the system, more AHL-LuxR complex is formed. The complex inhibits the subpopulation promoter. When the promoter is inhibited production of 434-cI-LVA will be suppressed and production of λ-cl will be activated. At a certain time point λ-cl takes control over the system, because 434-cI-LVA has a higher turnover rate than λ-cl. In this case more λ-cl results in more RFP.
In a later stage, to get the desired response, the quorum sensing system and the subpopulation system were combined. As shown in Figure 8, you can see how we intend to generate different cell populations. With this extended network we try to generate a model which predicts the behaviour of the subpopulations. In Figure 9 you can see the increasing RFP over time after many cell divisions, indicating an 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 biologically reasonable range between 0 and 1. For the analyses we used 100,000 parameter sets, 10 cells, random initial conditions between 0 and 1 and 60 timesteps. Tuneable parameters are used, each parameter set can produce dramatically different population dynamics. 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.
With the Latin Hypercube sampling we made parameter sets that are obtained from a lognormal distribution a lognormal distribution assigns probabilities to all positive values. However the distributions is skewed to favour smaller values. Biological reaction rates have been found to follow this distribution 8 with a parameter estimation based on Raue et al 7. In Figure 10 you can see an example.
With these confidence intervals Equation for confidence interval used the best parameter sets could be chosen.
In a later stage, to get the desired response, the quorum sensing system and the subpopulation system were combined. As shown in Figure 8, 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 9 you can see the increasing RFP over time after many cell divisions, indicating an 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 biologically reasonable range numbers between 0 and 1. For the analyses we used 100.000 parameter sets, 10 cells, random initial conditions and 60 timesteps. Tuneable parameters are used, each parameter set can produce dramatically different population dynamics. 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.
With the parameter numbers of the Latin Hypercube sampling we made parameter sets that are obtained from a lognormal distribution a lognormal distribution assigns probabilities to all positive values. However the distributions is skewed to favour smaller values. Biological reaction rates have been found to follow this distribution 8 with a parameter estimation based on Raue et al 7. Below you could see an example;
With these confidence intervals Equation for confidence interval used the best parameter sets could be chosen.
In conclusion
Quorum sensing ensures that the toxin is only produced when the density of
bacteria is high enough, this standardizes the amount of toxin produced by the bacteria
population. The subpopulation system was coupled to the quorum sensing system.
Together, quorum sensing and formation of non-producing subpopulations allow
bacteria to produce waves of toxin.
With the results of the combined system we can conclude that waves of toxins are
produced. Different parameters in the quorum sensing system elicit different GFP
responses. However, we can not expect to be able to make genetically identical cells with varying values for these parameters
with the subpopulation system we may be able to predict which RBSs of the library have the highest chance to successfully create subpopulations. The library in further research it could be tested in the lab.
Optogenetic Kill Switch Model
One important aspect of our project is the biocontainment of BeeT to the hive, preventing it from spreading into the environment. In collaboration with the wet-lab, we designed an optogenetic kill switch based on the blue light sensing pDusk and pDawn systems as described by Ohlendorf et al.1. The cell death is inflicted by the mazEF toxin-antitoxin (TA) system. The latter functions by the antitoxin (mazE) preventing the toxin (mazF) from cleaving mRNAs which ultimately kills the cell. With the underlying biology of the system in mind, we used synthetic bioengineering principles to mathematically describe our design and explore the dynamics of the system.
Our results show that we have a working mathematical model which describes the data of Ohlendorf et al.1. With this model, we now know where to look for the relative kinetic rates in the parameter space to give suggestions to the wet-lab on how to build a functioning optogenetic kill switch. Our differential equations of pDusk and pDawn can also be used by future iGEM teams to mathematically describe and build new optogenetic tools.
Light On
Modelling The Optogenetic Tool
For the first part of our analysis, we optimized the mathematical models of pDusk and pDawn using published data1. For now, we ignored the toxin-antitoxin system. This gave us the option to construct our scoring function to evaluate both systems simultaneously with a weighted means approach.
By constructing an accurate model of the optogenetic part of our overall kill switch system, we are confident that we are mathematically representing the behaviour of the microorganism in the lab. Results from the model can then be used as a reference point for building the toxin-antitoxin system into the kill switch model. We will search the parameter space to identify parameter sets which fit the data given by Ohlendorf et al.1. In addition, we will select the best fit to data based on a scoring function as described by Raue et al.4. Lastly, we provide a mathematical model which can be used by future iGEM teams to build new optogenetic tools.
System Design
We first studied the pDusk system in more detail to derive simplified equations which can describe the system behaviour. The genetic switches are based on the interactions between the light sensing protein YF1 and the response regulator FixJ as described by Möglich et al.2. In darkness, YF1 phosphorylates FixJ, which in turn activates the promoter pFixK2. This activation leads to the expression of the desired genes. Under light conditions, YF1 enters an excited light-state, which inhibits the phosphorylation of FixJ. In addition, it prevents the activation of the pFixK2 promoter and thus represses the target genes in Figure 11 for pDusk.
The pDawn system functions in the same way as the pDusk system, with the addition of cIλ being expressed depending on the activity of the pFixK2 promoter. The protein form of cIλ inhibits the expression of the RFP reporter gene in Figure 11 for pDawn.
Assumptions
To derive mathematical equations describing the above systems, we made some simplifying assumptions.
We neglect the effects of dilution/ growth. We thus assume the cell’s volume to be constant over time.
We assumed that the components in our system are neither affected by nor affect other cellular mechanisms.
As there is no additional information gained from modelling transcription and translation for the dark state of Yf1(yDD) and the inactive form of FixJ (ji) we lumped these processes and assumed that they can be described by a single parameter.
We also assumed the rates of production, binding and degradation of mRNAs and proteins to be linear which resulted in a first order differential equations system
To model the influence of light on the system, we assumed light activation to occur similar to the model of phytochrome B dimerization described in Klose et al.3 (). In addition, we consider in our system the different stages of Yf1 (yDD, yDL/LD, and yLL) as described by Möglich et al.2. Translated to our system, this means that with increasing light intensities (N), the pool of activated Yf1 (yDL/LD and yLL) would deplete the dark state of Yf1 (yDD), which is responsible for the phosphorylation and thus activation from inactive FixJ (ji) to active FixJ (ja). As all stages of Yf1 form a dimer, we assumed dimerization to occur quickly and be the dominant and relevant form for our system. Lastly, we assumed a quasi steady-state approximation (Michaelis-Menten kinetics) for the effect of activated FixJ (ja) on the expression downstream of the RFP (RFPm) reporter gene. A detailed system design is provided here.
Results
With our mathematical model we can describe the behaviour, as shown in Figure 12, of both systems as tested in the lab by Ohlendorf et al.1. We can thus say that we built a simplified mathematical representation of the pDusk and pDawn system which can describe the systems’ behaviour.
Preliminary results from the lab show that the RFPp response after 17 hours incubation time is weak using the pDusk system. The experiment was conducted in darkness and under
light intensity and the results are shown in Table 2.
System | Dark | Light | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
pDusk | |||||||||||||||||||||
pDawn |
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 |
Period and treatment | Colony death | Colony survival | Colony thriving |
---|---|---|---|
Sugar water, spring period | 6,6% | 80,6% | 12,8% |
Bee bread, spring | 0% | 2,9% | 97,1% |
Sugar water, winter | 15,1% | 80,7% | 4,2% |
Bee bread, winter | 0 | 57,6% | 42,4% |