Team:KU Leuven/Project/StickerSystem

From 2013.igem.org

(Difference between revisions)

Revision as of 16:14, 2 October 2013

iGem

Secret garden

Congratulations! You've found our secret garden! Follow the instructions below and win a great prize at the World jamboree!

A video shows that two of our team members are having great fun at our favourite company. Do you know the name of the second member that appears in the video?
For one of our models we had to do very extensive computations. To prevent our own computers from overheating and to keep the temperature in our iGEM room at a normal level, we used a supercomputer. Which centre maintains this supercomputer? (Dutch abbreviation)
We organised a symposium with a debate, some seminars and 2 iGEM project presentations. An iGEM team came all the way from the Netherlands to present their project. What is the name of their city?

Now put all of these in this URL:https://2013.igem.org/Team:KU_Leuven/(firstname)(abbreviation)(city), (loose the brackets and put everything in lowercase) and follow the very last instruction to get your special jamboree prize!

In this part we describe the design of an oscillator that could be useful in biological networks. We designed one ourselves since we have very specific demands and look forward to the challenge. We even tried to create a system that creates synchronised oscillations without depending heavily on the components used. So our proposal oscillates inherently, and depends only slightly on the parameters of the components used. In this text, we start with an explanation of how this oscillating model fits within the framework of our project. Second, we explain several necessities to obtain a synchronised oscillator, and how we managed to incorporate those within our network. For the thorough study of the network and to see what has been achieved in the lab, we refer to the modelling page and the wetlab page respectively.

Modelling

For those who are not afraid of having a more mathematical view on our oscillator, we invite you to visit our modelling page. The actual results we accomplished are mentioned here too.

Wetlab

A part of the oscillator was implemented in the wetlab. You can find the genes we chose for our oscillator here, as well as the results of the wetlab experiments.

Our initial system for the production of methylsalicylate and β-farnesene relied on direct interaction between the bacterium (BanAphids) and the aphid. This is ethically challenging since our BanAphids could end up in the environment. We therefore designed an alternative pheromone production system, whereby the bacteria are kept in semi-permeable pouches. These allow the pheromones to disperse in the air yet the bacteria themselves remain in the bags. In such a system bacteria have limited interactions with their environment. Consequently, honeydew would not touch the bacteria and cannot be used as a trigger, thus we have to adapt our pheromone expression system to these novel conditions. Our solution is an autonomous system. In its simplest form, this would be the constitutive expression of both pheromones. However, the constitutive production of β-farnesene rapidly renders aphids insensitive (Kunert, Reinhold and Gershenzon, 2010). The constant production of methyl-salicylate could be equally disadvantageous since ladybugs may become insensitive to the pheromone and the plant itself may end up in defence-mode too long, causing it to wilt. To prevent habituation β-farnesene en methyl-salicylate should fluctuate. This is typically achieved in an oscillator. Here we will concentrate on the modelling of a β-farnesene oscillator as a proof of principle. The production of methylsalicylate can be regulated similarly.

Colony-wide oscillations

Before we delve into the details of our oscillator we will first discuss the intricacies of oscillating one cell versus oscillating a colony, which consists of millions of cells. The repressilator of Elowitz and Leibler (2000) is a nice example of how to create oscillations in one cell. Their work has been a cornerstone for synthetic biology since the repressilator was among the first synthetic networks successfully introduced into bacteria. However, they did not succeed in a colony-wide synchronization. This means that even though each bacterium oscillates on its own, they did not oscillate together. For every bacterium in the colony, there will be one oscillating in opposite phase. The average of their signals would be a flat line in the case of perfect sinusoidal oscillations (Figure 1a). Clearly this underlines the need for synchronization on the colony-level. Providing this happens, the oscillations of the different cells would amplify each other (Figure 1b), resulting in an oscillating colony.

The importance of synchronization can also be seen in nature, where single organisms organize themselves into larger groups (Ioannou et al., 2007). A well-known example is the behaviour of relatively small fish that group into schools. This brings them potential benefits, one of which is exemplified in Figure 2.

Figure 1a| The summed input of two sinusoidal functions in anti-phase result in a flat line.

Figure 1b| The summed input of two sinusoidal functions in phase result in an overall sinusoidal function, with a higher amplitude.

Figure 2| Figure : This shows how small fish can confuse their predators when they work together in a synchronized fashion, something they cannot achieve on their own.

Colony-wide oscillations

Obviously, the first and foremost requirement for our oscillator is synchronization on the colony level. The iGEM team from Wageningen tried to attain exactly this in 2011, based on the model proposed by Danino et al. (2010). This model is thoroughly described by the Wageningen 2011 iGEM team. As they mention on their wiki, it heavily depends on parameter values and conditions. We refer to Box 1 for an explanation of parameters and conditions.
Prior to determining the parameters that will define our oscillating network, we have to establish the nature of the network. Following the repressilator of Elowitz and Leibler (2000) and the synchronized oscillator of Danino et al. (2010) we also choose a transcription factor (TF) network. Our TF network will consist of two modules. The first controls the production of β-farnesene, the second consists of oscillating transcription factors. We will design our TF network such that the oscillating module controls the crucial step in the β-farnesene production module, resulting in the oscillating production of β-farnesene.

Parameter dependency

We investigated currently available synthetic biology networks to estimate the feasibility of such a combined production system. Unfortunately we noticed that most are highly case-specific. First, they are heavily dependent on the parameters (promoter strength, transcription rate…) of their components (promoters, transcription factor …). Second, in natural conditions, environmental changes (temperature, pH …) strongly influence those parameters. The ramifications of these susceptibilities are that these oscillators can only function under very specific conditions, limiting their use in practical implementations. Summarized, the currently used TF networks are too responsive to parameter and condition changes. Clearly synthetic biology needs a general oscillator; without the previously mentioned liabilities. We aim to build a TF network where the oscillating behaviour is fairly insensitive to the components’ parameters. Following from the note in Box 1, this also renders the oscillating behaviour insensitive to the conditions. This implies that the components of the network are exchangeable without impeding its oscillating behaviour. Be aware that the wetlab challenge will still be choosing transcription factors that exhibit the proper interactions (with other transcription factors).

Figure 3: Logical circuit displaying our oscillating model, combined with its link to the production system

The most important feature of our model remains the sustained colony-wide oscillations under a broad range of parameters. The production of β-farnesene should not be constitutive, but the height of the production peaks and the time in between different peaks can vary as long as they remain within reasonable ranges. Therefore we do not pose stringent requirements for the amplitude and frequency of the β-farnesene production peaks. To build up the actual model, we started from the seminal work of Uri Alon (2006), a lot of coffee and nightly endeavours. The result of this slog is shown in Figure 3. Our model consists of six transcription factors (A, B, C, D, X and Y). The arrows represent the transcriptional activation of the target (e.g. an arrow from A to X means that transcription factor A induces the production of transcription factor X). Similarly, the inhibitory sign () represents the transcriptional repression of the target. The AND and OR gates are logical gates. For an AND gate to function both of the inputs must be ‘positive’ (e.g. for TF A to be transcribed, TF D must be present and TF C must be absent). For an OR gate to function one positive input suffices (e.g. TF C is transcribed when TF A or TF X is present or when both are present). One of those transcription factors must eventually linked to the production of β-farnesene. Based on some of our modelling, we selected TF A to be linked to the production of β-farnesene. The main reason being that TF A and TF B show a sharp production peak, the goal of an oscillating production system. This sharp production peak of TF A can also be seen in Figure 5c and 5d.

Oscillations of our system

We will now walk you through the network and how it reaches oscillations. A high level of TF A will induce the production of both TF C and TF X. After a little while, the level of TF C will be sufficient to initiate the repression of the top AND gate (and the stimulation of the bottom AND gate). Once the top AND gate is significantly repressed, the level of TF A starts to decline. When TF A drops underneath its threshold, the level of TF X starts to decline too. Be aware that at this point the level of TF C does not decline yet. Only when the level of TF X also dropped underneath its own threshold will the level of TF C start to wane. This prolonged expression of TF C results in an extended repression of the production of TF A. This ascertains the level of A drops sufficiently. On the other hand, an extended expression of TF C also results in an extended activation of the production of TF B, which reaches a high level. The same explanation as before can now be applied to TF B, TF D and TF Y. This eventually results in a decrease in the level of TF B and a high level of TF A, bringing the system back to its starting point. Every time this cycle is completed, the levels of each of the transcription factors dramatically change and eventually return to their original level, or in other words, oscillate. This network design inherently results in such a behaviour, meaning that the dependence on the parameter values is very low. This aspect of our model has been supported with in silico results, which can be found on the modelling page regarding the subject.

Synchronization

We achieved low parameter dependence through an intelligent network design. The other requirement is that the oscillation of the colony is synchronized. The oscillations of different cells are linked because two of the components of our oscillatory network can freely diffuse out of the cells. Diffusion is something that occurs very rapidly at the scale relevant for bacteria. It distributes the molecules almost evenly throughout the colony, at least as long as most partake in the production of these colony-wide molecules. This results in colony-wide oscillations of those molecules. Consequently, this is a very effective means of synchronizing a population. Using two colony-wide molecules that (indirectly) repress each other’s production allows the oscillation of a broader spectrum of colony densities. When there are more cells per volume the perceived production rate of the colony-wide molecules also increases. The reciprocal (indirect) repression of the two colony-wide molecules helps to cancel this effect and equalizes the oscillations for a larger amount of cell densities.
By studying the possibilities for colony-wide transcription factors, we found quorum-sensing molecules as good candidates, since the ones we encountered serve as transcription factors (combined with intracellular receptors) and can passively diffuse out of the cells (Fugua, Winans and Greenberg, 1994). Quorum-sensing molecules are produced by enzymes, which is thoroughly discussed on the oscillator wetlab page and the extra enzyme step alters the equation as is discussed on the modelling page. Danino et al. (2010) also opted for a quorum-sensing molecule for their synchronized oscillator, but they used only one. Our model would use 2 (displayed as A and B), to allow a broader range of colony densities.

Filling in the dots

For biologist the most interesting part is most likely giving a name to the transcription factors. The primary requirement would be that their biological interactions are according to the network displayed in Figure 3. For example in our wetlab attempts we used the transcription factor araC (biobrick C0080) to be TF X, which had a promoter (R0078) inducible by a quorum-sensing molecule. For more details and practical implications we refer you to the oscillator wetlab page.

A principal problem that goes hand in hand with colony synchronization, is the constant presence of noise. This noise is partitioned into two sources: intrinsic noise, which originates within the regarded subsystem and extrinsic noise, which originates outside of it. We will describe this specifically for gene expression since we built a transcription factor circuit with oscillating behaviour. The intrinsic noise is due to the stochastic effects involved in the reaction events leading to transcription and translation. This leads to fluctuations in timing and order of those events, even in cells that are in an equal state (equal nutritional status, place in the cell cycle, …). The extrinsic noise is for example due to differences in the number of RNA polymerase and ribosome molecules. Because they are gene products themselves, they are subject to their own intrinsic noise. Other factors that lead to extrinsic noise include the stage in the cell cycle, the quantity of the protein, the mRNA degradation machinery and the cell environment (Swain, Elowitz and Siggia, 2002). This substantial presence of noise has to be taken into account when developing a genetic circuit, either by suppressing it, or by building a network that is robust to it (Elowitz et al., 2002).
The presence of noise affects our system in two ways. First it means the different cells in a colony are in a different state and exhibit a variance in their parameters. Second it causes fractions of the colony to become unsynchronized. Both of these effects have been tested on the modelling page and the results show our designed network resists this very well. In the rest of this text we will discuss how the use of diffusible molecules and the shape of our network achieve the different requirements posed to an oscillator.

Coherent type 1 feed forward loop

As mentioned above, there is a prolonged production of TF C (D) after the disappearance of TF A (B). However, when there is TF A (B) present, the production of repressor TF C (D) starts immediately. This means there’s an asymmetric time delay for the production of the repressing molecules. The network motif that exhibits this behaviour is called a ‘coherent type 1 feed forward loop’ (C1-FFL) with an OR logical gate (Mangan and Alon, 2003), one of which is highlighted in Figure 4. This extended period in which one of the colony-wide molecules is repressed and the other produced, helps to reduce the effect of cell-to-cell variability in the different parameters, which is a necessity in order to have a synchronized oscillation. Even if not all cells produce a sufficient amount of repressing molecules, the prolonged repression by the others still results in an effective reduction in the amount of that colony-wide molecule, and analogously also a rise in the concentration of the other. The prolonged production of TF C, and similarly TF D, ascertains that the switching event they are responsible for is fully executed.

Figure 4 | Logical circuit displaying our oscillator, with one C1 FFL highlighted in green

A small desynchronized fraction of the cells cannot distort the oscillations

At the small space-scale that is relevant to bacteria, diffusion rapidly spreads out molecules throughout the colony. If for instance, the unsynchronized subpopulation produces the other colony-wide molecule, that concentration does not reach any significant level because of the rapid diffusion at that scale. This can be explained by using an approximation of the diffusion coefficient of a typical quorum sensing molecule; D(N-(3-Oxododecanoyl)-L-homoserine lactone) equals 4.9 * 10² µm²s^-1 (Stewart, 2003). The equation (Einstein, 1905) gives the average displacement of molecules because of diffusion in 3 dimensions after time t. In this example the average displacement after 1 second would be 54 µm, which is about equal to 50 times the size of one cell. This supports our claim that the pheromone production of one cell is rapidly dispersed throughout its environment and that only larger fractions of the colony can control the level of colony-wide molecules.

The colony-wide concentration of some transcription factors benefits rapid resynchronization

The distance between cells in moderate density cultures is approximately 16 µm (= 2*10⁸ cells/ml, Park et al., 2003) or one third of the diffusion length after one second. This implies that all cells experience an approximately equal concentration of diffusible molecules. If, by random occurrence, a certain amount of cells have an excess amount of non-diffusible molecules, as for instance one of the repressors, they will produce the colony-wide molecules at a different rate. The next switch in production, however, occurs for all cells approximately at the same time and serves as a resynchronization event. This can be explained because it is the colony-wide molecule that is being produced by the majority that first reaches the threshold needed to switch to the production of the other colony-wide molecule in all of the cells. Since the cells that were out of sync had not yet stopped producing that other molecule, they are resynchronized with the majority. This has to be seen in relation with the extended production of TF C, and TF D, responsible for the switching events.

Example of rapid resynchronization

Figure 5 shows an extreme example of this principle. These images have been created by solving a partial differential equation (PDE) with matlab (provided by MathWorks). The initial conditions in this PDE are that 40% of the cells start with a 4-fold excess of TF C and a quarter of TF D, with respect to the other 60% of the cells. Figures 5a and 5b show the spatial-temporal oscillations of a colony-wide molecule, here TF A, (Figure 5a) and a non-permeable molecule, here TF C (Figure 5b), respectively. Even though the population behaves differently in the beginning, they show a rapid resynchronization. Figure 5 c and d display the production rates of the colony-wide molecules and of the molecules that each repress one and induce the other colony-wide molecule in the two different cell subtypes. Figure 5 c displays this for a cell belonging to the majority (60%) and Figure 5 d for a minority (40%) cell.

The model shows only small differences between the production rates of the non-diffusible molecules (red and yellow) while protein production switches occur simultaneously. This is because those are controlled by the concentration of colony-wide molecules, which are approximately uniformly distributed. In reality this will be a stronger effect, since we chose a much smaller diffusion coefficient (2 * 10¹ µm²s^-1 instead of 4.9 * 10² µm²s^-1) in order to display the principles. The production of the colony-wide molecules (blue and cyan) show a big difference during the first oscillations, but those differences rapidly disappear; there is no significant difference anymore after the second oscillation and resynchronization is a fact. We also measured how the colony would react if cells would go “out of sync”: how quickly would the model reinstate colony-wide synchronization? We refer to the modelling page for details on these quantitative results and the algorithms used.

Figure 5 | Graphical reproduction of the rapid resynchronization | a, The spatial-temporal fluctuations of a colony-wide molecule in a population in which 40% initially behaves differently. b, The concentration of one of the non-diffusible molecules in a population in which 40% initially behaves differently. c, The evolution over time of the production rate of several molecules in a cell belonging to the majority of the population. d, The evolution over time of the production rate of several molecules in a cell belonging to the minority of the population.

Team:KU Leuven/Project/StickerSystem

From 2013.igem.org

Revision as of 16:14, 2 October 2013

Secret garden

The Oscillator

Modelling

Wetlab

An oscillator as an alternative solution

Colony-wide oscillations

Colony-wide oscillations

Parameter dependency

Our design

Oscillations of our system

Synchronization

Filling in the dots

Coping with noise

Coherent type 1 feed forward loop

A small desynchronized fraction of the cells cannot distort the oscillations

The colony-wide concentration of some transcription factors benefits rapid resynchronization

Example of rapid resynchronization

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+   Our initial system for the production of methylsalicylate and β-farnesene relied on direct interaction between the bacterium (BanAphids) and the aphid. This is ethically challenging since our BanAphids could end up in the environment. We therefore designed an alternative pheromone production system, whereby the bacteria are kept in semi-permeable pouches. These allow the pheromones to disperse in the air yet the bacteria themselves remain in the bags. In such a system bacteria have limited interactions with their environment. Consequently, honeydew would not touch the bacteria and cannot be used as a trigger, thus we have to adapt our pheromone expression system to these novel conditions. Our solution is an autonomous system. In its simplest form, this would be the constitutive expression of both pheromones. However, the constitutive production of β-farnesene rapidly renders aphids insensitive (Kunert, Reinhold and Gershenzon, 2010). The constant production of methyl-salicylate could be equally disadvantageous since ladybugs may become insensitive to the pheromone and the plant itself may end up in defence-mode too long, causing it to wilt. To prevent habituation β-farnesene en methyl-salicylate should fluctuate. This is typically achieved in an oscillator. Here we will concentrate on the modelling of a β-farnesene oscillator as a proof of principle. The production of methylsalicylate can be regulated similarly.</p>
-    <h3>Why would we use an oscillator?</h3>
-    <p align="justify">Continuous exposure of aphids to the alarm pheromone EBF leads to habituation within three generations. However, habituated aphids can also revert back to EBF sensitive ones in only three generations. This wants to say that there is no genetic mutation, the mechanism is situated at transcriptional level. In literature one can find different results of the use of continuous EBF emission. According to Devos et al. (2010) both continuous as well as periodic emission of EBF have their advantages. Continuous exposure to the alarm pheromone leads to habituation. This will give rise to EBF-insensitive aphids, that won’t be repelled anymore by EBF and that will also produce a larger progeny. On the other hand habituated aphids have a lower survival rate in the presence of ladybugs. This wants to say that periodic emission of EBF will repel the aphids but at the end their survival rate will be higher. This is all contradictory with an article published by Kunert et al. (2010) in which it’s written that continuous emission does not serve as a direct defence against aphids. While considering if we should implement an oscillator or not, we also found out that it’s unknown whether predators become habituated to EBF. If this would be the case, it would be better to make use of an oscillating model. For this reason and for what was mentioned in the article of Kunert et al. (2010), we decided to design an oscillator. This can also be useful for other teams in the future as one can imagine many projects that require and oscillating system.</br>
-In order to expand on the possibility of such a periodical production we investigated biological oscillating networks. A transcriptional network that exhibits oscillating behavior is the repressilator of Elowitz and Leibler (2000). This has been a cornerstone for synthetic biology since they were among the first to successfully introduce a synthetic model in a living organism. However, their paper mentions the lack of colony-wide synchronization. This is a necessity to achieve a periodical production, otherwise the variation will even out, resulting in a de facto constitutive expression. This means the repressilator does not suffice for a bacterial production unit with a periodical output.</p>
-   </div>
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-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/e/eb/Repressilator.png" alt="The repressilator"/>
-    <p>Figure 1ǀ The repressilator by Elowitz and Leibler</p>
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+  <h3>Colony-wide oscillations</h3>
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+   <p align = "justify">
+Before we delve into the details of our oscillator we will first discuss the intricacies of oscillating one cell versus oscillating a colony, which consists of millions of cells. The repressilator of Elowitz and Leibler (2000) is a nice example of how to create oscillations in one cell. Their work has been a cornerstone for synthetic biology since the repressilator was among the first synthetic networks successfully introduced into bacteria. However, they did not succeed in a colony-wide synchronization. This means that even though each bacterium oscillates on its own, they did not oscillate together. For every bacterium in the colony, there will be one oscillating in opposite phase. The average of their signals would be a flat line in the case of perfect sinusoidal oscillations (Figure 1a). Clearly this underlines the need for synchronization on the colony-level. Providing this happens, the oscillations of the different cells would amplify each other (Figure 1b), resulting in an oscillating colony.</p><br/>
+   <p align="justify">The importance of synchronization can also be seen in nature, where single organisms organize themselves into larger groups (Ioannou et al., 2007). A well-known example is the behaviour of relatively small fish that group into schools. This brings them potential benefits, one of which is exemplified in Figure 2.</p>
+   </div>
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-    <h3><br/></h3>
+   <img src="#"/>
-    <img src="https://static.igem.org/mediawiki/2011/e/e1/System3.png" alt="Wageningen Team 2011 project"/>
+   <p align="justify">Figure 1a| The summed input of two sinusoidal functions in anti-phase result in a flat line. </p><br/>
-    <p>Figure 2ǀ The oscillator of the Wageninen 2011 iGEM team.</p>
+   <img src="#"/>
+   <p align="justify">Figure 1b| The summed input of two sinusoidal functions in phase result in an overall sinusoidal function, with a higher amplitude.</p>
+   <img src="#"/>
+   <p align="justify">Figure 2| Figure : This shows how small fish can confuse their predators when they work together in a synchronized fashion, something they cannot achieve on their own.</p>
     </div>
-   <div class="span8">
-    <h3>A synchronized oscillator</h3>
-    <p align="justify">The <a href="https://2011.igem.org/Team:Wageningen_UR"> iGEM team from Wageningen</a> tried to attain colony wide oscillations in 2011, by using the model proposed by Danino et al. (2010). This model provides a next step in the engineering of genetic circuits and is thoroughly described by the Wageningen 2011 iGEM team. As they mention on their wiki, this model heavily depends on the parameter values. Because we want to use an oscillator as a pace regulator, the eventual system will have multiple other inserted genes. The introduction of another set of genes besides an oscillator means an extra load on the current genetic circuit and this can influence the parameters of the oscillator-network (Shiue and Prather, 2012). To have a synchronized oscillator module that functions ‘independently’ on the presence of other modules, we need a system that gives oscillations for a broad range of parameters. This way it can preserve its oscillating behavior independently of possible other loads on the cell’s metabolism.</p>
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-    <h3>Our very own oscillator</h3>
+  <h3>Colony-wide oscillations</h3>
-    <p align="justify">The most important feature of our model is the sustained colony wide oscillations for a broad range of parameters. Meanwhile, for both the amplitude and frequency we do not pose stringent requirements. This is because the production of β-farnesene should definitely not be constitutive, but the height of the peaks in production and the time in between different peaks can vary as long as they remain within reasonable ranges. Since we know very well what we exactly desire from the oscillator we decided to design one ourselves. Another, equally important, reason for this decision is the fact that this design would offer a great journey on its own and give us the opportunity to learn a tremendous amount of new things, which is one of the things iGEM is about. </p>
+   <p align = "justify">
+Obviously, the first and foremost requirement for our oscillator is synchronization on the colony level. The iGEM team from Wageningen tried to attain exactly this in 2011, based on the model proposed by Danino et al. (2010). This model is thoroughly described by the Wageningen 2011 iGEM team. As they mention on their wiki, it heavily depends on parameter values and conditions. We refer to Box 1 for an explanation of parameters and conditions.<br/>
+Prior to determining the parameters that will define our oscillating network, we have to establish the nature of the network. Following the repressilator of Elowitz and Leibler (2000) and the synchronized oscillator of Danino et al. (2010) we also choose a transcription factor (TF) network. Our TF network will consist of two modules. The first controls the production of β-farnesene, the second consists of oscillating transcription factors. We will design our TF network such that the oscillating module controls the crucial step in the β-farnesene production module, resulting in the oscillating production of β-farnesene.</p>
   </div>
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-<!-- The components -->
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-   <div class="row-fluid">
+   <h3>Parameter dependency</h3>
-   <div class="span4 greytext">
+    <p align = "justify">
-    <h3><br/></h3>
+We investigated currently available synthetic biology networks to estimate the feasibility of such a combined production system. Unfortunately we noticed that most are highly case-specific. First, they are heavily dependent on the parameters (promoter strength, transcription rate…) of their components (promoters, transcription factor …). Second, in natural conditions, environmental changes (temperature, pH …) strongly influence those parameters. The ramifications of these susceptibilities are that these oscillators can only function under very specific conditions, limiting their use in practical implementations. Summarized, the currently used TF networks are too responsive to parameter and condition changes. Clearly synthetic biology needs a general oscillator; without the previously mentioned liabilities. We aim to build a TF network where the oscillating behaviour is fairly insensitive to the components’ parameters. Following from the note in Box 1, this also renders the oscillating behaviour insensitive to the conditions. This implies that the components of the network are exchangeable without impeding its oscillating behaviour. Be aware that the wetlab challenge will still be choosing transcription factors that exhibit the proper interactions (with other transcription factors).</p>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid milking"/>
-    <p>Figure xǀ Tekst.</p>
-    </div>
-   <div class="span8">
-    <h3>The components</h3>
-    <p align="justify">We will design our model starting from an engineering perspective, inspired by the introduction to systems biology from Alon (2006). As the previously discussed models from the literature, we will also use a transcription factor network that creates oscillations. However, we also try to stretch the features of our model further by having the system not depend too much on what exactly are the used components. With this we mean that the several promoters and transcription factors we use, should be replaceable, without changing the fact that oscillations are produced. This is a very nice feature and is possible because our system will oscillate for a broad range of parameters. Previously we discussed the fact that a broad range of oscillating parameter is a necessity in order to preserve the oscillating behavior despite of other loads on the cell’s metabolism. However allowing components to be changed without altering the qualitative behavior of the system greatly increases the need for a broad range of oscillating parameters.</p>
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-<!-- TITLE -->
 <div id="header" class="row-fluid">
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-   <h3>How we attain synchronization</h3>
+   <h3 class="bg-green">Our design</h3>
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-<!-- Quorum Sensing. -->
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-    <h3>Quorum sensing molecules</h3>
+    <div class="span4 greytext">
-    <p align="justify">As for a means of synchronization we will use molecules that oscillate colony-wide, for which the quorum sensing molecules used by Danino et al. (2010) offer a good example. Instead of individual intracellular oscillations that are synchronized by a mechanism that influences the entire colony, we aim for a colony-wide oscillation, which is intrinsically synchronized.<br/>
+   <img src="#" alt="logical circuit">
-We will use two distinct colony-wide molecules, instead of only one, since that way we can have a less parameter sensitive oscillator. This happens when the two colony-wide molecules (indirectly) repress each other’s production, which will of course be the case in our model. When this is the case then when for instance there is an excess production of the colony-wide molecules, these excesses will partially repress each other. This implicates that a broader spectrum of colony densities should oscillate. As to make sure the evolution towards a stable steady state is avoided for reasonable parameters, we also require delaying steps to ascertain a separation in time of the successive peaks in production. By studying the possibilities for colony-wide transcription factors, we found quorum-sensing molecules as good candidates, since the ones we encountered serve as transcription factors (combined with intracellular receptors) and can diffuse out of the cells (Fugua, Winans and Greenberg, 1994). Because the quorum-sensing molecules are produced by enzymes, instead of being directly transcribed and translated, this extra step in which the enzymes are produced already induces an extra delay. On top of that the processes leading from the activation of a gene towards an active protein also take a finite amount of time, which also adds an extra delay. </p>
+   <p align="justify">Figure 3: Logical circuit displaying our oscillating model, combined with its link to the production system</p>
     </div>
-    <div class="span12">
-    <div class="span6 greytext">
+    <p align = "justify">
-    <img src="https://static.igem.org/mediawiki/2013/6/67/Quorum_sensing.png" alt="Quorum sensing molecules"/>
+The most important feature of our model remains the sustained colony-wide oscillations under a broad range of parameters. The production of β-farnesene should not be constitutive, but the height of the production peaks and the time in between different peaks can vary as long as they remain within reasonable ranges. Therefore we do not pose stringent requirements for the amplitude and frequency of the β-farnesene production peaks. To build up the actual model, we started from the seminal work of Uri Alon (2006), a lot of coffee and nightly endeavours. The result of this slog is shown in Figure 3. Our model consists of six transcription factors (A, B, C, D, X and Y). The arrows represent the transcriptional activation of the target (e.g. an arrow from A to X means that transcription factor A induces the production of transcription factor X). Similarly, the inhibitory sign () represents the transcriptional repression of the target. The AND and OR gates are logical gates. For an AND gate to function both of the inputs must be ‘positive’ (e.g. for TF A to be transcribed, TF D must be present <u>and</u> TF C must be absent). For an OR gate to function one positive input suffices (e.g. TF C is transcribed when TF A <u>or</u> TF X is present <u>or</u> when both are present). One of those transcription factors must eventually linked to the production of β-farnesene. Based on some of our modelling, we selected TF A to be linked to the production of β-farnesene. The main reason being that TF A and TF B show a sharp production peak, the goal of an oscillating production system. This sharp production peak of TF A can also be seen in Figure 5c and 5d.</p>
-    <p>Figure xǀ Possible quorum sensing molecules.</p>
     </div>
-   <div class="span6 greytext">
-    <img src="https://static.igem.org/mediawiki/2013/a/ac/Bacterial_Quorum_Sensing_by_CarolineDahl.png" alt="Quorum sensing model"/>
-    <p>Figure xǀ Typical model of quorum sensing.</p>
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-<!-- The logical circuit. -->
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+   <h3>Oscillations of our system</h3>
-   <div class="span4 greytext">
+    <p align = "justify">We will now walk you through the network and how it reaches oscillations. A high level of TF A will induce the production of both TF C and TF X. After a little while, the level of TF C will be sufficient to initiate the repression of the top AND gate (and the stimulation of the bottom AND gate). Once the top AND gate is significantly repressed, the level of TF A starts to decline. When TF A drops underneath its threshold, the level of TF X starts to decline too. Be aware that at this point the level of TF C does not decline yet. Only when the level of TF X also dropped underneath its own threshold will the level of TF C start to wane. This prolonged expression of TF C results in an extended repression of the production of TF A. This ascertains the level of A drops sufficiently. On the other hand, an extended expression of TF C also results in an extended activation of the production of TF B, which reaches a high level. The same explanation as before can now be applied to TF B, TF D and TF Y. This eventually results in a decrease in the level of TF B and a high level of TF A, bringing the system back to its starting point. Every time this cycle is completed, the levels of each of the transcription factors dramatically change and eventually return to their original level, or in other words, oscillate. This network design inherently results in such a behaviour, meaning that the dependence on the parameter values is very low. This aspect of our model has been supported with in silico results, which can be found on the <a href="https://2013.igem.org/Team:KU_Leuven/Project/Oscillator/modelling">modelling page</a> regarding the subject.</p>
-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid milking"/>
-    <p>Figure xǀ Tekst.</p>
-    </div>
-   <div class="span8">
-    <h3>The logical circuit</h3>
-    <p align="justify">Figure X displays a logical circuit with our proposal for an oscillating model. It consists of two analogous halves that are meant to exhibit sequential peaks. In this system A and B represent the colony-wide molecules. They are produced by enzymes, which is indicated by the dotted lines, and of which the expression is controlled by the logical AND gate. We incorporated this enzyme step already because we will propose a practical implementation that uses quorum-sensing molecules later on. We will first explain how this system produces oscillations and afterwards, with a more thorough explanation of the subsystems and components, we will show how this inherently creates a synchronized oscillation.</p>
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-<!-- Basic mechanism. -->
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+   <h3>Synchronization</h3>
-   <div class="span8">
+   <p align = "justify">We achieved low parameter dependence through an intelligent network design. The other requirement is that the oscillation of the colony is synchronized. The oscillations of different cells are linked because two of the components of our oscillatory network can freely diffuse out of the cells. Diffusion is something that occurs very rapidly at the scale relevant for bacteria. It distributes the molecules almost evenly throughout the colony, at least as long as most partake in the production of these colony-wide molecules. This results in colony-wide oscillations of those molecules. Consequently, this is a very effective means of synchronizing a population. Using two colony-wide molecules that (indirectly) repress each other’s production allows the oscillation of a broader spectrum of colony densities. When there are more cells per volume the perceived production rate of the colony-wide molecules also increases. The reciprocal (indirect) repression of the two colony-wide molecules helps to cancel this effect and equalizes the oscillations for a larger amount of cell densities.<br/>
-    <h3>Basic mechanism</h3>
+By studying the possibilities for colony-wide transcription factors, we found quorum-sensing molecules as good candidates, since the ones we encountered serve as transcription factors (combined with intracellular receptors) and can passively diffuse out of the cells (Fugua, Winans and Greenberg, 1994). Quorum-sensing molecules are produced by enzymes, which is thoroughly discussed on the <a href="https://2013.igem.org/Team:KU_Leuven/Project/Oscillator/wetlab">oscillator wetlab page</a> and the extra enzyme step alters the equation as is discussed on the <a href="https://2013.igem.org/Team:KU_Leuven/Project/Oscillator/modelling">modelling page</a>. Danino et al. (2010) also opted for a quorum-sensing molecule for their synchronized oscillator, but they used only one. Our model would use 2 (displayed as A and B), to allow a broader range of colony densities.</p>
-    <p align="justify">When there is a high level of A, this induces the production of both X and C, of which the latter will repress A and induce B. The production of C will not stop, even after A has disappeared below its threshold, since there is still X present that induces C. This effect creates an extended repression of A, in order to make sure the level of A drops sufficiently, so there is no production of X and C while the other halve of the system is active. This extended period in which C is present, also induces the production of B and the same story can be told for this halve. This means there are sequential peaks in the different components, which means this is an oscillating system.<br/>
-However, we aren’t satisfied yet with only this. Our ultimate goal is to provide synchronized oscillations throughout the colony with a low parameter dependence. In order to describe this system we will first explain the importance of the prolonged expression of C (or D). Second, we will describe how this system attains synchronization and rapid resynchronization and lastly we will discuss the other parameter dependencies. </p>
-   </div>
-   <div class="span4 greytext">
-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid colors"/>
-    <p>Figure xǀ Text</p>
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-  </div>
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-<!-- Prolonged production. -->
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+   <h3>Filling in the dots</h3>
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+    <p align = "justify">For biologist the most interesting part is most likely giving a name to the transcription factors. The primary requirement would be that their biological interactions are according to the network displayed in Figure 3. For example in our wetlab attempts we used the transcription factor araC (biobrick C0080) to be TF X, which had a promoter (R0078) inducible by a quorum-sensing molecule. For more details and practical implications we refer you to the <a href="https://2013.igem.org/Team:KU_Leuven/Project/Oscillator/wetlab">oscillator wetlab page</a>.</p>
-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid milking"/>
-    <p>Figure xǀ Tekst.</p>
-    </div>
-   <div class="span8">
-    <a id="Prolonged production"></a>
-    <h3>Prolonged production</h3>
-    <p align="justify">As mentioned above, there is a prolonged production of C (D) after the disappearance of A (B). However, when there is A (B) present, the production of C (D) starts immediately. This means there’s an asymmetric time delay for the production of the repressing molecules. The network motif that exhibits this behavior is called a ‘coherent type 1 feed forward loop’ (C1-FFL) with an OR logical gate (Mangan and Alon, 2003), of which one is highlighted in 3. This extended period in which one of the colony-wide molecules is repressed and the other produced, helps to reduce the effect of cell-to-cell variability in the different parameters, which is a necessity in order to have a synchronized oscillation. Even if not all cells produce a sufficient amount of repressing molecules, the prolonged repression by the others still results in an effective reduction in the amount of that colony-wide molecule, and analogously also a rise in the concentration of the other.</p>
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-    <h3>Rapid resynchronization</h3>
-    <p align="justify">The synchronized oscillation is an inherent property of this system. Because of the small space-scale, the diffusion distributes the molecules almost evenly throughout the colony, as long as most partake in the production. This colony-wide concentration of the diffusible molecules ascertains the rapid resynchronization of subpopulations that do not follow the others. If for instance, the unsynchronized subpopulation produces the other colony-wide molecule, that concentration does not reach any significant level because of the rapid diffusion at that scale. This can be explained by using an approximation of the diffusion coefficient of a typical quorum sensing molecule; The diffusion coefficient D of N-(3-Oxododecanoyl)-L-homoserine lactone equals 4.9 x 10<sup>2</sup> µm<sup>2</sup>s<sup>-1</sup>(Stewart, 2003). <b>The equation</b>  (Einstein, 1905) gives the average displacement of molecules because of diffusion in 3 dimensions after time t. In this example the average displacement after 1 second would be 54 µm, which is about equal to 50 times the size of one cell. This affirms the statement that the production of one cell is rapidly dispersed throughout its environment. Next, this also implies all cells have an approximately equal concentration, since the distance between cells in moderate density cultures is approximately 16 µm (= 2 x 10<sup>8</sup> cells/ml, Park et al., 2003). This distance corresponds with one third of the diffusion length after one second, if we assume the production is evenly distributed among the population. This colony-wide concentration holds the key to a rapid resynchronization as explained below. </p>
-   </div>
-   <div class="span4 greytext">
-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid colors"/>
-    <p>Figure xǀ Text</p>
-   </div>
-  </div>
- </div>
-</div>
-<!-- TITLE -->
 <div id="header" class="row-fluid">
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-   <h3>How we retain synchronization</h3>
+   <h3 class="bg-green">Coping with noise</h3>
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-<!-- Noise. -->
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   <div class="span12 white">
-  <div class="row-fluid">
+    <p align = "justify">A principal problem that goes hand in hand with colony synchronization, is the constant presence of noise. This noise is partitioned into two sources: intrinsic noise, which originates within the regarded subsystem and extrinsic noise, which originates outside of it. We will describe this specifically for gene expression since we built a transcription factor circuit with oscillating behaviour. The intrinsic noise is due to the stochastic effects involved in the reaction events leading to transcription and translation. This leads to fluctuations in timing and order of those events, even in cells that are in an equal state (equal nutritional status, place in the cell cycle, …). The extrinsic noise is for example due to differences in the number of RNA polymerase and ribosome molecules. Because they are gene products themselves, they are subject to their own intrinsic noise. Other factors that lead to extrinsic noise include the stage in the cell cycle, the quantity of the protein, the mRNA degradation machinery and the cell environment (Swain, Elowitz and Siggia, 2002). This substantial presence of noise has to be taken into account when developing a genetic circuit, either by suppressing it, or by building a network that is robust to it (Elowitz et al., 2002).<br/>
-    <div class="span4 greytext">
+The presence of noise affects our system in two ways. First it means the different cells in a colony are in a different state and exhibit a variance in their parameters.  Second it causes fractions of the colony to become unsynchronized. Both of these effects have been tested on the <a href="https://2013.igem.org/Team:KU_Leuven/Project/Oscillator/modelling">modelling page</a> and the results show our designed network resists this very well. In the rest of this text we will discuss how the use of diffusible molecules and the shape of our network achieve the different requirements posed to an oscillator.</p>
-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid milking"/>
-    <p>Figure xǀ Tekst.</p>
-   </div>
-   <div class="span8">
-    <h3>Coping with noise</h3>
-    <p align="justify">A principal problem that goes hand in hand with colony synchronization, is the constant presence of noise. This noise is partitioned into two sources: intrinsic noise, which originates within the regarded subsystem and extrinsic noise, which originates outside of it. We will describe this specifically for gene expression since we’ll build a genetic circuit with oscillating behavior. The intrinsic noise is due to the stochastic effects involved in the reaction events leading to transcription and translation. This leads to fluctuations in timing and order of those events, even in cells that are in an equal state. The extrinsic noise is for example due to a difference in the number of RNA polymerases and ribosomes and because they are gene products themselves are thus subject to their own intrinsic noise. Other factors that lead to extrinsic noise include the stage in the cell cycle, the quantity of the protein, the mRNA degradation machinery and the cell environment (Swain, Elowitz and Siggia, 2002). This substantial presence of noise has to be taken into account when developing a genetic circuit, either by suppressing it, or by building a network that is robust to it (Elowitz et al., 2002).</p>
-   </div>
-  </div>
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-<!-- Getting back in sync -->
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+  <h3>Coherent type 1 feed forward loop</h3>
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-    <h3>Getting back in sync</h3>
+   <p align = "justify">As mentioned above, there is a prolonged production of TF C (D) after the disappearance of TF A (B). However, when there is TF A (B) present, the production of repressor TF C (D) starts immediately. This means there’s an asymmetric time delay for the production of the repressing molecules. The network motif that exhibits this behaviour is called a ‘coherent type 1 feed forward loop’ (C1-FFL) with an OR logical gate (Mangan and Alon, 2003), one of which is highlighted in Figure 4. This extended period in which one of the colony-wide molecules is repressed and the other produced, helps to reduce the effect of cell-to-cell variability in the different parameters, which is a necessity in order to have a synchronized oscillation. Even if not all cells produce a sufficient amount of repressing molecules, the prolonged repression by the others still results in an effective reduction in the amount of that colony-wide molecule, and analogously also a rise in the concentration of the other. The prolonged production of TF C, and similarly TF D, ascertains that the switching event they are responsible for is fully executed.</p>
-    <p align="justify">The most important impact of noise on the occurrence of synchronized oscillations is the fact that at any time, a proportion of the cells may oscillate in a different phase. It is consequently imperative that our model has rapid resynchronization as a feature. Otherwise this would lead to a netto constitutive expression from the colony perspective.<br/>
-If, by random occurrence, a certain amount of cells have an excess amount of non-diffusible molecules, as for instance one of the repressors, they will produce the colony-wide molecules at a different rate. The next switch in production, however, occurs for all of the cells approximately at the same time and serves as a resynchronization event. This can be explained because it is the colony-wide molecule that is being produced by the majority that first reaches the threshold needed to switch to the production of the other colony-wide molecule in all of the cells. Since the cells that were out of sync had not yet stopped producing that other molecule, they are resynchronized with the majority. This has to be seen in relation with the asymmetric time delay, which prolong the production of molecules that execute the switching events, ascertaining that it does happen.</p>
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-   <div class="span4 greytext">
-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid colors"/>
-    <p>Figure xǀ Text</p>
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-<!-- An example -->
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-    <h3><br/></h3>
+     <img src="#" alt="C1FFL">
-     <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid milking"/>
+     <p align="justify">Figure 4 | Logical circuit displaying our oscillator, with one C1 FFL highlighted in green</p>
-     <p>Figure xǀ Tekst.</p>
     </div>
-   <div class="span8">
-    <h3>An example</h3>
-    <p align="justify">Figure x shows an example of this principle. These images have been created by solving a partial differential equation, in which 40% of the cells have initially a quadruple amount of one of the repressors and a quarter of the others, in respect to the other 60% of the cells. 2 a and b show the spatial-temporal oscillations of respectively a colony-wide molecule, like A, (2 a) and a non-permeable molecule, like C (2 b). 2 a displays the above mentioned nearly uniform concentration of diffusible molecules. Even though close to half of the population behaves differently, they show a rapid resynchronization. 2 c and d display the production rates of the colony-wide molecules and of the molecules that each repress one and induce the other colony-wide molecule in the two different kind of cells. 2 c displays this for a cell belonging to the majority and 2 d for the other 40%.<br/>
-They show only small differences between the production rates of the non-permeable molecules (red and yellow) and the switches in production happen at the same time. This is because those are controlled by the concentration of colony-wide molecules, which are approximately uniformly distributed. The production of the colony-wide molecules (blue and cyan) show a big difference during the first oscillations, but those differences rapidly disappear, until after the second oscillation there is no significant difference anymore and resynchronization is a fact.</p>
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-  <h3>Recapitulation</h3>
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-</div>
-<!-- Why an oscillator? -->
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+   <h3>A small desynchronized fraction of the cells cannot distort the oscillations</h3>
-   <div class="span8">
+   <p align = "justify">At the small space-scale that is relevant to bacteria, diffusion rapidly spreads out molecules throughout the colony. If for instance, the unsynchronized subpopulation produces the other colony-wide molecule, that concentration does not reach any significant level because of the rapid diffusion at that scale. This can be explained by using an approximation of the diffusion coefficient of a typical quorum sensing molecule; D(N-(3-Oxododecanoyl)-L-homoserine lactone) equals 4.9 * 10<sup>2</sup> µm<sup>2</sup>s<sup>-1</sup> (Stewart, 2003). The equation  (Einstein, 1905) gives the average displacement of molecules because of diffusion in 3 dimensions after time t. In this example the average displacement after 1 second would be 54 µm, which is about equal to 50 times the size of one cell. This supports our claim that the pheromone production of one cell is rapidly dispersed throughout its environment and that only larger fractions of the colony can control the level of colony-wide molecules. </p>
-    <h3>Low parameter dependence</h3>
-    <p align="justify">In the above we already mentioned all of the reasons why a low parameter dependence is a necessity. Here we will first run through those once more. First of all this is a necessity in order to accomplish our goal of having a synchronized oscillating system that does not depend heavily on the components (promoters and transcription factors). This definitely demands the lowest amount of parameter dependence, but it is also the least crucial part of our model. Secondly this is important in the respect of the principle of synthetic biology. Building new life requires well defined modules which can be used together in order to create a new function. This means that in a cell that has our oscillator inside of it, other modules will be used at the same time. In our case, for example, we would couple it to a β-farnesene producing module. However, since we are working with a highly complex internal metabolism of the cell, those modules will interact and influence each other’s behavior. This means our model should still produce oscillations despite of those interactions, and thus not change its behavior when the parameters are slightly altered. Lastly a low parameter dependence also means a low dependence on the cell densities, which has been a problem encountered by Danino et al. (2010).</p>
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-   <div class="span4 greytext">
-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid colors"/>
-    <p>Figure xǀ Text</p>
-   </div>
-  </div>
   </div>
 </div>
-<!-- Staying synchronized -->
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+   <h3>The colony-wide concentration of some transcription factors benefits rapid resynchronization</h3>
-   <div class="span4 greytext">
+   <p align = "justify">The distance between cells in moderate density cultures is approximately 16 µm (= 2*10<sup>8</sup> cells/ml, Park et al., 2003) or one third of the diffusion length after one second. This implies that all cells experience an approximately equal concentration of diffusible molecules.  If, by random occurrence, a certain amount of cells have an excess amount of non-diffusible molecules, as for instance one of the repressors, they will produce the colony-wide molecules at a different rate. The next switch in production, however, occurs for all cells approximately at the same time and serves as a resynchronization event. This can be explained because it is the colony-wide molecule that is being produced by the majority that first reaches the threshold needed to switch to the production of the other colony-wide molecule in all of the cells. Since the cells that were out of sync had not yet stopped producing that other molecule, they are resynchronized with the majority. This has to be seen in relation with the extended production of TF C, and TF D, responsible for the switching events.</p>
-    <h3><br/></h3>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid milking"/>
-    <p>Figure xǀ An ant 'milks' an aphid for his honeydew.</p>
-   </div>
-   <div class="span8">
-    <h3>Staying synchronized</h3>
-    <p align="justify">In the above we already showed why our model oscillates inherently and that shows that the system should not depend too heavily on differences in parameters. This is something that has been tested on the modeling page. We will also further elaborate on another aspect of parameter dependencies, namely the effect of cell-to-cell variability which means each of the cells will have slightly different parameters, even though they are genetically identical. This arises due to stochastic effects and our system makes the entire colony oscillate in sync despite this fact. We have already discussed that our system can withstand this thanks to the <a href="#Prolonged production"> asymmetric time-delays</a>. We will now also highlight several other features that counter this effect. The cell-to-cell variability in for instance the thresholds is partly compensated because of the fact that, even though some cells have already reached the threshold for repression, the production of colony-wide molecules does not instantaneously drop. This inherent delay in transcription networks helps to cancel out fluctuations in the height of the threshold. Fluctuations in the production of the colony-wide molecules are canceled out because of the rapid dispersion. Next, the production of the non-diffusible molecules is also subject to fluctuations. However since they are produced over an extended period of time, because of the asymmetric time delay, fluctuations are at least partially canceled out over time. </p>
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-  <h3>Further elaboration</h3>
- </div>
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-<!-- Tekst -->
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-    <p align="justify">This theoretical work was a lot of fun to develop and is further extended on the <a href= "https://2013.igem.org/Team:KU_Leuven/Project/Oscillator/modeling">modelling page about the subject</a>, where we study  each of the above mentioned features. On top of that we also begun the work of bringing it in to cells. Bringing the entire model into a living cell poses some problems however, of which the most important one is the required time for the many cloning steps. We do foresee that in the future this will become easier, when the field of synthetic biology gains importance. We chose to focus on a crucial part of the oscillator in the wetlab, since it serves as a useful network motif by itself and it can help other teams in further developing this oscillator. The transcriptional network motif we are making a biobrick of is a coherent type 1 feed forward loop which uses a quorum sensing molecule as the first transcription factor. The oscillator envelops this network motif twice, of which one is highlighted in green in figure x. The reason we have chosen this natural occurring network motif is because of its central role in our proposed oscillator model, as well as in many other natural systems (Mangan and Alon, 2003). For the implementation, we refer you to the <a href= "https://2013.igem.org/Team:KU_Leuven/Project/Oscillator/wetlab" >wetlab page</a>.</p>
+   <p align = "justify">Figure 5 shows an extreme example of this principle. These images have been created by solving a partial differential equation (PDE) with matlab (provided by MathWorks). The initial conditions in this PDE are that 40% of the cells start with a 4-fold excess of TF C and a quarter of TF D, with respect to the other 60% of the cells. Figures 5a and 5b show the spatial-temporal oscillations of a colony-wide molecule, here TF A, (Figure 5a) and a non-permeable molecule, here TF C (Figure 5b), respectively. Even though the population behaves differently in the beginning, they show a rapid resynchronization. Figure 5 c and d display the production rates of the colony-wide molecules and of the molecules that each repress one and induce the other colony-wide molecule in the two different cell subtypes. Figure 5 c displays this for a cell belonging to the majority (60%) and Figure 5 d for a minority (40%) cell. </p>
+The model shows only small differences between the production rates of the non-diffusible molecules (red and yellow) while protein production switches occur simultaneously. This is because those are controlled by the concentration of colony-wide molecules, which are approximately uniformly distributed. In reality this will be a stronger effect, since we chose a much smaller diffusion coefficient (2 * 10<sup>1</sup> µm<sup>2</sup>s<sup>-1</sup> instead of 4.9 * 10<sup>2</sup> µm<sup>2</sup>s<sup>-1</sup>) in order to display the principles. The production of the colony-wide molecules (blue and cyan) show a big difference during the first oscillations, but those differences rapidly disappear; there is no significant difference anymore after the second oscillation and resynchronization is a fact. We also measured how the colony would react if cells would go “out of sync”: how quickly would the model reinstate colony-wide synchronization? We refer to the <a href="https://2013.igem.org/Team:KU_Leuven/Project/Oscillator/modelling"> modelling page</a> for details on these quantitative results and the algorithms used.
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+   <img src="#" alt="5.1>
-    <img src="https://static.igem.org/mediawiki/2013/0/09/KU_Leuven_team2.png" alt="Aphid colors"/>
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-    <p>Figure xǀ Text</p>
+   <img src="#" alt="5.3>
+   <img src="#" alt="5.4>
+   <p align="justify">Figure 5 | Graphical reproduction of the rapid resynchronization | a, The spatial-temporal fluctuations of a colony-wide molecule in a population in which 40% initially behaves differently. b, The concentration of one of the non-diffusible molecules in a population in which 40% initially behaves differently. c, The evolution over time of the production rate of several molecules in a cell belonging to the majority of the population. d, The evolution over time of the production rate of several molecules in a cell belonging to the minority of the population.</p>
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-    <p align="justify">Alon, U. (2006). An introduction to systems biology: design principles of biological circuits. CRC Press, 301.<br/>
-Danino, T. et al. (2010). A synchronized quorum of genetic clocks. Nature, 463:326-330.<br/>
-De Vos, M., et al. (2010). Alarm pheromone habituation in Myzus persicae has fitness consequences and causes extensive gene expression changes. PNAS, 107: 14673-14678
-Einstein, A. (1905). On the movement of small particles suspended in stationary liquids required by the molecular-kinetic theory of heat. Annalen der Physik 17:549-560.<br/>
-Elowitz, M. B., and Leibler, S. (2000). A synthetic oscillatory network of transcriptional regulators. Nature, 403(6767):335-338.<br/>
-Elowitz, M. B. et al. (2002). Stochastic gene expression in a single cell. Science, 297(5584):1183-1186.<br/>
-Fuqua, W. C., Winans, S. C., and Greenberg, E. P. (1994). Quorum sensing in Bacteria: the luxR-luxI family of cell density-responsive transcriptional regulators. J. Bacteriol, 176:269-275.<br/>
-Kunert, G., Reinhold, C. and Gershenzon, J. (2010). Constitutive emission of the aphid alarm pheromone, (E)-β-farnesene, from plants does not serve as a direct defense against aphids. BMC Ecology, 10:23.<br/>
-Mangan, S., and Alon, U. (2003). Structure and function of the feed-forward loop network motif. PNAS, 100:11980-11985.
-Park, S. et al. (2003). Motion to form a quorum. Science, 301:188.<br/>
-Shiue, E., and Prather, K. L. J. (2012). Synthetic biology devices as tools for metabolic engineering. Biochemical Engineering Journal, 65:82-89.<br/>
-Stewart, P. S. (2003). Diffusion in biofilms. Journal of Bacteriology, 185:1485-1491.<br/>
-Swain, P. S., Elowitz, M. B., and Siggia, E. D. (2002). Intrinsic and extrinsic contributions to stochasticity in gene expression. PNAS, 99:12795-12800.</p>
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