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Tokyo Tech 2011

1. The Hands
2. The Judges
3. The Randomizers

Rock-Paper-Scissors game

Introduction

The Hands

The first step towards making an RPS game that can be played between humans and bacteria is giving each player a set of signaling molecules through which they can communicate their choice of rock, paper or scissors. For that purpose we created two sets of three signaling molecules corresponding each to rock, paper or scissors. For humans we used IPTG, aTc and salicylate, respectively. For E. coli we used 3OC6-HSL, 3OC12-HSL and AI-2, respectively.

The Judges

Although we defined a set of six signaling molecules that can be used to play the RPS game, we still need to find a way to know who wins the game. To know who the winner of each game is, we designed a set of E. coli that act as judges. Because there were no working parts related to AI-2 or 3OC12-HSL, we constructed new working lasI promoter, lsrA promoter and LsrR coding gene.

The Randomizers

Although our set of six signaling molecules allows us to play RPS with E. coli, we must make sure E. coli can choose any of its three signaling molecules with the same probability in order to be able to play RPS fairly and properly. To do so, we designed three kinds of randomizers.

1. The Hands

The first step towards making an RPS game that can be played between humans and bacteria is giving each player a set of signaling molecules through which they can communicate their choice of rock, paper or scissors. For that purpose we created two sets of three signaling molecules corresponding each to rock, paper or scissors. For humans we used IPTG, aTc and salicylate, respectively. For E. coli we used 3OC6-HSL, 3OC12-HSL and AI-2, respectively.

2. The Judges

Although we defined a set of six signaling molecules that can be used to play the RPS game, we still need to find a way to know who wins the game. To know who the winner of each game is, we designed a set of E. coli that act as judges. Each Judge E. coli has an AND-gate promoter and a fluorescent protein gene that is expressed when the AND-gate promoter is activated. In this way, the Judge E. coli can let us know its decision by producing GFP, RFP or CFP to indicate whether humans win, lose or it is a tie, respectively.

2.1 Using AND-Gate promoters to create Judges

The first step to make the Judge E. coli was to find a logic device which could allow the Judge to decide who the winner of the RPS game was. We found that the AND-gate promoters would fit perfectly for that purpose, since they can take two signaling molecules as inputs and produce one indicator as output. Since each of the players has a set of three different signaling molecules, we need a set of nine Judges, each of which has an AND-gate promoter that is activated only by one of the nine possible pairs of signaling molecules. These combinations are shown in the image below.

Our next mission was then to check if there were AND-gate promoters BioBricks that we could use. We searched in the Registry and found a potential AND-gate promoter designed by iGEM 2007's team Tokyo_Tech. This potential AND-gate promoter is designed to be activated by the addition of both IPTG and 3OC6-HSL. However, there was no data showing the IPTG dependency of this promoter, so we did experiments and confirmed this dependency for the first time in iGEM. We concluded that the addition of both IPTG and 3OC6-HSL regulates the activity of this AND-gate promoter. In this way, we completed the construction of one of the Judges E. coli, which proves in principle that our game is feasible. To know the detailed method about this assay, please see here.

Fig. 2.1 Tokyo_Tech AND-gate promoter

This Plux-lac hybrid promoter contains two LacI operators, a LuxR operator and luxR. We introduced this part into LacI expressing E. coli strain. Because IPTG controls the binding of LacI to two LacI-operator parts and 3OC6-HSL controls the binding of LuxR to a LuxR-operator part, the gfp gene activity of the reporter part is dually regulated by IPTG and 3OC6-HSL. We used promoterless pSB3K3-gfp (BBa_J54103) as a negative control, and pAC-Pλ-gfp (chloramphenicol-resistance), which constitutively expressed GFP, as a positive control. To know about the mechanism of this promoter click here.

2.2 Creating Parts that responded correctly to our set of Signaling Molecules

In the process of constructing enough AND-gates that could suffice the needs of our RPS game design, we discovered two faulty BioBricks: lsrA promoter (BBa_K117002) and las promoter (BBa_J64010). Because of these faulty parts, the Judge E. coli set we had designed could only sense the Player E. coli's signaling molecule 3OC6-HSL (Rock). This ultimately led to an unfair game because humans could win every time they played with the Paper signaling molecule (for more on the “Sad story of the Rock Player” click here).

To fix this problem, we improved the old defective las and lsrA promoters parts by making new parts that work! As can be seen in the experimental information below (see “Improving lsrA promoter” and “Improving las promoter”), we confirmed our lasI promoter (BBa_K649000) and lsrA promoter (BBa_K649100) work perfectly!

Since the lsrA promoter plays a key role in the correct functioning of AI-2, fixing these parts now allows us to use AI-2 as a signaling molecule, which is a promising advance because of the characteristics of the AI-2 mechanism. This mechanism prevents AI-2 from cross-talking with other signaling molecules such as AHL. Hence, this signaling molecule is a very powerful tool to build complex Synthetic Biology systems.

Finally, one thing we would like outline is that although the promoters we made are single input promoters, confirmation of their activity is required as a reference to construct AND gate promoters. Therefore, we solved important issues and made significant advances towards constructing AND-gate promoters. This allows E. coli to also choose the signaling molecules corresponding to Paper and Scissors, so we have again a working RPS game design.

2.3 Improving PlsrA

Fig. 2.2 Not working lsrA promoter(BBa_K117002)
activity and our new lsrA promoter(BBa_K649104) activity

We confirmed that the lsrA promoter (BBa_K117002) does not work properly (samples used our experiment are listed in Table 2.1 below). The fluorescence intensity of GFP of lsrA promoter-gfp((BBa_K117002)-gfp) was lower even than those of the negative control (Fig. 2.2), which clearly shows that lsrA promoter((BBa_K117002) does not work as expected. In this experiment, we measured transcriptional activity of lsrA promoter by introducing a gfp gene downstream of this promoter (Fig. 2.3).

Table 2.1 Samples used our experiment
Name	Strain	Plasmid
sample1	JD22597	Ptet-gfp on pSB1A2
sample2		Promoterless-gfp on pSB6A1
sample3		PlsrA-gfp on pSB1A2 (BBa_K649104)
sample4		PlsrA-gfp on pSB1A2 ((BBa_K117002)-gfp)

Fig. 2.3 lsrA promoter-gfp((BBa_K117002)-gfp)

To solve this problem, we created the first working iGEM lsrA promoter (BBa_K649100). Its fluorescence intensity was much higher than that from a promoter-less gfp negative control plasmid, showing that our new lsrA promoter works(Fig. 2.5). In this experiment, we measured the transcriptional activity of our lsrA promoter by introducing a gfp gene downstream of the promoter(BBa_K649104, Fig. 2.4). Details about this experiment can be found here.

Fig. 2.4 lsrA promoter-gfp(BBa_K649104)

Fig. 2.5 LsrR represses lsrA promoter.

Moreover, this promoter can be repressed by our new LsrR part(BBa_K649105). (samples used our experiments are listed in Table 2.2 below) The fluorescence intensity of GFP of sample 3 was three times as large as that of sample 4. This result shows that LsrR successfully repressed lsrA promoter. In this experiment, we measured LsrR repression activity by introducing a gfp gene downstream of lsrA promoter ((BBa_K649105, Fig. 2.6). Details about this experiment can be found here.

Table2.2 Samples used our experiment
Name	Strain	Plasmid
sample1	JM2.300	Ptet-gfp on pSB6A1
sample2	JM2.300	Promoterless-gfp on pSB3K3
sample3	MG1655	PlsrA-gfp on pSB3K3
sample4	MG1655	PlsrA-gfp-PlsrR-lsrR on pSB3K3

Fig. 2.6 lsrA promoter-gfp-lsrR promoter-lsrR(BBa_K649105)

2.4 Improving las promoter

Fig. 2.7 (a)

(b)

Fig. 2.7 (a): Not working lasI promoter (BBa_J64010). Fig. 2.7 (b): New working lasI promoter (BBa_K649000) we made. We confirmed it works as expected. In our assay, we used the same LasR regulator part used in the assay of BBa_ J64010. Clearly, for our part the fluorescence intensity of 3OC12-HSL+ was higher than that of 3OC12-HSL-.
To know detailed methods about these lasI promoter assay, please see here, previous part and new part.

To prove that the LasR regulator used in our PlasI assay works, we did another assay. Details about this assay can be found here.

3. The Randomizers

Although our set of six signaling molecules allows us to play RPS with E. coli, we must make sure E. coli can choose any of its three signaling molecules with the same probability in order to be able to play RPS fairly and properly. To do so, we designed three kinds of randomizers: one kind which needs of three types of bacteria (each of which produces one of the three RPS signaling molecules), and the other kind that needs of only one type of bacteria which can synthetize each of the three signaling molecules one at a time and randomly. Namely, the randomizers are Single Colony Isolation, Survival of one Strain and Conditional Knockout by Recombination.

3.1 Single Colony Isolation

This is our simplest randomizer design. To make sure E. coli chooses any of its signaling molecules with equal probability, we put the constructs for each molecule inside a different bacterium, so we create three types of bacteria: one synthetizing the corresponding signaling molecule for rock, other synthetizing the corresponding signaling molecule for paper, and lastly one synthetizing the corresponding signaling molecule for scissors. By randomly isolating a single colony out of the many colonies that result from the mixing between the three types of E. coli, we get a random output as E. coli's choice for the RPS game.

3.2 Conditional Knockout by Recombination

Our second randomizer differs from our other two randomizers in that all the three signaling molecules are produced one at a time and randomly by only one type of bacteria. We were inspired by a paper about “brainbow” research on mice to create this randomizer (Livet J et al., 2007), which is based on the recombination mechanism of the enzyme Cre and the lox sequences. We designed a Cre-Lox system which allows E. coli to express one of its three signaling molecules by means of conditional knockout. The design is depicted in Fig. 1. It should be noted this randomizer is designed to be used at a single-cell level. When this randomizer is used in groups of cells, the different signals released by the cells will mix. In this case, by using microfluidic devices or isolating single colony of bacteria, we can obtain only one of the signaling molecules produced by the initial group of cells.

Fig. 3.1 - (a) Cre recombinase construction. (b) lox cassettes distribution for the randomizer design

3.2.1 The Requirements

Basically, each pair of lox sites (indicated by the same color) mark the points which the enzyme Cre will excise (they will be cut off the backbone along with the sequence between them). For a design that allows choosing randomly one of E. coli’s three signaling molecules, at least two cassettes of lox sites are needed. When these two cassettes of lox sites and protein coding sequences are arranged as in Fig. 3.1(b), only one signaling molecule is produced.

Our design also required a way to control luxI gene's expression. To do so, we used an inducible promoter instead of a constitutive promoter. A constitutive promoter would have caused luxI gene to be expressed beforehand and could lead to an E. coli producing two signaling molecules at the same time (the equivalent of showing two hands in the RPS game). In contrast, the inducible promoter prevents a particular gene from expressing preferentially.

One last but not less important requirement for our randomizer is that it should express each of the three signals not only one at a time, but also with the same probability. This makes the game fair in the sense that E. coli’s choice in the RPS game is not predictable.

3.2.2 The Mechanism

When the blue cassette of Lox sites is excised (Fig. 3.1), the signaling molecule coded by lasI (3OC6-HSL) will be produced. Likewise, when the black Lox cassette is excised, the signaling molecule coded by luxS (AI-2) will be produced. On the other hand, a third possible outcome is that recombination does not take place. In this case, the signaling molecule coded by luxI (3OC6-HSL) will be produced. Also note that excision of one kind of lox cassette removes the remaining cassette, thereby preventing further recombination.

As mentioned before, one of the requirements for our randomizer was to have at least two lox cassettes. This prevents excision of lox sites from different cassettes (for example one blue lox site and one black lox site). Because the lox71-lox66 cassette and the lox2272-lox2272 cassette are incompatible (Zorana Carter and Daniela Delneri et al., Yeast 2010), we can use them to build our randomizer.

3.2.3 Testing the Lox Cassettes

As stated above, we need two lox cassettes of different recombination frequency for randomizer. Because there was no working lox parts in registry, we constructed three original BioBricks for testing whether lox2272 and lox71/66 cassettes work. For the convenience of testing, fluorescence expressing genes were used in place of signal molecular expressing genes in construction. After figuring out their working in vitro, we tested them in vivo by detecting red and green fluorescence through fluoro imager and flow cytometer. Furthermore, we compared the relative recombination frequency of two cassettes . Our lox Cassettes constructions were working properly, and their recombination frequency were different from each other.

PlacIQ-lox2272-gfp-lox2272(BBa_K649200)
PlacIQ-lox2272-rfp-lox2272-gfp(BBa_K649201)
PlacIQ-lox71-rfp-lox66-gfp(BBa_K649202)

The in vitro assay with K649200 was made in advance. The preliminary experiment allowed us to confirm that the Cre-mediated recombination on lox2272 cassette works as designed. In the assay, Cre recombinase was added to the linear DNA and incubated for 0.5, 2, and 4 hours. Images of the experiments have been added below.

When checking the result by electrophoresis, there were several bands in samples to which Cre was added(1st, 2nd lane from right which corresponds to 4 hr and 2 hr respectively). It indicates that excision of the lox sites successfully occurred. To know detailed about this assay, please see here, in vitro assay for lox2272

For the in vivo assay, by detecting fluorescenc levels of GFP and mCherry, we could determine whether recombination occured in K649201 and K649202 and compare relative recombination frequency between two of them. We prepared a competent cell JM2.300 into which P_BAD/araC-Cre(pSB1A2, BBa_I718008) had been constructed. Subsequently, our BioBrick was constructed into the cell.

sample		arabinose
1	PlacIQ-lox-rfp-lox-gfp(pSB3K3) P_BAD/araC-Cre(pSB1A2)	+
2	PlacIQ-lox-rfp-lox-gfp(pSB3K3) P_BAD/araC-Cre(pSB1A2)	-
3	PlacIQ-lox-rfp-lox-gfp(pSB3K3) : negative control	+

The strain was grown in a 3 mL liquid culture, and 75 µL of 2 M arabinose was added to induce Cre expression. We used two controls for the experiment. One was the same strain without arabinose induction, and the other was JM2.300 strain which was induced by arabinose and had only our BioBrick. All the strains were cultured each for periods of 0.5, 1, 2, and 4 hours, and in each case the florescence levels were measured by flow cytometer and FLA. To know the detailed method about this assay, please see here in vivo assay for lox cassettes.

We confirmed our results optically by taking florescence images. K649201 transformants with with 0.5 hr-induction of Cre in liquid medium and its two control strains were plated and incubated in 37°C for 12 hours. Images of the three conditions were taken using red florescence filter, green florescence filter and no filter as shown below, respectively.

	(a)
	(b)
	(c)

Fig. 3.2 Cre-meditated recombination at lox2272 cassette. Cre-induction period of 0.5 hr (a)Overlay of Green and Red channel. The leftmost is a negative control which don't have Cre-expressing plasmid. The center is an arabinose induced sample which has both Cre plasmid and BioBrick K649201. The rightmost is a uninduced strain which has both plasmid like as the center. (b)Detection of GFP. The order of samples is same as above. (c)Detection of mCherry. The order of samples is same as above.

On the sample with the P_BAD/araC-Cre construction, we found that recombination occurred when arabinose was added. In contrast to this result, when we measured the levels of the sample without the P_BAD/araC-Cre construction, we found that the GFP levels were far lower than those of the sample with the P_BAD/araC-Cre construction. This clearly proves that our lox constructions, both in K649201 and K649202, respond correctly to the effects of Cre recombinase. A slight detection of green florescence in plate absence of P_BAD/araC-Cre can be explained that there happened cross-talk to green channel by FMN(Flavin mononucleotide) or expression of GFP according to malfunction of terminator before gfp. We could also observe recombination occurred when arabinose was not added, which can be explained due to a leaking in the P_BAD/araC promoter.You can find that K649202 also works well from the images of K649202 on here.

Furthermore, we could observe that the arabinose(+) sample of K649202 has higher green/red ratio than that of K649201, which implying the frequency of lox71/66 casette is higher than that of lox2272.

Fig. 3.3 Image of six samples of K649201 (up) and K649202 (down) at period of 0.5 hr


(a)	(b)
	Fig. 3.4 identical plates with Fig. 3.3 (a)expression levels of red and green florescence of K649201 (b)expression levels of red and green florescence of K649202 (c)examined area for comparing between red and green florescence at each plate
(c)

As we examining green florescence in comparison to red florescence, green expression level was lower than red in K649201(Fig. 3.4(a)), which meaning that considerable plasmids in those cells yet. In contrast, green expression level exceeded red in K649202(Fig. 3.4(b)). This result implies that recombination frequency of lox71/66 cassette is relatively high than that of lox2272 cassette.

Fig. 3.5 Green fluorescence level of each cell was detected by flow cytometer.
(a)arabinose induced strain containing only K649201 and cre-expressing plasmid (b)arabinose supplied strain containing only K649201 (c)arabinose induced starin containing K649202 and cre-expressing plasmid (d)arabinose supplied strain containing only K649202

The higher recombination efficiency of lox71/66 compare to lox2272 was confirmed also by flow cytometer intensity of lox71/66 was higher than that of lox2272, which supports the result detected by FLA.

3.2.4 Playing Fair: Future Work

To make each of the outcomes (R, P, and S) equally probable, we are going to quantify the recombination frequency of each lox cassette. This information and adequate Cre induction will be likely to allow us to have an RPS player E. coli whose choice of either of rock, paper or scissors cannot be predicted.

In our next experiments, we are going to vary the reaction time and the distance between the lox sites of each cassette. We believe precise modification of this two parameters must lead to our goal of making a randomizer in which each of the signaling molecules can be expressed with the same frequency (which results in each of the outcomes being expressed with the same probability).

3.3 Survival of One strain

3.3.1 Introduction: Very small differences determine who will survive

In this section we will show a shocking scenario of evolution: the future of each of three different rival strains (whether the strain will die or survive) is marked by very small differences between the initial population densities of the strains (a phenomenon also known as the “butterfly effect”). Furthermore, we will also show that we can apply this very interesting result to create a randomizer that can be used in our Rock-Paper-Scissors game, due to the fact that only one of the rival strains will survive. More specifically, we assign to each of the three rival strains either of Rock, Paper or Scissors, make them compete for survival and take the surviving strain to represent the bacteria's choice for the RPS game.

3.3.2 Adjusting the Model to create a True Randomizer

The idea for creating this randomizer was born from a paper written in 1996 by Durrett and Levin. In it, the authors described a system of three types of bacteria that competed for survival in dynamic that resembled a Rock-Paper-Scissors (RPS) game. However, the model proposed in this paper is not fully appropriate for our RPS randomizer, since one of the three types of bacteria cannot ultimately survive (although it can dominate the system, i.e. have the highest population density, for definite periods of time). We will discuss more on the limitations we found in this model to be adopted as a randomizer and the modifications we made to create a true randomizer.

3.3.3 How the Three Types of Bacteria Compete for Survival

The three types of bacteria that compete for survival use three tactics to outcompete their rivals: the production of a toxin (a bacteriocin called colicin) that is toxic to other strains, resistance to the toxin produced by other strains, and a higher birth rate than their rival strains. Namely, the three types of bacteria are: colicin-producing E. coli (R), colicin-resistant E. coli (P) and colicin-sensitive E. coli (S). The colicin-producer outcompetes the colicin-sensitive by producing the colicin. The colicin-sensitive bacteria outcompetes the colicin-resistant because its birth rate is higher than that of the colicin-resistant. The colicin-resistant outcompetes the colicin producer because its birth rate is higher than that of the colicin producer. The colicin resistant bacteria are also able to produce colicin, but at a lower energetic cost, which allows them to have a higher birth rate.

The system was described by the following general differential equations

Where

3.3.4 The Old Model

In the model described by Durrett and Levin’s paper the equations were as follows:

Producer

Resistant

Sensitive

These equations show that the colicin-resistant bacteria are completely immune to colicin (there is not death factor associated to colicin in the equation for du₂/dt). However, as will be explained afterwards, this results in a loss of balance that does not allow building a true randomizing system.

Now, setting the parameters as follows, the graph below was created by Durrett and Levin.

3.3.5 Our New Model

As mentioned before, the model proposed by Durrett and Levin has critical limitations as a randomizer for the RPS game. To be able to create a true randomizer, we modified the differential equations of the model taking care to give it a biological meaning. With our new differential equations, any of the three types of bacteria can ultimately survive by outcompeting the other two strains, which will die. More specifically, we limited the resistance of the colicin-resistant bacteria in the sense that it would produce a type of bacteriocin that is only toxic to itself and to the sensitive strain, and additionally the resistant strain would also be vulnerable to the colicin produced by the colicin-producer. Since which strain will be the one that survives is determined by very small differences in the initial concentrations of the three different populations of bacteria, in practice this systems becomes a randomizer because of the imprecisions in the measurements that result, for example, when using micropipettes. This randomizer describes a new competition dynamic that could not be reproduced in the previous model proposed by Durrett and Levin due to the instability along the axis.

If we set the parameters as follows

and we graph this equations using a Matlab program, we get a graph which clearly shows there are stable points on each of the three axes (Fig. 1, Up).

Fig. 1 Up: Our New model. Down: The Old Model

These stable points (u₁,0,0), (0,u₂,0) and (0,0,u₃) indicate that for the equations we have set all of the three strains may ultimately survive for infinite peiriods of time. The differences between our model and the model of Durrett and Levin can be seen graphically in Fig. 1. These graphs were plotted using Matlab.

Note that the parameters we have set for our equations satisfy the initail conditions of the model proposed by Durrett and Levin (indicated in black font) new terms

3.3.6 The Biological Meaning of our Model

From a biological perspective, our model describes the existence of two strains of bacteria that produce two different types of bacteriocins. One of these strains is not completely resistant to its own bacteriocin nor to the bacteriocin produced by its rival strain. This can be justified as the consequence of insufficient/ineffective resistance protein production by the “resistant” strain. This limitation in the production of resistance protein could be thought of as a consequence of the “resistant” strain being a mutant of a colicin-sensitive strain.

3.3.7 Making it Obvious

From the graph of our new model (Fig. 1, left) it can be deduced that there are paths that converge at stable points (u₁,0,0), (0,u₂,0) and (0,0,u₃), and that this paths all have an approximately common origin. In this section we would like to show that the origin of these paths is practically the same, and that in that sense we have designed a true randomizer (since, as mentioned before, the imprecisions that result in the experimental measurements will make it impossible to make the initial population density of the three strains the same).

In the following set of graphs we will make it obvious that each of the three different strains of E. coli to survive in a random fashion by very small differences on the initial concentrations of each strain.

We modeled our results using Matlab. As can be seen in the graphs below, each of the strains can survive if their initial density in only tree hundredths (a.u.) greater than the other two strains' initial concentrations.



	With these graphs it becomes clear that the imprecisions in experimental measurements (i.e. pipetting) are enough to cause the outcome of Rock, Paper or Scissors signaling molecule to be random. Consequently, we can conclude that this randomizer is not only feasible but also practical and effective (let alone interesting).

References

Patrick C. Seed et al. “Activation of the Pseudomonas aeruginosa lasI Gene by LasR and the Pseudomonas Autoinducer PAI: an Autoinduction Regulatory Hierarchy” JOURNAL OF BACTERIOLOGY (1995)
Shotaro Ayukawa et al. “Construction of a genetic AND gate under a new standard for assembly of genetic parts” BMC Genomics (2010)
Robert Sidney Cox, III et al. “Programming gene expression with combinatorial promoters” molecular system biology (2007)
Rolf Lutz et al. “Independent and tight regulation of transcriptional units in Escherichia coli via the LacR/O, the TetR/O and AraC/I1-I2 regulatory elements” Nucleic Acids Research (1997)
Karina B.Xavier and Bonnie L.Bassler 2004. Regulation of Uptake and Processing of the Quorum-Sensing Autoinducer AI2 in Escherichia coli. JOURNAL OF BACTERIOLOGY, Jan. 2005, p. 238-248
Ting Xue, Liping Zhao, Haipeng Sun, Xianxuan Zhou, Baolon Sun 2009. LsrR-binding site recognition and regulatory characteristics in Escherichia coli AI-2 quorum sensing. Cell Research (2009), p.1258-1268
Liang Wang, Yoshifumi Hashimoto, Chen-Yu Tsao, James J.Valdes, and William E.Bentley 2004. Cyclic AMP(cAMP) and cAMP Receptor Protein Influence both Synthesis and Uptake of Extracellular Autoinducer 2 in Escherichia coli. JOURNAL OF BACTERIOLOGY, Mar. 2005, p. 2066-2076
Jean Livet, Tamily A. Weissman, Hyuno Kang, Ryan W. Draft, Ju Lu, Robyn A. Bennis, Joshua R. Sanes and Jeff W. Lichtman (2007). Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system. Nature.
Kimi Araki, Masatake Araki1 and Ken-ichi Yamamura (2002). Site-directed integration of the cre gene mediated by Cre recombinase using a combination of mutant lox sites, Nucleic Acids Research
Durrett, R., Levin, S. Allelopathy in Spatially Distributed Populations (1997). Journal of Theoretical Biology, 185, 165-171.

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-		position: related;
+		text-indent: 2em;
-		text-indent: 0.5em;
 	}
@@ Line 235: / Line 219: @@
 		}
 	}
+	function getElementsByClass() {
+	    var classElements = new Array();
+	    var allElements = document.getElementsByTagName("*");
+	    for (i = 0 ; i < allElements.length; i++) {
+			if (allElements[i].className == 'firstHeading') {
+			    allElements[i].style.display = 'none';
+			   // window.alert('発見。');
+			}
+	    }
+	}
-		window.onload = function() {
+	window.onload = function() {
+		getElementsByClass();
 		var menu = window.document.getElementById('TopMenu');
 		if(menu==null)
@@ Line 269: / Line 265: @@
 <!-- top box -->
 <div class="top">
-	<img src="https://static.igem.org/mediawiki/2011/2/24/TokyoTech_TOPlogo.png" alt="Tokyo Tech 2011" /><br />
+	<object classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,0,0" width="965" height="150" id="Yourfilename" align="">
+		<param name="movie" value="https://static.igem.org/mediawiki/2011/4/4d/Header.swf">
+		<param name="quality" value="high">
+		<param name="bgcolor" value="#FFFFFF">
+		<embed src="https://static.igem.org/mediawiki/2011/4/4d/Header.swf" quality="high" bgcolor="#FFFFFF" width="965" height="150" name="Yourfilename" align="" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer">
+		</embed>
+	</object>
 	<!-- list of top menu -->
 	<div id="navigation">
@@ Line 276: / Line 278: @@
 			<li id="menu_Project">
-				Projects
+				Project
 				<ul>
-					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/index.htm">RPS-game</a></li>
+					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/index.htm">RPS-Game</a></li>
-					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/making-rain/index.htm">rain</a></li>
+					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/making-rain/index.htm">Make it Rain</a></li>
-					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/Urea-cooler/index.htm">urea cooler</a></li>
+					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/Urea-cooler/index.htm">Urea Coolers</a></li>
 				</ul>
 			</li>
@@ Line 289: / Line 291: @@
 				Modeling
 				<ul>
-					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Modeling/RPS-game/RPS-game">RPS-game</a></li>
+					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Modeling/RPS-game/RPS-game">RPS-Game</a></li>
+					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Modeling/Urea-cooler/urea-cooler">Urea Coolers</a></li>
-					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Modeling/Urea-cooler/urea-cooler">urea cooler</a></li>
 				</ul>
 			</li>
@@ Line 300: / Line 301: @@
 			<li id="menu_Extra">
-				Extra
+				More
-				<ul>
+				<ul style="width:210px;">
 					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Safety">Safety</a></li>
 					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Attribution_and_Contributions.htm">Attribution and Contributions</a></li>
 					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/notebook">NoteBook</a></li>
 					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/team">Team</a></li>
-					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Sponsers.htm">Sponsers</a></li>
+					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Sponsers.htm">Sponsors</a></li>
 					<li><a href="https://2011.igem.org/Team:Tokyo_Tech/Collaboration.htm">Collaboration</a></li>
 				</ul>
@@ Line 320: / Line 321: @@
 <!-- left menu list -->
-<div style="min-height: 5000px; float: left;">
+<div style="min-height: 20600px; float: left;">
 <div id="LeftMenu">
 	<!--list of page menu: DO NOT WRITE LINKS NOT WRITTEN IN THIS PAGE -->
 	<ul>
+		<li><a href="#1">1. The Hands</a></li>
 		<li>
-			<a href="#1.">1. The Human-Bacteria Rock, Paper and Scissors game</a>
+			<a href="#2">2. The Judges</a>
 			<ul>
-				<li><a href="#1.1">1.1 The Hands</a></li>
+				<li><a href="#2.1">2.1 Using AND-Gate promoters to create Judges</a></li>
+				<li><a href="#2.2">2.2 Creating Parts that responded correctly to our set of Signaling Molecules</a></li>
+				<li><a href="#2.3">2.3 Improving PlsrA</a></li>
+				<li><a href="#2.4">2.4 Improving Plas</a></li>
+			</ul>
+		</li>
+		<li>
+			<a href="#3">3. The Randomizers</a>
+			<ul>
+				<li><a href="#3.1">3.1 Single Colony Isolation</a></li>
 				<li>
-					<a href="#1.2">1.2 The Judge</a>
+					<a href="#3.2">3.2 Conditional Knockout by Recombination</a>
 					<ul>
-						<li><a href="#1.2.1">1.2.1 Creating New Parts</a></li>
+						<li><a href="#3.2.1">3.2.1 The Requirements</a></li>
-						<li>
+						<li><a href="#3.2.2">3.2.2 The Mechanism</a></li>
-							<a href="#1.2.2">1.2.2 The Design</a>
+						<li><a href="#3.2.3">3.2.3 Testing the <i>Lox</i> Cassettes</a></li>
-							<ul>
+						<li><a href="#3.2.4">3.2.4 Playing Fair: Future Work</a></li>
-								<li><a href="#1.2.1.1">1.2.1.1</a></li>
-								<li><a href="#1.2.1.2">1.2.1.2</a></li>
-								<li>
-									<a href="#1.2.1.3">1.2.1.3</a>
-									<ul>
-										<li><a href="#1.2.1.3.1">1.2.1.3.1 Our new LsrR part</a></li>
-										<li><a href="#1.2.1.3.2">1.2.1.3.2 The AI-2 Mechanism</a></li>
-									</ul>
-								</li>
-							</ul>
-						</li>
 					</ul>
 				</li>
 				<li>
-					<a href="#1.3">1.3 The Randomizers</a>
+					<a href="#3.3">3.3 Survival of one strain</a>
 					<ul>
-						<li>
+						<li><a href="#3.3.1">3.3.1 Introduction: Very small differences determine who will survive</a></li>
-							<a href="#1.3.1">1.3.1 Three Randomizers</a>
+						<li><a href="#3.3.2">3.3.2 Adjusting the Model to create a True Randomizer</a></li>
-							<ul>
+						<li><a href="#3.3.3">3.3.3 How the Three Types of Bacteria Compete for Survival</a></li>
-								<li><a href="#1.3.1.1">1.3.1.1 Single Colony Isolation</a></li>
+						<li><a href="#3.3.4">3.3.4 The Old Model</a></li>
-								<li><a href="#1.3.1.2">1.3.1.2 survival of the Fittest</a></li>
+						<li><a href="#3.3.5">3.3.5 Our New Model</a></li>
-								<li>
+						<li><a href="#3.3.6">3.3.6 The Biological Meaning of our Model</a></li>
-									<a href="#1.3.1.3">1.3.1.3 Conditional Knockout by Recombination</a>
+						<li><a href="#3.3.7">3.3.7 Making it Obvious</a></li>
-									<ul>
-										<li><a href="#1.1.1.3.1">1.1.1.3.1</a></li>
-									</ul>
-								</li>
-							</ul>
-						</li>
 					</ul>
 				</li>
@@ Line 375: / Line 368: @@
 <!-- main contents -->
 <div class="main">
-	<!-- ############ Wrote main contents here ############### -->
+	<!-- ############ Write main contents here ############### -->
 	<!-- page title -->
 	<h1> Rock-Paper-Scissors game </h1>
+	<h2> Introduction </h2>
+	<div align= "center">
+		<span class="top"> The Hands </span><br />
+		<img src="https://static.igem.org/mediawiki/2011/4/48/Jyangken.png" width="300px" />
+	</div>
 	<p>
-		<h2 id="1.">1. The Human-Bacteria Rock, Paper and Scissors game</h2>
+		The first step towards making an RPS game that can be played
+		between humans and bacteria is giving each player a set of
+		signaling molecules through which they can communicate their
+		choice of rock, paper or scissors. For that purpose we created
+		two sets of three signaling molecules corresponding each to rock, paper or scissors.
+		For humans we used IPTG, aTc and salicylate, respectively.
+		For <span class="name">E. coli</span> we used 3OC6-HSL, 3OC12-HSL and AI-2, respectively.
+	</p>
+	<hr />
-		<h3 id="1.1">1.1 The Hands</h3>
+	<div align= "center">
+		<span class="top"> The Judges </span><br />
+		<img src="https://static.igem.org/mediawiki/2011/8/8a/Judge.png" width="350px" />
+		<table>
+			<tr>
+				<td><img src="https://static.igem.org/mediawiki/2011/2/24/BBa_K649001_graph3.png" width="360px" /></td>
+				<td><img src="https://static.igem.org/mediawiki/2011/f/fb/PlsrA3.png" width="400px" /></td>
+			</tr>
+		</table>
+	</div>
+	<p>
+		Although we defined a set of six signaling molecules that can be used to
+		play the RPS game, we still need to find a way to know who wins the game.
+		To know who the winner of each game is, we designed a set of
+		<span class="name">E. coli</span> that act as judges. Because there were no working parts related to AI-2 or 3OC12-HSL, we constructed new working  lasI promoter, lsrA promoter and LsrR coding gene.
+	</p>
+	<hr />
+	<div align= "center">
+		<span class="top"> The Randomizers </span><br />
+		<img src="https://static.igem.org/mediawiki/2011/7/79/Titech-rps-randomizers.png" width="750px" />
+	</div>
+	<p>
+		Although our set of six signaling molecules allows us to play RPS with
+		<span class="name">E. coli</span>, we must make sure <span class="name">E. coli</span>
+		can choose any of its three signaling molecules with the same probability
+		in order to be able to play RPS fairly and properly.
+		To do so, we designed three kinds of randomizers.
+	</p>
+	<p>
+		<h2 id="1">1. The Hands</h2>
+		<img src="https://static.igem.org/mediawiki/2011/7/75/The_hands.png" width="600px" style="float:right;" />
 		<p>
-			The first step towards making an RPS game that can be played between humans and
+			The first step towards making an RPS game that can be played between
-			bacteria is giving each player a set of signaling molecules through which
+			humans and bacteria is giving each player a set of signaling molecules
-			they can communicate their choice of rock, paper or scissors.
+			through which they can communicate their choice of rock, paper or scissors.
-			For that purpose we created two sets of three signaling molecules corresponding
+			For that purpose we created two sets of three signaling molecules
-			each to rock, paper or scissors. For humans we used IPTG, aTc and salicylate,
+			corresponding each to rock, paper or scissors. For humans we used IPTG,
-			respectively. For E. coli we used 3O-C6-HSL, 3O-C12-HSL and AI-2, respectively.
+			aTc and salicylate, respectively.
+			For <span class="name">E. coli</span> we used 3OC6-HSL, 3OC12-HSL and AI-2, respectively.
+		</p>
+		<h2 id="2" style="clear:both;">2. The Judges</h2>
+		<img src="https://static.igem.org/mediawiki/2011/8/8a/Judge.png" alt="the Judge" style="float: left;" />
+		<p>
+			Although we defined a set of six signaling molecules that can be used
+			to play the RPS game, we still need to find a way to know who wins the game.
+			To know who the winner of each game is,
+			we designed a set of <span class="name">E. coli</span> that act as judges.
+			Each Judge <span class="name">E. coli</span> has an AND-gate promoter and
+			a fluorescent protein gene that is expressed when the AND-gate promoter
+			is activated. In this way, the Judge <span class="name">E. coli</span> can
+			let us know its decision by producing GFP, RFP or CFP to indicate whether
+			humans win, lose or it is a tie, respectively.
+		</p>
+		<h3 id="2.1" style="clear:both;">2.1 Using AND-Gate promoters to create Judges</h3>
+		<p>
+			The first step to make the Judge <span class="name">E. coli</span> was to
+			find a logic device which could allow the Judge to decide who the winner of the RPS game was.
+			We found that the AND-gate promoters would fit perfectly for that purpose,
+			since they can take two signaling molecules as inputs and produce one indicator
+			as output. Since each of the players has a set of three different signaling
+			molecules, we need a set of nine Judges, each of which has an AND-gate promoter
+			that is activated only by one of the nine possible pairs of signaling molecules.
+			These combinations are shown in the image below.
 		</p>
-		<h3 id="1.2">1.2 The Judge</h3>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/3/36/Tt-image021.png" width="600px" />
+		</div>
 		<p>
-			We have our set of six signaling molecules that can be used to play the RPS game,
+			Our next mission was then to check if there were AND-gate promoters BioBricks
-			but we still need to find a way to know who wins the game.
+			that we could use. We searched in the Registry and found a potential AND-gate
-			To know who the winner of each game is, we designed a Judge E. coli that has a built
+			promoter designed by iGEM 2007's team Tokyo_Tech. This potential AND-gate
-			in AND-gate promoter and can let us know its decisions by expressing a particular
+			promoter is designed to be activated by the addition of both IPTG and 3OC6-HSL.
-			fluorescent protein. GFP, RFP or CFP to indicate whether humans win,
+			However, there was no data showing the IPTG dependency of this promoter,
-			lose or it is a tie, respectively.
+			so we did experiments and confirmed this dependency for the first time in iGEM.
+			We concluded that the addition of both IPTG and 3OC6-HSL regulates the activity
+			of this AND-gate promoter. In this way, we completed the construction of one of
+			the Judges <span class="name">E. coli</span>, which proves in principle that
+			our game is feasible. To know the detailed method about this assay,
+			please see <a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#4.">here</a>.
 		</p>
-		<h4 id="1.2.1">1.2.1 Creating New Parts</h4>
+		<div style="float:left">
+			<img src="https://static.igem.org/mediawiki/2011/b/be/BBa_I751101_graph3.png" width="400px" style="margin-right: 10px;"/><br />
+			<span class="graph_title">Fig. 2.1 Tokyo_Tech AND-gate promoter</span>
+		</div>
 		<p>
+			This Plux-lac hybrid promoter contains two LacI operators, a LuxR operator and luxR.
+			We introduced this part into LacI expressing <span class="name">E. coli</span> strain.
+			Because IPTG controls the binding of LacI to two LacI-operator parts and 3OC6-HSL
+			controls the binding of LuxR to a LuxR-operator part, the <span class="gene">gfp</span>
+			gene activity of the reporter part is dually regulated by IPTG and 3OC6-HSL.
+			We used promoterless pSB3K3-<span class="gene">gfp</span> (BBa_J54103) as a negative control,
+			and pAC-P&lambda;-<span class="gene">gfp</span> (chloramphenicol-resistance), which constitutively expressed GFP,
+			as a positive control. To know about the mechanism of this promoter click
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#4.0.">here</a>.
+		</p>
+		<h3 id="2.2" style="clear:both;">2.2 Creating Parts that responded correctly to our set of Signaling Molecules</h3>
 		<p>
-			The first step to make the Judge E. coli was to make sure there were AND-gates
+			In the process of constructing enough AND-gates that could suffice the needs
-			promoters that could work properly. We tested the AND-gate promoter designed by
+			of our RPS game design, we discovered two faulty BioBricks: lsrA promoter (BBa_K117002) and las promoter (BBa_J64010).
-			iGEM 2006's team Tokyo Alliance and confirmed it works well and can be used
+			Because of these faulty parts, the Judge <span class="name">E. coli</span>
-			as a logic device to know who the winner of the RPS game is.
+			set we had designed could only sense the Player <span class="name">E. coli</span>'s
-			Since in our human-bacteria RPS game each of the two players has one set of three
+			signaling molecule 3OC6-HSL (Rock). This ultimately led to an unfair game
-			different signaling molecules, we need 9 different AND-gate promoters,
+			because humans could win every time they played with the Paper signaling molecule
-			each corresponding to one of the 9 possible two signal combinations.
+			(for more on the &ldquo;Sad story of the Rock Player&rdquo; click
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/the_sad_stroy_of_the_rock_player">here</a>).
 		</p>
 		<p>
-			In the process of constructing enough AND-gates that could suffice the needs of
+			To fix this problem, we improved the old defective las and lsrA promoters parts
-			our RPS game design we discovered two faulty BioBricks and made new parts that can
+			by making new parts that work! As can be seen in the experimental information
-			replace them. Namely, we made a lasI promoter and a lsrR promoter that work well.
+			below (see “Improving lsrA promoter” and “Improving las promoter”),
-			These promoters are single input promoters but they are useful as a reference to
+			we confirmed our lasI promoter (<a href="http://partsregistry.org/Part:BBa_K649000">BBa_K649000</a>)
-			construct AND gate promoters. Also note that LsrR is essential for regulating the
+			and lsrA promoter (<a href="http://partsregistry.org/Part:BBa_K649100">BBa_K649100</a>) work perfectly!
-			AND gate promoter. Therefore, we solved important issues and made significant
-			advances towards constructing AND-gate promoters.
 		</p>
+		<p>
+			Since the lsrA promoter plays a key role in the correct functioning of AI-2,
+			fixing these parts now allows us to use AI-2 as a signaling molecule, which is a
+			promising advance because of the characteristics of
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#5.0.">the AI-2 mechanism</a>.
+			This mechanism prevents AI-2 from cross-talking with other signaling molecules
+			such as AHL. Hence, this signaling molecule is a very powerful
+			tool to build complex Synthetic Biology systems.
 		</p>
-		<h4 id="1.2.2">1.2.2 The Design</h4>
 		<p>
-			We designed AND-gate promoters that use two operators:
+			Finally, one thing we would like outline is that although the promoters we made
-			one that uses activators as regulators, and other that uses repressors as regulators.
+			are single input promoters, confirmation of their activity is required as a
-			After an activator binds to an inducer the resulting complex binds to the
+			reference to construct AND gate promoters. Therefore, we solved important issues
-			corresponding operator and activates it. However, since the AND-gate promoter needs
+			and made significant advances towards constructing AND-gate promoters. This allows
-			its both operators to be active, transcription will not start until the operator
+			<span class="name">E. coli</span> to also choose the signaling molecules
-			that uses repressors as regulators has been de-repressed by the appropriate signaling
+			corresponding to Paper and Scissors, so we have again a working RPS game design.
-			molecule. This mechanism assures that transcription will not start until both players
-			have added the corresponding signaling molecules to the place where the Judge
-			bacterium is, so it fits perfectly in our RPS game design. To see the game results
-			easily, we added a reporter gene downstream of the AND-gate promoter, so either of gfp,
-			rfp or cfp is expressed when humans win, lose or tie the game, respectively.
 		</p>
-		<h5 id="1.2.1.1">1.2.1.1</h5>
+		<h3 id="2.3">2.3 Improving PlsrA</h3>
- 		<p>
- 			<img alt="TokyoAliance AndGate" />
+		<div style="float: left;">
-			<div class="graph_title">Tokyo Alliance AND-gate promoter</div>
+			<img src="https://static.igem.org/mediawiki/2011/6/6e/PlsrA2.png" alt="activity" width="400px" /><br />
-			We used this Plux-lac hybrid promoter which contains a LacI operator,
+			<span class="graph_title">Fig. 2.2 Not working lsrA promoter(<a href="http://partsregistry.org/Part:BBa_K117002">BBa_K117002</a>) <br /> activity and our new lsrA promoter(<a href="http://partsregistry.org/Part:BBa_K649104">BBa_K649104</a>)</span> activity
-			a LuxR operator and luxR. We introduced this plasmid into a LacI expressing E. coli
+		</div>
-			strain pTrc99A (JM2.300). Because IPTG controls the binding of LacI to two
+		<p>
-			LacI-operator parts and 3OC6-HSL controls the binding of LuxR to a LuxR-operator part,
+			We confirmed that the lsrA promoter (<a href="http://partsregistry.org/Part:BBa_K117002">BBa_K117002</a>) does not work properly
-			GFP of the reporter part is dually regulated by IPTG and 3O-C6-HSL.
+			(samples used our experiment are listed in Table 2.1 below). The fluorescence intensity of GFP of lsrA promoter-<span class="gene">gfp</span>((<a href="http://partsregistry.org/Part:BBa_K117002">BBa_K117002</a>)-<span class="gene">gfp</span>) was lower
-			We also used promoterless pSB3K3-GFP (BBa_J54103) as a negative control, and Pλ-GFP
+			even than those of the negative control (Fig. 2.2), which clearly shows that
-			(chloramphenicol-resistance), which constitutively expressed GFP, as a positive control.
+			lsrA promoter((<a href="http://partsregistry.org/Part:BBa_K117002">BBa_K117002</a>) does not work as expected. In this experiment,
+			we measured transcriptional activity of lsrA promoter by introducing a
+			<span class="gene">gfp</span> gene downstream of this promoter (Fig. 2.3).
 		</p>
-		<h5 id="1.2.1.2">1.2.1.2</h5>
+		<table style="clear:both;margin-top: 20px;" border="1" align="center">
+			<caption>Table 2.1 Samples used our experiment</caption>
+			<tr>
+				<th>Name</th>
+				<th>Strain</th>
+				<th>Plasmid</th>
+			</tr>
+			<tr>
+				<td>sample1</td>
+				<td rowspan="4">JD22597</td>
+				<td>Ptet-<span class="gene">gfp</span> on pSB1A2</td>
+			</tr>
+			<tr>
+				<td>sample2</td>
+				<td>Promoterless-<span class="gene">gfp</span> on pSB6A1</td>
+			</tr>
+			<tr>
+				<td>sample3</td>
+				<td>PlsrA-<span class="gene">gfp</span> on pSB1A2 (<a href="http://partsregistry.org/Part:BBa_K649104">BBa_K649104</a>)</td>
+			</tr>
+			<tr>
+				<td>sample4</td>
+				<td>PlsrA-<span class="gene">gfp</span> on pSB1A2 ((<a href="http://partsregistry.org/Part:BBa_K117002">BBa_K117002</a>)-<span class="gene">gfp</span>)</td>
+			</tr>
+		</table>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/f/fb/PlsrAo.png" alt="Fig2.3" width="200px" /><br />
+			<span class="graph_title">Fig. 2.3 lsrA promoter-<span class="gene">gfp</span>((<a href="http://partsregistry.org/Part:BBa_K117002">BBa_K117002</a>)-<span class="gene">gfp</span>)</span>
+		</div>
 		<p>
-			<img alt="Signal table" />
+			To solve this problem, we created the first working iGEM lsrA promoter (<a href="http://partsregistry.org/Part:BBa_K649100">BBa_K649100</a>).
+			Its fluorescence intensity was much higher than that from a promoter-less
+			<span class="gene">gfp</span> negative control plasmid, showing that our new
+			lsrA promoter works(Fig. 2.5). In this experiment, we measured the transcriptional
+			activity of our lsrA promoter by introducing a <span class="gene">gfp</span> gene downstream of
+			the promoter(<a href="http://partsregistry.org/Part:BBa_K649104">BBa_K649104</a>, Fig. 2.4). Details about this experiment can be found
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#5.">here</a>.
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/6/60/PlsrAgfpx.png" alt="Fig2.4" width="200px"><br />
+			<span class="graph_title">Fig. 2.4 lsrA promoter-<span class="gene">gfp</span>(<a href="http://partsregistry.org/Part:BBa_K649104">BBa_K649104</a>)</span>
+		</div> <br />
-		<h5 id="1.2.1.3">1.2.1.3</h5>
+		<div align="center">
-		<p>
+			<img src="https://static.igem.org/mediawiki/2011/archive/6/6d/20111028133941%21LsrR_repression1.png" alt="Fig4" width="600px"><br />
-		<p>
+			<span class="graph_title">Fig. 2.5 LsrR represses lsrA promoter.</span>
-			When doing experiments to make more AND-gate promoters, we found that the parts
+		</div>
-			corresponding to the plasI promoter (BBa_###) and plsrA promoter (BBa_###) did not
-			work as expected.
- 		</p>
- 		<p>
- 			<img alt="PlasI previous" />
-			<div class="graph_title">Not working lasI promoter (BBa_J64010)</div>
-			<img alt="Plasmid map" />
-			<img alt="PlsrA prev" />
-			<div class="graph_title">Not working lsrA promoter (BBa_K117002)</div>
-		</p>
 		<p>
-			We confirmed that the lsrA promoter BBa_K117002 does not work
+			Moreover, this promoter can be repressed by our new LsrR part(<a href="http://partsregistry.org/Part:BBa_K649105">BBa_K649105</a>).
-			(samples used our experiments are listed in Table 1.)  We measured transcriptional
+			(samples used our experiments are listed in Table 2.2 below) The fluorescence
-			activity of lsrA promoter by introducing a gfp gene downstream of this promoter
+			intensity of GFP of sample 3 was three times as large as
-			(Fig.1).The intensity level of GFP fluorescence of BBa_1K17002 were lower
+			that of sample 4. This result shows that LsrR successfully repressed
-			even than those of the negative control (Fig.2), which clearly shows that
+			lsrA promoter. In this experiment, we measured LsrR repression activity by
-			lsrA promoter(BBa_K117002) does not work properly.
+			introducing a <span class="gene">gfp</span> gene downstream of lsrA promoter ((<a href="http://partsregistry.org/Part:BBa_K649105">BBa_K649105</a>, Fig. 2.6).
+			Details about this experiment can be found
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#6.">here</a>.
 		</p>
+		<table align="center" border="1">
+			<caption>Table2.2 Samples used our experiment</caption>
+			<tr>
+				<th>Name</th>
+				<th>Strain</th>
+				<th>Plasmid</th>
+			</tr>
+			<tr>
+				<td>sample1</td>
+				<td rowspan="2">JM2.300</td>
+				<td>Ptet-<span class="gene">gfp</span> on pSB6A1</td>
+			</tr>
+			<tr>
+				<td>sample2</td>
+				<td>Promoterless-<span class="gene">gfp</span> on pSB3K3</td>
+			</tr>
+			<tr>
+				<td>sample3</td>
+				<td rowspan="2">MG1655</td>
+				<td>PlsrA-<span class="gene">gfp</span> on pSB3K3</td>
+			</tr>
+			<tr>
+				<td>sample4</td>
+				<td>PlsrA-<span class="gene">gfp</span>-PlsrR-<span class="gene">lsrR</span> on pSB3K3</td>
+			</tr>
+		</table>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/d/dc/PlsrAPlsrR.png" alt="Fig.5" width="200px"><br />
+			<span class="graph_title">Fig. 2.6 lsrA promoter-<span class="gene">gfp</span>-lsrR promoter-<span class="gene">lsrR</span>(<a href="http://partsregistry.org/Part:BBa_K649105">BBa_K649105</a>)</span>
+		</div>
+		<h3 id="2.4">2.4 Improving las promoter</h3>
+		<table align="center">
+			<tr>
+			<td>
+                        <img src="https://static.igem.org/mediawiki/2011/8/80/BBa_J64010_graph3.png" align="left" height="330px" />
+                        <span class="graph_title">Fig. 2.7 (a)</span>
+                        </td>
+			<td>
+                        <img src="https://static.igem.org/mediawiki/2011/2/24/BBa_K649001_graph3.png" align="right" height="330px" />
+                        <span class="graph_title">(b)</span>
+                        </td>
+			</tr>
+		</table>
 		<p>
-			Because of these faulty parts, our game design became flawed and the Judge E. coli
+			Fig. 2.7 (a): Not working lasI promoter (BBa_J64010).
-			could only sense the Player E. coli's signaling molecule when the latter chose
+			Fig. 2.7 (b): New working lasI promoter (BBa_K649000) we made.
-			that signaling molecule corresponding to Rock.
+			We confirmed it works as expected. In our assay, we used the same LasR
+			regulator part used in the assay of BBa_ J64010. Clearly, for our
-			<img alt="e.coli in sad" />
+			part the fluorescence intensity of 3OC12-HSL+ was higher than that of 3OC12-HSL-.<br />
- 		</p>
+			To know detailed methods about these lasI promoter assay, please see here,
-		<p>
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#2.">previous part</a>
-			To solve this problem we made new parts that can replace these faulty parts.
+			and <a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#3.">new part</a>.
-			Below you can see that our plasI (BBa_###) and plasrA (BBa_###) work perfectly!
-			This allows E. coli to also chose the signaling molecules corresponding to
-			Paper and Scissors, so we have again a working RPS game design.
-			<img alt="human helped e.coli" />
-			<img alt="Assay data"/>
-			<img alt="plasmid map" />
- 		</p>
-		<p>
-			We made new lasI promoter and confirmed it works as expected. In our assay,
-			we used the same LasR regulator part used in the assay of BBa_ J64010. Clearly,
-			for our part the fluorescence intensity of 3OC12-HSL+ was higher than that of
-O-C12-HSL-. To see details about our assay method click here.
-			<img alt="assay data" />
 		</p>
 		<p>
-			We succeeded in the construction of the first working iGEM lsrA promoter
+			To prove that the LasR regulator used in our PlasI assay works, we did another assay.
-			((BBa_K649100) and made sure it works properly.  This lsrA promoter is repressed
+			Details about this assay can be found
-			by our new LsrR part. These working parts allow us to use AI-2 as a signaling molecule,
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#1.">here.</a>
-			which is a very powerful tool to build complex Synthetic Biology systems,
-			since AI-2's mechanism prevents it from cross-talking with other signaling molecules
-			such as AHL.
 		</p>
+		<h2 id="3">3. The Randomizers</h2>
 		<p>
-			In our experiment, we compared the transcriptional activity of the previous lsrA
+			Although our set of six signaling molecules allows us to play RPS with
-			promoter (BBa_K117002) and our new lsrA promoter (BBa_K649100). We measured the
+			<span class="name">E. coli</span>, we must make sure <span class="name">E. coli</span>
-			transcriptional activity of our lsrA promoter by introducing a gfp gene downstream of
+			can choose any of its three signaling molecules with the same probability
-			this promoter (Fig.3).  The intensity levels of GFP fluorescence of BBa_K649100 were
+			in order to be able to play RPS fairly and properly. To do so, we designed
-			much higher than BBa_117002 (Fig.4), which shows that our new lsrA promoter
+			three kinds of randomizers: one kind which needs of three types of bacteria
-			(BBa_K649100) works.
+			(each of which produces one of the three RPS signaling molecules),
-		</p>
+			and the other kind that needs of only one type of bacteria which can
+			synthetize each of the three signaling molecules one at a time and randomly.
+			Namely, the randomizers are Single Colony Isolation,
+			Survival of one Strain and Conditional Knockout by Recombination.
 		</p>
-		<h6 id="1.2.1.3.1">1.2.1.3.1 Our New LsrR part</h6>
+		<h3 id="3.1">3.1 Single Colony Isolation</h3>
+		<img src="https://static.igem.org/mediawiki/2011/d/d6/Image041.png" style="float:right;"/>
 		<p>
-			We confirmed that our new LsrR part represses the lsrA promoter.
+			This is our simplest randomizer design. To make sure <span class="name">E. coli</span>
-			We measured LsrR repression activity by introducing a gfp gene downstream of PlsrA
+			chooses any of its signaling molecules with equal probability, we put the constructs
-			(Fig.5).  The intensity of GFP fluorescence of sample3 was three times as large
+			for each molecule inside a different bacterium, so we create three types of bacteria:
-			as that of sample 4 (Fig.6). This result shows that LsrR successfully repressed PlsrA.
+			one synthetizing the corresponding signaling molecule for rock, other synthetizing
-			<img alt="assaydata" />
+			the corresponding signaling molecule for paper, and lastly one synthetizing the
-			<table>
+			corresponding signaling molecule for scissors. By randomly isolating a single colony
-				<tr>
+			out of the many colonies that result from the mixing between the three types of
-					<th>name</th>
+			<span class="name">E. coli</span>, we get a random output as
-					<th>strain</th>
+			<span class="name">E. coli</span>'s choice for the RPS game.
-					<th>plasmid</th>
-				</tr>
-				<tr>
-					<td>sample1</td>
-					<td>JM2.300</td>
-					<td>pSB6A1 Ptet GFP RBS1-12</td>
-				</tr>
-				<tr>
-					<td>sample2</td>
-					<td>JM2.300</td>
-					<td>pSB6A1 &Delta;P GFP</td>
-				</tr>
-				<tr>
-					<td>sample3</td>
-					<td>MG1655</td>
-					<td>pSB3K3 PlsrA GFP</td>
-				</tr>
-				<tr>
-					<td>sample4</td>
-					<td>MG1655</td>
-					<td>pSB3K3 PlsrA GFP PlsrR lsrR</td>
-				</tr>
-			</table>
 		</p>
-		<h6 id="1.2.1.3.2">1.2.1.3.2 The AI-2 Mechanism</h6>
+		<h3 id="3.2" style="clear:both">3.2 Conditional Knockout by Recombination</h3>
-		<p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/0/0c/Cre-lox_mechanism_1.png" width="550px" align="center" />
+		</div>
 		<p>
-			AI2 is synthesized by LuxS and accumulates extracellularly. Then AI2 is imported by
+			Our second randomizer differs from our other two randomizers in that all the
-			LsrACDB transporter and AI2 is phosphorylated by the LsrK kinase. Phospho-AI2
+			three signaling molecules are produced one at a time and randomly by only one type
-			relieves LsrR inhibition and LsrR is the repressor of the lsr operon and itself.
+			of bacteria. We were inspired by a paper about &ldquo;brainbow&rdquo; research
-			<img alt="AI2 signaling" />
+			on mice to create this randomizer (Livet J <i>et al.</i>, 2007), which is based
+			on the recombination mechanism of the enzyme Cre and the lox sequences.
+			We designed a Cre-Lox system which allows <span class="name">E. coli</span>
+			to express one of its three signaling molecules by means of conditional knockout.
+			The design is depicted in Fig. 1. It should be noted this randomizer is designed
+			to be used at a single-cell level. When this randomizer is used in groups of cells,
+			the different signals released by the cells will mix. In this case, by using microfluidic
+			devices or isolating single colony of bacteria, we can obtain only one of the signaling
+			molecules produced by the initial group of cells.
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/3/3d/Fig_3.1_-_in_one_cell_1.png" width="700px" align="center" />
+		</div>
+				<div class="graph_title">
+			Fig. 3.1 - (a) Cre recombinase construction. (b) lox cassettes distribution for the randomizer design
+		</div>
+		<h4 id="3.2.1">3.2.1 The Requirements</h4>
 		<p>
-			First AI-2 is synthesized by LuxS and accumulates outside the cell. Then AI-2 is
+			Basically, each pair of <i>lox</i> sites (indicated by the same color) mark the points
-			imported into the cell by the LsrACDB transporter. Inside the cell, AI-2 is
+			which the enzyme Cre will excise (they will be cut off the backbone along with the
-			phosphorylated by the LsrK kinase. Phospho-AI2 relieves LsrR inhibition from the
+			sequence between them). For a design that allows choosing randomly one of
-			lsr operon, therefore activating PlsrA.
+			<span class="name">E. coli</span>’s three signaling molecules, at least two
+			cassettes of lox sites are needed. When these two cassettes of lox sites and
+			protein coding sequences are arranged as in Fig. 3.1(b),
+			only one signaling molecule is produced.
 		</p>
-		</p>
-		<h3 id="1.3">1.3 The Randomizers</h3>
 		<p>
-			To complete our RPS game design, we need to make sure E. coli follows the rules of
+			Our design also required a way to control <span class="gene">luxI</span> gene's expression.
-			the game by synthetizing only one signaling molecule every time it plays. Additionally,
+			To do so, we used an inducible promoter instead of a constitutive promoter.
-			we want it to be able to choose its signal randomly. In view of these needs,
+			A constitutive promoter would have caused <span class="gene">luxI</span> gene to be expressed beforehand and
-			we designed three randomizers that satisfy the conditions for the game Single Colony
+			could lead to an <span class="name">E. coli</span> producing two signaling molecules
-			Isolation, Survival of the Fittest, and Conditional Knockout.
+			at the same time (the equivalent of showing two hands in the RPS game). In contrast,
+			the inducible promoter prevents a particular gene from expressing preferentially.
+		</p>
+		<p>
+			One last but not less important requirement for our randomizer is that it should
+			express each of the three signals not only one at a time, but also with the same
+			probability. This makes the game fair in the sense that
+			<span class="name">E. coli</span>’s choice in the RPS game is not predictable.
 		</p>
+		<h4 id="3.2.2">3.2.2 The Mechanism</h4>
-		<h4 id="1.3.1">1.3.1 Three Randomizers</h4>
-		<p>
 		<p>
-			Our set of six signaling molecules allows us to play RPS with E. coli, but in order
+			When the blue cassette of <i>Lox</i> sites is excised (Fig. 3.1), the signaling molecule
-			to be able to play properly we must make sure E. coli can chose either of its three
+			coded by lasI (3OC6-HSL) will be produced. Likewise, when the black <i>Lox</i> cassette
-			signaling molecules with the same probability. To do so, we designed three types of
+			is excised, the signaling molecule coded by luxS (AI-2) will be produced. On the other hand,
-			randomizers: two of them are three-bacterium randomizers and the other is a
+			a third possible outcome is that recombination does not take place. In this case,
-			single-bacterium randomizer.
+			the signaling molecule coded by <span class="gene">luxI</span> (3OC6-HSL) will be produced. Also note that excision
+			of one kind of lox cassette removes the remaining cassette,
+			thereby preventing further recombination.
 		</p>
 		<p>
-			Namely, the three-bacterium randomizers are Single Colony Isolation and Survival of
+			As mentioned before, one of the requirements for our randomizer was to have at least
-			the Fittest. The single-bacterium randomizer is Conditional Knockout by Recombination.
+			two lox cassettes. This prevents excision of <i>lox</i> sites from different cassettes
-		</p>
+			(for example one blue <i>lox</i> site and one black <i>lox</i> site). Because the <i>lox71-lox66</i> cassette and the l<i>ox2272-lox2272</i> cassette are incompatible (Zorana Carter and Daniela Delneri <i>et al.</i>, Yeast 2010), we can use them to build our randomizer.
 		</p>
-		<h5 id="1.3.1.1">1.3.1.1 Single Colony Isolation</h5>
+		<h4 id="3.2.3">3.2.3 Testing the Lox Cassettes</h4>
 		<p>
-			This is our simplest randomizer design. To make sure E. coli choses any of its signaling
+			As stated above, we need two lox cassettes of different recombination frequency
-			molecules with equal probability, we put the constructs for each molecule inside a
+			for randomizer. Because there was no working <i>lox</i> parts in registry, we constructed
-			different bacterium, so we create three types of bacteria: one synthetizing the
+			three original BioBricks for testing whether <i>lox2272</i> and <i>lox71/66</i> cassettes work. For
-			corresponding signaling molecule for rock, other synthetizing the corresponding
+			the convenience of testing, fluorescence expressing genes were used in place of signal
-			signaling molecule for paper, and lastly one synthetizing the corresponding signaling
+			molecular expressing genes in construction. After figuring out their working <i>in vitro</i>, we tested them <i>in vivo</i> by detecting red and green fluorescence through fluoro imager and flow cytometer. Furthermore, we compared the relative recombination frequency of two cassettes . Our <i>lox</i> Cassettes constructions
-			molecule for scissors. By randomly isolating a single colony out of these three
+			were working properly, and their recombination frequency were different from each other.
-			colonies we get a random output as E. coli's choice for the RPS game.
 		</p>
+		<ul>
+			<li>
+				PlacIQ-<i>lox2272</i>-<span class="gene">gfp</span>-<i>lox2272</i><a href="http://partsregistry.org/Part:BBa_K649200">(BBa_K649200)</a>
+				<img src="https://static.igem.org/mediawiki/2011/6/6d/Lox-gfp-lox_1.png" width="550px"/>
+			</li>
+			<li>
+				PlacIQ-<i>lox2272</i>-<span class="gene">rfp</span>-<i>lox2272</i>-<span class="gene">gfp</span><a href="http://partsregistry.org/Part:BBa_K649201">(BBa_K649201)</a>
+				<img src="https://static.igem.org/mediawiki/2011/2/2b/Lox2272-rfp-lox-gfp_1.png" width="550px"/>
+			</li>
+			<li>
+				PlacIQ-<i>lox71</i>-<span class="gene">rfp</span>-<i>lox66</i>-<span class="gene">gfp</span><a href="http://partsregistry.org/Part:BBa_K649202">(BBa_K649202)</a>
+				<img src="https://static.igem.org/mediawiki/2011/b/b4/Lox71-rfp-lox-gfp_1.png" width="550px"/>
+			</li>
+		</ul>
-		<h5 id="1.3.1.2">1.3.1.2 Survival of the Fittest</h5>
 		<p>
-		<p>
+			The <i>in vitro</i> assay with K649200 was made in advance. The preliminary experiment allowed
-			In 1996 Durret and Levin described a system of three types of bacteria that competed
+			us to confirm that the Cre-mediated recombination on <i>lox2272</i> cassette works as designed.
-			for survival in dynamic that resembled a Rock-Paper-Scissors (RPS) game. The bacteria
+			In the assay, Cre recombinase was added to the linear DNA and incubated for 0.5, 2, and 4 hours.
-			used two main evolutionary stable strategies (ESS) to outcompete their rivals:
+			Images of the experiments have been added below.
-			the production of a toxin (a bacteriocin called colicin) that was toxic to other
-			strains and a higher birth rate than their rival strains. The three types of bacteria
-			described in the model by Durret and Levin were colicin-producing E. coli (R),
-			colicin-resistant E. coli (P) and colicin-sensitive E. coli (S). The colicin producer
-			outcompeted the colicin sensitive by producing the colicin, the colicin sensitive
-			bacteria outcompeted the colicin resistant because it's birth rate was higher than
-			that of the colicin resistant, and the colicin resistant outcompeted the colicin
-			producer because it' birth rate was higher than that of the colicin producer.
-			The colicin resistant bacteria were also able to produce colicin, but at a lower
-			energetic cost, which allowed them to have a higher birth rate.
 		</p>
+		<img src="https://static.igem.org/mediawiki/2011/6/60/In_vitro_lox_gfp_lox.png" style="float: left;"/>
 		<p>
-			The system was described by the following general differential equations
+			When checking the result by electrophoresis, there were several bands in samples to
+			which Cre was added(1st, 2nd lane from right which corresponds to 4 hr and 2 hr respectively).
+			It indicates that excision of the <i>lox</i> sites successfully occurred.
+			To know detailed about this assay, please see here,
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#7."><i>in vitro</i> assay for <i>lox2272</i></a>
 		</p>
 		<p>
-			∑_(i=1)^n?u_i  &lt; 1<br />
+			For the <i>in vivo</i> assay, by detecting fluorescenc levels of GFP and mCherry,
-			(du_i)/dt=β_i u_i u_0- u_i ( δ_i+∑_(j=1)^(n-1)??γ_j u_j ?)<br />
+			we could determine whether recombination occured in K649201 and K649202 and compare
-			u_0=1-∑_(i=1)^n?u_i <br />
+			relative recombination frequency between two of them. We prepared a competent cell
-			Where<br />
+			JM2.300 into which P<sub>BAD</sub>/araC-Cre(pSB1A2, BBa_I718008) had been constructed.
+			Subsequently, our BioBrick was constructed into the cell.
-			u_i i's concentration in arbitrary units (a.u.)
-			β_i i's birth rate
-			δ_i i's death rate
-			γ_j i's death rate due to j's bacteriocin
-			u_0 carrying capacity
-			In the model described by Durret and Levin's paper the equations were as follows:
-			Producer
-			(du_1)/dt=β_1 u_1 u_0- u_1 δ_1
-			Resistant
-			(du_2)/dt=β_2 u_2 u_0- u_2 δ_2
-			Sensitive
-			(du_3)/dt=β_3 u_3 u_0- u_i ( δ_3+γ_1 u_1+ γ_2 u_2 )
-			Setting the parameters as follows, the following graph was created by Durret and Levin.
-			β_1=3, β_2=3.2, β_3=4
-			γ_1 = 3, γ_2 = 0.5
-			δ_1 = δ_2  = δ_3 =1
-			Note that these parameters satisfy the following relations:
-			β_3>β_2>β_1, γ_1> γ_2, and δ_1=δ_2= δ_3
 		</p>
+		<table border="1" align="center">
+			<tr>
+				<th colspan="2">sample</th>
+				<th>arabinose</th>
+			</tr>
+			<tr>
+				<td>1</td>
+				<td>PlacIQ-<i>lox</i>-<span class="gene">rfp</span>-<i>lox</i>-<span class="gene">gfp</span>(pSB3K3)<br />P<sub>BAD</sub>/araC-Cre(pSB1A2)</td>
+				<td style="text-align:center;">+</td>
+			</tr>
+			<tr>
+				<td>2</td>
+				<td>PlacIQ-<i>lox</i>-<span class="gene">rfp</span>-<i>lox</i>-<span class="gene">gfp</span>(pSB3K3)<br />P<sub>BAD</sub>/araC-Cre(pSB1A2)</td>
+				<td style="text-align:center;">-</td>
+			</tr>
+			<tr>
+				<td>3</td>
+				<td>PlacIQ-<i>lox</i>-<span class="gene">rfp</span>-<i>lox</i>-<span class="gene">gfp</span>(pSB3K3)<br /> : negative control </td>
+				<td style="text-align:center;">+</td>
+			</tr>
+		</table>
 		<p>
-			<img alt="Durret and Levin" />
+			The strain was grown in a 3 mL liquid culture, and 75 &micro;L of 2 M arabinose was added
-			Durret &amp; Levin (1996)<br />
+			to induce Cre expression. We used two controls for the experiment. One was the same strain
-			In this model, however, there is no case where the colicin-producer can survive for
+			without arabinose induction, and the other was JM2.300 strain which was induced by arabinose
-			infinitively long periods of time if the colicin-resistant's initial concentration
+			and had only our BioBrick. All the strains were cultured each for periods of 0.5, 1, 2, and 4 hours,
-			is greater than zero. This can be seen in the graph drawn by Durret and Levin,
+			and in each case the florescence levels were measured by flow cytometer and FLA.
-			where the lines along the axis for u_1 (in the rightmost lower corner) always converge
+			To know the detailed method about this assay, please see here
-			either to u_3 or u_2. We highlighted this fact by circling the point in the graph below.
+			<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#8."><i>in vivo</i> assay for <i>lox</i> cassettes</a>.
-			<img alt="Durret and Levin remark" />
-		</p>
- 		<p>
-			The existence of this instability along the u_1 axis does not allow us to construct a
-			randomizer that can function based on minimal differences in the initial concentrations
-			of the three different populations of bacteria. For that reason, we modified the
-			differential equations of the model so that any of the three types of bacteria could
-			win for infinitely long periods of time (could win definitely). More specifically,
-			we limited the resistance of the colicin-resistant bacteria in the sense that it would
-			produce a type of bacteriocin that is only toxic to itself and to the sensitive strain,
-			and additionally the resistant strain would also be vulnerable to the colicin produced
-			by the colicin producer.
 		</p>
 		<p>
-			Producer
+			We confirmed our results optically by taking florescence images.
-			(du_1)/dt=β_1 u_1 u_0- u_1 δ_1
+			K649201 transformants with with 0.5 hr-induction of Cre in liquid medium and its two control strains were                    plated and incubated in 37&deg;C for 12 hours. Images of the three conditions were taken using red
-			Limited Resistance
+			florescence filter, green florescence filter and no filter as shown below, respectively.
-			(du_2)/dt=β_2 u_2 u_0- u_2 (δ_2+γ_1' u_1+γ_2' u_2)
-			Sensitive
-			(du_3)/dt=β_3 u_3 u_0- u_3 ( δ_3+γ_1 u_1+ γ_2 u_2)
-			If we set the parameters as follows
-			β_3=3.1, β_2=3.2,? β?_1=4
-			γ_1=2,γ_2=0.5,? ? γ?_1'=0.1 ,γ?_2'=0.002
-			δ_1=δ_2= δ_3=1
 		</p>
+		<table align="center">
+			<tr>
+				<td><img src="https://static.igem.org/mediawiki/2011/1/1e/Image146.png" style="margin-top:10px;margin-bottom:10px;" width="500px" /></td>
+				<td style="text-align:center;">(a)</td>
+			</tr>
+			<tr>
+				<td><img src="https://static.igem.org/mediawiki/2011/thumb/7/76/Image144.png/800px-Image144.png" style="margin-top:10px;margin-bottom:10px;" width="500px" /></td>
+				<td style="text-align:center;">(b)</td>
+			</tr>
+			<tr>
+				<td><img src="https://static.igem.org/mediawiki/2011/thumb/2/27/Image142.png/800px-Image142.png" style="margin-top:10px;margin-bottom:10px;" width="500px" /></td>
+				<td style="text-align:center;">(c)</td>
+			</tr>
+		</table>
 		<p>
-			and we graph this equations using a Matlab program, we get a graph which clearly
+			Fig. 3.2 Cre-meditated recombination at <i>lox2272</i> cassette. Cre-induction period of 0.5 hr
-			shows there are stable points on each of the three axes.
+                        (a)Overlay of Green and Red channel. The leftmost is a negative control which don't have Cre-expressing
-			<img alt="new 3d" />
+                        plasmid. The center is an arabinose induced sample which has both Cre plasmid and BioBrick K649201.
- 		</p>
+			The rightmost is a uninduced strain which has both plasmid like as the center.
- 		<p>
+			(b)Detection of GFP. The order of samples is same as above.
-			These stable points (u_1,0,0), (0,u_2,0) and (0,0,u_3) indicate that for the
+			(c)Detection of mCherry. The order of samples is same as above.
-			equations we have set all of the three strains may ultimately survive for infinite
-			peiriods of time even if the initial density of the other two strains is positive.
 		</p>
 		<p>
-			To see the difference between our model and Durret and Levin's model more clearly,
+			On the sample with the P<sub>BAD</sub>/araC-Cre construction, we found that recombination occurred
-			we also plotted Durret and Levin's model using Matlab.
+			when arabinose was added. In contrast to this result, when we measured the levels of the sample
-			<img alt="prev. 3D" />
+			without the P<sub>BAD</sub>/araC-Cre construction, we found that the GFP levels were far lower than
-		</p>
+			those of the sample with the P<sub>BAD</sub>/araC-Cre construction. This clearly proves that our
- 		<p>
+			<i>lox</i> constructions, both in K649201 and K649202, respond correctly to the effects of Cre recombinase.
-			Note that the parameters we have set for our equations satisfy the initail conditions
+			A slight detection of green florescence in plate absence of P<sub>BAD</sub>/araC-Cre can be explained
-			of the model proposed by Durret and Levin (indicated in black font) in the sense
+                        that there happened cross-talk to green channel by FMN(Flavin mononucleotide) or expression of GFP according
-			that β_3&gt;β_2&gt;β_1, γ_1&gt;γ_2  &gt;γ_1'&gt;γ?_2', and δ_1=δ_2= δ_3.
+                        to malfunction of terminator before <span class="gene">gfp</span>. We could also observe recombination occurred when arabinose was not
-			The two new terms we added are indicated in red.
+                        added, which can be explained due to a leaking in the P<sub>BAD</sub>/araC promoter.You can find that K649202 also works well from the images of K649202 on<a href="https://2011.igem.org/Team:Tokyo_Tech/Projects/RPS-game/assay#8."> here</a>.
 		</p>
 		<p>
-			From a biological perspective, this model describes the existence of two strains of
+			Furthermore, we could observe that the arabinose(+) sample of K649202 has higher green/red ratio than that of K649201, which implying the frequency of <i>lox71/66</i> casette is higher than that of <i>lox2272</i>.
-			bacteria that produce two different types of bacteriocin. One of these strains is not
-			completely resistant to its own bacteriocin nor to the bacteriocin produced by its
-			rival strain. This can be explained by thinking that the strain with this limitation
-			in its bacteriocin resistance does not produce enough/effective resistance protein,
-			which could be a consequence of it being a mutant of a colicin-sensitive strain.
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/8/86/111001DK_30_eachpair_111003.png" /><br />
+			<span class="graph_title">Fig. 3.3 Image of six samples of K649201 (up) and K649202 (down) at period of 0.5 hr</span>
+		</div><br />
+		<table border="0">
+			<tr>
+				<td><img src="https://static.igem.org/mediawiki/2011/1/11/Proportion_2272_0.5hr.png" /></td>
+				<td><img src="https://static.igem.org/mediawiki/2011/b/bb/Proportion_7166_0.5hr.png" /></td>
+			</tr>
+			<tr>
+				<td style="text-align:center;">(a)</td>
+				<td style="text-align:center;">(b)</td>
+			</tr>
+			<tr>
+				<td><img src="https://static.igem.org/mediawiki/2011/archive/5/52/20111004160721%21Proportion_area.png" /></td>
+				<td>
+					Fig. 3.4 identical plates with Fig. 3.3<br />
+					(a)expression levels of red and green florescence of K649201<br />
+					(b)expression levels of red and green florescence of K649202<br />
+					(c)examined area for comparing between red and green florescence at each plate<br />
+			   </td>
+			</tr>
+			<tr>
+				<td style="text-align:center;">(c)</td>
+				<td> </td>
+			</tr>
+		</table>
 		<p>
-			The next step is to find a set of parameters that satisfy the conditions set by the
+			As we examining green florescence in comparison to red florescence, green expression level was lower than red in
-			model of Durret and Levin, the above condition of allowing stable points on each of
+			K649201(Fig. 3.4(a)), which meaning that considerable plasmids in those cells yet. In contrast, green	expression level exceeded red in K649202(Fig. 3.4(b)). This result implies that recombination frequency of
-			the three axes and also allow each of the three different strains of E. coli to
+			<i>lox71/66</i> cassette is relatively high than that of <i>lox2272</i> cassette.<br />
-			survive in a random fashion by minimal differences on the initial concentrations of
-			each strain.
-			<img alt="producer" />
-			<img alt="limit-registance" />
-			<img alt="sensitive" />
 		</p>
+			<center><img src="https://static.igem.org/mediawiki/2011/a/a2/Flow_cytometer.png"/ width="500px" ></center><br>
+                <p>     <span class="graph_title">Fig. 3.5 Green fluorescence level of each cell was detected by flow cytometer.<br>
+                        (a)arabinose induced strain containing only K649201 and cre-expressing plasmid (b)arabinose supplied strain containing only K649201 (c)arabinose induced starin containing K649202 and cre-expressing plasmid (d)arabinose supplied strain containing only K649202<br>
+                </p>
+                <p>
+                The higher recombination efficiency of <i>lox71/66</i> compare to <i>lox2272</i> was confirmed also by flow cytometer intensity of <i>lox71/66</i> was higher than that of lox2272, which supports the result detected by FLA.
+                </span>
+                </p>
+		<h4 id="3.2.4">3.2.4 Playing Fair: Future Work</h4>
 		<p>
-			We found, by writing another program in Matlab, that the following set of parameters
+			To make each of the outcomes (R, P, and S) equally probable, we are going to quantify the recombination frequency of each lox cassette. This information and adequate Cre induction will be likely to allow us to have an RPS player
-			satisfy all of the above mentioned conditions.
+			<span class="name">E. coli</span> whose choice of either of rock, paper or scissors cannot be predicted.
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/e/e6/Regulating_time_1.png" width="700px"/>
+		</div>
 		<p>
-			β_3=3, β_2=3.2,? β?_1=5.1
+			In our next experiments, we are going to vary the reaction time and the distance between the lox sites
-			γ_1=2,γ_2=1,? ? γ?_1'=0.2 ,γ?_2'=0.01
+			of each cassette. We believe precise modification of this two parameters must lead to our goal of
-			δ_1=δ_2= δ_3=1
+			making a randomizer in which each of the signaling molecules can be expressed with the same frequency
+			(which results in each of the outcomes being expressed with the same probability).
 		</p>
+		<h3 id="3.3">3.3 Survival of One strain</h3>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/2/28/Image042.png" width="500px" />
+		</div>
+		<h4 id="3.3.1">3.3.1 Introduction: Very small differences determine who will survive</h4>
 		<p>
-			As can be seen in the graphs below, each of the strains can survive if their initial
+			In this section we will show a shocking scenario of evolution:
-			density in only tree hundredths (a.u.) greater than the other two strains' initial
+			the future of each of three different rival strains (whether the strain will die or survive)
-			concentrations.
+			is marked by very small differences between the initial population densities of the strains (a phenomenon also known as the &ldquo;butterfly effect&rdquo;).
+			Furthermore, we will also show that we can apply this very interesting result to create a randomizer
+			that can be used in our Rock-Paper-Scissors game, due to the fact that only one of the rival strains
+			will survive. More specifically, we assign to each of the three rival strains either of Rock, Paper or Scissors,
+			make them compete for survival and take the surviving strain to represent the bacteria's choice for the RPS game.
 		</p>
+		<h4 id="3.3.2">3.3.2 Adjusting the Model to create a True Randomizer</h4>
 		<p>
-			The producer strain survives if u_1= 0.32, u_2= 0.29, u_3= 0.29 (a.u.).<br />
+			The idea for creating this randomizer was born from a paper written in
-			The limited-resistance strain survives if u_1= 0.29, u_2= 0.32, u_3= 0.29 (a.u.).<br />
+by Durrett and Levin. In it, the authors described a system of three types of bacteria that competed for
-			The sensitive strain survives if u_1= 0.29, u_2= 0.29, u_3= 0.32 (a.u.).<br />
+			survival in dynamic that resembled a Rock-Paper-Scissors (RPS) game.
-			In practice, this minimal variation of concentrations will cause the outcome of
+			However, the model proposed in this paper is not fully appropriate for our RPS randomizer,
-			Rock, Paper or Scissors signaling molecule to be random. Consequently, we can conclude
+			since one of the three types of bacteria cannot ultimately survive
-			that this randomizer is not only feasible but also practical and effective
+			(although it can dominate the system, i.e. have the highest population density, for definite periods of time).
-			(let alone interesting).
+			We will discuss more on the limitations we found in this model to be adopted as a
-		</p>
+			randomizer and the modifications we made to create a true randomizer.
 		</p>
+		<h4 id="3.3.3">3.3.3 How the Three Types of Bacteria Compete for Survival</h4>
-		<h5 id="1.3.1.3">1.3.1.3 Conditional Knockout by Recombination</h5>
 		<p>
-		<p>
+			The three types of bacteria that compete for survival use three tactics to outcompete their rivals:
-			Our third randomizer differs from our other two randomizers in that it is a
+			the production of a toxin (a bacteriocin called colicin) that is toxic to other strains,
-			single-bacterium randomizer.  It is based on the recombination mechanism of the enzyme
+			resistance to the toxin produced by other strains, and a higher birth rate than their rival strains.
-			Cre and the lox sequences. We designed a Cre-Lox system which allows E. coli to
+			Namely, the three types of bacteria are: colicin-producing <span class="name">E. coli</span> (R),
-			express one of its three signaling molecules by means of conditional knockout.
+			colicin-resistant <span class="name">E. coli</span> (P)
-			The design is depicted in Figure 1.
+			and colicin-sensitive <span class="name">E. coli</span> (S).
+			The colicin-producer outcompetes the colicin-sensitive by producing the colicin. The colicin-sensitive
+			bacteria outcompetes the colicin-resistant because its birth rate is higher than that of the colicin-resistant.
+			The colicin-resistant outcompetes the colicin producer because its birth rate is higher
+			than that of the colicin producer. The colicin resistant bacteria are also able to produce colicin,
+			but at a lower energetic cost, which allows them to have a higher birth rate.
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/b/bf/Image044.png" width="500px" />
+		</div>
+        <p>
+			The system was described by the following general differential equations
+		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/2/28/Colisin1.png" />
+		</div>
 		<p>
-			(a)
+			Where
-			<img alt="cre" />
-			(b)
-			 <img alt="plasmid" />
-			Figure 1 - (a) Cre recombinase construction.
-			(b) Lox cassettes distribution for the randomizer design
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/c/c0/Colisin2.png" />
+		</div>
+		<h4 id="3.3.4">3.3.4 The Old Model</h4>
 		<p>
-			Basically, each pair of lox sites (indicated by the same color) mark the points which
+			In the model described by Durrett and Levin’s paper the equations were as follows:
-			the enzyme Cre will excise (they will be cut off the backbone along with the
-			sequence between them). For a design that allows choosing randomly one of E. coli's
-			three signaling molecules, at least two cassettes of lox sites are needed.
-			When these two cassettes of lox sites and protein coding sequences are arranged as in
-			Figure 1(b), only one signaling molecule is produced.
 		</p>
+		<div align="center">
+			<p>Producer</p>
+			<img src="https://static.igem.org/mediawiki/2011/1/1d/Colisin3.png" /><br />
+			<p>Resistant</p>
+			<img src="https://static.igem.org/mediawiki/2011/0/04/Colisin4.png" /><br />
+			<p>Sensitive</p>
+			<img src="https://static.igem.org/mediawiki/2011/3/36/Colisin5.png" /><br />
+		</div>
 		<p>
-			For example, when the blue cassette of Lox sites is excised, the signaling molecule
+			These equations show that the colicin-resistant bacteria are completely immune to colicin
-			coded by LasI (3OC6-HSL) will be produced. Likewise, when the purple Lox cassette is
+			(there is not death factor associated to colicin in the equation for du<sub>2</sub>/dt).
-			excised, the signaling molecule coded by LuxS (AI-2) will be produced.
+			However, as will be explained afterwards, this results in a loss of
-			On the other hand, a third possible outcome is that recombination does not take place.
+			balance that does not allow building a true randomizing system.
-			In this case, the signaling molecule coded by LuxI (3OC6-HSL) will be produced.
-			Also note that excision of one kind of lox cassette removes the remaining cassette,
-			thereby preventing further recombination.
 		</p>
 		<p>
-			To avoid excision of lox sites from different cassetes (for example one blue lox site
+			Now, setting the parameters as follows, the graph below was created by Durrett and Levin.
-			and one purple lix site), we used a lox71-lox66 cassette and a lox2272-lox2272 cassette.
-			It is well known that lox71/lox2272 and lox66/lox2272 are incompatible
-			(Zorana Carter and Daniela Delneri et al, Yeast 2010).
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/4/41/Colisin6.png" /><br />
+			<img src="https://static.igem.org/mediawiki/2011/e/e3/Colisin7.png" />
+                        <img src="http://partsregistry.org/wiki/images/b/bd/Modeling1.png" width="354px"/><br />
+			<img src="https://static.igem.org/mediawiki/2011/thumb/b/b1/Colisin8.png/800px-Colisin8.png" width="800px"/><br />
+			<img src="https://static.igem.org/mediawiki/2011/5/55/Modeling2.png" width="354px"/><br />
+		</div>
+		<h4 id="3.3.5">3.3.5 Our New Model</h4>
 		<p>
-			Also, to be able to control the LuxI gene's expression, we used an inducible promoter
+			As mentioned before, the model proposed by Durrett and Levin has critical limitations as a randomizer for the RPS game.
-			instead of a constitutive promoter. A constitutive promoter will cause LuxI gene to be
+			To be able to create a true randomizer, we modified the differential equations of the model taking care to give it
-			expressed beforehand and could lead to an E.coli producing two signaling molecules
+			a biological meaning. With our new differential equations, any of the three types of bacteria can ultimately survive
-			at the same time (the equivalent of showing two hands in the RPS game). In contrast,
+			by outcompeting the other two strains, which will die. More specifically, we limited the resistance of the
-			the inducible promoter prevents a particular gene from expressing preferentially.
+			colicin-resistant bacteria in the sense that it would produce a type of bacteriocin that is only toxic to itself and
+			to the sensitive strain, and additionally the resistant strain would also be vulnerable to the colicin produced by
+			the colicin-producer.  Since which strain will be the one that survives is determined by very small differences in
+			the initial concentrations of the three different populations of bacteria, in practice this systems becomes a
+			randomizer because of the imprecisions in the measurements that result, for example, when using micropipettes.
+			This randomizer describes a new competition dynamic that could not be reproduced in the previous model proposed
+			by Durrett and Levin due to the instability along the
+			<img src="https://static.igem.org/mediawiki/2011/e/e0/Image088.png" alt="u1">axis.
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/c/c1/Colimodel1.png" alt="our new model" />
+		</div>
 		<p>
-			Now that we have designed a recombination mechanism that allows the expression of
+			If we set the parameters as follows
-			three signaling molecules one at a time, the next step towards making a randomizer
-			is to make sure these three signals are expressed with the same probability,
-			so that E. coli's choice in the RPS game cannot be predictable.
-			So, how can we make the probability of expressing each of these signals the same?
-		</p>
 		</p>
-		<h6 id="1.1.1.3.1">1.1.1.3.1</h6>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/0/00/Colimodel2.png" alt="new model's coefficient" />
+		</div>
 		<p>
-		<p>
+			and we graph this equations using a Matlab program,
-			How to make each of the Outcomes (R, P, and S) Equally Probable<br />
+			we get a graph which clearly shows there are stable points on each of the three axes
+			(Fig. 1, Up).
-			The first step towards making the probability of each of the three genes' expressions
-			to be the same, is to examine the recombination frequency of each lox cassette.
 		</p>
+		<div align="center">
+			<img src="https://static.igem.org/mediawiki/2011/b/b8/Model2.png" width="815px" style="float:center;"/><br />
+		<img src="https://static.igem.org/mediawiki/2011/0/05/Image106.png" width="815px" style="float:center;"/>
+</div>
+		<div align="center">
+			Fig. 1 Up: Our New model. Down: The Old Model
+		</div>
 		<p>
-			For that purpose, three kinds of BioBricks were constructed. Two of them are expected
+			These stable points (u<sub>1</sub>,0,0), (0,u<sub>2</sub>,0) and (0,0,u<sub>3</sub>) indicate that for the equations
-			to express GFP when the lox sites are excised and RFP when they are not: <br />
+			we have set all of the three strains may ultimately survive for infinite peiriods of time.
-			<ul>
+			The differences between our model and the model of Durrett and Levin can be seen graphically
-				<li>PlacIQ-lox2272-rfp-lox2272-gfp (BBa_640201)</li>
+			in Fig. 1. These graphs were plotted using Matlab.
-				<li>PlacIQ-lox71-rfp-lox66-gfp (BBa_640202),</li>
-			</ul>
-			By comparing levels of GFP fluorescence and RFP fluorescence we could determine the
-			relative recombination frequency of BBa_640201 and BBa_640202 (the recombination
-			frequency levels when compared to one another).
-			Besides these two BioBricks we made another one with the construction
-			PlacIQ-lox2272-gfp-lox2272(BBa_640200).  For this last BioBrick, in vivo and in vitro
-			assays were made.
 		</p>
 		<p>
-			The in vitro assay of BBa_640200 allowed us to confirm that the Cre-mediated
+			Note that the parameters we have set for our equations satisfy the initail conditions
-			recombination on lox2272 cassette works as designed.  In the assay, the part was
+			of the model proposed by Durrett and Levin (indicated in black font)
-			made linear using restriction enzymes. Cre recombinase (xconcentration, xvolume)
+			<img src="https://static.igem.org/mediawiki/2011/a/a4/Colimodel4.png" alt="new terms" width="800px"/>
-			was added to the linear DNA (x concentration, x volume) and incubated for 0.5, 2,
-			and 4 hours.  Images of the experiments have been added below.
 		</p>
+		<h4 id="3.3.6">3.3.6 The Biological Meaning of our Model</h4>
-		IMAGES
 		<p>
-			These images of the electrophoresis experiments show that there are several bands in
+			From a biological perspective, our model describes the existence of two strains of
-			samples to which Cre was added, which indicates that excision of the lox sites
+			bacteria that produce two different types of bacteriocins. One of these strains is not
-			successfully occurred.
+			completely resistant to its own bacteriocin nor to the bacteriocin produced by its
+			rival strain. This can be justified as the consequence of insufficient/ineffective
+			resistance protein production by the &ldquo;resistant&rdquo; strain. This limitation in the
+			production of resistance protein could be thought of as a consequence of the
+			&ldquo;resistant&rdquo; strain being a mutant of a colicin-sensitive strain.
 		</p>
+		<h4 id="3.3.7">3.3.7 Making it Obvious</h4>
 		<p>
-			For the in vivo assay, we prepared a competent cell JM2.300 into which
+			From the graph of our new model (Fig. 1, left) it can be deduced that there are paths
-			Pbad/araC-Cre(pSB1A2, BBa_ ####) had been constructed. Subsequently, our BioBrick
+			that converge at stable points (u<sub>1</sub>,0,0), (0,u<sub>2</sub>,0) and (0,0,u<sub>3</sub>), and that this paths all
-			was constructed into the cell's genome. The strain was grown in a 3ml liquid culture,
+			have an approximately common origin. In this section we would like to show that the
-			and 75μl of 2M arabinose was added to induce Cre expression. For the control
+			origin of these paths is practically the same, and that in that sense we have designed
-			experiments we used the same strain without arabinose induction and a JM2.300
+			a true randomizer (since, as mentioned before, the imprecisions that result in the
-			strain which had only our BioBrick.  All the strains were cultured each for periods of
+			experimental measurements will make it impossible to make the initial
-.5, 1, 2, and 4 hours, and in each case the florescence levels were measured by
+			population density of the three strains the same).
-			flow cytometer and fluorescence microscopy.
 		</p>
+		<p>
+			In the following set of graphs we will make it obvious that each of the three
+			different strains of E. coli to survive in a random fashion by very small
+			differences on the initial concentrations of each strain.
 		</p>
+		<p>
+			We modeled our results using Matlab.
+			As can be seen in the graphs below, each of the strains can survive if their
+			initial density in only tree hundredths (a.u.) greater than the other two strains'
+			initial concentrations.
+		</p>
+		<table>
+			<tr>
+				<td>
+					<a href="https://static.igem.org/mediawiki/2011/thumb/1/19/Image130.png/800px-Image130.png">
+						<img src="https://static.igem.org/mediawiki/2011/thumb/1/19/Image130.png/800px-Image130.png" alt="output1" Width="400px" />
+					</a>
+				</td>
+				<td>
+					<a href="https://static.igem.org/mediawiki/2011/thumb/a/a1/Image132.png/800px-Image132.png">
+						<img src="https://static.igem.org/mediawiki/2011/thumb/a/a1/Image132.png/800px-Image132.png" alt="output2" Width="400px" />
+					</a>
+				</td>
+			</tr>
+			<tr>
+				<td>
+						<img src="https://static.igem.org/mediawiki/2011/1/11/Tt-modeling1.png" alt="coefficient of output1" Width="400px"/>
+				</td>
+				<td>
+						<img src="https://static.igem.org/mediawiki/2011/9/99/Tt-modeling2.png" alt="coefficient of output2" Width="400px"/>
+				</td>
+			</tr>
+			<tr>
+				<td>
+					<a href="https://static.igem.org/mediawiki/2011/thumb/a/a2/Image134.png/800px-Image134.png">
+						<img src="https://static.igem.org/mediawiki/2011/thumb/a/a2/Image134.png/800px-Image134.png" alt="output3" Width="400px" />
+					</a>
+				</td>
+				<td rowspan="2">
+					With these graphs it becomes clear that the imprecisions in experimental measurements
+					(i.e. pipetting) are enough to cause the outcome of Rock, Paper or Scissors signaling
+					molecule to be random. Consequently, we can conclude that this randomizer is not
+					only feasible but also practical and effective (let alone interesting).
+				</td>
+			</tr>
+			<tr>
+				<td><img src="https://static.igem.org/mediawiki/2011/b/b7/Tt-modeling3.png" alt="coefficient of output3" Width="400px"/></td>
+			</tr>
+		</table>
+<h2>References</h2>
+	<p>
+	<ul>
+<li>Patrick C. Seed <i>et al</i>. &ldquo;Activation of the Pseudomonas aeruginosa lasI Gene by LasR and the Pseudomonas Autoinducer PAI: an Autoinduction Regulatory Hierarchy&rdquo; JOURNAL OF BACTERIOLOGY (1995)</li>
+<li>Shotaro Ayukawa <i>et al</i>. &ldquo;Construction of a genetic AND gate under a new standard for assembly of genetic parts&rdquo; BMC Genomics (2010)</li>
+<li>Robert Sidney Cox, III <i>et al</i>. &ldquo;Programming gene expression with combinatorial promoters&rdquo; molecular system biology (2007)</li>
+<li>Rolf Lutz <i>et al</i>. &ldquo;Independent and tight regulation of transcriptional units in Escherichia coli via the LacR/O, the TetR/O and AraC/I1-I2 regulatory elements&rdquo; Nucleic Acids Research (1997)</li>
+<li>Karina B.Xavier and Bonnie L.Bassler 2004. Regulation of Uptake and Processing of the Quorum-Sensing Autoinducer AI2 in Escherichia coli. JOURNAL OF BACTERIOLOGY, Jan. 2005, p. 238-248</li>
+<li>Ting Xue, Liping Zhao, Haipeng Sun, Xianxuan Zhou, Baolon Sun 2009. LsrR-binding site recognition and regulatory characteristics in Escherichia coli AI-2 quorum sensing. Cell Research (2009), p.1258-1268</li>
+<li>Liang Wang, Yoshifumi Hashimoto, Chen-Yu Tsao, James J.Valdes, and William E.Bentley 2004. Cyclic AMP(cAMP) and cAMP Receptor Protein Influence both Synthesis and Uptake of Extracellular Autoinducer 2 in Escherichia coli. JOURNAL OF BACTERIOLOGY, Mar. 2005, p. 2066-2076</li>
+<li>Jean Livet, Tamily A. Weissman, Hyuno Kang, Ryan W. Draft, Ju Lu, Robyn A. Bennis, Joshua R. Sanes and Jeff W. Lichtman (2007). Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system. Nature.</li>
+		<li>Kimi Araki, Masatake Araki1 and Ken-ichi Yamamura (2002). Site-directed integration of the cre gene mediated by Cre recombinase using a combination of mutant <i>lox</i> sites, Nucleic Acids Research</li>
+<li>Durrett, R., Levin, S. Allelopathy in Spatially Distributed Populations (1997). Journal of Theoretical Biology, 185, 165-171. </li>
+	</ul>
 	</p>
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