Rock-Paper-Scissors game

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 Judge

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 Alliance. This potential AND-gate promoter is designed to be activated by the addition of both IPTG and 3O-C6-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 3O-C6-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.

Tokyo Alliance 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: PlsrA (BBa_K117002) and PlasI (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 lasI and lsrA promoters parts by making new parts that work! As can be seen in the experimental information below (see “Improving PlsrA” and “Improving PlasI”), we confirmed our PlasI (BBa_K649000) and PlsrA (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 chose the signaling molecules corresponding to Paper and Scissors, so we have again a working RPS game design.

2.3 Improving PlsrA

LEFT: Not working PlsrA (BBa_K117002) RIGT: Working PlsrA (BBa_K649100)

We confirmed that the lsrA promoter BBa_K117002 does not work properly (samples used our experiments are listed in Table 1 below). We measured transcriptional activity of lsrA promoter by introducing a gfp gene downstream of this promoter (Fig.1).The intensity level of GFP fluorescence of BBa_1K17002 were lower even than those of the negative control (Fig.2), which clearly shows that lsrA promoter(BBa_K117002) does not work as expected.

To solve this problem, we created the first working iGEM lsrA promoter (BBa_K649100). This promoter can be repressed by our new LsrR part (BBa_K649107). We measured the transcriptional activity of our lsrA promoter by introducing a gfp gene downstream of the promoter. Its fluorescence intensity was much higher than that from a promoter-less GFP negative control plasmid, showing that our new lsrA promoter works. The parts we constructed can be found below.

2.4 Improving PlasI

LEFT: Not working lasI promoter (BBa_J64010). RIGHT: New working lasI promoter (BBa_K649000) we made. We confirmed it works as expected. In our assay, we used the same LsrR 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 prove that the problem resided in the PlasI part and not in the LasR part, we did another assay with a well characterized LasR part that we received and that is known to work well. Details about this assay can be found here

The constructions we made to test our promoter can be found below.

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 chose 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 the Fittest and Conditional Knockout by Recombination.

3.1 Single Colony Isolation

This is our simplest randomizer design. To make sure E. coli choses 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

3.2.1 The Requirements

3.2.2 The Mechanism

3.2.3 Testing the Lox Cassettes

3.2.4 Playing Fair: Future Work

3.3 Survival of one strain

控え

In 1996 Durret and Levin described a system of three types of bacteria that competed for survival in dynamic that resembled a Rock-Paper-Scissors (RPS) game. The bacteria used two main evolutionary stable strategies (ESS) to outcompete their rivals: 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. The system was described by the following general differential equations ∑_(i=1)^n?u_i < 1
(du_i)/dt=β_i u_i u_0- u_i ( δ_i+∑_(j=1)^(n-1)??γ_j u_j ?)
u_0=1-∑_(i=1)^n?u_i
Where
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 Durret & Levin (1996)
In this model, however, there is no case where the colicin-producer can survive for infinitively long periods of time if the colicin-resistant's initial concentration is greater than zero. This can be seen in the graph drawn by Durret and Levin, where the lines along the axis for u_1 (in the rightmost lower corner) always converge either to u_3 or u_2. We highlighted this fact by circling the point in the graph below. 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. Producer (du_1)/dt=β_1 u_1 u_0- u_1 δ_1 Limited Resistance (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 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. These stable points (u_1,0,0), (0,u_2,0) and (0,0,u_3) indicate that for the 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. To see the difference between our model and Durret and Levin's model more clearly, we also plotted Durret and Levin's model using Matlab. Note that the parameters we have set for our equations satisfy the initail conditions of the model proposed by Durret and Levin (indicated in black font) in the sense that β_3>β_2>β_1, γ_1>γ_2 >γ_1'>γ?_2', and δ_1=δ_2= δ_3. The two new terms we added are indicated in red. From a biological perspective, this model describes the existence of two strains of 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. The next step is to find a set of parameters that satisfy the conditions set by the model of Durret and Levin, the above condition of allowing stable points on each of the three axes and also allow each of the three different strains of E. coli to survive in a random fashion by minimal differences on the initial concentrations of each strain. We found, by writing another program in Matlab, that the following set of parameters satisfy all of the above mentioned conditions. β_3=3, β_2=3.2,? β?_1=5.1 γ_1=2,γ_2=1,? ? γ?_1'=0.2 ,γ?_2'=0.01 δ_1=δ_2= δ_3=1 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. The producer strain survives if u_1= 0.32, u_2= 0.29, u_3= 0.29 (a.u.).
The limited-resistance strain survives if u_1= 0.29, u_2= 0.32, u_3= 0.29 (a.u.).
The sensitive strain survives if u_1= 0.29, u_2= 0.29, u_3= 0.32 (a.u.).
In practice, this minimal variation of concentrations will 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).