Project

1. Introduction

In our E. coli’s version of Prisoner’s Dilemma game involving two prisoner coli, the results of their options define the profit they obtained. Here, profit means the growth of E. coli. Like the prisoners in the game theory, we genetically engineered two E. coli to act as the prisoners, Prisoner A and Prisoner B. The prisoner colis are able to cooperate or to defect in our game. The combinations of their options (cooperation or defection) affect the profit they obtained which equals to their growth. To cooperate, they produce AHL while to defect, they do not produce AHL. Each prisoner coli is designed to produce different type of AHL (C4HSL or 3OC12HSL). The act of producing AHL imposes a metabolic burden on both prisoner coli.

2. The original Prisoner’s Dilemma scenario in game theory

The original Prisoner’s Dilemma scenario involves two members of a criminal gang who were given an option-selection opportunity either to cooperate or to defect, in order to pursue for the best profit defined in the payoff matrix (Fig.2-1-2-1). This Prisoner’s Dilemma game is a typical example analyzed in game theory. The two gangs were arrested by the police. They were separated into two different rooms so that they can’t communicate. In these individual rooms, each prisoner was given an the opportunity either (1) to cooperate with the other prisoner by remaining silent, or (2) to defect the other criminal by confessing to his crime. Their corresponding punishment is shown in Fig.2-1-2-1. This table is called the payoff matrix.

Fig.2-1-2-1. The payoff matrix in Prisoner’s Dilemma (punishment = imprisoned years)

From the payoff matrix, one rational option combination, called the Nash equilibrium, is when both chooses defection. From A’s point of view, if B were to defect, A should choose to defect, comparing 10 years to 5 years of imprisonment. If B were to cooperate, A should choose to defect, comparing 2 years to 0 year of imprisonment. In other words, regardless of which option the other decides, each prisoner is punished less by defecting the other. B’s rational decision is the same as A, so combination of both prisoner’s defection is one rational option combination.

Although both prisoners’ defection result from the combination of selfish option selecting, the combination of both prisoners’ simultaneous cooperation actually brings more profit to both prisoners than the combination of such selfish selections. Apparently, 5 years imprisonment for both prisoners is more severe than 2 years imprisonment for both prisoners. Thus the combination of both prisoners’ defection is not called Pareto efficiency. This game with such payoff matrix where Nash equilibrium is not the Pareto efficient is called the Prisoner’s Dilemma.

3. Replication of the payoff matrix using E.coli

3.1 Prisoner coli’s dilemma payoff matrix

Referring to Fig.2-1-2-1 shown above, we replicated the payoff matrix using E. coli whose growth inhibition stand for punishment (Fig.2-1-3-1). Prisoner A and B are able to cooperate or to defect. As a result of combination of options, each prisoner coli is applied a corresponding growth inhibition, (none, low, middle, or high).

Fig.2-1-3-1. Our replicated payoff matrix for growth inhibition effect on Prisoner coli (A: Prisoner A, B: Prisoner B, C: Cooperation, D: Defection)

In the implementation of our replicated payoff matrix, combined effect by antibiotics and metabolic burden can apply 4 types of growth inhibitions (none, low, middle, high) which our prisoner coli will face with. Because our game procedure includes exchange of culture supernatant (Fig.2-1-3-2) (See the experiment page for detailed protocol), AHL produced by a prisoner’s cooperation induces the opponent’s expression of an antibiotic resistant gene, and thus circumvents growth inhibition of the opponent. Note that AHL produced by a prisoner has no effect to itself due to binding specificity among AHLs and corresponding transcription activator proteins. The production of AHL also cause metabolic burden in the cooperating prisoner coli. The initially designed genetic circuits of Prisoner A and B in cooperating and defecting mode are shown in Fig.2-1-3-3.

Fig.2-1-3-2. Experimental procedure in the implementation of our replicated payoff matrix

Fig.2-1-3-3. The genetic circuits of prisoner coli with the options of cooperation or defection

3.1.1 Both cooperation leads to low growth inhibition

When both prisoner coli cooperate, both of them will experience “low” growth inhibition caused by metabolic burden in producing AHL. By exchanging the culture’s supernatant, prisoner coli will receive their corresponding AHL, inducing the expression of chloramphenicol resistant gene (CmR). Thus, both of them will not receive any growth inhibition from antibiotic chloramphenicol (Cm), while both will experience metabolic burden by producing AHL (Fig.2-1-3-4). In this case, we define the growth inhibition as “low”.

Fig.2-1-3-4. Growth inhibition caused by metabolic burden in producing AHL as both prisoners cooperate>

3.1.2 Both defection leads to middle growth inhibition

In case of both prisoner coli defection which means absence of AHL induction, both of them will experience “middle” growth inhibition because lack of chloramphenicol resistant protein (CmR) does not circumvent antibiotic effect of Cm. Since defecting prisoner coli do not produce AHL, they will not receive their corresponding AHL during the exchange of culture supernatant. Thus, both of them will be freed from metabolic burden by producing AHL but receive moderate growth inhibition from Cm (Fig.2-1-3-5). In this case, we define the growth inhibition as “middle”.

Fig.2-1-3-5. Growth inhibition caused by Cm without CmR expression as both prisoners defect

3.1.3 When one is fooled, two types of growth inhibition (high and none)

When Prisoner A cooperates while Prisoner B defects, Prisoner A will experience “high” growth inhibition caused by metabolic burden and chloramphenicol (Cm) antibiotic while Prisoner B will experience “none” growth inhibition. By exchanging the culture supernatant, Prisoner A will not receive C4HSL, as being defected by B while Prisoner B will receive 3OC12HSL produced by cooperating A. Thus, Prisoner A will experience both of metabolic burden by producing AHL and moderate growth inhibition from Cm. On the other hand, Prisoner B will not experience any growth inhibition since Cm resistance is acquired (Fig.2-1-3-6). We define the growth inhibition as “high” and “none” respectively.

Fig.2-1-3-6. Growth inhibition caused by both metabolic burden in producing AHL and Cm antibiotic as cooperating prisoner being defected while nothing will happen to defecting prisoner being cooperated.

3.2 Modeling selected a solution for leaky expression problem to satisfy the requirement of the payoff matrix

At the first stage of wet experiment, initial designed circuits showed leaky expression of chloramphenicol resistant protein (CmR). “Middle” growth inhibition is required for implementation of our payoff matrix (Fig.2-1-3-7A) (See the experiment page for details). However, cells showed active growth even in the absence of AHL when the cell harboring either of our firstly designed genetic circuit Pcon_rhlR_TT_Plux_CmR in Prisoner A coli or Pcon_lasR_TT_Plux_CmR in Prisoner B coli (Fig.2-1-3-7B). Please refer to modeling page for Prisoner B coli’s results.

Fig.2-1-3-7. We compared the results in modeling and wet lab

To solve this problem, our series of modeling suggested us select next circuits design to add an ssrA degradation tag to the C-terminal of the chloramphenicol resistant protein (CmR). Firstly, we adjusted the model to include leaky expression of CmR protein (Fig.2-1-3-7C) (Further information of modeling is here). We then planned two solutions, each of which is evaluated by modeling, to circumvent the effect of leaky expressions (Fig.2-1-3-7DE). Because increase of degradation rate of CmR showed more effective suppression of growth than increase of Cm concentration, we created CmR coding sequence with an ssrA degradation tag (BBa_K1632020).

3.3 Improvement of CmR protein property by addition of an ssrA degradation tag

For precise implementation of our payoff matrix, suggestions from modeling allow us successfully improving the former plasmid by adding an ssrA tag right after the CmR gene (Fig.2-1-3-8). The ssrA tag helps to degrade the leaked chloramphenicol resistant protein (CmR). The improved parts (BBa_K1632020) was used for construction of BBa_K1632023 circuit for C4HSL inducible expression of CmR. Compared with circuits without an ssrA tag BBa_K1632025, our improved BBa_K1632023 indeed showed much slower growth which corresponds to “middle” growth inhibition (Fig.2-1-3-9 pink dotted line). Furthermore, addition of C4HSL recovers active cell growth which corresponds to “none” growth inhibition (Fig.2-1-3-9 blue line). These results show the improved function of AHL-dependent CmR expression by measuring the concentration of cells.

Fig.2-1-3-8. An improved plasmid is constructed by adding an ssrA tag to CmR

Fig.2-1-3-9. Our wet lab result suits the modeling result

3.4 Succeeded to replicate the payoff matrix through wet lab

Using the improved plasmids we constructed, our E.coli version payoff matrix is replicated through wet experiments. As mentioned earlier, we genetically engineered two prisoner coli, Prisoner A and Prisoner B. They are able to cooperate or to defect. The genetic circuits, with the improved chloramphenicol resistant protein (CmR) part, of Prisoner A and B are shown in Fig.2-1-3-10.

Fig.2-1-3-10. The genetic circuits of prisoner colis with the options of cooperation or defection

With the combination of four options between two prisoner coli, we succeeded to replicate the four types of growth inhibition (Fig.2-1-3-11) prisoner colis will face with in our payoff matrix. Because AHL production from those parts has already confirmed in descriptions in Partsregistry, in our experiment, corresponding AHL is added to prisoner colis when the opponent decided to cooperate. AHL is not added when the opponent decided to defect. Besides that, 100 microg/mL of chloramphenicol (Cm) is added to both prisoner colis. Prisoner coli will acquire Cm resistance when the opponent decided to cooperate. (Without Cm resistance, prisoner colis will face with growth inhibition.)

In the C4HSL presence which stand for cooperation of Prisoner B (Fig.2-1-3-11 case 1 and 2), Prisoner A acquired Cm resistance. Prisoner A showed “none” growth inhibition, because Prisoner A’s defection does not impose metabolic burden in the cell (case 1). On the other hand, additional cooperation by Prisoner A caused metabolic burden by producing AHL and showed “low” growth inhibition on Prisoner A (case 2)

In the C4HSL absence which stand for defection of Prisoner B (Fig.2-1-3-11 case 3 and 4), growth of Prisoner A is inhibited to some extents by Cm antibiotic effect. Even without metabolic burden, case 3, Prisoner A with defection, showed more severe growth inhibition than case 2. Furthermore, additional cooperation by Prisoner A (case 4) causes little growth due to metabolic burden by producing AHL. Thus we can define “middle” growth inhibition on case 3 and “high” growth inhibition on case 4.

The experiments using culture of Prisoner B cell and addition of 3OC12HSL resulted in the four types of growth inhibition effects similar to those for Prisoner A (Fig.2-1-3-12). (See here for more details on the wet experiments)

Fig.2-1-3-11. The results from our wet lab replicated the payoff matrix

Fig.2-1-3-12. The results from our wet lab replicated the payoff matrix

Considering the feedbacks we received from our school festival, we planned to give prisoner coli its own option selection opportunity without human involvement.

4. Prisoner coli decides its option : Cooperation or Defection

4.1 How to decide?

In order to enable a prisoner coli to randomly select its options between cooperation and defection, we noticed that a fim switch, which can invert a promoter sequence bidirectionally in the presence of FimB recombinase, is the part we need (Fig.2-1-4-1). Containing [ON] and [OFF] states, the fim switch controls the direction of transcriptions. The promoter in the fim switch directs transcription to the right when the fim switch is in the [ON] state. In the [OFF] state of the fim switch, on the other hand, the promoter directs transcription to the left. We further designed to allocate AHL-producing enzyme coding sequence at the left side of the fim switch. Note that, [ON] state fim switch will make prisoner coli to produce AHL, indicating cooperation. On the contrary, [OFF] state fim switch will prevent prisoner coli from AHL production, indicating defection. In the presence of FimB, random bidirectional inversion of the promoter-containing fim switch occurs, indicating random decision making.

Fig.2-1-4-1. In the presence of FimB recombinase, promoter in fim switch can be inverted at random.

To enable prisoner coli to have their own option selected randomly, we designed Decision making coli which expresses FimB protein (Fig.2-1-4-2A). Even only cooperation-mode plasmid was used for transformation of Decision making coli, two types of plasmids, ones in cooperation and defection mode, co-exist in the single cell due to inversion of the fim switch. We are then able to extract mixture of the both plasmid. When we use the plasmid mixture for transformation of prisoner coli, either one from the mixture will be introduced into a single cell. We thus cannot know the prisoner coli’s option selection at that moment. To confirm the activity by Decision making coli, we firstly used Fim switch GFP plasmids: GFP [ON] and GFP [OFF] (Fig.2-1-4-2B).

Fig.2-1-4-2. FimB allows Decision making coli to select option at random, inverting a promoter in a fim switch.

4.1.1 FimB assay : recombinase that inverts the fim switch at random

For implementation of Decision making coli, we newly constructed a plasmid, PBAD/araC_rbs_fimB (BBa_K1632012) that produces wild type FimB (Fig.2-1-4-3). We also prepared two other new plasmids, BBa_K1632007 and BBa_K1632008 (Fig.2-1-4-3). BBa_K1632012 enables arabinose-inducible expression of wild type FimB. In BBa_K1632007 and BBa_K1632008, either an [ON] or [OFF] fim switch is placed upstream of GFP coding sequence.

Fig.2-1-4-3. New plasmids we constructed to confirm the function of BBa_K1632012 plasmid for Decision making coli

From our wet lab results, FimB expressed from our new part, BBa_K1632012, is confirmed to randomly invert the fim switch bidirectionally, from [ON] to [OFF] state and from [OFF] to [ON] state (Fig.2-1-4-4, Fig.2-1-4-5, Fig.2-1-4-6). This is the first case in iGEM to show random inversion of a promoter. From the histogram C and D in Fig.2-1-4-4, forward move of the peak indicates increased accumulation of GFP by the FimB expression. This shows that some amount of fim switch[default OFF] state is into the [ON] state in the presence of FimB. Although only slight decrease of fluorescence from A to B was observed, the histogram B, after expression of FimB, shows close peak fluorescence to that in histogram C (Fig.2-1-4-4). This implies that fim switch[default ON] state is also inverted in some extent into the [OFF] state in the presence of FimB. Thus we tried to confirm such inversion by colony formation using plasmid mixture extracted cell expressing FimB, and by DNA sequencing of each plasmid obtained from each colony. Fig.2-1-4-5 and Fig.2-1-4-6 clearly shows inversion from [default ON] to [OFF] state; E. coli harboring the [ON] fim switch plasmid glows in green fluorescence while E.coli harboring the [OFF] fim switch plasmid does not glow under ultra violet light. Cells transformed by the plasmid mixture extracted from the experiment for histogram B formed two types of colonies: those with strong fluorescence and those with little background fluorescence. Also, sequence complementarity in the specific region of the switch shows intended inversion of the switch from [ON] to [OFF]. Furthermore, the nearly equal number of the colonies between fluorescent and non-fluorescent suggest random inversion of the fim switch by FimB expression. Similar analysis, by using the plasmid mixture extracted from the experiment for histogram C, also showed random inversion of default [OFF] plasmid. (Go to FimB Assay page)

Fig.2-1-4-4. The intensity of fluorescence in cells measured using flow cytometer

Fig.2-1-4-5. Colony formation using plasmid mixture extracted cell expressing FimB

Fig.2-1-4-6. DNA sequencing results of fim switch from [ON] to [OFF] stateDNA sequencing results of fim switch from [ON] to [OFF] state

We decided to make prisoner coli have their own strategies like humans, finding out that humans do have strategies while playing the game in our policy and practices.

5. Iterated game with several strategies

We decided to make prisoner coli to have their own strategies like human, finding out that humans do have strategies while playing the game in our policy and practices. In our game, we prepared four types of different strategies. Because evaluation of some strategies requires iterated games, we also created an E.coli version of iterated prisoner’s dilemma game.

5.1 The four strategies

We prepared four strategies: Random strategy, always cooperate strategy, always defect strategy and tit-for-tat strategy. In the in silico game tournaments around 1980, tit-for-tat strategy, written lastly in 5.1.4, was the most successful among the four.

5.1.1 Random strategy

TThe prisoner coli with this strategy makes every decisions randomly in each iterated game. Fig.2-1-5-1 shows random strategy by Prisoner A coli. After each game, the former cooperating or defecting plasmid in prisoner coli is recovered and introduced into Decision making coli. The Decision making coli expressing FimB will then produce two types of plasmids, cooperation and defection, in the single cell (refer 4.1). We cannot know if each molecule of the plasmid is either in the cooperating mode or the defecting mode. Because only one molecule of the plasmid is introduced to a competent prisoner cell, the decision will become random, regardless of what the other decides in the last game in the iterated games.

Fig.2-1-5-1. Prisoner A with random strategy in our iterated game

5.1.2 Always cooperate

The prisoner coli with this strategy will always cooperate no matter what the other decides. The plasmid will be recovered and again introduced into a fresh prisoner coli. By this, the fresh one will have the same plasmid with the previous prisoner coli. So, the certain prisoner coli (as shown in Fig.2-1-5-2) will always cooperate.

Fig.2-1-5-2. Prisoner A with always cooperate strategy in oue iterated game

5.1.3 Always defect

The prisoner coli with this strategy will always defect no matter what the other decides. Similarly, the plasmid will be recovered and again introduced into a fresh prisoner coli. By this, the fresh one will have the same plasmid as the previous prisoner coli. So, the certain prisoner coli (as shown in Fig.2-1-5-3) will always defect.

Fig.2-1-5-3. Prisoner A with always defect strategy in our iterated game

5.1.4 Tit-for-tat strategy

The prisoner coli with tit-for-tat strategy cooperates in the first game, then from second game onwards, copies the other’s decision from the previous game (Fig.2-1-5-4). Fig.2-1-5-4 shows tit-for-tat strategy by Prisoner A. If Prisoner B cooperated in the 1st game, Prisoner A’s option from the second game will be cooperation. In the third game, Prisoner A’s option will be defection given that Prisoner B defected in the last game. Prisoner A will just copy Prisoner B’s option from the previous game. Because mutual cooperation leads to the lowest growth inhibition while mutual defection leads to the highest growth inhibition, given that the opponent also experienced the same inhibition, tit-for-tat strategy becomes the most successful strategy.

Fig.2-1-5-4. The tit-for-tat strategy in our iterated game

To realize tit-for-tat strategy in prisoner coli, we designed an AHL-dependent modification of the prisoner plasmid. AHL released from the cooperation by opponent B from the previous game turns the Prisoner A plasmid into the cooperation mode (Fig.2-1-5-5). On the contrary, defection by opponent B from the previous game causes nothing to the Prisoner A plasmid which does not produce AHL at initial defection mode.

For Prisoner A’s mirroring the option of the opponent B from the previous game, we designed C4HSL-dependent expression of FimE, which inverts the fim switch unidirectionally (Fig.2-1-5-5). C4HSL released form the cooperating opponent B in the last game cause inversion of the switch and make Prisoner plasmid A produce C12HSL in the present game. Because all of the prisoner plasmid molecules extracted from Decision making coli in this case can produce 3OC12HSL, Prisoner A coli transformed by the plasmids shows cooperation by producing 3OC12HSL. Note that, in the presence of FimE, the fim switch can be inverted from [ON] to [OFF] but not from [OFF] to [ON]. Thus Prisoner plasmid A in this strategy is designed to initially have IasI-coding sequence in the opposite direction of the promoter in the [ON] switch. In the case of defection by the opponent from the previous game, the prisoner plasmid is not modified due to the absence of C4HSL from the last game, and thus does not produce 3OC12HSL, indicating mirrored defection by Prisoner A.　

Fig.2-1-5-5. Experimental procedure and genetic circuit for tit-for-tat strategy

5.1.4.1 FimE assay: recombinase that inverts fim switch in only one way

To confirm the function of fim switch in the presence of FimE, we constructed two new genetic circuit parts, BBa_K1632013 and BBa_K1632002 (Fig.2-1-5-6). BBa_K1632013 enables arabinose-inducible expression of wild type FimE. In BBa_K1632013 and BBa_K1632002, either [ON] or [OFF] fim switch is placed upstream of GFP coding sequence.

From our wet lab results, the FimE is confirmed to invert fim switch only from [ON] state to [OFF] state (Fig.2-1-5-7, Fig.2-1-5-8). From the histogram A and B in Fig.2-1-5-7, the peak moved backwards, indicating weakened intensity of the fluorescence in cells. This shows that fim switch[default ON] state is inverted into the [OFF] state in the presence of FimE. On the other hand, the peak hardly moved between the histograms C and D in Fig.2-1-5-7, indicating that fim switch[default OFF] state cannot be inverted into the [ON] state in the presence of FimE. We tried to confirm such inversion by colony formation by each plasmid molecule and DNA sequencing. Fig.2-1-5-8AB shows inversion from [default ON] to [OFF] state. (Go to FimE Assay page)

Fig.2-1-5-6. New plasmids we constructed to confirm the function of fim switch

Fig.2-1-5-7. The intensity of fluorescence in cells cells measured using flow cytometer

Fig.2-1-5-8. Colony formation by each plasmid molecule and DNA sequencing results of fim switch

6. Dilemma game in general public

Through the dilemma game we held among students in our Policy & Practices, we iGEM students realized the importance of continuously pursuing the process I nour project and, of the risk evaluation in synthetic biology as by ourselves. Initially, opinions from public received at our presentations at school festivals motivated us to investigate the stereotypes surrounding the sustainability, safety, and security of genetic modification. For integration of this concerned issue into our project, we designed and executed an expanded prisoner’s dilemma game played among high school and undergraduate students, who are people outside of iGEM. The game we designed, involving payoff matrices with or without dilemma and also payoff matrices associated with the idea of GMO, has four types of payoff matrix (Fig.2-1-6-1).

Fig.2-1-6-1. The four types of payoff matrices we designed

Through execution of the games, we found that the public chose the option which seems to be affected by the stereotype: “GMO is dangerous.” When we compared the total number of times the combination of options was selected among the participants in row 1, column 1 between Group 2 and 4’s payoff matrices (Fig.2-1-6-2), the result was 2% in Group 2, in which the idea of GMO was not associated, and 8% in Group 4, in which the idea of GMO was associated. Even though this combination of options (row 1, column 1) is not Pareto efficient, disfavor of GMO may have attracted more selections to this combination of options with less profit. (Further description is written here). A possible interpretation from this result is that the public’s option selection was affected by concerns for sustainability, safety, and security of genetic modification, which were not shown in the payoff matrix. To precisely examine further on this interpretation, we would like to increase the number of subjects playing the prisoner’s dilemma game.

Fig.2-1-6-2. Overall results of our expanded dilemma game among students

Interestingly, we found the example of a player who himself realized the irrationality of choosing the options adhered to the stereotypes of the term GMO in the middle of the iterated game. Player B, in Fig. Fig.2-1-6-3, experienced option selection influenced by preconceptions obtained when we first explained the original Prisoner’s Dilemma scenario. From the 4th round of the game, realizing that higher points is needed to win the game, Player B’s option became ‘use.’ So we temporarily thought of asserting that "each individual’s constant thinking of whether the payoff matrix is correct or not, will lead to the increase of the score for the entire society."

Fig.2-1-6-3. Results of a dilemma game held in between two students

However, from our full year experience in iGEM, we realized the necessity of verifying from a different point of view. In other words, we realized that we researchers ourselves must also continuously reflect on the risks and costs & benefits of the science we discover. In the workshop that we attended as our initial activity in iGEM, we learned from social scientists, the danger of grounding on the deficit model, which fixes on the idea that the general public is ignorant, and the importance of the two-way dialogue between society and researchers. From this past experience, we realized that it wasn’t the participants of the dilemma game who were misinterpreting the payoff matrix from the stereotype of the term GMO, but it might have been the members of iGEM Tokyo Tech who were misinterpreting both the costs and benefits of GMO. The scores of our payoff matrix in the dilemma game was indeed designed from assumptions for both the costs and benefits of GMO. Now we address that in order to understand the correct payoff matrix of technology, instead of forcing a concept that is constructed only by researchers, one-sidedly to the general public, the attitude of cooperating and thinking together with the general public, is important in social justice.（Click here to know more about our Policy & Practices）

From our full year of activities in iGEM, we realized the necessity of continuously reflecting on the risks and costs & benefits of the science we discover, and verifying thus science from a different point of view as a researchers ourselves.

From our full year of activities in iGEM, we realized the necessity of verifying continuously reflect on the costs, benefits, and risks of the science we discover from a different point of view as a researchers ourselves.

7. Reference

→ Bo Hu et al. (2010) An Environment-Sensitive Synthetic Microbial Ecosystem. PLoS ONE 5(5): e10619

→ John M. Abraham et al. (1985) An invertible element of DNA controls phase variation of type 1 fimbriae of Escherichia coli. Proc Natl Acad Sci USA 82(17):5724-7

→ Matthew P. McCusker et al. (2008) DNA sequence heterogeneity in Fim tyrosine-integrase recombinase-binding elements and functional motif asymmetries determine the directionality of the fim genetic switch in Escherichia coli K-12. Molecular Microbiology 67(1): 171-187

→ Hung M. et al. (2014) Modulating the frequency and bias of stochastic switching to control phenotypic variation. Nat Commun 5:4574. doi:10.1038/ncomms5574

→ McClain MS et al. (1991) Roles of fimB and fimE in site-specific DNA inversion associated with phase variation of type 1 fimbriae in Escherichia coli. J Bacteriol 173(17):5308-14.

→ Robert Axelrod (1980) Effective Choice in the Prisoner's Dilemma. The Journal of Conflict Resolution, Vol. 24, No. 1, pp. 3-25

Team:Tokyo Tech/Project