contents

1. Introduction?

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

3. Replication of the payoff matrix using E. coli

3.1 Prisoner coli’s dilemma payoff matrix

3.1.1 Both cooperation leads to low damage

3.1.2 Both defection leads to middle damage

3.1.3 When one is fooled, two types of damage

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

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

3.4 Succeeded to replicate the payoff matrix through wet lab

4. Prisoner coli decides its option : Cooperate or Defect

4.1 How to decide?

4.1.1 FimB assay: recombinase that inverts fim switch at random

5. Iterated game with several strategies

5.1 The four strategies

5.1.1 Random strategy

5.1.2 Always cooperate strategy

5.1.3 Always defect strategy

5.1.4 Tit-for-tat strategy

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

6. Dilemma game in general public

7. Reference

1. Introduction

We decided to replay the Prisoner’s Dilemma game, in which one’s profit depend on options of cooperation and defection, by using E. coli. The Prisoner’s Dilemma, a well-known game analyzed in game theory, involves dilemma between cooperation and defection. To pursue his or her own profit, one will choose to cooperate or to defect in the game.

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 according to the payoff matrix (Fig.2-1-2-1) in order to pursue for the best profit. This Prisoner’s Dilemma game is a typical example analyzed in game theory. Two members of a criminal gang 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 option. Each prisoner was given the opportunity either to cooperate with the other prisoner by remaining silent, or 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 Nash equilibrium, is both defections. 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 cooperate, 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. A’s judgement is the same to A, so option of both defections is one rational option combination.

Although both players’ defections result from combination of selfish option selections, the combination of both player’s simultaneous cooperation actually bring more profit to both players than the combination of selfish selections. Apparently, 2 years punishment for both prisoners is not severe than 5 years for both. Thus the combination of both defections is not called Pareto efficiency. This game with such payoff matrix where Nash equilibrium is not Pareto efficiency 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 option, 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, cooperation by a prisoner produces AHL to circumvent growth inhibition of the opponent which receives the AHL inducing expression of antibiotic resistant gene. 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.

3.1.1 Both cooperation leads to low growth inhibition

When two 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 experience metabolic burden by producing AHL. In this case, we define the growth inhibition as “low”.

3.1.2 Both defection leads to middle growth inhibition

When two prisoner coli defect, both of them will experience “middle” growth inhibition caused by Cm antibiotic without CmR expression in the absence of AHL. Since defecting prisoner coli do not produce AHL, they will not receive their corresponding AHL during the exchange of culture’s supernatant. Thus, both of them will free from metabolic burden by producing AHL but receive moderate growth inhibition from Cm. In this case, we define the growth inhibition as “middle”.

Fig.

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 Cm antibiotic while Prisoner B will experience “none” growth inhibition. By exchanging the culture’s 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 metabolic burden by producing AHL and moderate growth inhibition from Cm while Prisoner B will not experience any growth inhibition given that Cm resistance is acquired. We define the growth inhibition as “high” and “none” respectively.

Fig.

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 CmR. Although “middle” growth inhibition is required for implementation of our payoff matrix (Fig. 2.7A), 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- .). Please refer to modeling page for Prisoner B coli’s results.

Fig.2-1-3- .

To solve this problem, our series of modeling suggested us select next circuits design to add ssrA degradation tag to CmR protein. Firstly, we adjusted the model to include leaky expression of CmR protein (Fig. 2.7C). We then planned two solutions, each of which is evaluated by modeling, to circumvent the effect of leaky expressions (Fig. 2.7DE). Because increase of degradation rate of CmR showed more effective suppression of growth than increase of Cm concentration, we created CmR coding sequence with ssrA degradation tag (BBa_K1632020).

3.3 Improvement of CmR protein property by addition of 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-?). The ssrA tag helps to degrade the leaked CmR protein. The improved parts were used for construction of BBa_K1632020 circuit for C4HSL inducible expression of CmR. Compared with circuits without ssrA tag BBa_K395160, our improved BBa_K1632020 indeed showed much slower growth which corresponds to “middle” growth inhibition (Fig.2-1-3-??). Furthermore, addition of C4HSL recovers active cell growth which corresponds to “none” growth inhibition (Fig.2-1-3-??). These results show the improved function of AHL-dependent CmR expression by measuring the concentration of cells.

Fig.2-1-3-??

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 lab 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 CmR part, of Prisoner A and B are shown in Fig.2-1-3-???.

Fig.2-1-3-????

With the combination of four options between two prisoner coli, we succeeded to replicate the four types of growth inhibition (Fig. 2.12) prisoner colis will face in our payoff matrix. 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 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 growth inhibition.)

In the C4HSL presence which stand for cooperation of Prisoner B (Fig.2-1-3-????? case 1 and 2), Prisoner A acquired Cm resistance. Prisoner A showed “none” growth inhibition due to its defection (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-????? case 3 and 4), growth of Prisoner A is inhibited 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 experiment was also repeated by using 3OC12HSL, in this case Prisoner B showed similar results showing expected growth inhibition effects similar to those for Prisoner A (Fig.2-1-3-??????).