1. Mathematical Model

1.1 Introduction

1.2 Cell Population

1.3 Signaling Molecules

1.4 Bank

1.5 Company

1.6 Customer

2. Story Simulation Details

2.1 Company and Customer Co-culture Simulation

2.2 Introduction of Bank

2.3 Economic Wave

1. Mathematical Model

1.1 Introduction

・Table 4-1-1-1 Meaning of parameters

Detailed designs are shown below.

1.2 Cell Population

Fig. 4-1-1-3. Equations for cell population

The equations above describe how cells grow in the culture. Equation (1), (2), (3) describe the populations of Bank, Company, and Customer . All first terms of the equations are considered carrying capacity. Second terms of (2) and (3) describe the effect of chloramphenicol and chloramphenicol resistance gene. Note that in second terms  are set to 0 once the value becomes minus.

1.3 Signaling Molecules

Fig. 4-1-1-4. Equations for signaling molecules

These equations describe the concentrations of C4HSL and 3OC12HSL.
First and Second terms of (4) describe the production of C4HSL from RhlI in Bank and Customers cells. Third term is meant for the decomposition of C4HSL by AiiA in Bank cell. Fourth term is for the degradation of C4HSL.

Same goes on for 3OC12HSL. First term describes the production of 3OC12HSL from LasI in Company. Second term is for the decomposition of 3OC12HSL by AiiA in Bank cell. Third term is for the degradation of 3OC12HSL.

1.4 Bank

1.5 Company

In the presence of C4HSL, LasI and CmR will be expressed.

1.6 Customer

In the presence of 3OC12HSL, RhlI and CmR will be expressed.

2. Story Stimulation details

2.1 Company and Customer co-culture simulation

When the strength levels of Prhl and Plux promoters are in the red area, Company and Customer can grow well. Otherwise when strength levels are in the blue area, either Company or Customer cannot grow well.

With the optimized parameter values, Company and Customer can grow well as shown in Fig. 4-1-2-2.

2.2 Introduction of Bank

Company and Customer cannot grow well with less initial amounts than previous simulation as shown in Fig. 4-1-2-3.

But once we added the Bank to our system, they can grow well with the C4HSL produced by the Bank as shown in Fig. 4-1-2-4.

Along with the growth of the system, Bank eventually changes its state from distribution state to collection state. This is shown in Fig. 4-1-2-5.

As shown in Fig. 4-1-2-5, C4HSL concentration increases, RhlI concentration follows the blue line in the figure, lastly RhlI won't be expressed. On the other hand, when the C4HSL concentration decreases, RhlI concentration follows the green line in the figure, results in high expression of RhlI.

2.3 Economic wave

With the advice from entrepreneurs, we introduced economic wave to our system. Detail is shown in Economic Wave page in the modeling.

Once the economic wave is introduced to our system, Company and Customer cannot grow well because of the recession during the economic wave. This is shown in Fig. 4-1-2-6.

As in the real economy, we also introduced Bank to this system. The result was different depending on the harshness of the economic wave. If the economic wave is moderate, then the Bank can help Company and Customer grow well even in the presence of economic wave. This is shown in Fig. 4-1-2-7.

But if the economic wave is harsh, then Bank cannot help Company and Customer enough. The result is shown in Fig. 4-1-2-8.