# Team:Tokyo Tech/Modeling/Overview

Tokyo_Tech

## Modeling

Overview

Contents

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

# 1.1 Introduction

Since our genetic circuit is complex, it is very difficult to predict the system’s behavior intuitively. Thus we constructed mathematical models to predict the behavior.

Fig. 4-1-1-1. Genetic Circuit Design

Fig. 4-1-1-2. Corresponding Mathematical Model

### ・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

Fig. 4-1-1-5. Equations for Bank

Bank switches to two states during the cultivation. (6) and (7) describe the Distribution state. LacI represses the translation of TetR as described in first term of (8). RhlI will distribute C4HSL which represents money. On the other hand, (8) and (9) describe the Collection state. TetR represses LacI. AiiA decomposes C4HSL.

In order to achieve the state switching depend on the concentration of C4HSL, TetR and AiiA are regulated not only by LacI, but also by C4HSL. This makes the system be able to switch depends on the concentration of C4HSL.

# 1.5 Company

Fig. 4-1-1-6. Equations for Company

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

# 1.6 Customer

Fig. 4-1-1-7. Equations for Customer

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

# 2.1 Company and Customer co-culture simulation

The system which includes only Company and Customer was simulated before our experiments. From the analysis we performed, we noticed that strength levels of Prhl and Plux promoters should be equally strong as shown in Fig. 4-1-2-1.(Detailed analysis is shown in another modeling page.)

Fig. 4-1-2-1. Company and Customer growth dependency of Prhl and Plux promoters strength levels

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.

Fig. 4-1-2-2. Company and Customer can grow well with optimized parameters

# 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.

Fig. 4-1-2-3. Company and Customer cannot grow with less initial amounts

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.

Fig. 4-1-2-4. Addition of Bank make the system grow well

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.

Fig. 4-1-2-5. Bank changes its state from Distribution State to Collection State

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.

Fig. 4-1-2-6. Company and Customer cannot grow with economic wave

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.

Fig. 4-1-2-7. Bank can help Company and Customer even in the presence of economic wave

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.

Fig. 4-1-2-8. Bank cannot help Company and Customer enough in the presence of harsh economic wave