Team:Tokyo Tech/Modeling

1. Introduction

Detail designs are shown below.

1.2 Cell population

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

1.3 Signaling molecules

These equations describe concentrations of C4HSL and 3OC12HSL.

First and Second term of (4) describes production of C4HSL from RhlI in Bank and Company cells. Third term is meant for decomposition of C4HSL by AiiA in Bank cell. Fourth term is for degradation of C4HSL.

Same goes on 3OC12HSL. First term describes the production of 3OC12HSL from LasI in Bank. Second term is for decomposition of C12HSL by AiiA in Bank cell. Third term is for 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 C12, RhlI and CmR will be expressed.

2. Story simulation details

2.1. Company and Customer co-culture simulation

The result of simulation is shown below. To make the condition of the simulation same to the actual experiment, the cells are first cultured in a medium without chloramphenicol. Later chloramphenicol was added to the medium. The following graph only shows the simulated populations of Company and Customer in the latter condition.

As above graph shows, this simulation tells the population won’t grow in this condition.

1. 2.2 Co-culture simulation with Prhl_RL

In order to avoid the death of Company and Customer, We chose Plux on company cell regulating the expression of CmR and LasI. Detail of the choice of improvement is shown in the page : (still not decided name but will be on other page under modeling.)

Our improved promoter has the same amount of leakage and higher amount of maximum expression rate. In Fig. ?(equations), this corresponds to the higher alpha values on equation (5) and (6). According to the experimental result, the value of the maximum expression under Prhl are set to over 10 times larger than the original one.

The result of the simulation is shown below. To simulate in exact same condition to the experiment, the cells are first cultured in a medium without chloramphenicol. Later chloramphenicol was added to the medium. The following graph shows the result of simulation.

As shown in above graph, company and customer grows well in this condition.

The system with Bank was also simulated. Same to the above two simulations, the cells are first cultured in a medium without chloramphenicol. Later chloramphenicol was added to the medium. The result is shown below.

RhlI is expressed in distribution state. And AiiA is expressed in collection state. The above graph shows the Bank first stayed in distribution state and later changes to collection state.

3. Reference

1. Motivation

2. Reason for the choice

Since the system has fewest components to achieve the mutual dependency, what we can change is the values of parameters. In the parameters in the equations, modifiable parameters are listed below.

Leakage is not listed above because Company and Customer will be independent if the leakage increase.

2.2. Modifications

Since there was no time to modify two or more components in the system, we should be able to achieve the goal with just one modification of the components. In the following we will examine which one to change one by one.

2.2.2.C4HSL,3OC12HSL production rate by RhlI, LasI(corresponds to k in (3) and (4))
Signaling molecule production rate by RhlI, LasI can be changed by modifying RhlI ,LasI protein to make more signaling molecule. We set these values to be 0.05 originally. The following graph shows how the final populations of Company and Customer change depending on the value of signaling molecule production rate. In this simulation the value of k in equation (4) is varied.

As shown above, if the value is over 10^-1, then the final populations of Company and Customer get higher. This implies Company and Customer can grow well if the signaling molecule production rate was improved.

2.2.3.Degradation rate of C4HSL and C12HSL

Changing pH of the medium can change degradation rates of C4HSL and C12HSL. Degradation rates d of equation (3) and (4) are varied simultaneously because the variation of pH affects not only d of one signaling molecule, but both of them. In the following simulation the degradation rate is varied from 10^-4 to 10^0. The result is shown below.

2.2.4 maximum expression rate of proteins following Plux (corresponds to alpha in equation (5) and (6))

Mutating promoter can result improving the maximum production rate of the following proteins. Thus the dependency of the final populations of Company and Customer was examined by varying the value of maximum expression rate alpha. The result is shown below.

The parameter alpha was originally set to 10^2. From the graph, if the parameter value increase, the populations of Company and Customer also increase. This means improving promoter can result in increasing populations.

2.2.5. Degradation rates of RhlI,LasI, Cloramphenicol resistane(corresponds to d in equation (5),(6),(7),(8))

The final populations are simulated with varying the parameter values. First degradation rate of RhlI was changed. The original value was 2*10^-2. The following graph is the result of the simulation.

The graph tells populations of Company and Customer cannot be higher in any value of degradation rate.

About degradation rate of chloramphenicol resistance, there’s no meaning in changing values. What we can do is only increase the degradation rate, but that results in reducing the internal chloramphenicol resistance concentration. This means the cells becomes easy to be killed. This is not an expected outcome.

2.3. Result

From the examination of each parameters, parameters possibly change the growth of Company and Customer is only C4HSL,3OC12HSL production rate by RhlI, LasI and maximum expression rate of proteins following Plux.

Former one is about changing the nature of proteins. Latter one is about changing the nature of promoters. We decided to modify promoters because changing the nature of promoters is easier than changing the nature of proteins.

1. Motivation

On our story, Bank has to change its state from collection state to distribution state, and vice versa depending on the concentration of C4HSL.

We analyzed the parameter range which can realize the mechanism.  

2. Analysis

2.1.Problem formulation

RhlR is ignored in the equations because it is constantly expressed in the cell.

What we want to achieve is

1. 1) In the high concentration of C4HSL, Bank circuit is stably in collection state. TetR expresses highly and LacI doesn’t express much.

2. 2) In the low concentration of C4HSL, Bank circuit is stably in the distribution state. LacI expresses highly and TetR doesn’t express much.

1. 2.2. Nullclines and stable state

Since our aim is to estimate stable state, nullclines for each equation play crucial role. Equations for nullclines of each protein are described below.

In terms of these equations, our aim is translated as follows.

1. 1) When the value of [C4] is high, these nullclines have to have one intersection which has high value on [TetR] and low value on [LacI].

2. 2) When the value of [C4] is low, these nullclines have to have one intersection which has low value on [TetR] and high value on [LacI]

Parameter values which satisify above two conditions are restricted to the following striped area.