Model03

=Model3: Entire System Simulation

Simulation 3-1 Chemotaxis

Abstract

We simulated the chemotaxis of colony of 10⁸ E.coli using Asp diffusion model in model1 and the approximation of chemotaxis we derived in model2. The result was consistent with the experimental result.

Methods

We considered the dynamics of E.coli colony as following simultaneous partial differential equations.

We already knew the values of parameters V, D_E, D_A using model1 and model2. In this section we use the hypothesis that E.coli digests Asp. However, the digestion rate was not clear so we ran the simulation with some different digestion rates: k= 3.3×10^-21, 3.3×10^-20, and 3.3×10^-19 [mol]. To be exact, we had to consider the growth of E.coli, but the colony growth is so complex a process that we could not find out an appropriate colony growth model (i.e. A growth rate as a function of E.coli density). For this reason we did not consider the growth in our simulation. We simulated the time development of above equations using 1st order finite difference method. The initial state was shown in fig.1.

Following movies are the result of the simulation. Color strength indicates the concentration of E.coli. [mov1. 3.3*10^-21] [mov2. 3.3*10^-20] [mov3. 3.3*10^-19]

Figure 2 is the result of the experiment.

Judging from comparison between the movies and the result of experiment, the simulation whose digestion rate was k= 3.3×10^-20 reproduces the experimental result well. It can be said that we succeeded in simulating the Asp chemotaxis of E.coli.

Simulation 3-2 inducing to substrate

Aim

In our experiment we ended up not showing the entire system i.e. “Some E.coli detect substrates and they secret Asp and then make other E.coli assemble”. So we aimed to show it numerically and to present the advantage of this system by comparing with the old way.

Methods

We modified the program used in simulation 3-1 to replicate the Asp secretion in Substrate area.

According to the paper ^[1], we can make 50mg (dry weight) E.coli produce Asp at 0.1mmol/min. Given a single cell weighs 3.0×10^-13g (dry weight)^[2], the maximum Asp production rate is 10^-17 mol/(sec*cell). We used this value in the simulation.

We used k= 3.3×10^-20 as the Asp digestion rate.

We located E.coli colony at the center of agar gel and substrate area which diameter was 10mm at 25mm distant from the center. We ran the simulation and measured the cell density over time.

We also simulated E.coli with no Asp secretion as the control. This case was intended to replicate the old way that lets E.coli to diffuse and no induction happens.

Results

Following movies are the result of the simulation. [movie4]　with Asp induction [movie5]　mere diffusion

Discussion

The results clearly showed that Asp secretion significantly raised the cell density around substrate area.

This simulation has the limitation that it did not consider the factors that lead cell density to decrease (effect of E.coli density limit, Asp saturation etc) and therefore E.coli gathered at a single point with very high density.

Simulation 3-3　Bioremediation and the effect of “Arrest”

Aim

We aimed to show the validity of our system in bioremediation which is our ultimate objective. We also evaluated the effect of “Arrest”.

Methods

We evaluated the effectiveness of bioremediation by comparing the degradation rate of substrate. In this simulation E.coli degrades substrate and its degradation rate increases as the square of E.coli density. The reason for this was the Arrest system was suitable for the target which requires high E.coli density.

“Arrest” system was intended to slow down E.coli movement. When Arrest switch turns ON, the probability of “tumbling” increase and they become less mobile. In this simulation if E.coli detect substrate, the switch turns ON.

The DNA parts for “Arrest” was already made and the effect was verified experimentally. Figure 4 and Figure 5 are the result of the experiment.

At the beginning, E.coli colony was located at the center of the gel and both of them were same size. Figure 4 indicates the Arrest-ON colony after 20 hours of the beginning. Figure 5 indicates the Arrest-OFF. The area of colony in figure 4 was about ten times smaller than that in figure 5. According to the theory of physics, the area of material which is diffusing increases in proportional to its diffusion coefficient. So in our program, the diffusion coefficient was timed 1/10 when they are in substrate area.

We simulated following three cases. 1. mere diffusion 2. Asp induce only 3. with Arrest The initial states of E.coli and substrate are shown in fig. 2. We recorded the time development of total degradation amount in each case.

Results

[movie6] [movie7] [movie8]

Discussion

Victory!