Model2: A simple model for E.coli chemotaxis

iGEM UT-Tokyo

Aim

We derived a simple relationship between Asp concentration and E.coli chemotaxis so that we were able to simulate macroscopic ¥(n~10^8) E.coli colony chemotacitc behavior.

Background

We considered internal condition of E.coli (receptor methylation etc) by SPECS model^[1]. SPECS is a relatively accurate taxis model, and is suitable for simulation of approximately ten thousand E.coli for approximately 10 minutes. This model, however, take too much time to reproduce our system, because the system includes much more E.coli(about one hundred of million) and takes a relatively long time (a few days). So, by adapting SPECS model to our system, we have devised a new model that provides less calculation amount and enough accuracy. Concretely, we divided chemotactic motion of E.coli groups into two factors, that is, parallel translation and diffusion. Then we derived approximation equations that figure out the two respective values from Asp concentration and its gradient.

Method

In this study, we used SPECS method to simulate E.coli chemotactic motion. Here we introduce the brief overview of SPECS.

We processed Monte Carlo simulation for 20000 E.colis which behavior was based on SPECS in some different Asp concentration and its gradient. The gradient we used were exponential ¥[eqn 1]. We approximated E.colis movement as the combination of parallel translation and diffusion. We recorded the time course of average position <x> and root-mean-square <x²> and then calculated average velocity ¥[eqn 2] and the diffusion constant ¥[eqn 3].

For these results we derived the relationship between:

• Asp concentration and average velocity of E.coli
• Asp concentration and diffusion constant of E.coli
• gradient of Asp concentration and average velocity of E.coli
• gradient of Asp concentration and diffusion constant of E.coli

Finally we fitted approximated curve to these data.

Result

¥[fig1. relationship between Asp conc. and avg. velocity] ¥[fig2. relationship between gradient of Asp conc. and avg. velocity] ¥[fig3. relationship between Asp conc. and diffusion coef.] ¥[fig4. relationship between gradient of Asp conc. and diffusion coef.] fitted curveは次の式で与えられる。 ¥[eqn4](tanh(0.66*(log(A)+11.35))+1.0)*0.055*grad(log(A)) ¥[eqn5](tanh(0.65*(log(A)+11.5))+1.0)*(tanh(0.71*(grad(log(A))-2.05)+0.9)*0.0037+0.0047 ¥φ means Asp concentration.

References