1.Introduction

   To understand, predict and ultimately control the behavior of our engineered microbial group effect, we have developed dynamic model of the system, based on transerential equations which describe and integrate the individual processes. This model involves several entities going from the molecular level (genes, RNAs, proteins, and metabolites) up to the cellular and population levels, distinct intracellular and extracellular compartments, and a wide range of biological and physical processes (transcription, translation, signalling, growth, transusion, etc). Here we can show the concentrate of DspB and Enterobactin produced by our engineered bacteria and the biofilm and rust removing time through calculating.

2.Observations

  Naturally, when there is a certain amount of HSL in the environment, HSL complex with afeR proteins and bind to afeR promoter which regulate positively the genes downstream (as shown on the Figure 1) and on that our sensing system relies to produce DspB and enterobactin.

3.Goals

  Our goal of this model is to create a generic quorum sensing model so that:

  • We can determine the effect of afeR promoter and predict the production of DspB and enterobactin.

  • We can predict hao long our engineered bacteria would take to remove the biofilm and rust.

4.Materials and Methods

4.1 HSL Transfer

  HSL is produced by iron bacterias and realeased into the water environment. So the first step of our sensing is HSL transfering into our engineered E.coli from the water. And a passive transusion model is used for this process that the transfer rate of HSL can be described as this:

  • K_HSL,W-C : transfer coefficient through the membrane (s−1)

  • We can predict hao long our engineered bacteria would take to remove the biofilm and rust.

4.2 AfeR-HSL Complexation

  AfeR is produced by engineered E.coli and functions in cell and its concentration is obtained approximating the number of protein per cell, using the E.coli concentration (cell/L) and the Avogadro number.

  The AfeR-HSL complexation is simply formed that way:

  Assuming kinetics of AfeR-HSL complexation complexation is fast compared to the rest of the system, we assumed that the free and complexed forms are at equilibrum.

  • K _{eq, AfeR-HSL} : equilibrum constant of the AfeR-HSL complexation (mol/L)

4.3 DspB Production

  The production of the DspB from the DspB gene includes transcription and translation after activation. In addition, we should also consider its transport and degradation.

4.3.1 DspB Gene Activation

  This process is modeled using a Michaelian formalism depending on its activator (AfeR-HSL complexation) concentration. The promoter strength is also taken into account.

  • DspB DNA,0/cell : total number of DspB DNA per cell

  • DspB DNA/cell : number of activated DspB DNA per cell

  • K a, AfeR-HSL : activation constant of the AfeR-HSL complexation (mol/L)

  • k p, afeR : afeR promoter influence