Iron Sensing

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

4.3.2 DspB Transcription

The DspB transcription depends on the transcription rate of the strain and the length of the DspB gene. The Avogadro number is used to express the transcription velocity in molar concentration in one cell per time unit.

• k_transcript : E.coli transcription rate (nucleotides/s)

• RNA polymerase/gene: number of RNA polymerase per gene

• DNA length (DspB): number of nucleotides on the DspB gene

• V _intracell: volume of a bacterial cell (L)

For the convenience of mathematical operation, we merged the ktranscript、RNA polymerase/gene and "V" intracell to a constant.

4.3.3 DspB Translation

The DspB translation depends on the translation rate of the strain, the mRNA length and the quantity of mRNA. The translation velocity is expressed in molar concentration in one cell per time unit.

• k_translation : E.coli translation rate (nucleotides/s)

• Ribosomes/RNA: number of ribosomes per mRNA

• RNA length (DspB): number of nucleotides on the DspB mRNA

• [DspB mRNA] : DspB mRNA concentration in one E.coli cell

For the convenience of mathematical operation, we merge the ktranslation and Ribosomes/RNA and to a constant.

4.3.4 Degradation

Some of the DspB protein and mRNA are degraded. A degradation constant is used to model the degradation velocity.

• K_deg,DspB: DspB degradation constant (s−1)

• K_{deg,DspB mRNA}: DspB mRNA degradation constant (s−1)

4.3.5 DspB Transfer

DspB protein needs to be transferred to the water environment to function. This process is taken into account through a passive transusion model.

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

4.4 Biofilm Removel

The biofilm is removed by the DspB and the process is modeled assuming a Michaelis-Menten kinetics.

• kcat,DspB : catalytic constant of the DspB enzyme (s −1)

• "KM,D" : Michaelis constant of the DspB enzyme (mol/L)

4.5 EntE Production

We treat enterobactin enzymes gene cluster as a whole gene (EntE gene). The production of the enterobactin enzymes from the EntE gene includes transcription and translation after activation. In addition, we should also consider its degradation. Because the enterobactin enzymes function in the cell, we don't need to consider its transport to the water environment.

4.5.1 EntE 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.

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

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

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

• k p, afeR : afeR promoter influence

4.5.2 EntE Transcription

The EntE transcription depends on the transcription rate of the strain and the length of the EntE gene. The Avogadro number is used to express the transcription velocity in molar concentration in one cell per time unit.

• "EntE DNA,/cell" : number of EntE gene per cell

• ktranscript : E.coli transcription rate (nucleotides/s)