# Team:NYMU-Taipei/Modeling/ModSensors

National Yang Ming University

# Sensors

## Backgrounds

When Nosema enters the bees, it will trigger bees’ ROS (Reactive Oxygen Species) production, which in turn launches E. coli’s OxyR production. After that ROS and OxyR will form a complex and binds to AhpCp promoter, which function as a sensor/ switch to have the whole circuit opened when Nosema exists, and closed when Nosema is killed.. To increase the sensitivity of this switch, we add an additional circuit expressing OxyR regulated by a constitutive promoter to enhance the basal OxyR expression in E. coli.

The picture shows how oxyR and ROS form a complex:

## Objectives

1. To know the lag time between sensing the invasion and the production of the killing protein.
2. The minimal Oxidative stress that can activate the switch by choosing the proper constitutive promoter for boosting OxyR's concentration
3. To know the relation between ROS input and the AhpCp promoter open strength.
4. To see to which degree will AhpCp promoter influence the production of LuxI, LuxR, and TetR, which will influence the second and the third circuit.

## System

It is assumed that the concentration of ROS in bees is relative to the severity of Nosema infection, and that OxyR is so abundant that once ROS appears, it will soon bind to ROS to form OxyR* and reach equilibrium.

Equation1:

\frac{d[mRNA_O_x_y_R]}{dt}=PoPSconstitutive\times\frac{N}{V}-KdegmRNA[mRNAOxyR]

PoPSconstitutive = promoter strength of constitutive promoter (J23102)

N = number of plasmid in a single cell

V = volume of a cell

The aim of the equation is to know the production rate of mRNAOxyR, and choose the proper constitutive promoter for boosting OxyR's concentration.

Equation2:

\frac{d[OxyR]}{dt}=RBS\times[mRNAOxyR]-KdegOxyR[OxyR]

RBS = binding site strength

KdegOxyR = degrading constant of OxyR

The aim of the equation is to know the production rate of OxyR and when it can reach the concentration activating AhpCp promoter, which can in turn be deduced to get the lag time between sensing the invasion and the production of the killing protein.

Equation3:

[OxyR*]=KOxyR*\times[ROS]\times[OxyR]

KOxyR* = constant rate of ROS+OxyR→OxyR*

The aim of the equation is to know the concentration of OxyR* given the concentration of ROS and OxyR, which will know the relation between ROS input and the AhpCp promoter open time.

Equation4:

\frac{d[mRNA_L_a_c_I]}{dt}=\frac{ [mRNALuxI] }{dt}=\frac{ [mRNALuxR] }{dt} =\frac{ {[OxyR*]} ^{{n}^{OxyR*}}}{{{KdOxyR*}^{{n}^{OxyR*}}}+{[OxyR*]}^{{n}^{OxyR*}}}\times{PoPsAhpCp}\times\frac{N}{V}

PoPSconstitutive = promoter strength of constitutive promoter

N = number of plasmid in a single cell

V = volume of a cell

The aim of the equation is to know how AhpCp promoter strength (in PoPS) influences the production of TetR, LuxI, and LuxR.

## Results

This picture predicts the buildup of concentration of mRNAOxyR, mRNACI, OxyR, CI will reach in a newborn Bee. coli (without Nosema invasion).

Since naturally produced oxyR in Bee.coli (our E.coli) is not sufficient, we add a constitutive promoter before the oxyR-producing gene to increase oxyR concentration to reach the effective level (0.005M). The picture shows that after adding constitutive promoter, oxyR concentration can reach the effective level to activate ROS/oxyR complex-induced promoter 50 hours after Nosema infection.

## Discussion

The results shown in killing protein and ethanol production means that the adjusted OxyR concentration is high enough to swiftly form a complex after ROS is heighten, therefore turning on the switch.

In reality, the final centration of OxyR can reach much more higher than we had expected after a longer period of time. The inaccuracy will be discussed below.

The reason why the actual result of OxyR concentration differing from the expected one may be that we did not take the negative feedback of OxyR production.

This picture shows OxyR cycle in E. coli:

The top molecule is reduced form of OxyR, whose Cys199 to sulfoxide will be oxidized by hydrogen peroxide (the oxidative reagent as well as a kind of ROS).

After the water exclusion and disulfide bond formation, the reduced form of oxy turns into the oxidized one. Oxidized OxyR is an activator of target promoter, which stimulates downstream gene expression. However, Oxidized form of OxyR protein is transformed into reduced OxyR protein (inactivated) by thioredoxin reductase (GSH). Reduced OxyR protein (the top molecule)provides the autorepression of OxyR gene (a negative feedback).

## Parameters

Model Parameter Description Value Unit Reference
Sensor KdegOxyR OxyR degrading rate 107 M-1 x min-1 Regulation of the OxyR transcription factor by hydrogen peroxide and the cellular thiol—disulfide status
KdOxyR* Dissociation constant of OxyR* 10-7.33 M
KOxyR OxyR producing rate constant 5.012 x 1014 X
nOxyR* Hill coefficient of OxyR* Ranging from 0.75~3.5,depends on what kind of ROS it react with X OxyR: A Molecular Code for Redox-Related Signaling
N Copy number 887(cells containing 25％ plasmid bearing cells) Single piece
1. Escherichia coli Plasmid Copy Number Assay
2. Improved determination of plasmid copy number using quantitative real-time PCR for monitoring fermentation processes