# Team:NYMU-Taipei/Modeling/MainParts

### From 2013.igem.org

## Contents |

# Main parts

## Backgrounds

**Circuit regulators**

• ptet regulated promoter (ptet) : when ptet exists, it will bind to ptet regulated promoter (ptet) and represses the promoter.

• pLux/cI hybrid promoter (plux/cI) : when luxR/AHL exists, it will open pLux/cI hybrid promoter (plux/cI), while cI will repress the promoter. What’s more, plux/cI is cI-dominant, which means when cI exists, the hybrid promoter will be repressed whether luxR/AHL exists or not.

**Circuit regulation:**

• Circuit condition without *Nosema*:

Without *Nosema ceranae*, the first circuit will not open, and thus, no ptet will be produced. Since there is no ptet binding to ptet, ptet will not be repressed, which means cI will be produced. After that, cI will bind to pLux/cI hybrid promoter, leading the third circuit to be off.

• Circuit condition with* Nosema*:

When *Nosema ceranae* infects the bee, bee’s immune system will be activated, leading to the concentration of ROS (reactive oxygen species) to be high. In response, Bee. coli will enhance the production of oxyR, which forms a complex with ROS and binds to transcription binding site ahead of AhpCp (an oxyR-activated promoter; namely, the sensor), leading to the first circuit to be on.

Since the first circuit is on, the downstream ptet gene will be produced and bind to ptet, leading to the second circuit to be off.

After the second circuit is closed, no cI is produced, leading to the third circuit to be on (no repressor at all). And then, kill protein will be produced and kill *Nosema Ceranae*.

• Positive feedback:

Besides the LuxI and LuxR(which then form a complex called luxR/AHL) produced by first circuit, the third circuit will also produce LuxI and LuxR, which acts as a positive feedback and strongly enhances the production of killer protein.

The picture shows how LuxI will transfer to AHL, which then bind to LuxR to form a dimer:

• Circuit condition when *Nosema* is killed:

After *Nosema* is killed, the sensor will be off and no ptet will be produced.

Without ptet, the ptet will not be repressed, and the second circuit will be on, leading to the production of cI. After cI binds to pLux/cI hybrid promoter, the third circuit to be off. After that, the overall circuit will switch to the beginning stage when there is no* Nosema*.

## Objectives

1. To know how much time it needs from sensing to killing the *Nosema* after infection

2. To know whether the pathway is effective or not

3. To know the range of kill protein concentration (from the minimal concentration which Is effective to kill *Nosema* to the maximal concentration which will not do harm to the bees)

## System

It is assumed that AHL is abundant and thus the formation of AHL2LuxR complex is determined only by the concentration of LuxR; CI’s mechanism of binding to the promoter is assumed to act as hill effect form; kill protein will sustain a period of time before it is degraded naturally without any other types of decomposition.

**Equation1**

Kdptet = dissociation constant of CI

nptet = Hill coefficient of ptet

PoPSptet = promoter strength of ptet

kdegmRNA = degrading constant of sensor promoter mRNA

N = number of plasmid in a single cell

V = volume of a cell

** The aim of the equation is to know mRNA_C_I production rate and when it can reach the level to translate the desired concentration.**

**Equation2**

KdROSoxyR = dissociation constant ofROSoxyR

nROSoxyR = Hill coefficient of ROSoxyR

PoPSAhpCp = promoter strength of AhpCp

kdegmRNA = degrading constant of sensor promoter mRNA

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 ptet.**

**Equation3:**

PoPSconstitutive= promoter strength of constitutive promoter (J23102)

N = number of plasmid in a single cell

V = volume of a cell

kdegmRNA = degrading constant of sensor promoter mRNA

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

**Equation4:**

KdROSoxyR = dissociation constant ofROSoxyR

nROSoxyR = Hill coefficient of ROSoxyR

PoPSAhpCp = promoter strength of AhpCp

KdLuxRAHL = dissociation constant ofLuxRAHL

nLuxRAHL = Hill coefficient of LuxRAHL

KdcI = dissociation constant of CI

ncI = Hill coefficient of CI

PoPSLuxcI = promoter strength of LuxcI hybrid promoter

kdegmRNA = degrading constant of sensor promoter Mrna

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 LuxI. **

**Equation5:**

KdROSoxyR = dissociation constant ofROSoxyR

nROSoxyR = Hill coefficient of ROSoxyR

PoPSAhpCp = promoter strength of AhpCp

KdLuxRAHL = dissociation constant ofLuxRAHL

nLuxRAHL = Hill coefficient of LuxRAHL

KdcI = dissociation constant of CI

ncI = Hill coefficient of CI

PoPSLuxcI = promoter strength of LuxcI hybrid promoter

kdegmRNA = degrading constant of sensor promoter Mrna

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 LuxR. **

**Equation6**

KdLuxRAHL = dissociation constant ofLuxRAHL

nLuxRAHL = Hill coefficient of LuxRAHL

KdcI = dissociation constant of CI

ncI = Hill coefficient of CI

PoPSLuxcI = promoter strength of LuxcI hybrid promoter

kdegmRNA = degrading constant of sensor promoter mRNA

N = number of plasmid in a single cell

V = volume of a cell

**The aim of the equation is to know mRNA of kill protein production rate and when it can reach the level of the desired concentration. **

to learn more about how we characterize pLuxCI, click here

**Equation7**

KdROSoxyR = dissociation constant ofROSoxyR

nROSoxyR = Hill coefficient of ROSoxyR

PoPSAhpCp = promoter strength of AhpCp

KdT7 = dissociation constant of T7

NT7 = Hill coefficient of T7

PoPST7 = promoter strength of T7 promoter

kdegmRNA = degrading constant of sensor promoter mRNA

N = number of plasmid in a single cell

V = volume of a cell

**The aim of the equation is to know mRNA of T7 polymerase production rate and when it can reach the level to translate enough T7 polymerase. **

**Equation8:**

KdT7 = dissociation constant of T7

NT7 = Hill coefficient of T7

PoPST7 = promoter strength of T7 promoter

KdegmRNA = degrading constant of sensor promoter mRNA

N = number of plasmid in a single cell

V = volume of a cell

**The aim of the equation is to knowmRNA of enzyme PDC production rate and when it can reach the level to translate enough PDC. **

**Equation9:**

KdT7 = dissociation constant of T7

NT7 = Hill coefficient of T7

PoPST7 = promoter strength of T7 promoter

kdegmRNA = degrading constant of sensor promoter mRNA

N = number of plasmid in a single cell

V = volume of a cell

**The aim of the equation is to knowmRNA of enzyme ADH production rate and when it can reach the level to translate enough ADH. **

**Equation10 **

RBS = binding site strength

KdegCI = degrading constant of CI

**The aim of the equation is to know the production rate of CI and when it can reach the concentration to repress LuxCI hybrid promoter. **

**Equation11**

RBS = binding site strength

Kdegptet = degrading constant of ptet

**The aim of the equation is to known ptet production rate and when it can reach the concentration to repress promoter ptet.**

'*Equation12*

RBS = binding site strength

KAHL = LuxI to AHL rate constant

KdegLuxI = degrading constant of LuxI

**The aim of the equation is to know the production rate of LuxI concerning the LuxIAHL reaction and LuxI degrading. **

'*Equation13*

RBS = binding site strength

KmAHL =AHL to LuxI rate constant

KdegLuxR= degrading constant of LuxR

KonAHL = 2AHL + LuxR to (AHL)2/LuxR complex rate constant

KdegAHL = degrading constant of AHL

**The aim of the equation is to know the production rate of LuxR concerning the 2AHL + LuxR to (AHL)2/LuxR reaction , AHL to LuxI reaction, and LuxR, AHL degrading. **

'*Equation14:*

KAHL = LuxI to AHL rate constant

KonAHL = 2AHL + LuxR to (AHL)^2/LuxR complex rate constant

KoffAHL = (AHL)2/LuxR complex to 2AHL + LuxR rate constant

KdegAHL = degrading constant of AHL

**The aim of the equation is to know the production rate of AHL concerning the LuxIAHL reaction, 2AHL + LuxR to (AHL)2/LuxR reaction, (AHL)2/LuxR complex to 2AHL + LuxR reaction and AHL degrading. **

**Equation17**

RBS = binding site strength

PoPST7 = promoter strength of T7 promoter

N = number of plasmid in a single cell

V = volume of a cell

KdegADH = degrading constant of ADH (Acetaldehyde)

**The aim of the equation is to know ADH production rate and when it can reach the concentration of ethanol pathway equilibrium.**

**Equation18**

KAHL = LuxI to AHL rate constant

KonAHL = 2AHL + LuxR to (AHL)2/LuxR complex rate constant

KoffAHL = (AHL)2/LuxR complex to 2AHL + LuxR rate constant

KdegAHL = degrading constant of AHL

**The aim of the equation is to know the production rate of AHL concerning the LuxIAHL reaction, 2AHL + LuxR to (AHL)2/LuxR reaction, (AHL)2/LuxR complex to 2AHL + LuxR reaction and AHL degrading. **

**Equation19**

RBS = binding site strength

Kdegkill = degrading constant of kill

**The aim of the equation is to knowkiller protein production rate and when it can reach the effective concentration to kill Nosema. **

## Results

Figure1: This picture shows kill protein concentration to time under pLux/CI hybrid promoter’s control and LuxR, LuxI’s positive feedback. The result indicates that kill protein concentration will reach its effective level and kill *Nosema* in time (36 hours after *Nosema* infection)

Figure2: This picture is a control group model. It shows that without *Nosema* infection (ROS concentration=0), ethanol production is low enough to be ignored.

Figure3: This is the picture of kill protein concentration to time under promoter CI’s control only(control group)without pLux/CI's regulation.The result shows that kill protein's full expression is too low to kill *Nosema*.

## Discussion

Comparing to the ROS-level control group where ROS remains low when there’s no *Nosema* infection, kill protein production is highly boasted upon sensing *Nosema*.

The result indicates that kill protein concentration will reach its effective level and kill *Nosema* in time (36 hours after sensing *Nosema* infection, within the 5-day deadline when* Nosema* spores proliferates and the bee become incurable and infectious to other bees), at the given ROS changes and the enhanced OxyR expression (to learn more about our sensor model, click here).

## Circuit design and improvement

Upon using pCI to negatively regulate kill protein production, results show that kill protein's full expression while no CI present is too low to kill *Nosema*. To solve this problem we subsidized CI promoter into pLux/CI promoter for additional positive feedback to boast kill protein’s production. As the modeling results regarding the modified circuit shown, the consequences are positive. (click here to learn more about our circuit)

## Parameters:

Model | Parameter | Description | Value | Unit | Reference |
---|---|---|---|---|---|

Sensor
| KdegOxyR | OxyR degrading rate | 10^{7}
| 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 10^{14}
| 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 |
- Escherichia coli Plasmid Copy Number Assay
- Improved determination of plasmid copy number using quantitative real-time PCR for monitoring fermentation processes
| |

Ethanol
| pyruvate | Initial concentration of pyruvate in MG1655 | 1.18 x 2 | g/L | Expression of pyruvate carboxylase enhances succinate production in Escherichia coli without affecting glucose uptake |

nPDC | Hill coefficient of PDC | 2.1 | - | Purification, characterization and cDNA sequencing of pyruvate decarboxylase Zygosaccharomyces biporus | |

nADH | Hill coefficient of ADH | at high pH values, 30◦C, n=1; at low temperature, n=3 | - | Evidence for co-operativity in coenzyme binding to tetrameric Sulfolobus
solfataricus alcohol dehydrogenase and its structural basis: ﬂuorescence, kinetic and structural studies of the wild-type enzyme and non-co-operative N249Y mutant | |

SEIR(exponential)
| b | Infection rate constant of Nosema ceranae to the suspected
| 24/75 | Period(days)-1 | |

r1 | Infection rate constant of K12 to the suspected | 3/20 | Period(days)-1 | 1. Environment protection administration executive yuan of R.O.C Medical bacteriology of J.A.T | |

r2 | Infection rate constant of K12 to the latent | 3/20 | Period(days)-1 | 2. Environment protection administration executive yuan of R.O.C. 3. Medical bacteriology of J.A.T | |

e | rate of the latent turns infectious | 1/4 | Period(days)-1 | ||

u | Death rate of the infected | 1/8 | Period(days)-1 | ||

k | Rate of intaking capsule | 24/11 | Period(days)-1 | ||

SEIR(exponential&linear) | S | x(1) | Amount of total population | ||

E | x(2) | Amount of suspected individuals | |||

I | x(3) | Amount of individuals in the latent period | |||

R | x(4) | Amount of infected individuals |