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Team:NYMU-Taipei/Modeling/MainParts
Main part model
Background:
Circuit
regulators:
• LacI-regulated promoter (pLac) : when LacI exists,
it will bind to LacI-regulated promoter (pLac) 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 NosemaCeranae, the first circuit will not open, and thus, no LacI will be produced. Since there is no LacI binding to pLac, pLac will not be repressed, and thus 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 trxC (an oxyR-activated promoter; namely, the sensor), leading to the first circuit to be on.
Since the first circuit is on, the downstream LacI gene will be produced and bind to pLac, 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.
•Circuit condition when Nosema is killed:
After Nosema is killed, the sensor will be off and no lacI will be produced.
Without LacI, the pLac 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.
Aims:
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)
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:
KdLacI = dissociation constant of CI
nLacI = Hill coefficient of LacI
PoPSpLac = promoter strength of pLac
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 knowmRNACI production rate and when it can reach the level to translate the
desired concentration.
‧Equation2:
KdROSoxyR = dissociation constant ofROSoxyR
nROSoxyR = Hill coefficient of ROSoxyR
PoPStrxC = promoter strength of trxC
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 trxC promoter strength (in PoPS) influences the production of lacI.
‧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
PoPStrxC = promoter strength of trxC
KdLuxRAHL = dissociation constant ofLuxRAHL
nLuxRAHL = Hill coefficient of LuxRAHL
KdcI = dissociation constant ofcI
ncI = Hill coefficient ofCi
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 trxC promoter strength (in PoPS) influences the production of LuxI.
‧Equation5:
KdROSoxyR = dissociation constant ofROSoxyR
nROSoxyR = Hill coefficient of ROSoxyR
PoPStrxC = promoter strength of trxC
KdLuxRAHL = dissociation constant ofLuxRAHL
nLuxRAHL = Hill coefficient of LuxRAHL
KdcI = dissociation constant ofcI
ncI = Hill coefficient ofCi
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 trxC promoter strength (in PoPS) influences the production of LuxR.
‧Equation6:
KdLuxRAHL = dissociation constant ofLuxRAHL
nLuxRAHL = Hill coefficient of LuxRAHL
KdcI = dissociation constant ofcI
ncI = Hill coefficient ofCi
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 knowmRNA of kill protein production rate and when it can reach the level ofthe
desired concentration.
‧Equation7:
KdROSoxyR = dissociation constant ofROSoxyR
nROSoxyR = Hill coefficient of ROSoxyR
PoPStrxC = promoter strength of trxC
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 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
KdegLacI = degrading constant of LacI
The aim of the equation is
to knowLacI production rate and when it can reach the concentration to repress
promoter LacI
‧Equation12:
RBS = binding site strength
KAHL = LuxIàAHL rate constant
KdegLuxI = degrading constant of LuxI
The aim of the equation is
to know the production rate of LuxI concerning the LuxIàAHL reaction and LuxI degrading.
‧Equation13:
RBS = binding site strength
KmAHL =AHLàLuxI rate constant
KdegLuxR= degrading constant of LuxR
KonAHL = 2AHL + LuxRà(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 à (AHL)2/LuxR reaction , AHL à LuxI reaction, and LuxR, AHL degrading.
‧Equation14:
KAHL = LuxIàAHL rate constant
KonAHL = 2AHL + LuxRà(AHL)2/LuxR complex rate constant
KoffAHL = (AHL)2/LuxR complexà2AHL + LuxR rate constant
KdegAHL = degrading constant of AHL
‧Equation15:
RBS = binding site strength
KdegT7 = degrading constant of T7
The aim of the equation is
to know the threshold concentration of oxyR to conquer the terminal and when T7
polymerase can reach the required concentration to activate T7 promoter.
‧Equation16:
RBS = binding site strength
KdegPDC = degrading constant of PDC
The aim of the equation is
to know PDC production rate and when it can reach the concentration of ethanol
pathway equilibrium.
‧Equation17:
RBS = binding site strength
KdegADH = degrading constant of ADH
The aim of the equation is
to know ADH production rate and when it can reach the concentration of ethanol
pathway equilibrium.
‧Equation18:
KonAHL = 2AHL + LuxRà(AHL)2/LuxR complex rate constant
KoffAHL = (AHL)2/LuxR complexà2AHL + LuxR rate constant
The aim of the equation is to know (AHL/LuxR)complex production rate and when it can reach the concentration to activate LuxR/cI hybrid promoter
‧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 killNosema.
‧Equation20:
Kpyruvateacetaldehyde=
pyruvateàacetaldehyde
reaction rate constant
Kacetaldehydeethanol=
acetaldehyde à ethanol reaction
rate constant
Km =
ethanol àacetaldehyde
reaction rate constant
KdPDC = dissociation
constant of PDC
KdADH = dissociation
constant of ADH
The aim of the equation is to know ethanol production rate and when it can reach the concentration to kill the spores of NosemaCeranae.
Explanation
In this equation,
For the
section of the equation,
In this equation, RBS represents ribosome binding site strength, which is the affinity of ribosome to the starting site of mRNA.
For
the section of the equation,
Since LuxCI hybrid promoter is CI dominant, the presence of CI block the promoter and kill protein is not produced. This situation happens when there is no Nosema in bees.
In this equation,
For the section of the equation,
In this equation, RBS represents ribosome binding site strength, which is the affinity of ribosome to the starting site of mRNA.
For the section of the equation,
In this equation,
For the section of the equation,
In this equation,
For
the section of the equation,
In
this equation, RBS represents
ribosome binding site strength, which is the affinity of ribosome to the
starting site of mRNA;
For
the section of the equation,
LacI will repress pLac promoter, which leads to no production of CI. Without CI, LuxCI hybrid promoter will no longer be repressed, and kill protein can thus be generated. This situation happens when Nosema exist, and when the sensor promoter is turned on.
In this equation,
For the section of the equation,
In this equation, RBS represents ribosome binding site strength, which is the affinity of
ribosome to the starting site of mRNA;
For the section of the equation,
In this equation,
For the section of the equation,
Since
After trxC promoter is turned on by ROSoxyR complex and the downstream genes – LacI, LuxI, and LuxR starts to produce, which blocks the CI promoter and turns on the LuxCI hybrid promoter. After that, the gene encoded with kill protein downstream LuxCI hybrid promoter also begins to transcribe.
This equation shows production rate of mRNAkill.
For the section of the equation,
As for explanations of equation7, 8, 9, 15, 16, 17, 20, please see the ethanol wiki for more information.
Result:
After Nosema invasion (t=0), concentration of
kill protein will reach its constant level, which is
Similarly, the
effective concentration of ethanol to kill bees is
The benefits of our circuit are that the dissociation constant of T7 (KdT7) is small, which means it is sensitive (will swiftly open right after T7 polymerase reaches threshold) and that we use positive feedback to attain the goal of open this device like a switch.
Parameter:
|
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 |
|
KdROSOxyR |
Dissociation constant of ROS-OxyR complex |
10-7.33 |
M |
||
|
KoxyR |
OxyR producing rate constant |
5.012 x 1014 |
- |
||
|
nROSOxyR |
Hill coefficient of ROS-OxyR complex |
Ranging from0.75~ 3.5,depends on what kind of ROS it binds |
- |
OxyR: A Molecular Code for Redox-Related Signaling |
|
|
N |
Copy number |
887(cells containing25％ 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 |
|
|
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 4.
|
|
|
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 |
|
|
|
|
|
|
|
|
|
