Team:NYMU-Taipei/Modeling/MainParts

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Latest revision as of 02:40, 29 October 2013

National Yang Ming University

1 Main parts

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

\frac{d[mRNA_C_I]}{dt}= \frac{1-[ptet]^nptet}{ Kdptet^nptet+ [ptet]^nptet} \times PoPSconstitutive\times\frac{N}{V} -KdegmRNA\times [mRNA_C_I]

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.

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	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	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

Retrieved from "http://2013.igem.org/Team:NYMU-Taipei/Modeling/MainParts"

@@ Line 1: / Line 1: @@
 {{:Team:NYMU-Taipei/Header}}
+=Main parts=
+==Backgrounds==
-==Function of the parts:==
+'''Circuit regulators'''
-#'''circuit regulators:'''
-*'''LacIregulatedpromoter(pLac)''' : when LacI exists, it will bind to LacIregulatedpromoter(pLac) and represses the promoter.
-*'''pLux/cIhybridpromoter(plux/cI)''' : when luxR/AHL exists, it will open pLux/cIhybridpromoter(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:'''
-[[File:NYMU-Taipei_Circuit_condition_wo_nosema.jpg|center|700px|]]
+• ptet regulated promoter (ptet) : when ptet exists, it will bind to ptet regulated promoter (ptet) and represses the promoter.
-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, which means cI will be produced. After that, cIwill bind to pLux/cI-hybridpromoter, leading the third circuit to be off.
+• 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 condition with Nosema:
-[[File:NYMU-Taipei_Circuit_condition_w_nosema.jpg|center|700px]]
+'''Circuit regulation:'''
-When ''NosemaCeranae'' infects the bee, bee’s immune system will be activated, leading to the concentration of ROS(reactive oxygen species) to be high. In response, ''E. Kobee'' will enhance the production of oxyR, which binds to transcription binding site ahead of trxC (an oxyR-activated promoter; namely, the sensor), leading to the first circuit to be on.
+• Circuit condition without ''Nosema'':
+[[Image:NYMU_ Circuit condition without Nosema.png|center]]
-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.
+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.
-After the second circuit is closed, no cI is produced, leading to the third circuit to be on (no repressor at all). And then, killer protein will be produced and kill ''NosemaCeranae''.
+• Circuit condition with'' Nosema'':
-*Positive feedback:
+[[Image:NYMU_ Circuit condition with Nosema.png|center]]
-[[File:NYMU-Taipei_Mod_3.jpg|center|700px]]
+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.
-Besides the LuxI and LuxR(which then form a complex called luxR/AHL) produced by first circuit, the third circuit will also produce luxR/AHL, which acts as a positive feedback and strongly enhances the production of killer protein.
+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.
-*CircuitconditionwhenNosema is killed:
-[[File:NYMU-Taipei_Mod_4.jpg|center|700px]]
+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''.
-After '''Nosema''' is killed, the sensor will be off and no lacI will be produced.
+• Positive feedback:
-Without LacI, the pLac will not be repressed, and the second circuit will be on, leading to the production of cI. After cI binds topLux/cIhybridpromoter, the third circuit to be off.
+[[Image:NYMU_positive feedback.png|center]]
-The overall circuit will switch to the beginning stage when there is no Nosema.
+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 purpose of this modeling is:==
+The picture shows how LuxI will transfer to AHL, which then bind to LuxR to form a dimer:
-#To know how much time it needs from sensing to killing the Nosema after infection
-#To know whether the pathway is effectiveor not
+[[Image:NYMU_luxr ahl dimer.png|center]]
-#To know the range of killer 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 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 degration.
+• Circuit condition when ''Nosema'' is killed:
+[[Image:NYMU_ Circuit condition when Nosema is killed.png|center]]
+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==
+. To know how much time it needs from sensing to killing the ''Nosema'' after infection
+. To know whether the pathway is effective or not
+. 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'''
-===Equation1:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNACI]}{dt}=\frac{ 1-[LacI]^{nLacI} }{ KdLacI^{nLacI}+[LacI]^{nLacI} }\timesPoPSpLac\times\frac{N}{V}-kdegmRNA\times[mRNACI]
+\frac{d[mRNA_C_I]}{dt}= \frac{1-[ptet]^nptet}{ Kdptet^nptet+ [ptet]^nptet}
+\times PoPSconstitutive\times\frac{N}{V}
+-KdegmRNA\times [mRNA_C_I]
 </div>
 </html>
-KdLacI = dissociation constant of CI
+Kdptet = dissociation constant of CI
-nLacI = Hill coefficient of LacI
+nptet = Hill coefficient of ptet
-PoPSpLac = promoter strength of pLac
+PoPSptet = promoter strength of ptet
 kdegmRNA = degrading constant of sensor promoter mRNA
@@ Line 60: / Line 78: @@
 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.'''
+''' 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:===
+[[read more1]]
+'''Equation2'''
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNALacI]}{dt}=\frac{ [ROSoxyR]^{nROSoxyR} }{ KdROSoxyR^{nROSoxyR}+[ROSoxyR]^{nROSoxyR} }\timesPoPStrxC\times\frac{N}{V}-kdegmRNA\times[mRNAlacI]
+\frac{d[mRNA_L_a_c_I]}{dt}= \frac{1-[ROSoxyR]^nROSoxyR }{ KdROSoxyR ^nROSoxyR + [ROSoxyR]^nROSoxyR} PoPSAhpCp\times\frac{N}{V}-KdegmRNA[mRNA_L_a_c_I]
 </div>
 </html>
@@ Line 74: / Line 93: @@
 nROSoxyR = Hill coefficient of ROSoxyR
-PoPStrxC = promoter strength of trxC
+PoPSAhpCp = promoter strength of AhpCp
 kdegmRNA = degrading constant of sensor promoter mRNA
@@ Line 82: / Line 101: @@
 V = volume of a cell
-'''The aim of the equation is to know how trxC promoter strength (in PoPS) influences the production of lacI.'''
+''' The aim of the equation is to know how AhpCp promoter strength (in PoPS) influences the production of ptet.'''
+[[read more2]]
+'''Equation3:'''
-===Equation3:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNAoxyR]}{dt}=PoPSconstitutive\times\frac{N}{V}-KdegmRNA[mRNAoxyR]
+\frac{d[mRNA_O_x_y_R]}{dt}=PoPSconstitutive\times\frac{N}{V}-KdegmRNA\times [mRNAOxyR]</div>
-</div>
 </html>
@@ Line 99: / Line 120: @@
 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.'''
+''' The aim of the equation is to know the production rate ofmRNAoxyR, and choose the proper constitutive promoter for boosting OxyR's concentration.'''
-===Equation4:===
+[[read more3]]
-<html>
-<div lang="latex" class="equation">
+'''Equation4:'''
-<img src="https://static.igem.org/mediawiki/2013/e/ee/NYMU-Taipei_modmain_Image008.png"></img>
-</div>
+<html> <div lang="latex" class="equation">
-</html>
+\frac{d[mRNA_L_u_x_I]}{dt}= \frac{1-[ROSoxyR]^n ROSoxyR }{ Kd ROSoxyR ^n ROSoxyR + [ROSoxyR]^n ROSoxyR I} PoPSAhpCp\times\frac{N}{V}+\frac{1-[ LuxRAHL]^nLuxRAHL}{ KdLuxRAHL ^nLuxRAHL + [LuxRAHL]^nLuxRAHL}\times\frac{1-{1-[CI leak]^nCI}}{ KdCI^nCI+[CI]^nCI}\times PoPSLuxCI\times\frac{N}{V}-KdegmRNA[mRNALuxI]
+</div> </html>
 KdROSoxyR = dissociation constant ofROSoxyR
@@ Line 112: / Line 134: @@
 nROSoxyR = Hill coefficient of ROSoxyR
-PoPStrxC = promoter strength of trxC
+PoPSAhpCp = promoter strength of AhpCp
 KdLuxRAHL = dissociation constant ofLuxRAHL
@@ Line 118: / Line 140: @@
 nLuxRAHL = Hill coefficient of LuxRAHL
-KdcI = dissociation constant ofcI
+KdcI = dissociation constant of CI
-ncI = Hill coefficient ofCi
+ncI = Hill coefficient of CI
 PoPSLuxcI = promoter strength of LuxcI hybrid promoter
-kdegmRNA = degrading constant of sensor promoter mRNA
+kdegmRNA = degrading constant of sensor promoter Mrna
 N = number of plasmid in a single cell
@@ Line 130: / Line 152: @@
 V = volume of a cell
-'''The aim of the equation is to know how trxC promoter strength (in PoPS) influences the production of LuxI.'''
+''' The aim of the equation is to know how AhpCp promoter strength (in PoPS) influences the production of LuxI. '''
-===Equation5:===
+[[read more4]]
-<html>
-<div lang="latex" class="equation">
+'''Equation5:'''
-<img src="https://static.igem.org/mediawiki/2013/f/fd/NYMU-Taipei_modMain_Image009.png"></img>
-</div>
+<html> <div lang="latex" class="equation">
-</html>
+\frac{d[mRNA_L_u_x_R]}{dt}= \frac{1-[ROSoxyR]^n ROSoxyR }{ Kd ROSoxyR ^n ROSoxyR + [ROSoxyR]^n ROSoxyR I} \times PoPSAhpCp\times\frac{N}{V}+\frac{1-[ LuxRAHL]^nLuxRAHL}{ KdLuxRAHL ^nLuxRAHL + [LuxRAHL]^nLuxRAHL}\times\frac{1-{1-[CI leak]^nCI}}{ KdCI^nCI+[CI]^nCI}\times PoPSLuxCI\times\frac{N}{V}-KdegmRNA[mRNALuxR]
+</div> </html>
 KdROSoxyR = dissociation constant ofROSoxyR
@@ Line 143: / Line 166: @@
 nROSoxyR = Hill coefficient of ROSoxyR
-PoPStrxC = promoter strength of trxC
+PoPSAhpCp = promoter strength of AhpCp
 KdLuxRAHL = dissociation constant ofLuxRAHL
@@ Line 149: / Line 172: @@
 nLuxRAHL = Hill coefficient of LuxRAHL
-KdcI = dissociation constant ofcI
+KdcI = dissociation constant of CI
-ncI = Hill coefficient ofCi
+ncI = Hill coefficient of CI
 PoPSLuxcI = promoter strength of LuxcI hybrid promoter
-kdegmRNA = degrading constant of sensor promoter mRNA
+kdegmRNA = degrading constant of sensor promoter Mrna
 N = number of plasmid in a single cell
@@ Line 161: / Line 184: @@
 V = volume of a cell
-'''The aim of the equation is to know how trxC promoter strength (in PoPS) influences the production of LuxR.'''
+''' The aim of the equation is to know how AhpCp promoter strength (in PoPS) influences the production of LuxR. '''
-===Equation6:===
+[[read more5]]
-<html>
-<div lang="latex" class="equation">
+'''Equation6'''
-<img src="https://static.igem.org/mediawiki/2013/a/ab/NYMU-Taipei_modMain_Image010.png"></img>
-</div>
+<html> <div lang="latex" class="equation">
-</html>
+\frac{d[mRNA_k_i_l_l]}{dt}= \frac{1-[ LuxRAHL]^nLuxRAHL}{ KdLuxRAHL ^nLuxRAHL + [LuxRAHL]^nLuxRAHL}\times\frac{1-{1-[CI leak]^nCI}}{ KdCI^nCI+[CI]^nCI}\times PoPSLuxCI\times\frac{N}{V}-KdegmRNA[mRNA_k_i_l_l]
+</div> </html>
 KdLuxRAHL = dissociation constant ofLuxRAHL
@@ Line 174: / Line 198: @@
 nLuxRAHL = Hill coefficient of LuxRAHL
-KdcI = dissociation constant ofcI
+KdcI = dissociation constant of CI
-ncI = Hill coefficient ofCi
+ncI = Hill coefficient of CI
 PoPSLuxcI = promoter strength of LuxcI hybrid promoter
@@ Line 186: / Line 210: @@
 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.'''
+'''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. '''
-===Equation7:===
+[[read more6]]
-<html>
-<div lang="latex" class="equation">
+[[to learn more about how we characterize pLuxCI, click here]]
-<img src="https://static.igem.org/mediawiki/2013/6/64/NYMU-Taipei_modMain_Image011.png"></img>
-</div>
-</html>
+'''Equation7'''
+<html> <div lang="latex" class="equation">
+\frac{d[mRNA_t_7]}{dt}= \frac{1-[ROSoxyR]^n ROSoxyR }{ Kd ROSoxyR ^n ROSoxyR + [ROSoxyR]^nROSoxyR }\timesPoPSAhpCp\times\frac{N}{V}\times {a}+ \frac{1-[T7]^nT7}{ Kd T7^nT7 + [T7]^nT7}\times{PoPST7}\times\ frac{N}{V}-KdegmRNA\times [mRNA_T_7]
+</div> </html>
 KdROSoxyR = dissociation constant ofROSoxyR
@@ Line 199: / Line 227: @@
 nROSoxyR = Hill coefficient of ROSoxyR
-PoPStrxC = promoter strength of trxC
+PoPSAhpCp = promoter strength of AhpCp
 KdT7 = dissociation constant of T7
@@ Line 213: / Line 241: @@
 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.'''
+'''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. '''
+[[read more7]]
+'''Equation8:'''
-===Equation8:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNAPDC]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\timesPoPST7\times\frac{N}{V}-kdegmRNA\times[mRNAPDC]
+\frac{d[mRNA_P_D_C]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\times\frac{N}{V}-KdegmRNA\times[mRNAPDC]
 </div>
 </html>
+<br>
 KdT7 = dissociation constant of T7
@@ Line 228: / Line 259: @@
 PoPST7 = promoter strength of T7 promoter
-kdegmRNA = degrading constant of sensor promoter mRNA
+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.'''
+'''The aim of the equation is to knowmRNA of enzyme PDC production rate and when it can reach the level to translate enough PDC. '''
+[[read more8]]
+'''Equation9:'''
-===Equation9:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNAADH]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\timesPoPST7\times\frac{N}{V}-kdegmRNA\times[mRNAADH]
+\frac{d[mRNA_A_D_H]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\times\frac{N}{V}-KdegmRNA\times[mRNAADH]
 </div>
 </html>
@@ Line 255: / Line 289: @@
 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.'''
+'''The aim of the equation is to knowmRNA of enzyme ADH production rate and when it can reach the level to translate enough ADH. '''
+[[read more9]]
+'''Equation10 '''
-===Equation10:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[CI]}{dt}=RBS\times[mRNAcI]-KdegCI[CI]
+\frac{d[CI]}{dt}={RBS}\times{[mRNA_C_I]} -KdegCI\times{[CI]}
 </div>
 </html>
@@ Line 268: / Line 306: @@
 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.'''
+'''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. '''
+[[read more10]]
+'''Equation11'''
-===Equation11:===
 <html>
 <div lang="latex" class="equation">
-\frac{[LacI]}{dt}=RBS\times[mRNALacI]-KdegCI[LacI]
+\frac{d[ptet]}{dt}={RBS}\times{[mRNA_L_a_c_I]} - {Kdeg ptet} \times{[ptet]}
 </div>
 </html>
@@ Line 279: / Line 320: @@
 RBS = binding site strength
-KdegLacI = degrading constant of LacI
+Kdegptet = degrading constant of ptet
-'''The aim of the equation is to knowLacI production rate and when it can reach the concentration to repress promoter LacI'''
+'''The aim of the equation is to known ptet production rate and when it can reach the concentration to repress promoter ptet.'''
+[[read more11]]
+'''Equation12''
-===Equation12:===
 <html>
 <div lang="latex" class="equation">
-\frac{[LacI]}{dt}=RBS\times[mRNALacI]-KdegCI[LacI]
+\frac{d[LuxI]}{dt}={RBS}\times{[mRNA_L_u_x_I]} -KAHL\times{[LuxI]}
+ -Kdeg {[LuxI]} \times{[LuxI]}
 </div>
 </html>
@@ Line 292: / Line 337: @@
 RBS = binding site strength
-KAHL = LuxIAHL rate constant
+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 LuxIAHL reaction and LuxI degrading.'''
+'''The aim of the equation is to know the production rate of LuxI concerning the LuxIAHL reaction and LuxI degrading. '''
+[[read more12]]
+'''Equation13''
-===Equation13:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[LuxR]}{dt}=RBS\times[mRNALuxR]-KmAHL[AHL]-KdegLuxR[LuxR]-KonAHL\times[AHL]^2\times[LuxR]-KdegAHL[AHL]
+\frac{d[LuxR]}{dt}={RBS}\times{[mRNA_L_u_x_R]} – {KmAHL}\times{[AHL]}
+-	{Kdeg LuxR} \times{[LuxR]} \times {KmAHL}\{times[AHL]^{2}} \times{[LuxR]}- KdegAHL\times{[AHL]}
 </div>
 </html>
@@ Line 307: / Line 356: @@
 RBS = binding site strength
-KmAHL =AHLLuxI rate constant
+KmAHL =AHL to LuxI rate constant
 KdegLuxR= degrading constant of LuxR
-KonAHL = 2AHL + LuxR(AHL)2/LuxR complex rate constant
+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&harr;(AHL)2/LuxR reaction , AHL&rarr;LuxI reaction, and LuxR, AHL degrading.'''
+'''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. '''
+[[read more13]]
+'''Equation14:''
-===Equation14:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[AHL]}{dt}=KAHL\times[LuxI]+2\timesKoffAHL\times[AHLLuxR]-2\timesKonAHL\times[AHL]^2\times[LuxR]-KdegAHL[AHL]
+\frac{d[AHL]}{dt}={KAHL}\times{[LuxI]}+2\times KoffAHL \times [AHLLuxR] - 2\times KonAHL \times {[AHL]}^{2}\times {[LuxR]} - KdegAHL\times{[AHL]}
 </div>
 </html>
-KAHL = LuxIAHL rate constant
+KAHL = LuxI to AHL rate constant
-KonAHL = 2AHL + LuxR(AHL)2/LuxR complex rate constant
+KonAHL = 2AHL + LuxR to (AHL)^2/LuxR complex rate constant
-KoffAHL = (AHL)2/LuxR complex2AHL + LuxR 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 LuxI&rarr;AHL reaction, 2AHL + LuxR&harr;(AHL)2/LuxRreaction and AHL degrading.'''
+'''The aim of the equation is to know the production rate of AHL concerning the LuxIAHL reaction, 2AHL + LuxR to (AHL)2/LuxR reaction, (AHL)2/LuxR complex to 2AHL + LuxR reaction and AHL degrading. '''
+[[read more14]]
+'''Equation17'''
-===Equation15:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[T7]}{dt}=RBS\times[mRNAT7]-KdegT7[T7]
+\frac{d[ADH]}{dt}=RBS\times{PoPST7effect}\times\frac{N}{V}-{KdegADH}\times{[ADH]}
 </div>
 </html>
+<br>
 RBS = binding site strength
-KdegT7 = degrading constant of T7
+PoPST7 = promoter strength of T7 promoter
-'''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.'''
+N = number of plasmid in a single cell
-===Equation16:===
+V = volume of a cell
-<html>
-<div lang="latex" class="equation">
-\frac{d[PDC]}{dt}=RBS\times[mRNAPDC]-KdegPDC[PDC]
-</div>
-</html>
-RBS = binding site strength
+KdegADH = degrading constant of ADH (Acetaldehyde)
-KdegPDC = degrading constant of PDC
+'''The aim of the equation is to know ADH production rate and when it can reach the concentration of ethanol pathway equilibrium.'''
-'''The aim of the equation is to know PDC production rate and when it can reach the concentration of ethanol pathway equilibrium.'''
+[[read more17]]
-===Equation17:===
+'''Equation18'''
 <html>
 <div lang="latex" class="equation">
-\frac{d[ADH]}{dt}=RBS\times[mRNAADH]-KdegADH[ADH]
+\frac{d[AHL]}{dt}=\times KonAHL \times [AHL]^{2}\times{[LuxR]}- {KoffAHL} \times {[AHLLuxR]} - KdegAHL\times{[AHL]}
 </div>
 </html>
-RBS = binding site strength
+KAHL = LuxI to AHL rate constant
-KdegADH = degrading constant of ADH
+KonAHL = 2AHL + LuxR to (AHL)2/LuxR complex rate constant
-'''The aim of the equation is to know ADH production rate and when it can reach the concentration of ethanol pathway equilibrium.'''
+KoffAHL = (AHL)2/LuxR complex to 2AHL + LuxR rate constant
-===Equation18:===
+KdegAHL = degrading constant of AHL
-<html>
-<div lang="latex" class="equation">
-\frac{d[LuxRAHL]}{dt}=KonAHL\times[AHL]^2\times[LuxR]-KoffAHL\times[AHLLuxR]
-</div>
-</html>
-KonAHL = 2AHL + LuxR&rrar;(AHL)2/LuxR complex rate constant
+'''The aim of the equation is to know the production rate of AHL concerning the LuxIAHL reaction, 2AHL + LuxR to (AHL)2/LuxR reaction, (AHL)2/LuxR complex to 2AHL + LuxR reaction and AHL degrading. '''
-KoffAHL = (AHL)2/LuxR complex&rarr;2AHL + LuxR rate constant
+[[read more18]]
-'''KonAHL = 2AHL + LuxR&rarr;(AHL)2/LuxR complex rate constant
+'''Equation19'''
-KoffAHL = (AHL)2/LuxR complex&rarr;2AHL + LuxR rate constant'''
-===Equation19:===
 <html>
 <div lang="latex" class="equation">
-\frac{d[kill]}{dt}=RBS\times[mRNAkill]-Kdegkill[kill]
+\frac{d[kill]}{dt}={RBS}\times{[mRNA_k_i_l_l]} –Kdegkill\times{[kill]}
 </div>
 </html>
@@ Line 398: / Line 443: @@
 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.'''
+'''The aim of the equation is to knowkiller protein production rate and when it can reach the effective concentration to kill ''Nosema''. '''
-===Equation20:===
+[[read more19]]
-<html>
-<div lang="latex" class="equation" style="width: 800px;">
-\frac{d[ethanol]}{dt}=Kpyruvateacetaldehyde\timesKacetaldehydeethanol\times\frac{ [PDC]^{nPDC} }{ KdPDC^{nPDC}+[PDC] }\times\frac{ [ADH]^{nADH} }{ KdADH^{nADH}+[ADH] }\times[pyruvate]-Km\times\frac{ [ADH]^{nADH} }{ KdADH^{nADH}+[ADH]^{nADH} }\times[ethanol]
-</div>
-</html>
-Kpyruvateacetaldehyde= pyruvate&rarr;acetaldehyde reaction rate constant
-Kacetaldehydeethanol= acetaldehyde&rarr;ethanol reaction rate constant
-Km = ethanol&rarr;acetaldehyde reaction rate constant
+==Results==
+[[File:NYMU_defensin normal.png]]
-KdPDC = dissociation constant of PDC
+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)
-KdADH = dissociation constant of ADH
+[[File:NYMU_defensin witout ROS.png]]
-'''The aim of the equation is to know ethanol production rate and when it can reach the concentration to kill the spores of NosemaCeranae.'''
+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.
-==Explanation==
+[[File:NYMU_defensin only CI.png]]
-<html>
+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''.
-<div lang="latex" class="equation" style="width: 800px;">
-\frac{d[mRNACI]}{dt}=\frac{ 1-[LacI]^{nLacI} }{ KdLacI^{nLacI}+[LacI]^{nLacI} }\times{PoPSpLac}\times\frac{N}{V}-kdegmRNA\times[mRNACI]
-</div>
-</html>
-In this equation, PoPSpLac represents the promoter strength of LacI promoter, which is measured by the rate of RNApolymerase binding to the starting site of DNA transcription;<html><span lang="latex">\frac{ 1-[LacI]^{nLacI} }{ KdLacI^{nLacI}+[LacI]^{nLacI} }</span></html>represents the hill effect of repressor LacI to LacI promoter. Because LacI is a repressor, the numerator is <html><span lang="latex">\1-{LacI}^{nLacI}</span></html>
+==Discussion==
-For the section of the equation, <html><span lang="latex">\frac{ 1-[LacI]^{nLacI} }{ KdLacI^{nLacI}+[LacI]^{nLacI} }\times{PoPSpLac}\times\frac{N}{V}</span></html>represents the synthesizing rate of mRNACI under the influence of LacI and LacI promoter; -kdegmRNA×[mRNACI] represents the degrading rate of mRNACI
-<html>
-<div lang="latex" class="equation" style="width: 800px;">
-\frac{d[CI]}{dt}=RBS\times{[mRNAcI]}-KdegCI\times\[CI]}
-</div>
-</html>
-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, RBS×[mRNAcI] represents the synthesizing rate of CI; -kdegCI×[CI] represents the degrading rate of CI.
-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.
-<html>
+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''.
-<div lang="latex" class="equation" style="width: 800px;">
-\frac{d[mRNACI]}{dt}=\frac{ [ROSoxyR]^nROSoxyR }{ {[KdROSoxyR]^nROSoxyR}+{[ROSoxyR]^nROSoxyR} }\times{PoPStrxC}\times\frac{N}{V}-kdegmRNA\times[mRNACI]
+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)]].
-</div>
-</html>
+==Circuit design and improvement==
-In this equation, PoPStrxC represents the promoter strength of promotertrxC, which is measured by the rate of RNApolymerase binding to the starting site of DNA transcription;
+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:==
+{|class="wikitable" !Model!!Parameter!!Description!!Value!!Unit!!Reference
+! style="text-align: center;"|Model
+! style="text-align: center;"|Parameter
+! style="text-align: center;"|Description
+! style="text-align: center;"|Value
+! style="text-align: center;"|Unit
+! style="text-align: center;"|Reference
+|-
+|rowspan=5 style="text-align: center;"|'''Sensor'''
+| style="text-align: center;"|KdegOxyR
+|OxyR degrading rate
+| style="text-align: center;"|10<sup>7</sup>
+| style="text-align: center;"|M<sup>-1</sup> x min<sup>-1</sup>
+|rowspan=3|Regulation of the OxyR transcription factor by hydrogen peroxide and the cellular thiol—disulfide status
+|-
+| style="text-align: center;"|KdOxyR*
+|Dissociation constant of OxyR*
+| style="text-align: center;"|10<sup>-7.33</sup>
+| style="text-align: center;"|M
+|-
+| style="text-align: center;"|KOxyR
+|OxyR producing rate constant
+| style="text-align: center;"|5.012 x 10<sup>14</sup>
+| style="text-align: center;"|X
+|-
+| style="text-align: center;"|nOxyR*
+|Hill coefficient of OxyR*
+|Ranging from 0.75~3.5,depends on what kind of ROS it react with
+| style="text-align: center;"|X
+|OxyR: A Molecular Code for Redox-Related Signaling
+|-
+| style="text-align: center;"|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
+|-
+| rowspan="3" style="text-align: center;" | Ethanol
+| colspan="1" style="text-align: center;" |pyruvate
+| colspan="1" style="text-align: center;" | Initial concentration of pyruvate in MG1655
+| colspan="1" style="text-align: center;" | 1.18 x 2
+| colspan="1" style="text-align: center;" | g/L
+| colspan="1" style="text-align: center;" |Expression of pyruvate carboxylase enhances succinate production in Escherichia coli without affecting glucose uptake
+|-
+|style="text-align: center;" | nPDC
+| Hill coefficient of PDC
+| style="text-align: center;" |2.1
+| style="text-align: center;" | -
+|Purification, characterization and cDNA sequencing of pyruvate decarboxylase Zygosaccharomyces biporus
+|-
+|style="text-align: center;" |nADH||Hill coefficient of ADH|| style="text-align: center;" |at high pH values, 30◦C, n=1; at low temperature, n=3
+|style="text-align: center;" |  -
+|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
+|-
+|-
+| rowspan="6" | SEIR(exponential)
+| colspan="1" style="text-align: center;" | b
+| colspan="1" style="text-align: center;" | Infection rate constant of ''Nosema'' ceranae to the suspected
+| colspan="1" style="text-align: center;" | 24/75
+| colspan="1" style="text-align: center;" | Period(days)-1
+| colspan="1" style="text-align: center;" |
+|-
+|style="text-align: center;" | r1
+| Infection rate constant of K12 to the suspected
+| style="text-align: center;" |3/20
+| Period(days)-1
+| 1. Environment protection administration executive yuan of R.O.C Medical bacteriology of J.A.T
+|-
+|style="text-align: center;" |r2||Infection rate constant of K12 to the latent|| style="text-align: center;" |3/20  ||Period(days)-1||rowspan="2" | 2. Environment protection administration executive yuan of R.O.C.<br> 3. Medical bacteriology of J.A.T
+|-
+|style="text-align: center;" | e ||rate of the latent turns infectious||style="text-align: center;" |1/4||Period(days)-1
+|-
+|style="text-align: center;" | u || Death rate of the infected || style="text-align: center;" |1/8||Period(days)-1||
+|-
+|style="text-align: center;" | k || Rate of intaking capsule ||style="text-align: center;" |24/11||Period(days)-1||
+|-
+| rowspan="4" |SEIR(exponential&linear)
+| colspan="1" style="text-align: center;" | S
+| colspan="1" style="text-align: center;" | x(1)
+| colspan="1" style="text-align: center;" | Amount of total population
+| colspan="1" style="text-align: center;" |
+| colspan="1" style="text-align: center;" |
+|-
+|style="text-align: center;" | E
+| style="text-align: center;" |x(2)
+|style="text-align: center;" | Amount of suspected individuals
+|
+|
+|-
+|style="text-align: center;" |I||style="text-align: center;" |x(3)|| style="text-align: center;" |Amount of individuals in the latent period || ||
+|-
+|style="text-align: center;" | R ||style="text-align: center;" |x(4)||style="text-align: center;" |Amount of infected individuals||  ||
+|-
+|}
 {{:Team:NYMU-Taipei/Footer}}