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 part=
+=Main parts=
-==Function of the parts:==
+==Backgrounds==
-circuit regulators:
+'''Circuit regulators'''
-• LacI regulated promoter(pLac) : when LacI exists, it will bind to LacI regulated promoter(pLac) and represses the promoter.
+• 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.
+• 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 regulation:'''
-• Circuit condition without Nosema:
+• Circuit condition without ''Nosema'':
 [[Image:NYMU_ Circuit condition without Nosema.png|center]]
-Without Nosema Ceranae, 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, cI will bind to pLux/cI hybrid promoter, leading the third 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.
-• Circuit condition with Nosema:
+• Circuit condition with'' Nosema'':
 [[Image:NYMU_ Circuit condition with Nosema.png|center]]
-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.
+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 LacI gene will be produced and bind to pLac, leading to the second circuit to be off.
+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.
+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:
+• Positive feedback:
 [[Image:NYMU_positive feedback.png|center]]
 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:
+The picture shows how LuxI will transfer to AHL, which then bind to LuxR to form a dimer:
+[[Image:NYMU_luxr ahl dimer.png|center]]
+• 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 lacI will be produced.
+After ''Nosema'' is killed, the sensor will be off and no ptet 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.
+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''.
-==Aims==
+==Objectives==
-. To know how much time it needs from sensing to killing the Nosema after infection
+. 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)
+. 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.
-==Equations==
+==System==
-'''Equation1:'''
+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'''
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNACI]}{dt}= \frac{1-[LacI]^nLacI}{ KdLacI^nLacI+ [LacI]^nLacI}
+\frac{d[mRNA_C_I]}{dt}= \frac{1-[ptet]^nptet}{ Kdptet^nptet+ [ptet]^nptet}
 \times PoPSconstitutive\times\frac{N}{V}
--KdegmRNA\times [mRNACI]
+-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 73: / 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.'''
+[[read more1]]
-'''Equation2:'''
+'''Equation2'''
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNALacI]}{dt}= \frac{1-[ROSoxyR]^nROSoxyR }{ KdROSoxyR ^nROSoxyR + [ROSoxyR]^nROSoxyR} PoPStrxC\times\frac{N}{V}-KdegmRNA[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 86: / 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 94: / 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:'''
@@ Line 100: / Line 109: @@
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNAOxyR]}{dt}=PoPSconstitutive\times\frac{N}{V}-KdegmRNA\times [mRNAOxyR]</div>
+\frac{d[mRNA_O_x_y_R]}{dt}=PoPSconstitutive\times\frac{N}{V}-KdegmRNA\times [mRNAOxyR]</div>
 </html>
@@ Line 113: / Line 122: @@
 ''' The aim of the equation is to know the production rate ofmRNAoxyR, and choose the proper constitutive promoter for boosting OxyR's concentration.'''
+[[read more3]]
 '''Equation4:'''
 <html> <div lang="latex" class="equation">
-\frac{d[mRNALuxI]}{dt}= \frac{1-[ROSoxyR]^n ROSoxyR }{ Kd ROSoxyR ^n ROSoxyR + [ROSoxyR]^n ROSoxyR I} PoPStrxC\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]
+\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>
@@ Line 124: / Line 134: @@
 nROSoxyR = Hill coefficient of ROSoxyR
-PoPStrxC = promoter strength of trxC
+PoPSAhpCp = promoter strength of AhpCp
 KdLuxRAHL = dissociation constant ofLuxRAHL
@@ Line 142: / 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. '''
+[[read more4]]
 '''Equation5:'''
 <html> <div lang="latex" class="equation">
-\frac{d[mRNALuxR]}{dt}= \frac{1-[ROSoxyR]^n ROSoxyR }{ Kd ROSoxyR ^n ROSoxyR + [ROSoxyR]^n ROSoxyR I} \times PoPStrxC\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]
+\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>
@@ Line 154: / Line 166: @@
 nROSoxyR = Hill coefficient of ROSoxyR
-PoPStrxC = promoter strength of trxC
+PoPSAhpCp = promoter strength of AhpCp
 KdLuxRAHL = dissociation constant ofLuxRAHL
@@ Line 172: / 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. '''
+[[read more5]]
-'''Equation6:'''
+'''Equation6'''
 <html> <div lang="latex" class="equation">
-\frac{d[mRNAkill]}{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[mRNAkill]
+\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>
@@ Line 190: / Line 204: @@
 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 196: / 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]]
+[[to learn more about how we characterize pLuxCI, click here]]
+'''Equation7'''
 <html> <div lang="latex" class="equation">
-\frac{d[Mrnat7]}{dt}= \frac{1-[ROSoxyR]^n ROSoxyR }{ Kd ROSoxyR ^n ROSoxyR + [ROSoxyR]^nROSoxyR }\timesPoPStrxC\times\frac{N}{V}\times {a}+ \frac{1-[T7]^nT7}{ Kd T7^nT7 + [T7]^nT7}\times{PoPST7}\times\ frac{N}{V}-KdegmRNA\times [mRNAT7]
+\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>
@@ Line 208: / Line 227: @@
 nROSoxyR = Hill coefficient of ROSoxyR
-PoPStrxC = promoter strength of trxC
+PoPSAhpCp = promoter strength of AhpCp
 KdT7 = dissociation constant of T7
@@ Line 216: / Line 235: @@
 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
@@ Line 222: / 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:'''
@@ Line 228: / Line 249: @@
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNAPDC]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\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>
@@ Line 245: / Line 266: @@
 '''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:'''
@@ Line 250: / Line 273: @@
 <html>
 <div lang="latex" class="equation">
-\frac{d[mRNAADH]}{dt}=\frac{ [T7]^{nT7} }{ KdT7^{nT7}+[T7]^{nY7} }\times{PoPST7}\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 268: / Line 291: @@
 '''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: '''
+[[read more9]]
+'''Equation10 '''
 <html>
 <div lang="latex" class="equation">
-\frac{d[CI]}{dt}={RBS}\times{[mRNACI]} -KdegCI\times{[CI]}
+\frac{d[CI]}{dt}={RBS}\times{[mRNA_C_I]} -KdegCI\times{[CI]}
 </div>
 </html>
@@ Line 282: / Line 308: @@
 '''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:'''
+[[read more10]]
+'''Equation11'''
 <html>
 <div lang="latex" class="equation">
-\frac{d[LacI]}{dt}={RBS}\times{[mRNA LacI]} - {Kdeg LacI} \times{[LacI]}
+\frac{d[ptet]}{dt}={RBS}\times{[mRNA_L_a_c_I]} - {Kdeg ptet} \times{[ptet]}
 </div>
 </html>
@@ Line 292: / 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.'''
-'''Equation12:''
+[[read more11]]
+'''Equation12''
 <html>
 <div lang="latex" class="equation">
-\frac{d[LuxI]}{dt}={RBS}\times{[mRNA LuxI]} -KAHL\times{[LuxI]}
+\frac{d[LuxI]}{dt}={RBS}\times{[mRNA_L_u_x_I]} -KAHL\times{[LuxI]}
   -Kdeg {[LuxI]} \times{[LuxI]}
 </div>
@@ Line 313: / Line 343: @@
 '''The aim of the equation is to know the production rate of LuxI concerning the LuxIAHL reaction and LuxI degrading. '''
-'''Equation13:''
+[[read more12]]
+'''Equation13''
 <html>
 <div lang="latex" class="equation">
-\frac{d[LuxR]}{dt}={RBS}\times{[mRNA LuxR]} – {KmAHL}\times{[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>
@@ Line 333: / Line 365: @@
 '''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:''
@@ Line 352: / Line 386: @@
 '''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. '''
-'''Equation15:''
+[[read more14]]
-<html>
-<div lang="latex" class="equation">
-\frac{d[T7]}{dt}={RBS}\times{[mRNAT7]} –KdegT7\times{[T7]}
-</div>
-</html>
-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:''
-<html>
-<div lang="latex" class="equation">
-\frac{d[PDC]}{dt}=RBS\times{PoPST7effect}\times\frac{N}{V}-{kdegPDC}\times{[PDC]}
-</div>
-</html>
-RBS = binding site strength
-PoPST7 = promoter strength of T7 promoter
-N = number of plasmid in a single cell
-V = volume of a cell
-KdegPDC = degrading constant of PDC (pyruvate decarboxylase)
-'''The aim of the equation is to know PDC production rate and when it can reach the concentration of ethanol pathway equilibrium.'''
-'''Equation17:''
+'''Equation17'''
 <html>
@@ Line 407: / Line 410: @@
 '''The aim of the equation is to know ADH production rate and when it can reach the concentration of ethanol pathway equilibrium.'''
-'''Equation18:''
+[[read more17]]
+'''Equation18'''
 <html>
 <div lang="latex" class="equation">
@@ Line 425: / Line 429: @@
 '''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. '''
-'''Equation19:''
+[[read more18]]
+'''Equation19'''
 <html>
 <div lang="latex" class="equation">
-\frac{d[kill]}{dt}={RBS}\times{[mRNAkill]} –Kdegkill\times{[kill]}
+\frac{d[kill]}{dt}={RBS}\times{[mRNA_k_i_l_l]} –Kdegkill\times{[kill]}
 </div>
 </html>
@@ Line 437: / 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">
-\frac{d[ethanol]}{dt}=Kpyruvateacetaldehyde\times{Kacetaldehydeethanol}\times\frac{[PDC]^{nPDC} }{ KdPDC^{nPDC}+[PDC]^{nPDC}}\times\frac{[ADH]^{nADH} }{ KdADH^{nADH}+[ADH]^{nADH}}-Km\times\frac{[ADH]^{nADH}}{ KdADH^{nADH}+[ADH]^{nADH}}\times{[ethonal]}
-</div>
-</html>
-<br>
-Kpyruvateacetaldehyde = pyruvate→acetaldehyde reaction rate constant
-Kacetaldehydeethanol = acetaldehyde→ethanol reaction rate constant
+==Results==
+[[File:NYMU_defensin normal.png]]
+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)
+[[File:NYMU_defensin witout ROS.png]]
+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.
+[[File:NYMU_defensin only CI.png]]
+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''.
-Km = ethanol→acetaldehyde reaction rate constant
+==Discussion==
-KdADH = dissociation constant of ADH
+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 aim of the equation is to know ethanol production rate and when it can reach the concentration to kill the spores of Nosema Ceranae.''
+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:==
 {|class="wikitable" !Model!!Parameter!!Description!!Value!!Unit!!Reference
@@ Line 527: / Line 540: @@
 | 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;" | 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