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Miyoshi et al. 2007

Miyoshi F, Nakayama Y, Kaizu K, Iwasaki H, Tomita M (2007) A mathematical model for the Kai-protein-based chemical oscillator and clock gene expression rhythms in Cyanobacteria. J Biol Rhythms 22:69-8

In the cyanobacterium, Synechococcus elongatus, most promoters are regulated by a circadian clock under continuous light (LL) conditions. Nevertheless, the basic circadian oscillation is primarily generated by alternating KaiC phosphorylation/dephosphorylation reactions at the posttranslational level. Indeed, the KaiC phosphorylation cycle was recently reconstituted in vitro by incubating KaiA, KaiB, and KaiC proteins with ATP. However, the molecular dynamics of this chemical oscillation and the mechanism that drives the circadian transcription/translation rhythms remain unknown. In this report, the KaiC phosphorylation cycle and the gene regulatory network in the cyanobacterial circadian system have been modeled. The model reproduces the robust KaiC phosphorylation cycle in the absence of de novo gene expression as is observed in vitro, as well as its coupling to transcriptional/translational feedback in LL conditions in vivo. Moreover, the model is consistent with most previous experiments, including various combinations of genetic knockout or overexpression of kai genes. It also predicts that multiple KaiC phosphorylation states and dynamic Kai protein interactions may be required for the cyanobacterial circadian system.


model:Miyoshi et al. (2007)

Miyoshi F, Nakayama Y, Kaizu K, Iwasaki H, Tomita M (2007) A mathematical model for the Kai-protein-based chemical oscillator and clock gene expression rhythms in Cyanobacteria. J Biol Rhythms 22:69-80.


publication:Miyoshi et al. (2007)
Contains:
Initial expression: 1
Simulation type: fixed
Details
Initial expression: 139.22
Simulation type: reaction
Details
Initial expression: 779.158
Simulation type: reaction
Details
Initial expression: 1229.563
Simulation type: reaction
Details
Initial expression: 932.446
Simulation type: reaction
Details
Initial expression: 110.829
Simulation type: reaction
Details
Initial expression: 3251.369
Simulation type: reaction
Details
Initial expression: 0.173
Simulation type: reaction
Details
Initial expression: 1130
Simulation type: reaction
Details
Initial expression: 166.559
Simulation type: reaction
Details
Initial expression: 9.998
Simulation type: reaction
Details
Initial expression: 2.856
Simulation type: reaction
Details
Initial expression: 2.865
Simulation type: reaction
Details
Initial expression: 51.022
Simulation type: reaction
Details
Equation: KaiA2B4 -> KaiB4
Function: Mass Action (irreversible)
Reaction rate: k12*KaiA2B4
Kinetic rate constant Value
k12 0.08788
Details
Equation: KaiA2 -> KaiA2B4
Function: Mass Action (irreversible)
Reaction rate: k11*KaiB4 * KaiA2
Kinetic rate constant Value
k11 0.0008756
Details
Equation: KaiA2 -> KaiA
Function: Mass Action (irreversible)
Reaction rate: k7*KaiA2
Kinetic rate constant Value
k7 0.162
Details
Equation: KaiA -> KaiA2
Function: Mass Action 2nd order (irreversible)
Reaction rate: k8*KaiA*KaiA
Kinetic rate constant Value
k8 0.268
Details
Equation: KaiA ->
Function: light-dependend Mass Action (irreversible)
Reaction rate: kpdeg1*KaiA*L_
Kinetic rate constant Value
kpdeg1 0.008
L_ 1
Details
Equation: -> KaiA
Modifiers: kaiA_mRNA
Function: Light dependend inflow (irreversible)
Reaction rate: ktl1*L_*kaiA_mRNA
Kinetic rate constant Value
L_ 1
ktl1 0.008239
k1
Details
Equation: kaiA_mRNA ->
Function: Mass Action (irreversible)
Reaction rate: kmdeg1*kaiA_mRNA
Kinetic rate constant Value
kmdeg1 0.133
Details
Equation: -> KaiC
Modifiers: kaiBC_mRNA
Function: Light dependend inflow (irreversible)
Reaction rate: ktl2*L_*kaiBC_mRNA
Kinetic rate constant Value
ktl2 170.1
L_ 1
Details
Equation: KaiB ->
Function: light-dependend Mass Action (irreversible)
Reaction rate: kpdeg2*KaiB*L_
Kinetic rate constant Value
kpdeg2 0.49
L_ 1
Details
Equation: KaiB4i -> KaiB4
Modifiers: CPKaiC6
Function: Michaelis-Menten irreversible (irreversible)
Reaction rate: (kcat_b2*CPKaiC6*KaiB4i)/(Km_b2 + KaiB4i)
Kinetic rate constant Value
kcat_b2 0.346
Km_b2 66.75
Equation: KaiB4 -> KaiB4i
Modifiers: PPKaiC6
Function: Michaelis-Menten irreversible (irreversible)
Reaction rate: (kcat_b1*PPKaiC6*KaiB4)/(Km_b1 + KaiB4)
Kinetic rate constant Value
Km_b1 0.602
kcat_b1 2.423
Equation: KaiB4 -> KaiB
Function: Mass Action (irreversible)
Reaction rate: k10*KaiB4
Kinetic rate constant Value
k10 0.0001615
Details
Equation: KaiB -> KaiB4
Function: Mass Action 4th order (reversible)
Reaction rate: k9*KaiB*KaiB*KaiB*KaiB
Kinetic rate constant Value
k9 7.393e-17
Details
Equation: KaiC6 -> PPKaiC6
Function: Mass Action (irreversible)
Reaction rate: k21*KaiC6
Kinetic rate constant Value
k21 1.079e-08
Details
Equation: KaiC6 -> KaiC
Function: Mass Action (irreversible)
Reaction rate: k1*KaiC6
Kinetic rate constant Value
k1 1.615
Details
Equation: KaiC -> KaiC6
Function: Mass Action 6th order (reversible)
Reaction rate: k2*KaiC*KaiC*KaiC*KaiC*KaiC*KaiC
Kinetic rate constant Value
k2 2.039e-16
Details
Equation: KaiC6 -> PPKaiC6
Modifiers: KaiA2
Function: Michaelis-Menten irreversible (irreversible)
Reaction rate: (kcat1*KaiA2*KaiC6)/(Km1 + KaiC6)
Kinetic rate constant Value
kcat1 0.539
Km1 602
Details
Equation: KaiC ->
Function: light-dependend Mass Action (irreversible)
Reaction rate: kpdeg3*KaiC*L_
Kinetic rate constant Value
kpdeg3 1.3
L_ 1
Details
Equation: CPKaiC6 -> PPKaiC6
Function: Mass Action (irreversible)
Reaction rate: k24*CPKaiC6
Kinetic rate constant Value
k24 1.079e-08
Details
Equation: CPKaiC6 -> PPKaiC6
Modifiers: KaiA2B4
Function: Michaelis-Menten irreversible (irreversible)
Reaction rate: (kcat4*KaiA2B4*CPKaiC6)/(Km4 + CPKaiC6)
Kinetic rate constant Value
kcat4 0.89
Km4 0.602
Details
Equation: CPKaiC6 -> PKaiC
Function: Mass Action (irreversible)
Reaction rate: k5*CPKaiC6
Kinetic rate constant Value
k5 0.162
Details
Equation: PKaiC -> CPKaiC6
Function: Mass Action 6th order (reversible)
Reaction rate: k6*PKaiC*PKaiC*PKaiC*PKaiC*PKaiC*PKaiC
Kinetic rate constant Value
k6 1.019e-10
Details
Equation: -> kaiA_mRNA
Modifiers: CPKaiC6, PPKaiC6
Function: Enzyme-modulated light-dependend transcription (irreversible)
Reaction rate: ka1*(kbts1*RNAP)/(1+kbts1*RNAP)*(CPKaiC6/PPKaiC6)*L_
Kinetic rate constant Value
RNAP 5000
ka1 10170000
kbts1 3.657e-12
L_ 1
Details
Equation: kaiBC_mRNA ->
Function: Mass Action (irreversible)
Reaction rate: kmdeg2*kaiBC_mRNA
Kinetic rate constant Value
kmdeg2 0.178
Details
Equation: -> kaiBC_mRNA
Modifiers: CPKaiC6, PPKaiC6
Function: Enzyme-modulated light-dependend transcription (irreversible)
Reaction rate: ka2*(kbts2*RNAP)/(1+kbts2*RNAP)*(CPKaiC6/PPKaiC6)*L_
Kinetic rate constant Value
RNAP 5000
ka2 64580000
kbts2 1e-12
L_ 1
Details
Equation: PPKaiC6 -> KaiC6
Function: Mass Action (irreversible)
Reaction rate: k22*PPKaiC6
Kinetic rate constant Value
k22 1.079e-05
Details
Equation: PPKaiC6 -> CPKaiC6
Function: Mass Action (irreversible)
Reaction rate: k23*PPKaiC6
Kinetic rate constant Value
k23 1.079e-06
Details
Equation: PPKaiC6 -> KaiC6
Modifiers: KaiA2B4
Function: Michaelis-Menten irreversible (irreversible)
Reaction rate: (kcat2*KaiA2B4*PPKaiC6)/(Km2 + PPKaiC6)
Kinetic rate constant Value
kcat2 0.539
Km2 602
Details
Equation: PPKaiC6 -> PKaiC
Function: Mass Action (irreversible)
Reaction rate: k3*PPKaiC6
Kinetic rate constant Value
k3 0.0001615
Details
Equation: KaiC + PKaiC -> PPKaiC6
Function: Specific hexamer formation (Myioshi) (reversible)
Reaction rate: k4*KaiC*KaiC*KaiC*PKaiC*PKaiC*PKaiC
Kinetic rate constant Value
k4 1.019e-14
Details
Equation: PPKaiC6 -> CPKaiC6
Modifiers: KaiA2
Function: Michaelis-Menten irreversible (irreversible)
Reaction rate: (kcat3*KaiA2*PPKaiC6)/(Km3 + PPKaiC6)
Kinetic rate constant Value
kcat3 1.079
Km3 0.602
Details
Equation: PKaiC ->
Function: light-dependend Mass Action (irreversible)
Reaction rate: kpdeg4*PKaiC*L_
Kinetic rate constant Value
kpdeg4 0.2
L_ 1
Details

Constant quantities

Initial expression: 1.019e-14
Simulation type: fixed
Initial expression: 0.0001615
Simulation type: fixed
Initial expression: 2.039e-16
Simulation type: fixed
Initial expression: 0.162
Simulation type: fixed
Initial expression: 1.615
Simulation type: fixed
Initial expression: 1.019e-10
Simulation type: fixed
Initial expression: 0.162
Simulation type: fixed
Initial expression: 0.268
Simulation type: fixed
Initial expression: 7.393e-17
Simulation type: fixed
Initial expression: 0.0001615
Simulation type: fixed
Initial expression: 0.0008756
Simulation type: fixed
Initial expression: 0.08788
Simulation type: fixed
Initial expression: 1.079e-08
Simulation type: fixed
Initial expression: 1.079e-05
Simulation type: fixed
Initial expression: 1.079e-06
Simulation type: fixed
Initial expression: 1.079e-08
Simulation type: fixed
Initial expression: 10170000
Simulation type: fixed
Initial expression: 64580000
Simulation type: fixed
Initial expression: 0.539
Simulation type: fixed
Initial expression: 0.539
Simulation type: fixed
Initial expression: 1.079
Simulation type: fixed
Initial expression: 0.89
Simulation type: fixed
Initial expression: 2.423
Simulation type: fixed
Initial expression: 0.346
Simulation type: fixed
Initial expression: 0.133
Simulation type: fixed
Initial expression: 0.178
Simulation type: fixed
Initial expression: 0.008
Simulation type: fixed
Initial expression: 0.49
Simulation type: fixed
Initial expression: 1.3
Simulation type: fixed
Initial expression: 0.2
Simulation type: fixed
Initial expression: 0.008239
Simulation type: fixed
Initial expression: 170.1
Simulation type: fixed
Initial expression: 3.657e-12
Simulation type: fixed
Initial expression: 1e-12
Simulation type: fixed
Initial expression: 602
Simulation type: fixed
Initial expression: 602
Simulation type: fixed
Initial expression: 0.602
Simulation type: fixed
Initial expression: 0.602
Simulation type: fixed
Initial expression: 0.602
Simulation type: fixed
Initial expression: 66.75
Simulation type: fixed
Initial expression: 5000
Simulation type: fixed
Initial expression: 1
Simulation type: fixed

Assigned quantities

Initial expression: KaiC/(KaiC+PKaiC)
Simulation type: assignment
Initial expression: PKaiC/(KaiC+PKaiC)
Simulation type: assignment
Name Value
cytosol 1
KaiC6 139.22
PPKaiC6 779.158
CPKaiC6 1229.563
KaiC 932.446
PKaiC 110.829
KaiB4i 3251.369
KaiB4 0.173
KaiB 1130
KaiA2 166.559
KaiA 9.998
kaiA_mRNA 2.856
kaiBC_mRNA 2.865
KaiA2B4 51.022

Constant quantities

Name Value
k4 1.019e-14
k3 0.0001615
k2 2.039e-16
k5 0.162
k1 1.615
k6 1.019e-10
k7 0.162
k8 0.268
k9 7.393e-17
k10 0.0001615
k11 0.0008756
k12 0.08788
k21 1.079e-08
k22 1.079e-05
k23 1.079e-06
k24 1.079e-08
ka1 10170000
ka2 64580000
kcat1 0.539
kcat2 0.539
kcat3 1.079
kcat4 0.89
kcat_b1 2.423
kcat_b2 0.346
kmdeg1 0.133
kmdeg2 0.178
kpdeg1 0.008
kpdeg2 0.49
kpdeg3 1.3
kpdeg4 0.2
ktl1 0.008239
ktl2 170.1
kbts1 3.657e-12
kbts2 1e-12
Km1 602
Km2 602
Km3 0.602
Km4 0.602
Km_b1 0.602
Km_b2 66.75
RNAP 5000
L_ 1

Assigned quantities

Name Value
KaiC_rel KaiC/(KaiC+PKaiC)
PKaiC_rel PKaiC/(KaiC+PKaiC)
Name Value
Simulation Start 0  
Simulation End 120  
Number of Steps 60  
Title of Y-axis Species [molecules/cell]  
SemiLogX Scale 0  

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Matrix analysis

Matrix
Description: Dissolved oxygen was measured externally by PSI OxyCorder