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John Tyson's Computational Cell Biology Lab created a mathematical model for M-phase control in Xenopus oocyte (frog egg) extracts [Marlovits et al. 1998]. The M-phase control model shows principles by which you can apply phosphorylation and regulatory loops in your own models. Publications typically list systems of ordinary differential equations (ODEs) that represent a model system. This example shows you how to interpret these ODEs in the form of reaction pathways that are easier to represent and visualize in SimBiology software.
The model is centered around M-phase promoting factor (MPF). There are two positive feedback loops where MPF increases its synthesis and a negative feedback loop where MPF decreases its amount by increasing its degradation.
Cyclin B (CycB) dimerizes with Cdc2 kinase (Cdc2) to form M-phase promoting factor (MPF).
Positive feedback loops with M-phase promoting factor (MPF) activate the Cdc25 phosphatase and deactivate the Wee1 kinase. A negative feedback loop with MPF activates anaphase-promoting complex (APC) that regulates the degradation of the Cyclin B subunit.
Models in systems biology are commonly described in the literature with differential rate equations. However, SimBiology software defines a model using reactions. This section shows you how to convert models published in the literature to a SimBiology format. The equation numbers match the published paper for this model [Marlovits et al. 1998]. Equations that are missing in the sequence involve the Cdk inhibitor (CKI) protein, which is not currently modeled in the SimBiology version.
The rules for writing reaction and reaction rate equations from differential rate equations include not only the equations but also an understanding of the reactions. dx/dt refers to the species the differential rate equation is defining. kinetics refers to the species in the reaction rate.
Positive terms: Rate species are placed on right side of the reactions; reaction rate equation species are placed on the left.
Negative terms: Rate species are placed on the left side of the reaction because the species are being used up in some way; reaction rate equation species are also placed on left. You need to deduce the products from additional information about the model.
The following table will help you deduce the products for a reaction. In this example, by convention, phosphate groups on the right side of a species name are activating while phosphate groups on left are inhibiting.
| Enzyme | Description | Reaction |
|---|---|---|
| wee1 | Kinase, add inhibiting phosphate group | MPF —> P-MPF |
| cdc25 | Phosphatase, remove inhibiting phosphate group | P-MPF —> MPF + P |
| kcak | Kinase, add activating phosphate group | MPF —> MPFp |
| kpp | Phosphatase, remove activating phosphate group | MPF-P —> MPF + P |
| MPF | Kinase, add activating or inhibiting phosphate group | Wee1/Cdc25/IE —> X-P or P-X |
| ki | Add inhibiting Cki | Cki + MPF —> Cki:MPF |
| kir | Remove inhibiting Cki | Cki:MPF —> Cki + MPF |
Differential rate equation for cyclin B [Marlovits et al. 1998].
Rate rule using SimBiology format for the differential rate equation 1. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Rule 1 [CycB] = k1 - K2*[CycB] - k3*[Cdc2]*[CycB]
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules.
Reaction 1 AA -> CycB v = k1 Reaction 2 CycB -> AA v = K2*[CycB] Reaction 3 Cdc2 + CycB -> MPF v = k3*[Cdc2]*[CycB]
Differential rate equation for M-phase promoting factor (MPF) [Marlovits 1998]. Note that the parameter name kcakr [Marlovits et al. 1998] is changed to kpp [Borisuk 1998] in the following reaction equations. MPF is a heterodimer of cdc2 kinase and cyclin B.
Rate rule using SimBiology format for the differential rate equation 1. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Rule 2 MPF = kpp*MPFp - (Kwee1 + kcak + K2)*MPF + Kcdc25*pMPF + k3*Cdc2*CycB
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules. A reaction name in parentheses denotes a reaction repeated in another differential rate equation.
(Reaction 3) Cdc2 + CycB -> MPF v = k3*[Cdc2]*[CycB] Reaction 4 MPF -> Cdc2 + AA v = K2*[MPF] Reaction 5 MPFp -> MPF v = kpp*[MPFp] Reaction 6 MPF -> MPFp v = kcak*[MPF] Reaction 7 pMPF -> MPF v = Kcdc25*[pMPF] Reaction 8 MPF -> pMPF v = Kwee1*[MPF]
Differential rate equation for inhibited M-phase promoting factor (pMPF) [Marlovits 1998].
Rate rule using SimBiology format for the differential rate equation 3. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Rule 3 pMPF = Kwee1*MPF - (Kcdc25 + kcak + K2)*pMPF + kpp*pMPFp
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules.
Reaction 11 pMPF -> Cdc2 + AA v = K2*[pMPF] Reaction 12 pMPFp -> pMPF v = kpp*[pMPFp] Reaction 13 pMPF -> pMPFp v = kcak*[pMPF] (Reaction 8) MPF -> pMPF v = Kwee1*[MPF] (Reaction 7) pMPF -> MPF v = Kcdc25*[pMPF]
Differential rate equation for inhibited and activated M-phase promoting factor (pMPFp) [Marlovits 1998].
Rate rule using SimBiology format for the differential rate equation. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Rule 4 pMPFp = Kwee1*MPFp - (kpp + Kcdc25 + K2)*pMPFp + kcak*pMPF
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules.
Reaction 15 pMPFp -> Cdc2 + AA v = K2*[pMPFp] (Reaction 13) pMPF -> pMPFp v = kcak*[pMPF] (Reaction 12) pMPFp -> pMPF v = kpp*[pMPFp] Reaction 16 MPFp -> pMPFp v = Kwee1*[MPFp] Reaction 17 pMPFp -> MPFp v = Kcdc25*[pMPFp]
Differential rate equation for activated M-phase promoting factor (MPFp) [Marlovits 1998].
Rate rule using SimBiology format for the differential rate equation 1. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Rule 5 MPFp = kcak*MPF - (kpp + Kwee1 + K2)*MPFp + Kcdc25*pMPFp
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules.
Reaction 19 MPFp -> MPF + AA v = K2*[MPFp] (Reaction 6) MPF -> MPFp v = kcak*[MPF] (Reaction 5) MPFp -> MPF v = kpp*[MPFp] (Reaction 17) pMPFp -> MPFp v = Kcdc25*[pMPFp] (Reaction 16) MPFp -> pMPFp v = Kwee1*[MPFp]
Differential rate equation for activating and deactivating Cdc25 [Marlovits 1998].
Rate rule in SimBiology format for the differential rate equation 1. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules. Note that since there isn't a rate rule for Cdc25, its amount is written as (TotalCdc25 - Cdc25p).
Rule 11 Cdc25p = (k25*MPFp*(TotalCdc25 - Cdc25p))/(Km25 + (TotalCdc25 - Cdc25p)) - (k25r*PPase*Cdc25p)/(Km25r + Cdc25p)
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules.
Reaction 36 Cdc25 -> Cdc25p, v = k25*[MPFp]*[Cdc25]/(Km25 + [Cdc25]) Reaction 37 Cdc25p -> Cdc25, v = k25r*[Cdc25p]/(Km25r + [Cdc25p])
Differential rate equation for activating and deactivating Wee1 kinase [Marlovits 1998]. The kinase (MPFp) phosphorylates active Wee1 (Wee1) to its inactive form (Wee1p). The dephosphorylation of inactive Wee1 (Wee1p) is by an unknown phosphatase.
Rate rule in SimBiology format for the differential rate equation 1. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Rule 12 Wee1p = (kw*MPFp*(TotalWee1 - Wee1p))/(Kmw + (TotalWee1 - Wee1p)) - (kwr*Wee1p)/(Kmwr + Wee1p)
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules.
reaction 38 Wee1 -> Wee1p, v = (kw*[MPFp]*[Wee1])/(Kmw + [Wee1]) reaction 39 Wee1p -> Wee1, v = (kwr*[Wee1p])/(Kmwr + [Wee1p])
Differential rate equation for activating and deactivating the intermediate enzyme (IE) [Marlovits 1998]. The active kinase (MPFp) phosphorylates the inactive intermediate enzyme (IE) to its active form (IEp).
Rate rule in SimBiology format for the differential rate equation 1. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Rule 13 IEp = (kie*MPFp*(TotalIE - IEp))/(Kmie + (TotalIE - IEp)) - (kier*IEp)/(Kmier + IEp)
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules.
reaction 40 IE -> IEp, v = (kie*[MPFp]*[IE])/(Kmie + [IE]) reaction 41 IEp -> IE, v = (kier*[IEp])/(Kmier + [IEp])
Differential rate equation for [Marlovits 1998].
Rate rule in SimBiology format for the differential rate equation 1. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Rule 14 APCa = (kap*IEp*(TotalAPC - APCa))/(Kmap + (TotalAPC - APCa)) - (kapr*APCa)/(Kmapr + APCa)
Reaction and reaction rate equations derived from the differential rate equation. For a model using these reactions, see SimBiology Model with Reactions and Algebraic Rules.
Reaction 42 APCi -> APCa, v = (kap*[IEp]*[APCi])/(Kmap + [APCi]) Reaction 43 APCa -> APCi, v = (kapr*[APCa])/(Kmapr + [APCa])
Algebraic equation to define the rate parameter K2 [Marlovits 1998]. Inactive APC (APCi) is catalyzed by IE (intermediate enzyme) to active APC (APCa).
Algebraic rule in SimBiology format for the algebraic equation 17. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Algebraic Rule 17 V2i*(TotalAPC - APCa) + V2a*APCa - K2
Algebraic rule when simulating with reactions. For a model using this rule with reactions, see SimBiology Model with Reactions and Algebraic Rules. V2' is renamed to V2i and V2"is renamed to V2a. APCi (APC) is the inactive form of the enzyme while APCa (APC') is the active form. K2 is the independent variable.
Algebraic Rule 1 (V2i*APCi) + (V2a*APCa) - K2
Algebraic equation to define the rate parameter Kcdc25 [Marlovits 1998]. Inactive Cdc25 (Cdc25) is phosphorylated by MPF to active Cdc25 (Cdc25p).
Algebraic rule in SimBiology format for the algebraic equation 18. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Algebraic Rule 18 V25i*(TotalCdc25 - Cdc25p) + V25a*Cdc25p - Kcdc25
Algebraic rule when simulating with reactions. Kcdc25 is the independent variable. For a model using this rule with reactions, see SimBiology Model with Reactions and Algebraic Rules.
Algebraic Rule 2 (V25i*Cdc25) + (V25a*Cdc25p) - Kcdc25
Algebraic equation to define the rate parameter [Marlovits 1998]. Active Wee1 (Wee1) is phosphorylated by MPF to inactive Wee1 (Wee1p).
Algebraic rule in SimBiology format for rate parameter equation 19. For a model using this rule, see SimBiology Model with Rate and Algebraic Rules.
Algebraic Rule 19 Vwee1i*Wee1p + Vwee1a*(TotalWee1 - Wee1p) - Kwee1
Algebraic rule when simulating with reactions. Kwee1 is the independent variable. For a model using this rule with reactions, see SimBiology Model with Reactions and Algebraic Rules.
Algebraic Rule 3 (Vwee1i*Wee1p) + (Vwee1a*Wee1) - Kwee1
There is one rate rule for each equation defining a species and one algebraic rule for each variable parameter in the M-phase control model [Marlovits 1998]. For a list and description of the equations, see M-Phase Control Equations.
A basic model includes rate rules 1 to 5 and 11 to 14 with algebraic rules 17, 18, and 19.
Writing differential rate equations in an unambiguous format that a software program can understand is a simple process when you follow the syntax rules for programming languages.
Use an asterisk to indicate multiplication. For example, k[A] is written k*A or k*[A]. The brackets around the species A do not indicate concentration.
SimBiology uses square brackets around species and parameter name to allow names that are not valid MATLAB variable names. For example, you could have a species named glucose-6-phosphate dehydrogenase but you need to add brackets around the name in reaction rate and rule equations.
[glucose-6-phosphate dehydrogenase]
Use parentheses to clarify the order of evaluation for mathematical operations. For example, do not write Henri-Michaelis-Menten reaction rates as Vm*C/Kd + C, because Vm*C is divided by Kd before adding C to the result. Instead, write this reaction rate as (Vm*C)/(Kd + C).
The following table lists species in the model with their initial amounts. There are three variable parameters modeled as species (K2, Kcdc25, and KWee1). You could also model the variable parameters as parameters with the property ConstantAmount cleared.
The following table lists parameters in the model with their initial values. The property ConstantValue is selected for all of the parameters.
The rate rule is from Equation 1, Cyclin B.
rate rule: CycB = k1 - K2*CycB - k3*Cdc2*CycB
species: CycB = 0 nM
Cdc2 = 100 nM, [x]constant
parameters: k1 = 1 nM/minute
K2 = 0 1/minute, []constant
k3 = 0.005 1/(nM*minute)K2 is a variable rate parameter whose value is defined by an algebraic rule. See Algebraic Rule 17, Rate Parameter K2. Its value varies from 0.005 to 0.25 1/minute.
The rate rule is from Equation 2, M-Phase Promoting Factor.
rate rule: MPF = kpp*MPFp - (Kwee1 + kcak + K2)*MPF + Kcdc25*pMPF + k3*Cdc2*CycB
species: MPF = 0 nM
MPFp = 0 nM
pMPF = 0 nM
parameters: kpp = 0.004 1/minute
kcak = 0.64 1/minute
k3 = 0.005 1/(nM*minute)
K2 = 0 1/minute
Kcdc25 = 0 1/minute
Kwee1 = 0 1/minuteK2, Kcdc25, and Kwee1 are variable rate parameters whose values are defined by algebraic rules. See Algebraic Rule 17, Rate Parameter K2, Algebraic Rule 18, Rate Parameter Kcdc25, and Algebraic Rule 19, Rate Parameter Kwee1.
The rate rule is from Equation 3, Inhibited M-Phase Promoting Factor.
rate rule: pMPF = Kwee1*MPF - (Kcdc25 + kcak + K2)*pMPF + kpp*pMPFp
The rate rule is from Equation 4, Inhibited and Activated M-Phase Promoting Factor.
rate rule: pMPFp = Kwee1*MPFp - (kpp + Kcdc25 + K2)*pMPFp + kcak*pMPF
The rate rule is from Equation 5, Activated M-Phase Promoting Factor.
rate rule: MPFp = kcak*MPF - (kpp + Kwee1 + K2)*MPFp + Kcdc25*pMPFp
The rate rule is from Equation 11, Cell Division Control 25.
rate rule: Cdc25p = (k25*MPFp*(TotalCdc25 - Cdc25p))/(Km25 + (TotalCdc25 - Cdc25p)) - (k25r*PPase*Cdc25p)/(Km25r + Cdc25p)
The rate rule is from Equation 12, Wee1 Activation/Deactivation.
rate rule: Wee1p = (kw*MPFp*(TotalWee1 - Wee1p))/(Kmw + (TotalWee1 - Wee1p)) - (kwr*PPase*Wee1p)/(Kmwr + Wee1p)
The rate rule is from Equation 13, Intermediate Enzyme Activation/Deactivation.
rate rule: IEp = (kie*MPFp*(TotalIE - IEp))/(Kmie + (TotalIE - IEp)) - (kier*PPase*IEp)/(Kmier + IEp)
The rate rule is from Equation 14, APC Activation/Deactivation.
rate rule: APCa = (kap*IEp*(TotalAPC - APCa))/(Kmap + (TotalAPC - APCa)) - (kapr*AntiAPC*APCa)/(Kmapr + APCa)
K2 is a variable rate parameter whose value is determined by the amount of active and inactive APC. The algebraic rule is from Equation 17, Rate Parameter K2.
algebraic rule: V2i*(TotalAPC - APCa) + V2a*APCa - K2
species: APCi = 1 nM
APCa = 0 nM
TotalAPC = 1 nM [x]constant
parameters: K2 = 0 or 0.25 1/minute, []constant
V2i = 0.005 1/(nM*minute)
V2a = 0.25 1/(nM*minute)
Kcdc25 is a variable rate parameter whose value is determined by the amount of active and inactive Cdc25. The algebraic rule is from Algebraic Rule 18, Rate Parameter Kcdc25.
algebraic rule: V25i*(TotalCdc25 - Cdc25p) + V25a*Cdc25p - Kcdc25
Kwee1 is a variable rate parameter whose value is determined by the amount of active and inactive Wee1. The algebraic rule is from Equation 19, Rate Parameter Kwee1.
algebraic rule: Vweei*Wee1p + Vweea*(TotalWee1 - Wee1p) - Kwee1
Reaction 15, Degradation of Cyclin B on Active but Inhibited MPF
Reaction 40, Activation of Intermediate Enzyme by Active MPF
There can be one or more reactions for an equation defining a species and one algebraic rule for each variable parameter in the M-phase control model [Marlovits 1998]. For a list and description of the equations, see M-Phase Control Equations.
A basic model includes reactions 1 to 8, 11 to 13, 15 to 17, 19, and 36 to 43 with algebraic rules from equations 17, 18, and 19.
Cyclin B is synthesized at a constant rate.
reaction: AA -> CycB
reaction rate: k1 nM/minute
parameter: k1 = 1 nM/minute
species: CycB = 0 nM
AA = 100 nM [x]constant [x]boundarySimulate reaction 1 with the sundials solver.
Cyclin B is degraded at the end of the M-phase.
reaction: CycB -> AA
reaction rate: K2*CycB nM/minute
parameters: K2 = 0 1/minute, []constant, variable by rule
V2i = 0.005 1/nM*minute
V2a = 0.25 1/nM*minute
species: CycB = 0 nM
APCi = 1 nM
APCa = 0 nM
AA = 100 nM [x]constant [x]boundary
algebraic rule: (V2i*APCi) + (V2a*APCa) - K2Initially, Cyclin B degradation is low. This implies the amount of active APC (APCa) = 0 and inactive APC (APCi) = APCtotal = 1 nM.
Test the algebraic rule by simulating reactions 1 and 2 with APCi = 0 and APCa = 1.
Cyclin B dimerizes with Cdc2 kinase to form M-phase promoting factor (MPF).
reaction: Cdc2 + CycB -> MPF
reaction rate: k3*Cdc2*CycB nM/minute
parameters: k3 = 0.005 1/(nM*minute)
species: Cdc2 = 100 nM
CycB = 0 nM
MPF = 0 nMTest the model by simulating with K2 = 0.25.
Cyclin B is tagged with ubiquitin groups and degrades while bound to Cdc2.
reaction: MPF -> Cdc2 + AA
reaction rate: K2*[MPF]
parameters: K2 = 0 or 0.25 1/minute, variable by rule
v2i = 0.005 1/(nM*minute)
v2a = 0.25 1/(nM*minute)
species: MPF = 0 nM
APCi = 1 nM
APCa = 0 nM
AA = 100 nM [x]constant [x]boundary
algebraic rule: (v2i*APCi) + (v2a*APCa) - K2
Test the simulation with APCa = 1 and APCi = 0. Because the amount of APCa (active) is high, K2 increases and the degradation starts to balance the synthesis of MPF.
Active MPF (MPFp) is dephosphorylated on Thr-161 by an unknown phosphatase (PP) to inactive MPF (MPF).
reaction: MPFp -> MPF
reaction rate: kpp*[MPFp]
parameters: kpp = 0.004 1/minute
species: MPFp = 0 nM
MPF = 0 nMkcakr = 0.004 1/minute [Marlovits 1998, p. 175], but is renamed to kpp [Borisuk 1998].
Test simulation with APCa = 1 and APCi = 0. MPF increases without reaching steady state.
Inactive MPF (MPF) is phosphorylated on Thr-161 by an unknown cyclin activating kinase (CAK).
reaction: MPF -> MPFp
reaction rate: kcak*[MPF]
parameters: kcak = 0.64 1/minute
species: MPF = 0 nM
MPFp = 0 nMThe kinase reaction that phosphorylates MPF to the active form is 160 times faster than the phosphatase reaction that dephosphorylates active MPF.
Simulate the model with reactions 1 to 6. Notice that after adding reaction 6, most of the product goes to active MPF (MPFp).
Cdc25 phosphatase removes the inhibiting phosphate groups at the threonine 14 and tyrosine 15 residues on Cdc2 kinase.
reaction: pMPF -> MPF
reaction rate: Kcdc25*[pMPF]
parameters: Kcdc25 = 0.0 1/minute or 0.017 1/minute, variable by
algebraic rule
V25i = 0.017 1/(mM*minute)
V25a = 0.17 1/mM*minute
species: pMPF = 0 nM
MPF = 0 nM
Cdc25 = 1 nM (inactive)
Cdc25p = 0 nM (active)
algebraic rule: (V25i*Cdc25) + (V25a*Cdc25p) - Kcdc25Initially, all of the Cdc25 phosphatase is in the inactive form (Cdc25).
Enter the initial value for Kcdc25 as 0.0 and let the first time step calculate the value from the rule, or enter an initial value using the rule.
Initially, set ConstantAmount for Cdc25 and Cdc25p to test reactions 1 through 7. Then after you can add the reactions to regulate the Cdc25 phosphatase by clearing the ConstantAmount property.
Addition of inhibiting phosphate groups by Wee1 kinase to inhibit active M-phase promoting factor (MPF). Myt1 kinase is also involved with the phosphorylation, but its contribution is grouped with Wee1.
reaction: MPF -> pMPF
reaction rate: Kwee1*[MPF]
parameters: Kwee1 = 0.0 1/minute or 0.01 1/minute, variable by
algebraic rule
Vwee1i = 0.01 1/(nM*minute)
Vwee1a = 1.0 1/(nM*minute)
species: MPF = 0 nM
pMPF = 0 nM
Wee1p = 1 nM (inactive)
Wee1 = 0 nM (active)
algebraic rule: (Vwee1i*Wee1p) + (Vwee1a*Wee1) - Kwee1The initial capitalization for the parameter Kwee1 is a convention to indicate that this value changes during the simulation.
Test the simulation for reactions 1 through 8 with Wee1p (inactive) = 1 and Wee1 (active) = 0.
Test the simulation with Wee1p (inactive) = 0 and Wee1 (active) = 1.
Degradation of cyclin B (CycB) on inhibited MPF (pMPF). Cyclin B is tagged with ubiquitin groups and degrades while bound to Cdc2.
reaction: pMPF -> Cdc2 + AA
reaction rate: K2*[pMPF] nM/minute
parameters: K2 = 0 or 0.25 1/minute, variable by rule
V2i = 0.005 1/nM*minute
V2a = 0.25 1/nM*minute
species: MPF = 0 nM
APCi = 1 nM
APCa = 0 nM
AA = 100 nM [x]constant [x]boundary
Cdc2 = 100 nm
algebraic rule: (V2i*APCi) + (V2a*APCa) - K2
Test the simulation with Wee1 active (Wee1 = 1) and APC active (APCi = 1).
Inhibited/active MPF (pMPFp) is dephosphorylated on Thr-161 by an unknown phosphatase (PP) to inhibited MPF (pMPF). Compare reaction 12 with reaction 5.
reaction: pMPFp -> pMPF
reaction rate: kpp*[pMPFp]
parameters: kpp = 0.004 1/minute
species: pMPFp = 0 nM
pMPF = 0 nM
Inhibited MPF (pMPF) is phosphorylated on Thr-161 by an unknown cyclin-activating kinase (CAK). Compare reaction 13 with reaction 6.
reaction: pMPF -> pMPFp
reaction rate: kcak*[pMPF] nM/minute
parameters: kcak = 0.64 1/minute
species: pMPF = 0 nM
pMPFp = 0 nM
Test the simulation with Wee1p = 1 (inactive)/ Wee1 = 0 and then test with Wee1p = 0 (inactive)/ Wee1 = 1.
Degradation of cyclin B (CycB) on inhibited MPF (pMPF). Cyclin B is tagged with ubiquitin groups and degrades while bound to cdc2 kinase.
reaction: pMPFp -> Cdc2 + AA
reaction rate: K2*[pMPFp] nM/minute
parameters: K2 = 0 or 0.25 1/minute, variable by rule
v2i = 0.005 1/nM*minute
v2a = 0.25 1/nM*minute
species: MPF = 0 nM
APCi = 1 nM
APCa = 0 nM
AA = 100 nM [x]constant [x]boundary
Cdc2 = 100 nm
algebraic rule: (V2i*APCi) + (V2a*APCa) - K2
Addition of inhibiting phosphate groups by Wee1 kinase to inhibit active M-phase promoting factor (MPF). Myt1 kinase is also involved with the phosphorylation, but its contribution is grouped with Wee1.
reaction: MPFp -> pMPFp
reaction rate: Kwee1*[MPFp] nM/minute
parameters: Kwee1 = 1/minute []constant, variable by rule
Vweei = 0.01 1/nM*minute
Vweea = 1 1/nM*minute
species: MPFp = 0 nM
pMPFp = 0 nM
Wee1p = 1 nM (inactive)
Wee1 = 0 nM (active)
algebraic rule: (Vwee1i*Wee1p) + (Vwee1a*Wee1) - Kwee1Remove the inhibiting phosphate group from pMPFp with cdc25 phosphatase.
reaction: pMPFp -> MPFp
reaction rate: Kcdc25*[pMPFp]
parameters: Kcdc25 = 0 1/minue, []constant, variable by rule
V25i = 0.017 1/nM*minute
V25a = 0.17 1/nM*minute
species: pMPFp = 0 nM
MPFp = 0 nM
algebraic rule: (V25i*Cdc25) + (V25a*Cdc25p) - Kcdc25
Degradation of cyclin B (CycB) on inhibited MPF (pMPF). Cyclin B is tagged with ubiquitin groups and degrades while bound to cdc2 kinase.
reaction: MPFp -> MPF + AA
reaction rate: K2*[MPFp] nM/minute
parameters: K2 = 0 or 0.25 1/minute, variable by rule
V2i = 0.005 1/nM*minute
V2a = 0.25 1/nM*minute
species: MPF = 0 nM
MPFp = 0 nM
APCi = 1 nM
APCa = 0 nM
AA = 100 nM [x]constant [x]boundary
Cdc2 = 100 nm
algebraic rule: (V2i*APCi) + (V2a*APCa) - K2
Activation of cdc25 phosphatase by phosphorylation with active M-phase promoting factor (MPFp).
reaction: Cdc25 + (MPFp) -> Cdc25p + (MPFp)
reaction rate: (k25*[MPFp]*[Cdc25])/(Km25 + [Cdc25])
parameters: k25 = 0.02 1/minute
Km25 = 0.1 nM
species: Cdc25 = 1 nM (inactive)
Cdc25p = 0 nM (active)
Initially MPF is inhibited (MPF* reacts to pMPF*).
Deactivation of cdc25 phosphatase by dephosphorylation with an unknown phosphatase.
reaction: Cdc25p -> Cdc25
reaction rate: (k25r*[Cdc25p])/(Km25r + [Cdc25p])
parameters: k25r = 0.1 nM/minute
Km25r = 1 nM
species: Cdc25 = 1 nM (inactive)
Cdc25p = 0 nM (active)
Deactivation of Wee1 kinase by phosphorylation with active M-phase promoting factor (MPFp).
reaction: Wee1 + (MPFp) -> Wee1p + (MPFp)
reaction rate: (kw*[MPFp]*[Wee1])/(Kmw + [Wee1]) nM/minute
parameters: kw = 0.02 1/minute
Kmw = 0.1 nM
species: Wee1p = 1 nM (inactive)
Wee1 = 0 nM (active)Initially MPF is inhibited (MPF* reacts to pMPF*).
Activation of Wee1 kinase by dephosphorylation with an unknown kinase.
reaction: Wee1p -> Wee1
reaction rate: (kwr*[Wee1p])/(Kmwr + [Wee1p]) nM/minute
parameters: kwr = 0.1 nM/minute
Kmwr = 1 nM
species: Wee1p = 1 nM (inactive)
Wee1 = 0 nM (active)The inactive intermediate enzyme (IE) is activated by phosphorylation with active M-phase promoting factor (MPFp).
reaction: IE + (MPFp) -> IEp + (MPFp)
reaction rate: (kie*[MPFp]*[IE])/(Kmie + [IE])
parameters: kie = 0.02 1/minute
Kmie = 0.01nM
species: IE = 1 nM (inactive)
IEp = 0 nM (active)
The active intermediate enzyme (IE) is deactivated by dephosphorylation.
reaction: IEp -> IE
reaction rate: (kier*[IEp])/(Kmier + [IEp])
parameters: kier = 0.15 nM/minute
Kmier = 0.01 nM
species: IE = 1 nM (inactive)
IEp = 0 nM (active)
Anaphase-promoting complex (APC) is activated by an active intermediate enzyme (IEp).
reaction: APCi + IEp -> APCa + IEp
reaction rate: (kap*[IEp]*[APCi])/(Kmap + [APCi])
parameters: kap = 0.13 1/minute
Kmap = 0.01 nM
species : APCi = 1 nM
APCa = 0 nMAnaphase-promoting complex (APC) is deactivated.
reaction: APCa -> APCi
reaction rate: (kapr*[APCa])/(Kmapr + [APCa])
parameters: kapr = 0.13 nM/minute
Kmapr = 1 nM
species : APCi = 1 nM
APCa = 0 nM
[1] Borisuk M, Tyson J (1998), "Bifurcation analysis of a model of mitotic control in frog eggs," Journal of Theoretical Biology, 195(1):69–85, PubMed 9802951.
[2] Marlovits G, Tyson C, Novak B, Tyson J (1998), "Modeling M-phase control in Xenopus oocyte extracts: the surveillance mechanism for unreplicated DNA," Biophysical Chemistry, 72(1-2):169–184, PubMed 9652093.
[3] Novák B, Tyson J (1993), "Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos," Journal of Cell Science, 106(4):1153–1168, PubMed 8126097.
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