leloup3

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000074) This is model in continous darkness (DD) described in the article Toward a detailed computational model for the mammalian circadian clock This model features the full interlocked negative and positive regulation of Per,Cry,Bmal and REV-ERBalpha. The model exhibits robust oscillations quite independent of the initial conditions for teh parameters given. Each species is assigned zero as initial value, and the graph started at time=120h. Simulation results could be reproduced using Copasi 4.0.19(development) and roadRunner online. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

None

None

None

None

None

None

Toward a detailed computational model for the mammalian circadian clock.

  • Jean-Christophe Leloup
  • Albert Goldbeter
Proc. Natl. Acad. Sci. U.S.A. 2003; 100 (12): 7051-7056
Abstract
We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
3600.0 second
1e-09 mole
Id Name Spatial dimensions Size
compartment_0 cell 3.0 1.0
Id Name Initial quantity Compartment Fixed
species_0 Mb 0.0 compartment_0 (cell)
species_1 Bc 0.0 compartment_0 (cell)
species_10 PCc 0.0 compartment_0 (cell)
species_11 PCcp 0.0 compartment_0 (cell)
species_12 PCn 0.0 compartment_0 (cell)
species_13 Bnp 0.0 compartment_0 (cell)
species_14 PCnp 0.0 compartment_0 (cell)
species_15 In 0.0 compartment_0 (cell)
species_16 Mr 0.0 compartment_0 (cell)
species_17 Rc 0.0 compartment_0 (cell)
species_18 Rn 0.0 compartment_0 (cell)
species_2 Bcp 0.0 compartment_0 (cell)
species_3 Bn 0.0 compartment_0 (cell)
species_4 Cc 0.0 compartment_0 (cell)
species_5 Mc 0.0 compartment_0 (cell)
species_6 Ccp 0.0 compartment_0 (cell)
species_7 Mp 0.0 compartment_0 (cell)
species_8 Pc 0.0 compartment_0 (cell)
species_9 Pcp 0.0 compartment_0 (cell)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
reaction_0 Mb synthesized ∅ > species_0

compartment_0 * function_0(vsb, K, m, species_18)
reaction_1 Mb translated into protein ∅ > species_1

compartment_0 * function_1(k, species_0)
reaction_10 Mp translated into protein ∅ > species_8

compartment_0 * function_1(k, species_7)
reaction_11 Pcp specific degradation species_9 > ∅

compartment_0 * function_2(V, species_9, Km)
reaction_12 Pc phospholation species_8 > species_9

compartment_0 * function_2(V, species_8, Km)
reaction_13 Cc and Pc produce PCc species_4 + species_8 = species_10

compartment_0 * (k1 * species_4 * species_8 - k2 * species_10)
reaction_14 PCc phospholation species_10 > species_11

compartment_0 * function_2(V, species_10, Km)
reaction_15 PCcp specific degradation species_11 > ∅

compartment_0 * function_2(V, species_11, Km)
reaction_16 PCc transfered into nuclear species_10 = species_12

compartment_0 * (k1 * species_10 - k2 * species_12)
reaction_17 PCnp nonspecific degradation species_14 > ∅

compartment_0 * k1 * species_14
reaction_18 Bcp nonspecific degradation species_2 > ∅

compartment_0 * k1 * species_2
reaction_19 Bnp nonspecific degradation species_13 > ∅

compartment_0 * k1 * species_13
reaction_2 Mb nonspecific degradation species_0 > ∅

compartment_0 * k1 * species_0
reaction_20 Mc synthesis ∅ > species_5

compartment_0 * function_3(Vs, species_3, n, K)
reaction_21 PCn phospholation species_12 > species_14

compartment_0 * function_2(V, species_12, Km)
reaction_22 Mp nonspecific degradation species_7 > ∅

compartment_0 * k1 * species_7
reaction_23 Per_Cry and Clock_Bmal form inactive complex species_12 + species_3 = species_15

compartment_0 * (k1 * species_12 * species_3 - k2 * species_15)
reaction_24 Mb specific degradation species_0 > ∅

compartment_0 * function_2(V, species_0, Km)
reaction_25 Mc specific degradation species_5 > ∅

compartment_0 * function_2(V, species_5, Km)
reaction_26 Mp specific degradation species_7 > ∅

compartment_0 * function_2(V, species_7, Km)
reaction_27 Pc nonspecific degradation species_8 > ∅

compartment_0 * k1 * species_8
reaction_28 Cc nonspecific degradation species_4 > ∅

compartment_0 * k1 * species_4
reaction_29 Pcp nonspecific degradation species_9 > ∅

compartment_0 * k1 * species_9
reaction_3 Bc phosphorylation species_1 > species_2

compartment_0 * function_2(V, species_1, Km)
reaction_30 Ccp nonspecific degradation species_6 > ∅

compartment_0 * k1 * species_6
reaction_31 PCcp nonspecific degradation species_11 > ∅

compartment_0 * k1 * species_11
reaction_32 PCc nonspecific degradation species_10 > ∅

compartment_0 * k1 * species_10
reaction_33 PCnp specific degradation species_14 > ∅

compartment_0 * function_2(V, species_14, Km)
reaction_34 Bc nonspecific degradation species_1 > ∅

compartment_0 * k1 * species_1
reaction_35 Bcp specific degradation species_2 > ∅

compartment_0 * function_2(V, species_2, Km)
reaction_36 Bn phospholation species_3 > species_13

compartment_0 * function_2(V, species_3, Km)
reaction_37 Bnp specific degradation species_13 > ∅

compartment_0 * function_2(V, species_13, Km)
reaction_38 In nonspecific degration species_15 > ∅

compartment_0 * k1 * species_15
reaction_39 In specific degradation species_15 > ∅

compartment_0 * function_2(V, species_15, Km)
reaction_4 Bc transfered from cytosolic to nuclear species_1 = species_3

compartment_0 * (k1 * species_1 - k2 * species_3)
reaction_40 Bn nonspecific degradation species_3 > ∅

compartment_0 * k1 * species_3
reaction_41 Bcp dephospholation species_2 > species_1

compartment_0 * function_2(V, species_2, Km)
reaction_42 Bnp dephospholation species_13 > species_3

compartment_0 * function_2(V, species_13, Km)
reaction_43 Ccp dephospholation species_6 > species_4

compartment_0 * function_2(V, species_6, Km)
reaction_44 Pcp dephospholation species_9 > species_8

compartment_0 * function_2(V, species_9, Km)
reaction_45 PCnp dephospholation species_14 > species_12

compartment_0 * function_2(V, species_14, Km)
reaction_46 PCn nonspecific degradation species_12 > ∅

compartment_0 * k1 * species_12
reaction_47 PCcp dephospholation species_11 > species_10

compartment_0 * function_2(V, species_11, Km)
reaction_48 Mr synthesized ∅ > species_16

compartment_0 * function_3(Vs, species_3, n, K)
reaction_49 Mr nonspecific degradation species_16 > ∅

compartment_0 * k1 * species_16
reaction_5 Mc translated into protein ∅ > species_4

compartment_0 * function_1(k, species_5)
reaction_50 Mr specific degradation species_16 > ∅

compartment_0 * function_2(V, species_16, Km)
reaction_51 Mr translated into protein ∅ > species_17

compartment_0 * function_1(k, species_16)
reaction_52 Rc transfered into nuclear species_17 = species_18

compartment_0 * (k1 * species_17 - k2 * species_18)
reaction_53 Rc specific degradation species_17 > ∅

compartment_0 * function_2(V, species_17, Km)
reaction_54 Rc nonspecific degradation species_17 > ∅

compartment_0 * k1 * species_17
reaction_55 Rn specific degradation species_18 > ∅

compartment_0 * function_2(V, species_18, Km)
reaction_56 Rn nonspecific degradation species_18 > ∅

compartment_0 * k1 * species_18
reaction_6 Mc nonspecific degradation species_5 > ∅

compartment_0 * k1 * species_5
reaction_7 Cc phosphorylation species_4 > species_6

compartment_0 * function_2(V, species_4, Km)
reaction_8 Ccp specific degradation species_6 > ∅

compartment_0 * function_2(V, species_6, Km)
reaction_9 Mp synthesis ∅ > species_7

compartment_0 * function_3(Vs, species_3, n, K)

Global parameters

Id Value

Local parameters

Id Value Reaction
k1 0.02 reaction_49 (Mr nonspecific degradation)
Km 0.4 reaction_24 (Mb specific degradation)
V 1.6 reaction_50 (Mr specific degradation)
Km 0.4 reaction_50 (Mr specific degradation)
k 1.7 reaction_51 (Mr translated into protein)
k1 0.8 reaction_52 (Rc transfered into nuclear)
k2 0.4 reaction_52 (Rc transfered into nuclear)
vsb 1.8 reaction_0 (Mb synthesized)
K 1.0 reaction_0 (Mb synthesized)
V 4.4 reaction_53 (Rc specific degradation)
m 2.0 reaction_0 (Mb synthesized)
k 0.32 reaction_1 (Mb translated into protein)
k1 0.02 reaction_2 (Mb nonspecific degradation)
V 1.4 reaction_3 (Bc phosphorylation)
Km 1.006 reaction_3 (Bc phosphorylation)
k1 0.8 reaction_4 (Bc transfered from cytosolic to nuclear)
k2 0.4 reaction_4 (Bc transfered from cytosolic to nuclear)
k 3.2 reaction_5 (Mc translated into protein)
k1 0.02 reaction_6 (Mc nonspecific degradation)
Km 0.3 reaction_53 (Rc specific degradation)
V 1.2 reaction_7 (Cc phosphorylation)
k1 0.02 reaction_54 (Rc nonspecific degradation)
V 0.8 reaction_55 (Rn specific degradation)
Km 1.006 reaction_7 (Cc phosphorylation)
V 1.4 reaction_8 (Ccp specific degradation)
Km 0.3 reaction_8 (Ccp specific degradation)
Km 0.3 reaction_55 (Rn specific degradation)
Vs 2.4 reaction_9 (Mp synthesis)
n 2.0 reaction_9 (Mp synthesis)
K 0.6 reaction_9 (Mp synthesis)
k 1.2 reaction_10 (Mp translated into protein)
V 3.4 reaction_11 (Pcp specific degradation)
Km 0.3 reaction_11 (Pcp specific degradation)
k1 0.02 reaction_56 (Rn nonspecific degradation)
V 9.6 reaction_12 (Pc phospholation)
Km 1.006 reaction_12 (Pc phospholation)
k1 0.8 reaction_13 (Cc and Pc produce PCc)
k2 0.4 reaction_13 (Cc and Pc produce PCc)
V 2.4 reaction_14 (PCc phospholation)
Km 1.006 reaction_14 (PCc phospholation)
V 1.4 reaction_15 (PCcp specific degradation)
Km 0.3 reaction_15 (PCcp specific degradation)
k1 0.8 reaction_16 (PCc transfered into nuclear)
k2 0.4 reaction_16 (PCc transfered into nuclear)
k1 0.02 reaction_17 (PCnp nonspecific degradation)
k1 0.02 reaction_18 (Bcp nonspecific degradation)
k1 0.02 reaction_19 (Bnp nonspecific degradation)
Vs 2.2 reaction_20 (Mc synthesis)
n 2.0 reaction_20 (Mc synthesis)
K 0.6 reaction_20 (Mc synthesis)
V 2.4 reaction_21 (PCn phospholation)
Km 1.006 reaction_21 (PCn phospholation)
k1 0.02 reaction_22 (Mp nonspecific degradation)
k1 1.0 reaction_23 (Per_Cry and Clock_Bmal form inactive complex)
k2 0.2 reaction_23 (Per_Cry and Clock_Bmal form inactive complex)
V 1.3 reaction_24 (Mb specific degradation)
V 2.0 reaction_25 (Mc specific degradation)
Km 0.4 reaction_25 (Mc specific degradation)
V 2.2 reaction_26 (Mp specific degradation)
Km 0.3 reaction_26 (Mp specific degradation)
k1 0.02 reaction_27 (Pc nonspecific degradation)
k1 0.02 reaction_28 (Cc nonspecific degradation)
k1 0.02 reaction_29 (Pcp nonspecific degradation)
k1 0.02 reaction_30 (Ccp nonspecific degradation)
k1 0.02 reaction_31 (PCcp nonspecific degradation)
k1 0.02 reaction_32 (PCc nonspecific degradation)
V 1.4 reaction_33 (PCnp specific degradation)
Km 0.3 reaction_33 (PCnp specific degradation)
k1 0.02 reaction_34 (Bc nonspecific degradation)
V 3.0 reaction_35 (Bcp specific degradation)
Km 0.3 reaction_35 (Bcp specific degradation)
V 1.4 reaction_36 (Bn phospholation)
Km 1.006 reaction_36 (Bn phospholation)
V 3.0 reaction_37 (Bnp specific degradation)
Km 0.3 reaction_37 (Bnp specific degradation)
k1 0.02 reaction_38 (In nonspecific degration)
V 1.6 reaction_39 (In specific degradation)
Km 0.3 reaction_39 (In specific degradation)
k1 0.02 reaction_40 (Bn nonspecific degradation)
V 0.2 reaction_41 (Bcp dephospholation)
Km 0.1 reaction_41 (Bcp dephospholation)
V 0.4 reaction_42 (Bnp dephospholation)
Km 0.1 reaction_42 (Bnp dephospholation)
V 0.2 reaction_43 (Ccp dephospholation)
Km 0.1 reaction_43 (Ccp dephospholation)
V 0.6 reaction_44 (Pcp dephospholation)
Km 0.1 reaction_44 (Pcp dephospholation)
V 0.2 reaction_45 (PCnp dephospholation)
Km 0.1 reaction_45 (PCnp dephospholation)
k1 0.02 reaction_46 (PCn nonspecific degradation)
V 0.2 reaction_47 (PCcp dephospholation)
Km 0.1 reaction_47 (PCcp dephospholation)
Vs 1.6 reaction_48 (Mr synthesized)
n 2.0 reaction_48 (Mr synthesized)
K 0.6 reaction_48 (Mr synthesized)

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Definition
function_0(vsb, K, m, Bn) = vsb * pow(K, m) / (pow(K, m) + pow(Bn, m))
function_1(k, mRNA) = k * mRNA
function_2(V, substrate, Km) = V * substrate / (Km + substrate)
function_3(Vs, B, n, K) = Vs * pow(B, n) / (pow(K, n) + pow(B, n))
Trigger Assignments