leloup2

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000073) Biomodels notes: This model is according to the paper Toward a detailed computational model for the mammalian circadian clock . In this model only interlocked negative and positive regulation of Per, Cry, Bmal gene are involved. Some initial values were not provided, therefore they were chosen to fit the curve from the paper. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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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
cell cell 3.0 1.0
Id Name Initial quantity Compartment Fixed
species_0 Mb 9.0 cell (cell)
species_1 Bc 2.0 cell (cell)
species_10 PCc 0.0 cell (cell)
species_11 PCcp 0.0 cell (cell)
species_12 PCn 1.0 cell (cell)
species_13 Bnp 0.0 cell (cell)
species_14 PCnp 0.0 cell (cell)
species_15 In 0.0 cell (cell)
species_2 Bcp 0.0 cell (cell)
species_3 Bn 1.9 cell (cell)
species_4 Cc 0.0 cell (cell)
species_5 Mc 1.4 cell (cell)
species_6 Ccp 0.0 cell (cell)
species_7 Mp 1.6 cell (cell)
species_8 Pc 0.0 cell (cell)
species_9 Pcp 0.0 cell (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

cell * function_0(vsb, K, m, species_3)
reaction_1 Mb translated into protein ∅ > species_1

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

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

cell * function_2(V, species_9, Km)
reaction_12 Pc phosphorylation species_8 > species_9

cell * function_2(V, species_8, Km)
reaction_13 Cc and Pc produce complex Per_Cry species_4 + species_8 = species_10

cell * (k1 * species_4 * species_8 - k2 * species_10)
reaction_14 PCc phosphorylation species_10 > species_11

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

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

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

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

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

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

cell * k1 * species_0
reaction_20 Mc synthesis ∅ > species_5

cell * function_3(Vs, species_3, n, K)
reaction_21 PCn phosphorylation species_12 > species_14

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

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

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

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

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

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

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

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

cell * k1 * species_9
reaction_3 Bc phosphorylation species_1 > species_2

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

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

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

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

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

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

cell * function_2(V, species_2, Km)
reaction_36 Bn phosphorylation species_3 > species_13

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

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

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

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

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

cell * k1 * species_3
reaction_41 Bcp dephosphorylation species_2 > species_1

cell * function_2(V, species_2, Km)
reaction_42 Bnp dephosphorylation species_13 > species_3

cell * function_2(V, species_13, Km)
reaction_43 Ccp dephosphorylation species_6 > species_4

cell * function_2(V, species_6, Km)
reaction_44 Pcp dephosphorylation species_9 > species_8

cell * function_2(V, species_9, Km)
reaction_45 PCnp dephosphorylation species_14 > species_12

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

cell * k1 * species_12
reaction_47 PCcp dephosphorylation species_11 > species_10

cell * function_2(V, species_11, Km)
reaction_5 Mc translated into protein ∅ > species_4

cell * function_1(k, species_5)
reaction_6 Mc nonspecific degradation species_5 > ∅

cell * k1 * species_5
reaction_7 Cc phosphorylation species_4 > species_6

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

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

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

Global parameters

Id Value

Local parameters

Id Value Reaction
vsb 1.0 reaction_0 (Mb synthesized)
K 2.2 reaction_0 (Mb synthesized)
m 2.0 reaction_0 (Mb synthesized)
k 0.12 reaction_1 (Mb translated into protein)
k1 0.01 reaction_2 (Mb nonspecific degradation)
V 0.5 reaction_3 (Bc phosphorylation)
Km 0.1 reaction_3 (Bc phosphorylation)
k1 0.4 reaction_4 (Bc transfered from cytosolic to nuclear)
k2 0.2 reaction_4 (Bc transfered from cytosolic to nuclear)
k 1.6 reaction_5 (Mc translated into protein)
k1 0.01 reaction_6 (Mc nonspecific degradation)
V 0.6 reaction_7 (Cc phosphorylation)
Km 0.1 reaction_7 (Cc phosphorylation)
V 0.7 reaction_8 (Ccp specific degradation)
Km 0.3 reaction_8 (Ccp specific degradation)
Vs 1.5 reaction_9 (Mp synthesis)
n 4.0 reaction_9 (Mp synthesis)
K 0.7 reaction_9 (Mp synthesis)
k 0.6 reaction_10 (Mp translated into protein)
V 0.7 reaction_11 (Pcp specific degradation)
Km 0.3 reaction_11 (Pcp specific degradation)
V 0.4 reaction_12 (Pc phosphorylation)
Km 0.1 reaction_12 (Pc phosphorylation)
k1 0.4 reaction_13 (Cc and Pc produce complex Per_Cry)
k2 0.2 reaction_13 (Cc and Pc produce complex Per_Cry)
V 0.4 reaction_14 (PCc phosphorylation)
Km 0.1 reaction_14 (PCc phosphorylation)
V 0.7 reaction_15 (PCcp specific degradation)
Km 0.3 reaction_15 (PCcp specific degradation)
k1 0.4 reaction_16 (PCc transfered into nuclear)
k2 0.2 reaction_16 (PCc transfered into nuclear)
k1 0.01 reaction_17 (PCnp nonspecific degradation)
k1 0.01 reaction_18 (Bcp nonspecific degradation)
k1 0.01 reaction_19 (Bnp nonspecific degradation)
Vs 1.1 reaction_20 (Mc synthesis)
n 4.0 reaction_20 (Mc synthesis)
K 0.6 reaction_20 (Mc synthesis)
V 0.4 reaction_21 (PCn phosphorylation)
Km 0.1 reaction_21 (PCn phosphorylation)
k1 0.01 reaction_22 (Mp nonspecific degradation)
k1 0.5 reaction_23 (Per_Cry and Clock_Bmal form inactive complex)
k2 0.1 reaction_23 (Per_Cry and Clock_Bmal form inactive complex)
V 0.8 reaction_24 (Mb specific degradation)
Km 0.4 reaction_24 (Mb specific degradation)
V 1.0 reaction_25 (Mc specific degradation)
Km 0.4 reaction_25 (Mc specific degradation)
V 1.1 reaction_26 (Mp specific degradation)
Km 0.31 reaction_26 (Mp specific degradation)
k1 0.01 reaction_27 (Pc nonspecific degradation)
k1 0.12 reaction_28 (Cc nonspecific degradation)
k1 0.01 reaction_29 (Pcp nonspecific degradation)
k1 0.01 reaction_30 (Ccp nonspecific degradation)
k1 0.01 reaction_31 (PCcp nonspecific degradation)
k1 0.01 reaction_32 (PCc nonspecific degradation)
Km 0.3 reaction_35 (Bcp specific degradation)
V 0.7 reaction_33 (PCnp specific degradation)
Km 0.3 reaction_33 (PCnp specific degradation)
k1 0.01 reaction_34 (Bc nonspecific degradation)
V 0.5 reaction_35 (Bcp specific degradation)
V 0.5 reaction_36 (Bn phosphorylation)
Km 0.1 reaction_36 (Bn phosphorylation)
V 0.6 reaction_37 (Bnp specific degradation)
Km 0.3 reaction_37 (Bnp specific degradation)
k1 0.01 reaction_38 (In nonspecific degration)
V 0.8 reaction_39 (In specific degradation)
Km 0.3 reaction_39 (In specific degradation)
k1 0.01 reaction_40 (Bn nonspecific degradation)
V 0.1 reaction_41 (Bcp dephosphorylation)
Km 0.1 reaction_41 (Bcp dephosphorylation)
V 0.2 reaction_42 (Bnp dephosphorylation)
Km 0.1 reaction_42 (Bnp dephosphorylation)
V 0.1 reaction_43 (Ccp dephosphorylation)
Km 0.1 reaction_43 (Ccp dephosphorylation)
V 0.3 reaction_44 (Pcp dephosphorylation)
Km 0.1 reaction_44 (Pcp dephosphorylation)
V 0.1 reaction_45 (PCnp dephosphorylation)
Km 0.1 reaction_45 (PCnp dephosphorylation)
k1 0.01 reaction_46 (PCn nonspecific degradation)
V 0.1 reaction_47 (PCcp dephosphorylation)
Km 0.1 reaction_47 (PCcp dephosphorylation)

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