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goldbeter5

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goldbeter5

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000016) Biomodels notes: Figure 2 reproduced with COPASI 4.1 (build 21) 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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Manuscript information

A model for circadian oscillations in the Drosophila period protein (PER).

  • Albert Goldbeter
Proc. Biol. Sci. 1995; 261 (1362): 319-324
Abstract
The mechanism of circadian oscillations in the period protein (PER) in Drosophila is investigated by means of a theoretical model. Taking into account recent experimental observations, the model for the circadian clock is based on multiple phosphorylation of PER and on the negative feedback exerted by PER on the transcription of the period (per) gene. This minimal biochemical model provides a molecular basis for circadian oscillations of the limit cycle type. During oscillations, the peak in per mRNA precedes by several hours the peak in total PER protein. The results support the view that multiple PER phosphorylation introduces times delays which strengthen the capability of negative feedback to produce oscillations. The analysis shows that the rhythm only occurs in a range bounded by two critical values of the maximum rate of PER degradation. A similar result is obtained with respect to the rate of PER transport into the nucleus. The results suggest a tentative explanation for the altered period of per mutants, in terms of variations in the rate of PER degradation.

Unit definitions 2

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
— 1e-06 mole
— 3600.0 second

Compartments 3

Id Name Spatial dimensions Size
CYTOPLASM — 3.0 0.000000000000001
compartment_0000004 NUCLEUS 3.0 0.000000000000001
default — 3.0 0.000000000000001

Species 7

Id Name Initial quantity Compartment Fixed
EmptySet — 0.0 default ✔
M PER mRNA 0.1 CYTOPLASM ✘
P0 unphosphorylated PER 0.25 CYTOPLASM ✘
P1 monophosphorylated PER 0.25 CYTOPLASM ✘
P2 biphosphorylated PER 0.25 CYTOPLASM ✘
Pn nuclear PER 0.25 compartment_0000004 (NUCLEUS) ✘
Pt total PER 1.0 CYTOPLASM ✘

Initial assignments 0

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
Reactions 10
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
rM transcription of PER EmptySet > M

default * Vs * pow(KI, n) / (pow(KI, n) + pow(Pn, n))
rP01 first phosphorylation of PER P0 > P1

CYTOPLASM * V1 * P0 / (K1 + P0)
rP10 removal of the first PER phosphate P1 > P0

CYTOPLASM * V2 * P1 / (K2 + P1)
rP12 second phosphorylation of PER P1 > P2

CYTOPLASM * V3 * P1 / (K3 + P1)
rP21 removal of the second PER phosphate P2 > P1

CYTOPLASM * V4 * P2 / (K4 + P2)
rP2n translocation of PER to the nucleus P2 > Pn

k1 * P2 * CYTOPLASM
rPn2 translocation of PER to the cytoplasm Pn > P2

k2 * Pn * compartment_0000004
rTL translation of PER EmptySet > P0

ks * M * default
rVd degradation of PER P2 > EmptySet

CYTOPLASM * Vd * P2 / (Kd + P2)
rmRNAd degradation of PER mRNA M > EmptySet

Vm * M * CYTOPLASM / (Km + M)

Parameters 18   0

Global parameters

Id Value

Local parameters

Id Value Reaction
Vs 0.76 rM (transcription of PER)
KI 1.0 rM (transcription of PER)
n 4.0 rM (transcription of PER)
ks 0.38 rTL (translation of PER)
V1 3.2 rP01 (first phosphorylation of PER)
K1 2.0 rP01 (first phosphorylation of PER)
V2 1.58 rP10 (removal of the first PER phosphate)
K2 2.0 rP10 (removal of the first PER phosphate)
V3 5.0 rP12 (second phosphorylation of PER)
K3 2.0 rP12 (second phosphorylation of PER)
V4 2.5 rP21 (removal of the second PER phosphate)
K4 2.0 rP21 (removal of the second PER phosphate)
k1 1.9 rP2n (translocation of PER to the nucleus)
k2 1.3 rPn2 (translocation of PER to the cytoplasm)
Km 0.5 rmRNAd (degradation of PER mRNA)
Vm 0.65 rmRNAd (degradation of PER mRNA)
Vd 0.95 rVd (degradation of PER)
Kd 0.2 rVd (degradation of PER)

Rules 0   0   1

Assignment rules

Definition
Pt = P0 + P1 + P2 + Pn

Rate rules

Definition

Algebraic rules

Definition

Events 0

Trigger Assignments