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BIOMD0000000350 - Troein2011_ClockCircuit_OstreococcusTauri


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Reference Publication
Publication ID: 21219507
Troein C, Corellou F, Dixon LE, van Ooijen G, O'Neill JS, Bouget FY, Millar AJ.
Multiple light inputs to a simple clock circuit allow complex biological rhythms.
Plant J. 2011 Apr; 66(2): 375-385
School of Biological Sciences, University of Edinburgh and Centre for Systems Biology at Edinburgh, Edinburgh EH93JD, UK.  [more]
Original Model: BIOMD0000000350.origin
Submitter: Andrew J Millar
Submission ID: MODEL1107230000
Submission Date: 23 Jul 2011 07:25:34 UTC
Last Modification Date: 30 Aug 2011 12:39:23 UTC
Creation Date: 09 Aug 2011 16:20:30 UTC
Encoders:  Andrew J Millar
   Vijayalakshmi Chelliah
   Troein Carl
set #1
bqbiol:isVersionOf KEGG Pathway map04710
Gene Ontology circadian rhythm
bqbiol:occursIn Taxonomy Ostreococcus tauri

This model is from the article:
Multiple light inputs to a simple clock circuit allow complex biological rhythms
Troein C, Corellou F, Dixon LE, van Ooijen G, O'Neill JS, Bouget FY, Millar AJ. Plant J. 2011 Apr;66(2):375-85. 21219507 ,
Circadian clocks are biological timekeepers that allow living cells to time their activity in anticipation of predictable environmental changes. Detailed understanding of the circadian network of higher plants, such as Arabidopsis thaliana, is hampered by the high number of partially redundant genes. However, the picoeukaryotic alga Ostreococcus tauri, which was recently shown to possess a small number of non-redundant clock genes, presents an attractive alternative target for detailed modelling of circadian clocks in the green lineage. Based on extensive time-series data from in vivo reporter gene assays, we developed a model of the Ostreococcus clock as a feedback loop between the genes TOC1 and CCA1. The model reproduces the dynamics of the transcriptional and translational reporters over a range of photoperiods. Surprisingly, the model is also able to predict the transient behaviour of the clock when the light conditions are altered. Despite the apparent simplicity of the clock circuit, it displays considerable complexity in its response to changing light conditions. Systematic screening of the effects of altered day length revealed a complex relationship between phase and photoperiod, which is also captured by the model. The complex light response is shown to stem from circadian gating of light-dependent mechanisms. This study provides insights into the contributions of light inputs to the Ostreococcus clock. The model suggests that a high number of light-dependent reactions are important for flexible timing in a circadian clock with only one feedback loop.

Note: Two-gene model of the Ostreococcus circadian clock

This is a model of the circadian clock of Ostreococcus tauri, with a negative feedback loop between TOC1 and CCA1 (a.k.a. LHY) and multiple light inputs. It was used and described in Troein et al., Plant Journal (2011).

The model incorporates luciferase reporters, and in this SBML model the four different versions of the model for transcriptional and translational reporter lines (pTOC1::LUC, pCCA1::LUC, TOC1-LUC and CCA1-LUC) are all accessible by setting one of the rep_X parameters to 1 and the others to 0. You can also set all four to 0 to only simulate the non-reporter core of the system.

Input to the system should be provided by modifying the "light" function. An implementation of LD 12:12 is provided as an example, but the model was also used with more complicated light regimes that vary between data sets and are not convenient to express directly in SBML.

The functions "ox_cca1" and "ox_toc1" can be altered to add overexpression of CCA1 and TOC1. Setting either to x gives additional, constitutive transcription at x times the maximal (and typically not realizable) transcription rate of the native gene. The overexpression mutant fits in Figure 7 of Troein et al. (2011) used ox_cca1 = 0.115 and oc_toc1 = 0.0584, respectively.

The functions "copies_toc1" and "copies_cca1" are normally 1 but can be lowered to simulate knockdown experiments. The functions "transcription", "translation" and "proteasome" can be modified to simulate the effects of altering the overall rate of transcription, translation and protein degradation.

The parameters were fitted specifically to data from transgenic reporter lines TOC8, pTOC3, LHY7 and pLHY7 (Corellou et al., Plant Cell 2009). Parameters that begin with "effcopies" describe the effective number of copies of CCA1 or TOC1 in the respective translational fusion lines, with anything above 1 due to the fusion proteins.

For the model fitting, the initial values were fitted to the data in the various time courses. The initial values given here correspond to the limit cycle of the system in LD 12:12. The system converges to the limit cycle in just a few days under most light conditions, so these initial values are biologically meaningful.

The species cca1luc_c and cca1luc_n have been merged into cca1luc (which corresponds to the observable luminescence signal), because Copasi refused to run the system otherwise. For TOC1-LUC, the predicted output signal is the sum of toc1luc_1 and toc1luc_2.

This model originates from BioModels Database: A Database of Annotated Published Models ( It is copyright (c) 2005-2011 The Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

Publication ID: 21219507 Submission Date: 23 Jul 2011 07:25:34 UTC Last Modification Date: 30 Aug 2011 12:39:23 UTC Creation Date: 09 Aug 2011 16:20:30 UTC
Mathematical expressions
Light accumulator increase Light accumulator decrease TOC1 transcription TOC1 degradation
TOC1 translation TOC1 conversion TOC1 mRNA degradation CCA1 transcription
CCA1 mRNA degradation CCA1 translation CCA1 nuclear transport CCA1 degradation, cytosol
CCA1 degradation, nucleus LUC transcription, pTOC1 LUC mRNA degradation LUC translation
LUC decay TOC1-LUC transcription TOC1-LUC mRNA degradation TOC1-LUC translation
TOC1-LUC conversion TOC1-LUC degradation TOC1-LUC(1) deactivation TOC1-LUC(2) deactivation
LUC transcription, pCCA1 CCA1-LUC transcription CCA1-LUC mRNA degradation CCA1-LUC translation
CCA1-LUC degradation CCA1-LUC deactivation    
Assignment Rule (variable: toc1luc)      
Physical entities
Compartments Species
compartment acc toc1_mrna toc1_1
toc1_2 cca1_mrna cca1_c
cca1_n toc1luc_mrna toc1luc_1
toc1luc_2 cca1luc_mrna cca1luc
luc_mrna luc  
Global parameters
toc1luc D_luc D_mrna_luc acc_rate
R_toc1_cca1 H_toc1_cca1 L_toc1 R_toc1_acc
D_mrna_toc1 T_toc1 Di_toc1_12_l Di_toc1_12_d
D_toc1_2_l D_toc1_2_d H_cca1_toc1 R_cca1_toc1_2_l
R_cca1_toc1_2_d D_mrna_cca1 T_cca1 Di_cca1_cn
D_cca1_l D_cca1_d effcopies_cca1_LHY7 effcopies_toc1_TOC8
T_luc rep_TOC1 rep_pTOC1 rep_CCA1
Reactions (30)
 Light accumulator increase  → [acc];  
 Light accumulator decrease [acc] → ;  
 TOC1 transcription  → [toc1_mrna];   {acc} , {cca1_n}
 TOC1 degradation [toc1_2] → ;  
 TOC1 translation  → [toc1_1];   {toc1_mrna}
 TOC1 conversion [toc1_1] → [toc1_2];  
 TOC1 mRNA degradation [toc1_mrna] → ;  
 CCA1 transcription  → [cca1_mrna];   {toc1_2}
 CCA1 mRNA degradation [cca1_mrna] → ;  
 CCA1 translation  → [cca1_c];   {cca1_mrna}
 CCA1 nuclear transport [cca1_c] → [cca1_n];  
 CCA1 degradation, cytosol [cca1_c] → ;  
 CCA1 degradation, nucleus [cca1_n] → ;  
 LUC transcription, pTOC1  → [luc_mrna];   {acc} , {cca1_n}
 LUC mRNA degradation [luc_mrna] → ;  
 LUC translation  → [luc];   {luc_mrna}
 LUC decay [luc] → ;  
 TOC1-LUC transcription  → [toc1luc_mrna];   {acc} , {cca1_n}
 TOC1-LUC mRNA degradation [toc1luc_mrna] → ;  
 TOC1-LUC translation  → [toc1luc_1];   {toc1luc_mrna}
 TOC1-LUC conversion [toc1luc_1] → [toc1luc_2];  
 TOC1-LUC degradation [toc1luc_2] → ;  
 TOC1-LUC(1) deactivation [toc1luc_1] → ;  
 TOC1-LUC(2) deactivation [toc1luc_2] → ;  
 LUC transcription, pCCA1  → [luc_mrna];   {toc1_2}
 CCA1-LUC transcription  → [cca1luc_mrna];   {toc1_2}
 CCA1-LUC mRNA degradation [cca1luc_mrna] → ;  
 CCA1-LUC translation  → [cca1luc];   {cca1luc_mrna}
 CCA1-LUC degradation [cca1luc] → ;  
 CCA1-LUC deactivation [cca1luc] → ;  
Rules (1)
 Assignment Rule (name: toc1luc) toc1luc = toc1luc_1+toc1luc_2
Functions (21)
 LD1212 lambda(tod, ceil(sin(pi*tod/12)/2))
 Light accumulator decrease lambda(acc_rate, acc, acc_rate*acc)
 light lambda(tod, LD1212(tod))
 transcription lambda(t, 1+0*t)
 ox_toc1 lambda(t, 0*t)
 copies_toc1 lambda(t, 1+0*t)
 copies_cca1 lambda(t, 1+0*t)
 ox_cca1 lambda(t, 0*t)
 translation lambda(t, 1+0*t)
 proteasome lambda(t, 1+0*t)
 Translation lambda(t, T, mrna, translation(t)*T*mrna)
 Light-dependent protein decay lambda(t, D_l, D_d, level, proteasome(t)*(light(t)*D_l+(1-light(t))*D_d)*level)
 Light-dependent transport lambda(t, Di_l, Di_d, level, (light(t)*Di_l+(1-light(t))*Di_d)*level)
 LUC transcription for pTOC1 lambda(t, R_toc1_acc, acc, R_toc1_cca1, cca1_n, H_toc1_cca1, rep_pTOC1, L_toc1, rep_pTOC1*transcription(t)*(L_toc1+R_toc1_acc*acc)/(1+L_toc1+R_toc1_acc*acc+(R_toc1_cca1*cca1_n)^H_toc1_cca1))
 TOC1-LUC transcription lambda(t, R_toc1_acc, acc, R_toc1_cca1, cca1_n, H_toc1_cca1, rep_TOC1, L_toc1, rep_TOC1*transcription(t)*copies_toc1(t)*(L_toc1+R_toc1_acc*acc)/(1+L_toc1+R_toc1_acc*acc+(R_toc1_cca1*cca1_n)^H_toc1_cca1))
 LUC transcription for pCCA1 lambda(t, toc1_2, R_cca1_toc1_2_l, R_cca1_toc1_2_d, H_cca1_toc1, rep_pCCA1, rep_pCCA1*transcription(t)*(toc1_2*(light(t)*R_cca1_toc1_2_l+(1-light(t))*R_cca1_toc1_2_d))^H_cca1_toc1/((toc1_2*(light(t)*R_cca1_toc1_2_l+(1-light(t))*R_cca1_toc1_2_d))^H_cca1_toc1+1))
 CCA1-LUC transcription lambda(t, toc1_2, R_cca1_toc1_2_l, R_cca1_toc1_2_d, H_cca1_toc1, rep_CCA1, rep_CCA1*transcription(t)*copies_cca1(t)*(toc1_2*(light(t)*R_cca1_toc1_2_l+(1-light(t))*R_cca1_toc1_2_d))^H_cca1_toc1/((toc1_2*(light(t)*R_cca1_toc1_2_l+(1-light(t))*R_cca1_toc1_2_d))^H_cca1_toc1+1))
 tf_output lambda(reporter, effcopies, tf, (1+reporter*(effcopies-1))*tf)
 Light accumulator increase lambda(acc_rate, t, acc_rate*light(t))
 TOC1 transcription lambda(R_toc1_acc, acc, R_toc1_cca1, H_toc1_cca1, cca1_n, t, L_toc1, rep_CCA1, effcopies_cca1_LHY7, transcription(t)*(ox_toc1(t)+copies_toc1(t)*(L_toc1+R_toc1_acc*acc)/(1+L_toc1+R_toc1_acc*acc+(R_toc1_cca1*tf_output(rep_CCA1, effcopies_cca1_LHY7, cca1_n))^H_toc1_cca1)))
 CCA1 transcription lambda(t, toc1_2, R_cca1_toc1_2_l, R_cca1_toc1_2_d, H_cca1_toc1, rep_TOC1, effcopies_toc1_TOC8, transcription(t)*(ox_cca1(t)+copies_cca1(t)*(tf_output(rep_TOC1, effcopies_toc1_TOC8, toc1_2)*(light(t)*R_cca1_toc1_2_l+(1-light(t))*R_cca1_toc1_2_d))^H_cca1_toc1/((tf_output(rep_TOC1, effcopies_toc1_TOC8, toc1_2)*(light(t)*R_cca1_toc1_2_l+(1-light(t))*R_cca1_toc1_2_d))^H_cca1_toc1+1)))
 compartment Spatial dimensions: 3.0  Compartment size: 1.0
Compartment: compartment
Initial concentration: 0.272067372878265
Compartment: compartment
Initial concentration: 0.0385665277682963
Compartment: compartment
Initial concentration: 0.206521274112594
Compartment: compartment
Initial concentration: 0.312711901675853
Compartment: compartment
Initial concentration: 0.104555645465821
Compartment: compartment
Initial concentration: 0.051315426489096
Compartment: compartment
Initial concentration: 3.07283764226433
Compartment: compartment
Initial concentration: 0.0
Compartment: compartment
Initial concentration: 0.0
Compartment: compartment
Initial concentration: 0.0
Compartment: compartment
Initial concentration: 0.0
Compartment: compartment
Initial concentration: 0.0
Compartment: compartment
Initial concentration: 0.0
Compartment: compartment
Initial concentration: 0.0
Global Parameters (29)
Value: 0.182881217463259
Value: 1.0
Value: 0.0820132250303287
Value: 1.08706126858966
Value: 2.07807738692343
Value: 1.0E-4
Value: 0.231107032949407
Value: 0.29213049778373
Value: 0.769970172977886
Value: 0.136490583368648
Value: 0.326619492089715
Value: 0.461550559180802
Value: 0.356613920551118
Value: 2.5007062880634
Value: 3.27520292103832
Value: 1.38563901682266
Value: 1.33082080954527
Value: 4.90486610428652
Value: 10.0
Value: 0.424177877449438
Value: 0.269380178154091
Value: 1.13965755508623
Value: 1.0
Value: 1.0
Representative curation result(s)
Representative curation result(s) of BIOMD0000000350

Curator's comment: (updated: 10 Aug 2011 17:15:18 BST)

Figure 2 of the reference publication has been reproduced. The plots can be obtained by setting rep_X (X=CCA1, TOC1, pCCA1, or pTOC1) parameters to "1". All these four parameters equals "0", denote the non-reporter core of the system.
The y-axis of the curation figure is not consistent with that of the reference publication. This is because, in the paper the simulated data has been rescaled (multiplied by an aribitrary factor) to fit the experimental data.
Simulation was done using RoadRunner online simulator ( Data were obtained from RoadRunner simulator and plotted using Gnuplot.