1. Supporting Document Bayesian Experts in Exploring Reaction Kinetics of Transcription Circuits - On Transcriptional Circuit Model for Mammalian Circadian Clock - Yoshida, R., Saito, M.M., Nagao, H. and Higuchi, T. The Institute of Statistical Mathematics, ROIS

2. Mammalian Clock and Clock-Controlled Genes in the Model Clock Bmal1 (Arntl or Mop3) Per1 Per2 Cry1 RevErbA α (Nr1d1) Rora (Ror αlpha) Dbp Helix-loop-helix-PAS transcription factors Orphan nuclear hormone receptors According to the TF promoter analysis of Ueda et al. (2005), we have developed a model on transcription factor regulatory networks, involving 19 clock-related state variables in below: Clock-Regulating 8 Transcription Factors bZip-family (transcription factor) clock bmal1 (arntl or mop3) per1 per2 cry1 revErbA α (nr1d1) rora (ror αlpha) dbp 8 mRNAs 3 TF complexes Clock/Bmal1 Per1/Cry1 Per2/Cry1

3. Network Diagram of the Transcriptional Circuits (Hybrid Functional Petri Net) Ror(a)ror(a) Rev-ErbA α rev-erbA α Per2/Cry1 Per1/Cry1 Bmal1/Clock per1 per2 cry1 Per1 Per2 Cry1 Clock Bmal1 clock bmal1 Dbp dbp Normal arc Inhibitory arc Test arc Continuous placeTransition All the diagrams relevant to the baseline and degradation are omitted.

4. The circuit model describes a regulatory mechanism of the endogenous variables based on the following 19 ODEs. The Mathematical Form of ODE Model mRNA Protein or Protein complex Notations involving mRNA Three types of regulatory elements in promoters E/E’ box D box RRE Notations involving Protein and Protein Complex TF binding sites on promoters E/E’ box D box RRE Activators or Inhibitor? R R A A

5. The Mathematical Form of ODE Model Variable: per1; Description: Transcription; Variable ID: 1 Regulatory elements in promoter: E/E’ box, D box Activators: Bmal1/Clock, Dbp Inhibitors: Per1/Cry1, Per2/Cry2 E/E’ box D box Variable : per2; Description: Transcription; Variable ID: 2 Regulatory elements in promoter: E/E’ box, D box Activators: Bmal1/Clock, Dbp, Npas2 Inhibitors: Per1/Cry1, Per2/Cry2, Per3, Dec1 E/E’ box D box

6. Variable: cry1; Description: Transcription; Variable ID: 3 Regulatory elements in promoter: E/E’ box, RRE Activators: Bmal1/Clock, Rora, Inhibitors: Per1/Cry1, Per2/Cry2, Rev/ErbA E/E’ box RRE Variable: rev/erbA; Description: Transcription; Variable ID: 4 Regulatory elements in promoter: E/E’ box D box Activators: Bmal1/Clock, Dbp Inhibitors: Per1/Cry1, Per2/Cry1 E/E’ box D box The Mathematical Form of ODE Model

7. Variable: clock; Description: Transcription; Variable ID: 6 Regulatory elements in promoter: RRE Activators: Rora Inhibitors: Rev/ErbA RRE Variable: rora; Description: Transcription; Variable ID: 5 Regulatory elements in promoter: D box Activators: Dbp Inhibitors: D box The Mathematical Form of ODE Model

8. Variable: bmal1; Description: Transcription; Variable ID: 7 Regulatory elements in promoter: RRE Activators: Rora, Per1/Cry1, Per2/Cry1 Inhibitors:, Rev/ErbA Variable: dec1; Description: Transcription; Variable ID: 8 Regulatory elements in promoter: E/E’box Activators: Bmal1/Clock Inhibitors: Per1/Cry1, Per2/Cry2 RRE E/E’ box The Mathematical Form of ODE Model

9. Variable: Per1; Description: Translation, Biding; Variable ID: 9 Bind to: Cry1 Bind Variable : Per2; Description: Translation, Binding; Variable ID: 10 Bind to: Cry1 Variable: Cry1; Description: Translation, Binding; Variable ID: 11 Bind to: Per1, Per2 Bind Variable: Rev/ErbA; Description: Translation; Variable ID: 12 RRE R R The Mathematical Form of ODE Model

10. Variable: Clock; Description: Translation, Binding; Variable ID: 13 Bind to: Bmal1 Variable: Bmal1; Description: Translation; Variable ID: 14 Bind to: Clock Variable: Rora; Description: Translation; Variable ID: 15 RRE Bind A A Variable: Dbp; Description: Translation, Biding; Variable ID: 16 D box A A The Mathematical Form of ODE Model

11. Variable: Per1/Cry1; Description: Binding; Variable ID: 17 Variable: Per2/Cry1; Description: Binding; Variable ID: 18 Variable: Bmal1/Clock; Description: Binding; Variable ID: 19 E/E’ box R R R R A A The Mathematical Form of ODE Model

12. A Principle of Transcriptional Activities in Circadian Clocks Ueda et al., Nature Genetics, 2005 Bhlh b2 Bhlh b3 Per1 Per2 Per3 Cry1 Cloc k Npas 2 Bmal 1 Nfil3 Dbp RevE rbAα Nr1d 2 Rora Rorb Rorc E/E’ box D box RRE E/E’ box D box E/E’ box RRE Set of genes binding to RRE elements in promoters (purple: repressors; green: activators) Set of genes binding to D box elements in promoters (purple: repressors; green: activators) Set of genes binding to E/E’ box elements in promoters (purple: repressors; green: activators) Order of increase in daily transcriptional activities. Each gene is first categorized into the three elements (in rows) according to its target binding element, and further classified (in columns) according to its regulatory elements (combinations of the three regulatory sequences). about 24 hours