Table 1.
Parameter values used for the simulation of the different rat tissue core-clock gene array data (Eqs 1–5).
Transcriptional delays (τi) and degradation rates (di) were varied using literature-based values in order to simulate the observed data. Other parameters were set constant to their original values [14]. The All-Tissues parameters were calculated when gene array data from all tissues (liver, muscle, adipose, lung) were used in parameter estimation.
Fig 1.
After heterodimerizing and translocating to the nucleus, CLOCK/BMAL1 induces the expression of target genes retaining an Ebox at their promoter (e.g. Rev-Erba, Per2, Cry1, Dbp). The PER/CRY heterocomplexes further inhibit this CLOCK/BMAL1 driven transcription. The REV-ERBa and DBP conclude the core-clock gene network by inhibiting or inducing genes that retain either an RRE or a DBP complex in their promoter regions. Clock-controlled genes (CCGs) are further regulated by core-clock transcription factors through binding to the respective Ebox, RRE, or Dbox elements at the promoter of the target gene.
Fig 2.
Model fittings (curves) of core-clock gene expression (mRNA—circles) in different rat’s tissues.
Time of light/dark cycles are denoted by white/grey shading.
Fig 3.
Transcriptional delay and degradation rate parameters estimated to describe the expression of core-clock genes for the different tissues.
Error bars represent the 95% confidence interval. The y-axis provides the parameter values with definitions and units listed in Table 1. All-tissue depicts the parameter values resulting from fitting the data of all tissues concurrently (consensus model).
Fig 4.
Responses of the consensus model describing the overall data from four tissues.
Bold lines represent the joint model responses (sim) and thin lines the experimental data of core-clock genes in the different tissues. Light/dark periods are denoted by white/grey shading.
Fig 5.
Local sensitivity analysis of the phases of core-clock genes upon changing transcriptional delays and degradation rates.
Different subplots represent different sensitivity outputs that are the phases of the various core-clock genes (Bmal1, Rev-Erba, Per2, Cry1, Dbp). Bars indicate the sensitivity indices resulting by varying different parameters (transcriptional delays, degradation rates). The y-axis represents the absolute values of the normalized sensitivity coefficients (Eq 20).
Fig 6.
Model predictions relative to experimental data for clock-controlled genes oscillating jointly in pairs of rat tissues.
The solid line depicts identity (y = x).
Fig 7.
Ebox/RRE/Dbox regulation factor (RegFac) dynamics for the genes maintaining the highest phase difference among two tissues.
Upper panel shows model simulations together with the experimental data for the genes that maintain the largest phase differences. For each subplot of the upper panel, the two lower panels indicate the regulation factor dynamics (BMAL1, PER2, CRY1, REVERBA, DBP) for the tissues shown in upper panel and indicated in the title. Regulation factors dynamics are normalized based on the mean values in order to better represent the factor that most clearly influences the clock-controlled gene expression.
Fig 8.
Relation between phase difference of the same gene in two tissues, and the variation of transcription regulation via BMAL1, PER2, CRY1, REVERBA, DBP mediated transcription (Eqs 12–16).