Fig. 8: Performance of the Rao-Blackwell identification algorithm on the yeast transcription system with simulated data.

A Inference of a 3-gene-state system. We first simulated a 3-gene-state system (see Fig. 7B) with parameters k₁ = 0.3, k₂ = 0.4, k₃ = 0.3, k₄ = 0.3, \({k}_{{p}_{1}}=3\), and \({k}_{{p}_{2}}=5\) (all in units per minute); its mRNA dynamics and time-course measurements are depicted in the top-left panel. Next, we utilized our algorithm to identify the model parameters using the simulated measurements. The sample size of our algorithm was set to 10,000, and the result is presented in the box surrounded by the dash lines. The results illustrate that our algorithm accurately infers the hidden model parameters. The bottom-left panel compares the stationary distributions of the target system and the inferred model (with parameters being the maximum a posteriori estimates). Due to ergodicity, the stationary distribution of the target system was approximated by the occupation time distribution of the mRNA measurements. This bottom-left panel shows a close match between the two stationary distributions, suggesting the accuracy of the inferred model. B Inference of a 2-gene-state system. We tested our approach when the system had only two gene states. We first simulated the system with parameters the same as before, except that \({k}_{3}={k}_{4}={k}_{{p}_{2}}=0\), i.e., the system had only one active gene state. The mRNA dynamics and its time-course measurements are presented in the top-left panel. Then, we used our algorithm to identify the model parameters with the sample size set to 10,000; the result is presented in the box surrounded by the dash lines. The results illustrate that our algorithm accurately infers the parameters k₁, k₂, k₃, and \({k}_{{p}_{1}}\); as the maximum a posteriori estimate of k₃ is zero, our algorithm correctly identifies the two-gene-state model. For the irrelevant parameters k₄ and \({k}_{{p}_{2}}\), our algorithm expectedly gives conditional distributions close to uniform distributions (the prior distribution). The bottom-left panel shows a close match between the stationary distributions of the target system and the inferred model, suggesting the accuracy of the identification result. Source data are provided as a Source Data file.