Fig. 6: Filtering results for the genetic toggle switch.
From: Advanced methods for gene network identification and noise decomposition from single-cell data
A Genetic toggle switch where two gene expression systems repress each other. The first protein is fluorescent, and its trajectory is measured with the observation noise intensity of 1. Our approach classifies all the genes as the leader-level species and all the proteins as the follower-level species. B Performance of different filters in estimating the conditional mean of the second protein given a discrete-time trajectory of the first protein. The error bars represent the interval of the conditional mean ± conditional standard deviation (SD). The exact filter is approximated by the FSP method. The particle filter (PF) and the Rao-Blackwellized particle filter (RB-PF) have 105 samples and 104 samples, ensuring that their computational time is similar. This panel shows that all the filters have similar performance in estimating the conditional mean of the second protein. C L1 errors of the PF and the RB-PF at different time points. D Average L1 errors of the filters in estimating the marginal distributions. E Evaluation of marginal conditional distribution at the first observation time (t = 20). Panels (C) to (E) show that the RB-PF significantly outperforms the PF in terms of the L1 error, and the major advantage lies in the estimates of the follower system. F Performance of the filters under different observation noise intensities. The PF and RB-PF have, respectively, 105 samples and 104 samples, ensuring that their computational time is similar. The performance is evaluated by the average L1 error over 10 observation time points; the same applies in panels (G) and (H). This panel shows that the performance of both filters is robust to the intensity of the observation noise. G Convergence of the filters under a fixed observation noise intensity (σ = 1). H Convergence of the Monte Carlo method and the RB-CME solver in computing the CME of the genetic toggle switch at time 200. Panels (G) and (H) show that the RB-CME solver and RB-PF have similar performance in their associated problems given the same sample size or the same computational time. The same result also applies to the Monte Carlo method and PF. Source data are provided as a Source Data file.
