Fig. 2: Applying the framework to NFκB signaling dynamics.

a When macrophages encounter a stimulus, the single-cell signaling response of NFκB under each of the five types of stimuli was measured. Different concentrations of stimuli have been added, with in total 13 different conditions (Supplementary Fig. S1). Two representative examples of the experimental data are shown: under 10 ng/ml TNF, 100 ng/ml LPS, and more examples are in Supplementary Fig. S2. In each heatmap, the color code denotes signaling activities in different cells (y-axis) over time (x-axis). Source data are provided as a Source Data file. b The sampled trajectories from the time-inhomogeneous Markov model (upper row) and the hidden Markov model (lower row), for the two stimulus conditions marked by the stimuli symbols. The time-inhomogeneous Markov model has 32 states, and the hidden Markov model has 64 hidden states and 32 emission states. c Quantification on the training performance for the two models by three measures: the ratio between KL (Kullback–Leibler) divergence (of sample and data) and entropy (of data) at each timepoint (orange), the false k-nearest neighbor probability (blue), and the rescaled log-likelihood (green). Each dot is the mean value of the measure on all the 13 stimulus conditions, and the error bar denotes the standard deviation on the 13 stimulus conditions. The numbers of hidden states and emission states have a fixed ratio 2 here. The cases of ratio 1 and individually varying the number of states can be found in Supplementary Fig. S4, while the overfitting quantification in Supplementary Fig. S5.