Fig. 1

Local decomposition of gene expression noise in cell state space. a Coefficient of variation as a function of the mean expression on logarithmic scale. The explained variability and its components, Poissonian noise and total UMI count variability, are highlighted. Dot plots correspond to two individual neighborhoods of 101 cells each from a Kit+ hematopoietic progenitor dataset [22]. Violin plots to the right show the distribution of UMI counts and the number of detected features per cell barcode for each of the individual neighborhoods. b Negative binomial model for the UMI counts \({X}_{i,j}\). The variance is split into three components: Poissonian noise, total UMI count variability, and residual biological noise. c Estimation of the dispersion parameter \({r}_{j}^{t}\) for the two individual neighborhoods shown in a. Mean-normalized total UMI counts \(\beta_{j}\) are fitted by a Gamma distribution, with shape parameter \({\alpha }_{j}^{t}\) equal to the dispersion parameter \({r}_{j}^{t}\) in b. d UMAP plot highlighting \({r}_{j}^{t}\) estimates across the hematopoietic progenitor dataset. MPP, multipotent progenitors; Ly, lymphocytic; Mo, monocytic; GN, granulocytic neutrophil; Ba, basophylic; Mk, megakaryocytic; Ery, erythroid. e Comparison of \(\varepsilon\) estimates obtained by maximum likelihood (ML) estimation (black) and maximum a posteriori (MAP) estimation (red). A simulated dataset with three levels of gene expression noise was used (see “Methods” and Additional file 1: Figure S1b). Here, only \(\varepsilon\) estimates corresponding to the highest noise level are shown. f \(\varepsilon\) estimates for the simulated dataset with three different biological noise levels (“Methods”). Colors highlight groups of genes with different simulated biological noise levels (low, medium, or high). Simulated ground truths of noise values (dashed lines), and median values of the \(\varepsilon\) estimates (solid lines) are indicated for each group. Hyperparameter γ = 1