a Observed discrepancies in real data between single-nucleus and bulk expression for selected marker genes (left) for six individuals. Each color corresponds to a gene. On the left, observed bulk expression on the x axis is plotted against the pseudo-bulk expression on the y axis, where pseudo-bulk expression is calculated by summing the single-cell-based reference with cell proportions as weights. On the right, the Bisque transformation of bulk expression is on the x axis. Bisque recovers a one-to-one relationship by transforming the bulk expression for improved decomposition accuracy (right). b Simulation of bulk expression for six individuals based on true adipose snRNA-seq data with increasing gene-specific differences. These differences are modeled as a linear transformation of the summed snRNA-seq counts with coefficient and intercept sampled from half-normal distributions with parameter as indicated on the x axis. At σ = 0, the simulated bulk is simply the sum of the observed single-cell read counts. Performance on y axis measured in global Pearson correlation (R) (left) and root-mean squared deviation (RMSD) (right). Shaded regions indicate 95% confidence intervals based on bootstrapping with central lines indicating the mean observed value. Bisque remains robust to increasing gene-specific variation between single-cell and bulk expression levels. Source data are provided as a Source Data file.