Single-cell generalized trend model (scGTM): a flexible and interpretable model of gene expression trend along cell pseudotime

Modeling single-cell gene expression trends along cell pseudotime is a crucial analysis for exploring biological processes. Most existing methods rely on nonparametric regression models for their flexibility; however, nonparametric models often provide trends too complex to interpret. Other existing methods use interpretable but restrictive models. Since model interpretability and flexibility are both indispensable for understanding biological processes, the single-cell field needs a model that improves the interpretability and largely maintains the flexibility of nonparametric regression models. Here we propose the single-cell generalized trend model (scGTM) for capturing a gene's expression trend, which may be monotone, hill-shaped, or valley-shaped, along cell pseudotime. The scGTM has three advantages: (1) it can capture non-monotonic trends that are still easy to interpret, (2) its parameters are biologically interpretable and trend informative, and (3) it can flexibly accommodate common distributions for modeling gene expression counts. To tackle the complex optimization problems, we use the particle swarm optimization algorithm to find the constrained maximum likelihood estimates for the scGTM parameters. As an application, we analyze several single-cell gene expression data sets using the scGTM and show that it can capture interpretable gene expression trends along cell pseudotime and reveal molecular insights underlying the biological processes. We also provide an open-access Python package for fitting the scGTM at https://github. com/ElvisCuiHan/scGTM.