D-SPIN: constructing regulatory network models from single-cell RNA-seq perturbation data with probabilistic graphical models

D-SPIN (Dimension-scalable Single-cell Perturbation Integration Network) is a computational framework for constructing regulatory network models from large-scale single-cell perturbation data. D-SPIN models the transcriptional state of cells as a set of individual genes or gene programs that interact through a condition-dependent spin network model or Markov random field. A single unified network is learned across multiple conditions, where the perturbations modulate the activity of individual network nodes. The architecture allows information integration between different perturbation conditions and supports efficient inference algorithms that scale to thousands of genes, thousands of conditions, and millions of single cells. For interpretability, D-SPIN can also operate at the level of programs of co-expressing gene sets, which are extracted via unsupervised orthogonal non-negative matrix factorization (oNMF). Here we present the theory and detailed procedures for applying D-SPIN to build program-level or gene-level network models from single-cell data. With a public immune dictionary dataset, we illustrate multiple applications of D-SPIN, including identifying gene programs and network modules, classifying perturbation responses of cytokines, and nominating key regulators that mediate cytokine responses.