Stochastic models for single-cell data: Current challenges and the way forward

Mathematical Modeling and Inference of Epidermal Growth Factor-Induced Mitogen-Activated Protein Kinase Cell Signaling Pathways

The mitogen-activated protein kinase (MAPK) pathway is an important intracellular signaling cascade that plays a key role in various cellular processes. Understanding the regulatory mechanisms of this pathway is essential for developing effective interventions and targeted therapies for related diseases. Recent advances in single-cell proteomic technologies have provided unprecedented opportunities to investigate the heterogeneity and noise within complex, multi-signaling networks across diverse cells and cell types. Mathematical modeling has become a powerful interdisciplinary tool that bridges mathematics and experimental biology, providing valuable insights into these intricate cellular processes. In addition, statistical methods have been developed to infer pathway topologies and estimate unknown parameters within dynamic models. This review presents a comprehensive analysis of how mathematical modeling of the MAPK pathway deepens our understanding of its regulatory mechanisms, enhances the prediction of system behavior, and informs experimental research, with a particular focus on recent advances in modeling and inference using single-cell proteomic data.

DeepVelo: deep learning extends RNA velocity to multi-lineage systems with cell-specific kinetics

Existing RNA velocity estimation methods strongly rely on predefined dynamics and cell-agnostic constant transcriptional kinetic rates, assumptions often violated in complex and heterogeneous single-cell RNA sequencing (scRNA-seq) data. Using a graph convolution network, DeepVelo overcomes these limitations by generalizing RNA velocity to cell populations containing time-dependent kinetics and multiple lineages. DeepVelo infers time-varying cellular rates of transcription, splicing, and degradation, recovers each cell's stage in the differentiation process, and detects functionally relevant driver genes regulating these processes. Application to various developmental and pathogenic processes demonstrates DeepVelo's capacity to study complex differentiation and lineage decision events in heterogeneous scRNA-seq data.

To the proteome and beyond: advances in single-cell omics profiling for plant systems

Recent advances in single-cell proteomics for animal systems could be adapted for plants to increase our understanding of plant development, response to stimuli, and cell-to-cell signaling.