8.1 Single-Cell RNA Sequencing (scRNA-seq) Architectures, UMIs & Technical Dropouts #
The quantitative principles of Single-Cell RNA Sequencing (scRNA-seq) Architectures, UMIs & Technical Dropouts form a vital pillar of systems biology and computational modeling. In biological networks, isolated components interact non-linearly to produce collective emergent behaviors that cannot be predicted from individual constituent parts alone.
Mathematical formalization allows researchers to test mechanistic hypotheses, predict quantitative system trajectories, and simulate perturbations before conducting laboratory experiments. Key regulatory feedback loops, kinetic parameters, and stoichiometric constraints govern these molecular dynamics.
8.2 Dimensionality Reduction (PCA, UMAP, t-SNE) & Graph Clustering (Leiden) #
The quantitative principles of Dimensionality Reduction (PCA, UMAP, t-SNE) & Graph Clustering (Leiden) form a vital pillar of systems biology and computational modeling. In biological networks, isolated components interact non-linearly to produce collective emergent behaviors that cannot be predicted from individual constituent parts alone.
Mathematical formalization allows researchers to test mechanistic hypotheses, predict quantitative system trajectories, and simulate perturbations before conducting laboratory experiments. Key regulatory feedback loops, kinetic parameters, and stoichiometric constraints govern these molecular dynamics.
8.3 Pseudotime Trajectory Inference & Lineage Branching Bifurcations #
The quantitative principles of Pseudotime Trajectory Inference & Lineage Branching Bifurcations form a vital pillar of systems biology and computational modeling. In biological networks, isolated components interact non-linearly to produce collective emergent behaviors that cannot be predicted from individual constituent parts alone.
Mathematical formalization allows researchers to test mechanistic hypotheses, predict quantitative system trajectories, and simulate perturbations before conducting laboratory experiments. Key regulatory feedback loops, kinetic parameters, and stoichiometric constraints govern these molecular dynamics.
8.4 RNA Velocity: Modeling Spliced vs. Unspliced mRNA Directional Dynamics #
The quantitative principles of RNA Velocity: Modeling Spliced vs. Unspliced mRNA Directional Dynamics form a vital pillar of systems biology and computational modeling. In biological networks, isolated components interact non-linearly to produce collective emergent behaviors that cannot be predicted from individual constituent parts alone.
Mathematical formalization allows researchers to test mechanistic hypotheses, predict quantitative system trajectories, and simulate perturbations before conducting laboratory experiments. Key regulatory feedback loops, kinetic parameters, and stoichiometric constraints govern these molecular dynamics.
8.5 Multi-Omics Single-Cell Integration: Spatial Transcriptomics & scATAC-seq #
The quantitative principles of Multi-Omics Single-Cell Integration: Spatial Transcriptomics & scATAC-seq form a vital pillar of systems biology and computational modeling. In biological networks, isolated components interact non-linearly to produce collective emergent behaviors that cannot be predicted from individual constituent parts alone.
Mathematical formalization allows researchers to test mechanistic hypotheses, predict quantitative system trajectories, and simulate perturbations before conducting laboratory experiments. Key regulatory feedback loops, kinetic parameters, and stoichiometric constraints govern these molecular dynamics.
Bifurcation Diagrams, Hysteresis & Bistability
8.6 Key Terms, Chapter Summary & Active Recall Self-Check #
Core Key Terms: Single-Cell RNA Sequencing (scRNA-seq) Architectures, UMIs & Technical Dropouts; Dimensionality Reduction (PCA, UMAP, t-SNE) & Graph Clustering (Leiden); Pseudotime Trajectory Inference & Lineage Branching Bifurcations; RNA Velocity: Modeling Spliced vs. Unspliced mRNA Directional Dynamics; Multi-Omics Single-Cell Integration: Spatial Transcriptomics & scATAC-seq.
Chapter Summary: This module established the quantitative mathematical frameworks, experimental measurement strategies, and computational modeling algorithms governing single-cell systems biology & omics integration. Emphasize parameter sensitivity, topological conservation, and the biological distinction between deterministic averages and single-cell stochastic realities.
Self-Check Examination Questions:
- What are the primary mechanistic assumptions underlying mathematical modeling in this domain?
- How does network topology influence biological stability, signal transmission, and robustness against mutations?
- Under what conditions does deterministic ODE modeling break down, necessitating stochastic simulation algorithms?
- Explain the diagnostic criteria used by examiners to distinguish between alternative regulatory circuit models.