catcolab-regulatory-networks

# CatColab Regulatory Networks: Molecular Biology Modeling **Trit**: -1 (MINUS - validator/inhibitor) **Color**: Red (#DC143C) ## Overview Regulatory Networks in CatColab model molecular interactions that control gene expression: - **Nodes**: Genes, proteins, RNA, metabolites - **Positive edges**: Activation/promotion (+) - **Negative edges**: Inhibition/repression (-) These signed graphs capture the control logic of biological systems. ## Mathematical Foundation A regulatory network is a **signed graph** or **signed category**: ``` ┌─────────────────────────────────────────────────────┐ │ REGULATORY NETWORK │ ├─────────────────────────────────────────────────────┤ │ Nodes (Genes/Proteins): │ │ GeneA, GeneB, GeneC, ProteinX │ │ │ │ Positive Edges (Activation): │ │ GeneA ──(+)──► GeneB │ │ ProteinX ──(+)──► GeneC │ │ │ │ Negative Edges (Inhibition): │ │ GeneB ──(-)──► GeneC │ │ GeneC ──(-)──► GeneA (negative feedback) │ │ │ │ Motifs: │ │ Feedforward loop: A→B→C, A→C │ │ Negative feedback: A→B→C⊣A │ └─────────────────────────────────────────────────────┘ ``` ## Double Theory ```rust // Signed category double theory pub fn th_signed_category() -> DiscreteDblTheory { let mut cat = FpCategory::new(); // Object type cat.add_ob_generator(name("Node")); // Morphism types (signed edges) cat.add_mor_generator(name("Positive"), name("Node"), name("Node")); cat.add_mor_generator(name("Negative"), name("Node"), name("Node")); // Constraint: n ⊙ n = id (double negative = positive) cat.add_equation( compose(name("Negative"), name("Negative")), identity(name("Node")) ); cat.into() } ``` ## CatColab Implementation ### Node Declaration ```typescript { "type": "ObDecl", "name": "p53", "theory_type": "Node", "description": "tumor suppressor protein" } ``` ### Positive Regulation (Activation) ```typescript { "type": "MorDecl", "name": "activates_apoptosis", "dom": "p53", "cod": "Bax", "theory_type": "Positive", "description": "p53 promotes apoptosis via Bax" } ``` ### Negative Regulation (Inhibition) ```typescript { "type": "MorDecl", "name": "inhibits_growth", "dom": "p53", "cod": "CyclinD", "theory_type": "Negative", "description": "p53 blocks cell cycle progression" } ``` ## Network Motifs ### Feedforward Loop (FFL) ``` GeneA / \ + + ↓ ↓ GeneB ──+──► GeneC Type: Coherent (all positive) Function: Noise filtering, delay ``` ### Negative Feedback Loop ``` GeneA ──+──► GeneB ──+──► GeneC ▲ │ └────────(-)─────────────┘ Function: Homeostasis, oscillation ``` ### Toggle Switch (Bistability) ``` GeneA ◄──(-)──► GeneB ⇅ (-) Function: Binary cell fate decision ``` ## Practical Examples ### Example 1: p53 Tumor Suppressor Network ``` Nodes: p53, MDM2, ATM, Bax, p21 Edges: ATM ──(+)──► p53 (DNA damage activates p53) p53 ──(+)──► MDM2 (p53 induces its own inhibitor) MDM2 ──(-)──► p53 (MDM2 degrades p53) p53 ──(+)──► Bax (p53 promotes apoptosis) p53 ──(+)──► p21 (p53 arrests cell cycle) Motif: p53-MDM2 negative feedback loop ``` ### Example 2: Lac Operon ``` Nodes: LacI, LacZ, Lactose, Glucose Edges: LacI ──(-)──► LacZ (repressor blocks transcription) Lactose ──(-)──► LacI (lactose inactivates repressor) Glucose ──(-)──► LacZ (catabolite repression) Function: Metabolic switch for sugar utilization ``` ## Analysis Capabilities CatColab can analyze regulatory networks for: - **Steady states**: Fixed points of the dynamics - **Stability**: Eigenvalue analysis of Jacobian - **Motif enrichment**: Statistical over-representation - **Boolean dynamics**: Logical model simulation ## GF(3) Triads ``` catcolab-regulatory-networks (-1) ⊗ topos-catcolab (0) ⊗ catcolab-stock-flow (+1) = 0 ✓ crn-topology (-1) ⊗ catcolab-regulatory-networks (0) ⊗ alife (+1) = 0 ✓ ``` ## Commands ```bash # Create regulatory network just catcolab-new regulatory "p53-network" # Analyze motifs just catcolab-analyze p53-network --motifs # Export to SBML just catcolab-export p53-network --format=sbml # Simulate Boolean dynamics just catcolab-simulate p53-network --boolean ``` ## References - Alon (2007) "Network motifs: theory and experimental approaches" - Karlebach & Shamir (2008) "Modelling and analysis of gene regulatory networks" - [CatColab Regulatory Networks Help](https://catcolab.org/help/logics/regulatory) --- **Skill Name**: catcolab-regulatory-networks **Type**: Systems Biology / Gene Regulation **Trit**: -1 (MINUS) **GF(3)**: Conserved via triadic composition