Emergence (networks & collective dynamics)

1. Networks:

• Simple biological modules:
  • Transcription regulation; lac operon
  • Genetic switches
  • Signal transduction
  • Repressilator: a simple clock
• Statistics of complex networks:
  • Random (Erdös-Rényi) networks
  • Percolation, diameter, degree distribution
  • Scale free networks, construction and properties

2. Spatio-temporal patterns:

• Dynamics on a network:
  • fixed points and stability
• Hopfield neural network
• Cycles
  • Biological clocks The Belousov-Zhabotinsky Reaction
  • Biological clocks
  • Synchronization
• Turing instability

3. Emergence of cell state in the nucleus:

• Inferring compactification and structure of chromosomes
• Transcriptional condensates