The systems biology course aims at providing mathematical models helping to understand the dynamic interactions occurring within and between cells. This course gives the mathematical tools to model and analyze gene transcription networks and enzymatic reactions. To this end, both deterministic and stochastic approaches are exploited.
Transcription networks (TNs): graph properties and ODE approach to model gene regulation. Network motifs and their biological functions: speed up of the response time, increase robustness, produce oscillations. Enzymatic reactions: Reaction Rate Equations and Quasi Steady-State Approximations (QSSA). Master Chemical Equations: mathematical development and stochastic numerical simulations. The Gillespie algorithm.