Systems biology

Unit Coordinator: Alessandro Borri
Programme: Erasmus Mundus
ECTS Credits: 6
Semester: 1
Year: 2
Campus: University of L'Aquila
Language: English

Systems biology is an emerging research area, which aims at providing mathematical models helping to understand the dynamic interactions occurring within and among cells. This course provides the basic mathematical tools to model and analyze gene transcription as well as biochemical reaction networks: the most important network motifs are investigated exploiting both deterministic and stochastic approaches.

  • Review of basic concepts of biology and probability; deterministic vs. stochastic approach.
  • Transcription factors and transcription networks; gene expression: transcription and translation; separation of time scales and the Quasi-Steady-State Approximation (QSSA); activators and repressors; Hill and logic input functions; dynamics of simple regulation and switching production in ordinary differential equation (ODE) form; response time; mass action kinetics and conservation equation; the Michaelis-Menten kinetics; cooperativity; dependent and independent bindings; multi-dimensional input functions.
  • Network Motifs: real and randomized networks; the Erdos-Renyi (ER) model; graph properties; negative autoregulation (NAR) and stability analysis; three-node network motifs: feedback loops (FBLs) and feedforward loops (FFLs); coherent and incoherent FFLs; sign-sensitive delay, output pulse generation, speed up of response time, biphasic response curves in I1-FFL; review of the other types of FFL; examples: Arabinose system, Galactose system, flagella motor genes in E. Coli.
  • Introduction to Numerical Simulation in Systems Biology; MATLAB: introduction and basic notions; integration of non-stiff differential equations via ode45; randomized computation, Monte Carlo simulation, construction of randomized networks (E-R models) and digraphs.
  • General Transcription and Interaction Networks: Single-Input Module (SIM), Multi-Output Feedforward Loop, LIFO and FIFO temporal programs, bi-fans and Densely Overlapping Regulons (DORs), interlocked FFLs; positive autoregulation (PAR) and response slow-down; two-node positive feedback: double-positive (lock-on) and double-negative (toggle-switch) circuits; three-node motives; protein-protein interaction (PPI) networks and hybrid motifs; network motifs in real-world networks: food webs, social networks, electrical circuits, neuronal networks. Examples: sporulation of bacterium Bacillus subtilis, phosphorylation, response to pain stimuli in humans.
  • Biological Oscillations: the role of negative feedback and delay; time-separation, feedback strength and cooperativity; noise-induced and delay oscillations; bistability and hysteresis; robustness in biological circuits; models at a higher level of organization: tissues and organs; the glucose-insulin feedback loop.
  • The stochastic approach in Systems Biology: motivation, Chemical Reaction Networks, Continuous-Time Markov Chains; the Chemical Master Equation (CME) and its properties, characterization of the CME stationary distribution, the macroscopic equation, one-step processes; stochastic simulation in Systems Biology, inverse sampling method, Gillespie Stochastic Simulation Algorithm (SSA); examples.
  • Mesoscopic models and noise: extrinsic vs intrinsic noise, bursty reactions, the Chemical Langevin Equation, the Wiener Process, the Euler-Maruyama integration of Stochastic Differential Equations (SDEs).
  • Biological and biomedical examples: metabolism, tumors, epidemics, pharmacokinetics and pharmacodynamics (PKPD), environmental pollution, ecology.

Basic notions of mathematical analysis, dynamical systems and probability.

Reading list:

 Uri Alon, An introduction to systems biology: design principles of biological circuits, CRC press, 2019.

 E. Klipp, W. Liebermeister, C. Wierling, and A. Kowald, Systems biology: a textbook, John Wiley & Sons, 2016.


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