Systems Biology: Theory and Algorithms

Systems Biology: theory and algorithms

Systems biology is the study of the interactions between the components of a biological system, and how these interactions give rise to the function and behavior of that system.
This course gives the basic systems biology algorithmic approaches, in particular in application to analysis of highthroughput omics data.

Major topics covered are:
Functional genomics and highthroughput technologies in biomedicine.
Systems biology approaches: static and dynamic networks, Boolean static networks, Bayesian static and dynamic networks
Autoregulation and multistability in the biological systems:
Modeling genetics and biochemical networks as chemical reactions via ordinary differential equations (ODE): equilibrium points and linearization, nullclines, limit cycles, Hopf bifurcations.
ODE network inference: ODE inference from perturbations.
Biochemical kinetics via Markov process: Markov chains and continuous Markov processes, forward and backward Kolmogorov equations, Gillespie algorithm, exact and approximate simulation strategies.
Bayesian inference and MCMC: Gibbs sampler, the Metropolis-Hasting algorithm
Inference for stochastic kinetic models: inference given complete data, discrete-time observations.
Modeling genetics and biochemical networks via stochastic differential equations (SDE): stochastic time discrete approximations (strong and weak)
Case studies:
auto-regulatory genetic network,
bifurcations  in processes with micro RNA regulations,
the lac operon, genetic toggle,
inference of the expression regulation network
mutations and adaptive evolution

Bibliography:
J.D.Murray, Mathematical Biology, 1989
D.Wilkinson Stochastic Modelling for Systems Biology, Chapman & Hall/CRC ,2006
E Klipp, R Herwig, A Kowald, C Wierling, and H Lehrach. Systems Biology in Practice. Wiley-VCH: 2005
Z. Szallasi, J. Stelling, and V.Periwal (eds.) System Modeling in Cellular Biology: From Concepts to Nuts and Bolts, MIT Press: 2006
B Palsson, Systems Biology – Properties of Reconstructed Networks. Cambridge University Press: 2006
U Alon. An Introduction to Systems Biology: Design Principles of Biological Circuits. CRC Press: 2006
Y.Rozanov. Probability theory: a concise course. Dover publications Inc. 2000
P.Kloeden, E.Platen, H.Schurz. Numerical Solutions of SDE Through Computer Experiments, Springer, 2003
Wilke C.O.2001. Adaptive evolution on neural networks, Bulletin of Mathematical Biology, 63(4): 715-730

Lectures:

  1. TOPIC1_ODE_Dimer
  2. TOPIC2_ODE_ChemReactions
  3. TOPIC3_BayesianNetwork
  4. TOPIC4_PreyPredator
  5. TOPIC5_ODE_LinearSystems
  6. TOPIC6_ODE_EquilibriumPoints_Linearization
  7. TOPIC7_NonLinearSystems_Nullclines
  8. TOPIC8_TypesOfEquilibriumPoints
  9. TOPIC9_CompetitiveSpecies
  10. TOPIC10_LimitCycleHopfBifurcation
  11. TOPIC11_BelousovJabotinsky
  12. TOPIC12_MicroRNAbifurcation
  13. TOPIC13_TSNI
  14. TOPIC14_NIR
  15. TOPIC15_GeneticToggle
  16. TOPIC16_Probability
  17. TOPIC17_MarcovChain
  18. TOPIC18_MarcovProcess
  19. TOPIC19_StationaryMarkovProcess