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1. What is Systems Biology any why do we need it

  • Material:
    • cf. Chapter 1 of Skript (Very Draft Lecture Notes) (These lecture notes are created for a full systems biology lectures; nevertheless you can use the respective chapters for this lecture, too.)

  • What is Systems Biology?
  • What is a System?
  • Motivation - Why a systems approach? - Emergent Phenomena
  • Major Innovations of Systems Biology
    • Standards
    • Tight integration of experiment and theory
    • Automation of the scientific cycles
  • Example: SBML - Systems Biology Markup Language (very briefly)
  • Basic Approaches to Describe a System
  • Dynamical System and State Space
  • Model - System with Purpose to Abstract System Phenomena
  • Types of Systems

2. Reaction networks and modeling with differential equations.

  • Material:
    • Explained in Chapter 2 of Skript (Very Draft Lecture Notes) if your notes from the lecture should not be sufficient. The chapter contains also further examples for exercise.

  • How to translate biochemical reactions to differential equations?
  • Reaction network = set of species + set of reaction rules
  • Stoichiometric matrix
  • flux vector = kinetic laws
  • Mass action kinetics
  • Chemical differential equation
  • Dynamical interpretation / simulation
  • Example: Transcription factor activating a gene.

3. From reaction networks (RN) to gene regulatory networks (GRN)

  • Material:
  • With RNs we can create very detailed models of genes, their dynamics, and interactions.
  • The derived dynamical model is usually a differential equation (ODE), dx/dt = f(x), which can be used in three different ways:
    1. Find an explicit solution. (Only possible for very simple equations like dx/dt = k x, exponential growth)
    2. Simulation. E.g., by the simple scheme: x(t+dt) = x(t) + dt * f(x) with dt being the time-step.
    3. Qualitative analysis. E.g., by deriving the steady state, simply by solving f(x) = 0.
  • Overall picture, noting that there are different timescales, e.g., three time scales:
    1. very fast: activation of a protein, e.g., by phosphorylation [ignored in this lecture, assumed to be instantaneous]
    2. medium: binding of TF to promoter region, going into steady state; [focus of this lecture]
    3. slow: expression of a gene, creation of gene product (here, protein), [focus of next lectures]
  • As an exercise: "detailed" mode of gene Y being activated by transcription factor X forming a complex before binding to promotor region.
    • Time scale: medium
    • Approach: (2) Simulation (shown by using octave).
  • One dimensional model of gene activation:
    • n X + Yoff -> n X + Yon, Yon -> Yoff
    • Deviation of Hill-kinetics, beta(x).
    • Discussion of parameters: n and k.

4. Gene regulatory network motifs I (cf. U. Alon)

  • Basic model of a a factor X* activation a gene Y: dy/dt = beta(x) - alpha y
    • Steady state: y_st = beta(x) / alpha
    • Response time / half level activation time t1/2 = log 2 / alpha (independent of activation rate).
    • Graphical illustration of steady state and the dynamics towards steady state.
  • Negative feedback loop
    • Basic model dy/dt = beta(y) - alpha y * Use inhibitory Hill-kinetics for beta(y) similar to kinetics derived in previous lecture.
    • Deviation of core properties:
      • Reduces response time (gene switches quicker)
      • Increases robustness, with respect to decay rate alpha and max-level activation beta_m, but not according to k (binding kinetic constants).
    • Graphical illustration of steady state and the dynamics towards steady state.

  • Positive feedback loop
    • Basic model dy/dt = beta(y) - alpha y * Uuse Hill-kinetics for beta(y) as derived in previous lecture.
    • Deviation of core properties:
      • Can be bi-stable (if decay rate is not too high).
      • Decreases robustness,
      • Increases response time.
    • Graphical illustration of steady state and the dynamics towards steady state.

5. Gene regulatory network motifs II (cf. U. Alon)

6. Gene regulatory network motifs III (cf. U. Alon)

7. Boolean networks for modeling gene regulatory networks

8. Practical Exercise (planned)

  • Simulation using COPASI/Matlab (practical exercise, Location: FRZ Linux Pool)

X. Stochastic systems (not this year)

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Topic revision: r8 - 2019-11-05 - PeterDittrich
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