- 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

- 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.

- 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:
- Find an explicit solution. (Only possible for very simple equations like dx/dt = k x, exponential growth)
- Simulation. E.g., by the simple scheme: x(t+dt) = x(t) + dt * f(x) with dt being the time-step.
- 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:
- very fast: activation of a protein, e.g., by phosphorylation [ignored in this lecture, assumed to be instantaneous]
- medium: binding of TF to promoter region, going into steady state; [focus of this lecture]
- 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.

- Material:
- Look at the Cell Snapshot: http://www.sciencedirect.com/science/article/pii/S0092867410011360
- You can also watch Uri Alons video lectures (Lecture 2 - 4) avaiable at youtube. I basically took all the content from there. Except the relation between a reaction network and a regulatory network, which I showed at the beginning of the lecture. An analog deviation can be found in Alon's book "Systems Biology".
- Uri Alon's lectures at youtube

- 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.

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

- Paper: Gillespie1977 (just the first pages)

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

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