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---> Material for the lecture (slides, papers, software) <---

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

• 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.

• 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.

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  Edit Attach Copyright © 2008-2022 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
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