Tags:
create new tag
, view all tags
---> 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.

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

• Motifs with three genes
• 13 possible non-trivial networks (directed graphs) with three genes
• Common motif: feed forward loop (FFL)
• When distinguishing activation and inhibition: 8 Feed forward loops (4 x coherent and 4 x incoheren); only one coherent and one incoherent is very common (Type 1).
• Coherent feed forward loop Type 1 with
• AND (delayed on, immediate off, filters transient on pulses)
• OR (immediate on, delayed off, filter transient off pulses)
• Incoherent feed forward loop Type 1 with
• AND (pulse generator, deviation of input signal, can detect an increase in the input, reduces response time)
• Motifs with more than three genes
• Single input multiple output (SIM): Primitive sequential "program" execution. Timing can be evolved by altering kon, koff
• More complex motifs; e.g. for a spiked program, which combines Incoherent Type 1 loops with Coherent AND FFLs (see Cell Snapshot).
• Notes:
• The motifs studied so far are common in all organisms, and in particular in bacteria (e.g., E. Coli)
• In particular in organisms with different cell types and complex morphogenesis other motifs can be found, in particular feedback loops involving more than one gene. (see lecture on Boolean networks).

## 6. Boolean networks for modeling gene regulatory networks

• Motivation: Study large networks with many complex feedback loops and many atractors.
• Rough history: since 200 years theory, since 100 years for computer engineering, since 50 years for biology (Stuart Kauffman)
• So, a lot of extremely powerful theory and tools available when modeling a GRN as a Boolean network.
• Boolean network - basic definition and dynamics
• N : number of genes = number of nodes / gates
• x_i(t) from {0, 1} : at time t state of gene i (can be either 0=false or 1=true), i = 1, ..., N
• x(t) = (x_1(t), ... x_n(t)) : global state of the network, just putting all gene states into one vector x.
• f_i : update function of gene i
• x_i(t+1) = f_i(x(t)) : Gene i is updated using the update function f_i
• Note that an update function f_i of gene i usually depends only on subset of other genes. K_i denotes the size of this set.
• K_i : number of inputs of gene i
• If all genes have the same number of inputs (i.e., K_i = K for all i = 1, ..., N), we call the network: "NK Boolean Network" or "NK-Network" for short.
• Global dynamics x(t+1) = F(x(t)) with x(t) an N-dimensional Boolean vector denoting the state of the network at time t.
• Fixed point (stationary state): A state x is a stationary state, if F(x) = x.
• Atractor (or cycle) A: a set of states A = {x(0), x(1), ..., x(n-1)} with x(i+1 mod n) = F(x(i)) for i = 0, ..., n-1.
• n is called the period (or cycle length) of the atractor (cycle).
• A fixed point is an attractor with period (cycle length) 1.
• A basin of atraction B of an attractor A is the set of states that eventually lead to the attractor A, i.e., for all states x from B holds: F(2^N) is contained in A.
• An attractor (and a fixed point in particular) can be equated with a cell type.
• Random networks get easily chaotic (e.g. when there K>2 inputs per gene).
• Real networks are more ordered through canalizing functions.
• For modeling complex real networks (e.g., flower development) genes with three states are often used.

## 7. Stochastic dynamics in genetic systems

• Have a good feeling that we can do it this semester (19/20).
• But with an adapted, mathematically simplified, enhanced content.
• Background literature for the simulation algorithm:
• Motivation:
• The problem: when molecular counts get low, stochasticity comes in.
• GRNs can become stochastic when transcription factor concentration or mRNA concentration is very low.
• This might explain cell-cell variability and bursting gene expression.
• Can be useful: E.g. for decision making, switching dependent on stress (Yomo et al. model)
• Basic idea of stochastic simulation
• Gillespie Algorithm
• Draw one random number for deciding WHEN the next reaction happens.
• Draw another random number for deciding WHICH reaction then happens.
• Update current time and state accordingly.
• Note the difference of macro and micro rates: 2 S1 -> S3 vs. S1 + S2 -> S3
• Example simulation: Bursting gene expression

## 8. Practical Exercise (planned)

• Simulation using COPASI/Matlab (practical exercise, Location: FRZ Linux Pool) OR
• Practical exercises with pen and paper. Not the exciting but very useful.
Topic revision: r9 - 2019-11-25 - PeterDittrich   Copyright © 2008-2021 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding TWiki? Send feedback