BIOINF 4120
Bioinformatik II
- Structures and Systems Oliver Kohlbacher
SS 2010
20. Signaling Networks and
Cellular Dynamics
Abt. Simulation biologischer Systeme
WSI/ZBIT, Eberhard Karls Universität Tübingen
Signal Transduction
• Signal transduction is the process by which a
cell translates one stimulus into another
• Most signal transduction events start with the
activation of a membrane receptor
• The signal of that receptor is then passed on
along a signal transduction cascade
• Signal transduction can involve various types
of processes in a sequences (cascade):
– Ligand-receptor binding
– Biochemical reactions (e.g., phosphorylation)
– Gene regulation
Signal Transduction
• Signal transduction can trigger a wide array
of cellular responses
– Activation of genes
– Changes in the metabolism
– Cell proliferation
– Cell death (apoptosis!)
– Cell locomotion (chemotaxis!)
• We will examine some examples of signaling
patterns that frequently occur as well as
examples of more complex signaling networks
Example: Phosphorylation
• Phosphorylation and dephosphorylation is a very
common mechanism for protein (de-)activation
• It is frequently used in signal cascades
• A kinase catalyzes the phosphorylation, while a
phosphatase catalyzes the reverse reaction
Kholodenko, Nat. Rev. Cell Biol. (2006), 7, 165
Example: G-Proteins
• G-proteins can bind GDP or GTP
• Other proteins (GEFs – guanine exchange factors and
GAPs – GTPase activating proteins) can toggle the
system between the two states
Kholodenko, Nat. Rev. Cell Biol. (2006), 7, 165
Example: MAP Kinases
• Single-site phosphorylation cycles often form whole cascades
• A prominent example is the so-called MAP kinase pathway
• Here, MAP kinase (MAPK, M1) is activated by MAP kinase kinase
(MAPKK, M2), which in turn is activated by MAP kinase kinase
kinase (MAPKKK, M3)
Kholodenko, Nat. Rev. Cell Biol. (2006), 7, 165
Example: Dictyostelium
• Dictyostelium discoideum is a
slime mold
• It can move as loose cell
aggregates that show
chemotaxis
• Under certain conditions, it
can also form fruit bodies
containing spores
• cAMP is emitted by the
individual cells periodically
• This induces synchronous
movements of cell aggregates
through chemotaxis
http://www.ailab.si/supp/bi-visprog/dicty/cycle.gif
http://www.youtube.com/watch?v=Ql7i_TLUurM
Example: Dictyostelium
Periodic emission of cAMP is controlled by a small network
–
–
–
cAMP binds to membrane-bound receptor CAR1, which activates MAP kinase
ERK2 and adenylyl cyclase A (ACA)
MAP kinase ERK2, which phosphorylates cAMP phosphodiesterase REG A
High internal cAMP concentration activates protein kinase A (PKA), which in
turn inhibit ERK2 and CAR1
Laub MT, Loomis WF. Mol Biol Cell. 1998, 9(12):3521
Phases of Signal Transduction
Signaling is often broken down into three phases:
• Reception
– Primary detection of the signal by a receptor (often binding)
• Transduction
– The receptor structure is altered
– A cascade of reactions (signal transduction) is triggered
• Response
– At the end of the transduction pathway some final response is
triggered (or more than one)
– This can be almost anything: gene expression, rearrangement
of the cytoskeleton, activation of enzymes, etc.
– The signal is usually amplified along the cascade, a single
molecule can thus lead to a significant response
Modeling Signaling
• Like metabolic processes, signaling events can be
modeled qualitatively or quantitatively
• Since signaling networks can involve metabolic
processes and regulatory events, a unified modeling
of these is required
• Since the essential part of signal transduction is the
dynamics of these systems (how fast does the signal
occur?), time-invariant modeling approaches are less
useful here
• The most common model is thus kinetic modeling
using ordinary differential equations (ODEs)
Modeling Kinetics with ODEs
• The law of mass action gives rise to a straight-forward
description of biological processes
• Assume the simple reaction
A+B­2C
• The law of mass action states that the equilibrium
constant K for this reaction is:
where c(…) is the concentration (more precisely: the
activity, which is usually approximated by the
concentration) of the corresponding substrate/product
• In equilibrium, the reaction rates for the forward and
backward direction v+ and v- are equal
Enzyme Kinetics
• Simple enzymatic reaction
k
k-1
k
2
E + S ­1 ES !
E+P
Enzyme (E) and substrate (S) form an intermediate,
the enzyme-substrate complex (ES)
• ES reacts (irreversibly) to E and product (P)
• This yields the well-known Michaelis-Menten kinetics:
where Vmax describes the maximum capacity of the
enzyme and KM is the Michaelis-Menten constant
Types of Signaling Circuits
• In the simplest case there is a linear response
between a signal (S, e.g., a concentration) and a
response (R)
• In this case above, it is a simple synthesis and
degradation of a signal element
R ! RP
where RP is the phosphorylated (active) form of the
response element
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Types of Signaling Circuits
R ! RP
• The rate equations for this process are thus:
where S, R, RP are concentrations and RT = RP + R
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Types of Signaling Circuits
• Usually the response of the chemical reaction
induced is fast compared to the change in the signal
(e.g., external concentration)
• We can thus assume a steady state
• This yields a linear steady-state response Rss:
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Types of Signaling Circuits
• Simple cycles where the activation path follows a
Michaelis-Menten kinetics and the inactivation a
linear kinetics yield a hyperbolic activation profile:
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Types of Signaling Circuits
• Sigmoidal signal-response curves occur if
phosphorylation and dephosphorylation events are
governed by Michaelis-Menten kinetics
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Types of Signaling Circuits
• In this case the steady-state is the solution of a
quadratic equation:
• The biochemically acceptable solution of this
equation (0 < RP < RT) is the Goldbeter-Koshland
function G(u, v, J, K):
with
Types of Signaling Circuits
• Mutual activation of two reactions leads to an
irreversible switch: once a critical signal level has
been reached, the element will remain activated
even after the signal disappears
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Types of Signaling Circuits
• Mutual inhibition realizes a toggle switch: if the
signal falls back below a certain threshold, the
element becomes inactivated again
• The difference in the two critical signal levels
required leads to a hysteresis in the signal response
• The lac operon is a prominent example for a toggle
switch
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Types of Signaling Circuits
• Negative feedback can lead to oscillations
• At least three species are required to create
sustained oscillations
X ! Y ! R ––| X
• There are two ways to close the negative feedback
loop
– Inhibition of synthesis of X by RP
– Activation of degradation of X by RP
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Astable Multivibrator
• A simple oscillator based on two
transistors is constructed in basically
the same fashion
• This so-called astable multivibrator
uses a feedback loop to create an
oscillation
• If transistor Q1 is turned on (base
voltage of Q1 > 0.6 V), it holds R1/C1
junction close to 0V and C1 is being
charged through R2
• If the base voltage of Q2 reaches 0.6
V, it is turned on and pulls the R4/C2
junction to 0V, the base voltage of Q1
drops and Q1 is turned off
• Now we begin from start with
swapped roles for Q1 and Q2
http://en.wikipedia.org/wiki/Multivibrator
Dynamic Networks
• The signaling elements shown are just a selection of
the most important elements
• As in electronics, there exists a set of versatile
building blocks in signaling that can be assembled
into larger networks
• These elements do not occur individually, but they
are embedded in the context of larger, more
complex networks and coupled to other elements
• When analyzing the components of these networks
one can often identify these functional elements
• A well-studied example is the yeast cell cycle
Cell Cycle
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Cell Cycle - G1/S Module
The G1/S module implements a toggle switch
consisting of the Cdk1:CycB and CKI
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Cell Cycle - G2/M Module
The G2/M module implements a second toggle
switch consisting of the Cdk1:CycB and Wee1
as well as mutual activation between Cdk1:CycB
and Cdc25
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Cell Cycle - M/G1 Module
The M/G1 module finally implements a
negative feedback oscillator formed by
Cdk1:CycB ! APC ! Cdc20 –––| CycB
Tyson et al., Curr. Opin. Cell Biol. (2003), 15:221
Artificial Circuits
• One can also use the knowledge on these constructs to engineer
artificial circuits
• Elowitz and Leibler constructed a minimal oscillatory circuit in
E. coli based on negative feedback
• They inserted a ‘repressilator’ and a reporter plasmid
• The repressilator plasmid encodes for three genes that encode
a negative feedback cycle
• The reporter plasmid encodes for green fluorescent protein
(GPF) and is repressed by TetR
Elowitz, Leibler, Nature (2000), 403:335
Artificial Circuits
This circuit shows oscillatory fluorescence in E. coli!
Elowitz, Leibler, Nature (2000), 403:335
Solving ODEs
• Complex systems of ODEs as we consider them here
do not possess closed analytical solutions
• We thus have to resort to numerical methods to solve
these problems
• There are various algorithms for the numerical
solution of systems of ODEs available
– Deterministic methods
– Stochastic methods
• Dealing with efficient methods for solving ODEs is
beyond the scope of this lecture, though
• In many cases, we can use existing software packages
(LSODE, Mathematica, etc.) to solve the problems
once the system of ODEs has been formulated
Modeling with ODEs
• Modeling with ODEs requires
– Accurate stoichiometric modeling
– Knowledge about kinetic constants
• Much of the latter can be reconstructed from
biochemical literature
• The majority of kinetic constants is unknown, though
• They can be either
– Estimated from related enzymatic reactions
– Determined in a global optimization procedure based on
exptl. (metabolomics) data or on general model stability
• There are various software tools for modeling
dynamic systems
• To facilitate the exchange of complex models, there
are common data exchange formats like SBML
SBML
• Metabolic network models can by now be readily exchanged
through a common standard, the Systems Biology Markup
Language (SBML)
• SBML is an XML-based standard for biochemical reaction
networks
• It allows the exchange of metabolic network models in a
standardized fashion
<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2" level="2" version="1"> <model
id="MAP" name="M. tuberculosis Mycolic Acid Pathway"> <listOfCompartments>
<compartment id="default"/>
</listOfCompartments>
<listOfSpecies>
<species id="G001" name="acpS" compartment="default" …./>
<species id="X001" name="coenzyme-A" compartment="default" …/>
<species id="X002" name="apo-AcpM" compartment="default" …/>
<species id="X003" name="ADP" compartment=“…/>
</listOfSpecies>
…
http://www.sbml.org
SBML
<listOfReactions>
<reaction id="J001" reversible="false" fast="false">
<listOfReactants>
<speciesReference species="X001"/>
<speciesReference species="X002"/>
</listOfReactants>
<listOfProducts>
<speciesReference species="X003"/>
<speciesReference species="X004"/>
</listOfProducts>
<listOfModifiers>
<modifierSpeciesReference species="G001"/>
</listOfModifiers>
</reaction>
…
</listOfReactions>
http://www.sbml.org
CellDesigner
• CellDesigner is a network editor for systems
biology that allows the construction,
verification, and modification of biological
networks
• CellDesigner
– is written in Java
– reads and writes models as SBML
– can directly connect to various online SBML model
repositories
– Implements SBGB (Systems Biology Graphical
Notation), a graphical language that is being
established as a standard for systems biology
http://www.celldesigner.org
JWS Model Database
• JWS Model Database is a repository of curated models
• Models can be downloaded in various formats (e.g., SBML)
• The website also allows the online simulation of these models
through the web interface
http://www.jjj.bio.vu.nl
JWS Model Database
http://www.jjj.bio.vu.nl
JWS Model Database
http://www.jjj.bio.vu.nl
JWS Model Database
http://www.jjj.bio.vu.nl
COPASI
• The Complex Pathway Simulator (COPASI) is a tool for
analysis and simulation of biochemical networks
• It can handle steady-state analysis (EP, FBA) as well as
dynamic simulations
• It can use both deterministic and stochastic solvers for
differential equations
• It can read various model formats, including SBML
www.copasi.org
COPASI
COPASI
COPASI
References
Papers
• Laub MT, Loomis WF. A molecular network that produces spontaneous
oscillations in excitable cells of Dictyostelium. Mol Biol Cell. 1998,
9(12):3521-32
• Kholodenko, BN. Cell-signaling dynamics in time and space. Nat. Rev.
Cell Biol. (2006), 7, 165
Links
• CellDesigner
www.celldesigner.org
• Copasi
www.copasi.org
• JWS
www.jjj.bio.vu.nl
• More on Dictyostelium
http://www-biology.ucsd.edu/~firtel/movies.html