23. Lecture WS 2005/06 Bioinformatics III 1 V23 Stochastic simulations of cellular signalling Traditional computational approach to chemical/biochemical kinetics: (a) start with a set of coupled ODEs (reaction rate equations) that describe the time-dependent concentration of chemical species, (b) use some integrator to calculate the concentrations as a function of time given the rate constants and a set of initial concentrations. Successful applications : studies of yeast cell cycle, metabolic engineering, whole-cell scale models of metabolic pathways (E-cell), ... Major problem: cellular processes occur in very small volumes and frequently involve very small number of molecules. E.g. in gene expression processes a few TF molecules may interact with a single gene regulatory region. E.coli cells contain on average only 10 molecules of Lac
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23. Lecture WS 2005/06Bioinformatics III1 V23 Stochastic simulations of cellular signalling Traditional computational approach to chemical/biochemical.
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23. Lecture WS 2005/06
Bioinformatics III 1
V23 Stochastic simulations of cellular signalling
Traditional computational approach to chemical/biochemical kinetics:
(a) start with a set of coupled ODEs (reaction rate equations) that describe the
time-dependent concentration of chemical species,
(b) use some integrator to calculate the concentrations as a function of time given
the rate constants and a set of initial concentrations.
Successful applications : studies of yeast cell cycle, metabolic engineering,
whole-cell scale models of metabolic pathways (E-cell), ...
Major problem: cellular processes occur in very small volumes and frequently
involve very small number of molecules.
E.g. in gene expression processes a few TF molecules may interact with a single
gene regulatory region.
E.coli cells contain on average only 10 molecules of Lac repressor.
23. Lecture WS 2005/06
Bioinformatics III 2
Include stochastic effects
(Consequence1) modeling of reactions as continuous fluxes of matter is no
Architecture of signaling network: bow-tie structure
Oda et al.
Mol.Syst.Biol. 1 (2005)
23. Lecture WS 2005/06
Bioinformatics III 17
Network control
Several system controls define the overall behavior of the signaling network:
- 2 positive feedback loops
- Pyk2/c-Src activates ADAMs, which shed pro-HB-EGF so that the
amount of HB-EGF will be increased and enhance the signalling
- active PLC/ produces DAG which results in the cascading activation
of protein kinase C (PKC), phospholipase D, and PI5 kinase.
- 6 negative feedback loops
- inhibitory feed-forward paths
There are also a few positive and negative feedback loops that affect ErbB
pathway dynamics.
Oda et al. Mol.Syst.Biol. 1 (2005)
23. Lecture WS 2005/06
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Process diagram
Oda et al. Mol.Syst.Biol. 1 (2005)
23. Lecture WS 2005/06
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Modification and localization of proteins
Oda et al. Mol.Syst.Biol. 1 (2005)
23. Lecture WS 2005/06
Bioinformatics III 20
Precise association states between EGFR and adaptorsOda et al. Mol.Syst.Biol. 1 (2005)
Ellipsis in drawing association states of proteins using an ‘address’. (A) Precise association states between EGFR and adaptors. Three adaptor proteins, Shc, Grb2, and Gab1, bind to the activated EGFR via its autophosphorylated tyrosine residues. Shc binds to activated EGFR and is phosphorylated on its tyrosine 317. Grb2 binds to activated EGFR either directly or via Shc bound to activated EGFR. Gab1 also binds to activated EGFR either directly or via Grb2 bound to activated EGFR, and is phosphorylated on its tyrosine 446, 472, and 589.
23. Lecture WS 2005/06
Bioinformatics III 21
Cells of living organism sense their
environment and respond to
environmental stimuli.
Cellular signaling mechanisms govern how information
from the environment is decoded, processed and transferred to the appropriate
locations within the cell.
Signaling through the receptor tyrosine kinase (RTK) family of receptors regulates
a wide range of biological phenomena, including cell proliferation and
differentiation.
Integrated PW-DMC Model of Epidermal Growth Factor Receptor Trafficking and Signal Transduction
Diagram showing the compartments involved in
receptor trafficking and the receptor movement
pathways within the cell.
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
Bioinformatics III 22
Integrated Model of Epidermal Growth Factor Receptor Trafficking and Signal Transduction
Signaling pathways of various RTKs are reasonably well characterized.
Common features:
- receptor self-phosphorylation on tyrosine residues
- subsequent interaction with molecules containing SH2 and phospho-Tyr
residues.
The signal from the receptor is transmitted to downstream effector molecules
through a series of protein-protein interactions, such as the MAP kinase cascade.
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
Bioinformatics III 23
Integrated Model of Epidermal Growth Factor Receptor Trafficking and Signal Transduction
The EGF receptor can be activated by the
binding of any one of a number of different
ligands.
Each ligand stimulates a somewhat different
spectrum of biological responses.
The effect of different ligands on EGFR
activity is quite similar at a biochemical level
the mechanisms responsible for their
differential effect on cellular responses are
unkown.
After binding of any of its ligands, EGFR is
rapidly internalized by endocytosis.
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
Bioinformatics III 24
Integrated Model of Epidermal Growth Factor Receptor Trafficking and Signal Transduction
Different EGFR ligands vary in their ability to bind to EGFR as a function of
receptor microenvironment such as intravesicular pH.
After endocytosis, receptor-ligand complexes pass through several different
compartments that vary in their intravesicular milieu.
Receptor movement among cellular compartments („receptor trafficking“) can
exert a significant effect on the activity of the complexes.
The different intracellular compartments also vary in their access to some of the
substrates of the EGFR kinase.
This coupled relationship between substrate access and ligand-dependent
activity in different endocytic compartments suggests that trafficking could
function to „decode“ the information unique to each ligand.
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
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3 functions of trafficking
(1) controlling the magnitude of the signal
(2) controlling the specificity of the response
(3) controlling the duration of the response.
Understanding the relative contribution of these 3 aspects for any given
combination of cells, conditions, and ligands is very difficult
use computational models!
Resat et al. Biophys Journal 85, 730 (2003)
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Computational modelling of EGF receptor system
(1) trafficking and ligand-induced endocytosis
(2) signaling through Ras or MAP kinases
This work combines both aspects into a single model.
Most approaches to building computational kinetic models have severe
drawbacks when representing spatially heterogenous processes on a cellular
scale.
Review: In the traditional approach, we
- formulate set of coupled ODEs (reaction rate equations) for the time-dependent
concentration of chemical species
- use integrator to propagate the concentrations as a function of time given the
rate constants and a set of initial concentrations.
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
Bioinformatics III 27
Multiple time scale problemIn Dynamic Monte Carlo, reactions are considered events that occur with certain
probabilities over set intervals of time.
The event probabilities depend on the rate constant of the reaction and on the
number of molecules participating in the reaction.
In many interesting natural problems, the time scales of the events are spread
over a large spectrum.
Therefore it is very inefficient to treat all processes at the time scale of the fastest
individual reaction.
In the EGFR signaling network,
- receptor phosphorylation after ligand binding occurs almost instantaneously
- vesicle formation or sorting to lysosomes requires many minutes.
Resat et al. Biophys Journal 85, 730 (2003)
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Solution to multiple time scale problem
Computing millions and billions non-correlated random numbers can become a
time-consuming process.
Resat et al. (2001) introduced Probability-Weighted DMC to speed-up the
simulation by factor 20 – 100.
Different processes are only tested at variant times depending on their
probabilities
= very unlikely processes compute MC decision very infrequently.
Resat et al. Biophys Journal 85, 730 (2003)
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Signal transduction model of EGF receptor signaling pathway
Resat et al. Biophys Journal
85, 730 (2003)
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Bioinformatics III 30
Species in the EGF receptor signaling model
Resat et al. Biophys Journal
85, 730 (2003)
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Receptor and ligand group definitions
Resat et al. Biophys Journal 85, 730 (2003)
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Rate constants of the ligand:receptor interactions
Resat et al. Biophys Journal 85, 730 (2003)
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Early endosome inclusion coefficients
Resat et al. Biophys Journal 85, 730 (2003)
These are adjusted to yield the experimentally determined rates of
ligand-free and ligand-bound receptor internalization.
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Bioinformatics III 34
Time course of phosphorylated EGF receptors(a) Total number of phosphorylated EGF
receptors in the cell. Curves represent the
number of activated receptors when the cell is
stimulated with different ligand doses at the
beginning. The y axis represents the number of
receptors in thousands.
(b ) Ratio of the number of phosphorylated
receptors that are internalized to that of the
phosphorylated surface receptors.
(c) Ratio of the number of internalized
receptors to the number of surface receptors.
Curves are colored as:
[L] = 0.2 (magenta), 1 (blue), 2 (green), and 20
(red) nM.
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
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Distribution of the receptors among cellular compartments
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
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Stimulation of EGFR signaling pathway by different ligands
Comparison of the results when the EGFR
signaling pathway is stimulated with its ligands
EGF (red) and TGF- (green).
(a ) Total number of receptors in the cell as a
function of time after 20 nM ligand is added to the
system. Red diamond (EGF) and green square
(TGF-) points show the experimental results.
(b) Distribution of the receptors between
intravesicular compartments and the cell
membrane.
(c) Distribution of the phosphorylated receptors
between intravesicular compartments and the cell
membrane. In the figures, y axes represent the
number of receptors in thousands.
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
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Ratio of internal/surface receptors
The ratio of the In/Sur ratios when
the EGFR signaling pathway is
stimulated with its ligands EGF and
TGF- at 20 nM ligand
concentration.
Comparison of computational (solid
lines) and experimental (points)
results.
Ratio of the ratios for the
phosphorylated (i.e., activated)
(blue), and total (phosphorylated +
unphosphorylated) number
(magenta) of receptors.
Resat et al. Biophys Journal 85, 730 (2003)
23. Lecture WS 2005/06
Bioinformatics III 38
SummaryLarge-scale simulations of the kinetics of biological signaling networks are
becoming feasible.
Here, the model consisted of hundreds of distinct compartments and ca. 13.000
reactions/events that occur on a wide spatial-temporal range.
The exact Dynamic Monte Carlo algorithm of Gillespie (1976/1977) was a
breakthrough for simulations of stochastic systems.
Problem: simulations can become very time-consuming. In particular if the
processes occur on different time scales.
Methods like the probability-weighted DMC are promising tools for studying
complex cellular systems using molecular quanta.
Many other variants of DMC have and are being development.