illia horenko wilhelm huisinga & einführungsvortrag zum seminar modellierung dynamischer...
Post on 22-Dec-2015
214 views
TRANSCRIPT
Illia HorenkoWilhelm Huisinga &
Einführungsvortrag zum Seminar
Modellierung dynamischer Prozesse in der Zellbiologie
Freie Universität Berlin, 17. April 2003
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eBiological processes
signal pathways, metabolism, cell cycle,
membrane transport and pumps, excitability of ion channels
intercellular communication, pheromone response
A few examples:reference for graphics below
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eCommon modelling strategies
detailed description: (1) positional information of every molecule (2) interaction with others molecules
only suitable for (very) small subsystems
most common simplifying assumptions: (1’) well-stired mixture=spatial homogeneity (2’) reaction rates & law of mass action or reaction probabilities & combinatorics
representation of species according to (1’) by (a) concentrations deterministic differential equations (ODEs) (b) number of molecules stochastic simulation algorithm (Markov process)
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eExample
Conversion of substrate to product catalysed by enzymes:
PEES
ESSE
k
k
k
3
1
2
][]][[][ 21 ESkSEkSt
deterministic stochastic
state: concentration [X](t) of species X at time t
state: number of molecules X(t) (random variable) of species S at time t
])([ nextnext ,ttX|τn, TR P
equation of motion: ODE equation of motion: Markov Process
…
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
e Efficient Modelling of heterogeneity
compartment models (partially heterogeneous): (1) well-stirred within compartment (ODE,MP) & (2) interaction between compartment (consistent coupling)
reaction-diffusion models (fully heterogeneous) (a) concentration in time and space (deterministic PDE) or (b) 3d-molecular positions (random walk and reaction probabilities)
photo: http://genome-www.stanford.edu/Saccharomyces/yeast_images.shtml
Note: the more complex the model, the more parameters it needs!
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eFor example yeast
Saccharomyces cerevisiae
photo: http://genome-www.stanford.edu/Saccharomyces/yeast_images.shtml
„Yeast have many genes with homologs in humans. Has our understanding of these genes helped our understanding of human biology or disease? In his Perspective, Botstein argues "yes„ […]“
Botstein, Chervitz&Cherry, GENETICS: Yeast as a Model Organism
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eSaccharomyces cerevisiae
photo: http://genome-www.stanford.edu/Saccharomyces/yeast_images.shtml
“MAP (Mitogen Activated protein) kinase pathways play key roles in cellular response towards extracellular signals.” van Drogen & Peter Biology of the Cell 93 (2001)
http://mips.gsf.de/proj/yeast/CYGD/db/index.html
model of the MAPK signalling pathways of yeast:
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eSaccharomyces cerevisiae
photo: http://genome-www.stanford.edu/Saccharomyces/yeast_images.shtml
Question: how does yeast adapt to different osmotic conditions?
signalling pathway based on osmosensors
“Yeast cells in their natural habitats must adapt to extremes of osmoticconditions such as the saturating sugar of drying fruits and the nearlypure water of rain” (Posas et al., Cell 86, 1996)
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eyeast’s two osmosensors
de Nadal, Alepus & Posas, EMBO reports 3 (2002)
“Our current knowledge confirms that many principles of osmoadaptationare conserved across eukaryotes, and therefore the use of yeast as basicmodel system has been of great value elucidating the signal transduction mechanisms underlying the response to high osmolarity.”
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
e
)(1 tk
t
1-
0 500-
osmotic shock
Phosphorelay module
Sln1
Ypd1P Ypd1
Ssk1 Ssk1P
Sln1AP
Sln1HP)(11 tkk 22 k
503 k
504 k
3.05 k
M1.0 Sln1APSln1HPSln1 M1.0 Ypd1PYpd1 M1.0 Ssk1PSsk1
l14105.6 volumecell Molecules) 3915M1.0(
in cooperation with Edda Klipp&group
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
e
)(1 tk
t
1-
0 500-
osmotic shock
stochastic Markov process model
Sln1
Ypd1P Ypd1
Ssk1 Ssk1P
Sln1AP
Sln1HP)(11 tkk 22 k
503 k
504 k
3.05 k
in cooperation with Edda Klipp&group
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
e
)(1 tk
t
1-
0 500-
osmotic shock
deterministic ODE model
Sln1
Ypd1P Ypd1
Ssk1 Ssk1P
Sln1AP
Sln1HP)(11 tkk 22 k
503 k
504 k
3.05 k
in cooperation with Edda Klipp&group
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eComparison of results
sto
cha
stic
Mar
kov
Pro
cess
mod
el
det
erm
inis
tic O
DE
mo
del
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
e
),(),(),()(),( tRctRcktRcR
RDR
tRct i
llliiii
Species i is described through concentration and diffusionconstant
Modelling heterogeneity (PDE)
),( tRci
)(RDi
11
11 ),(),(),(
jj
jijijiR RR
tRctRctRc
1.Spatial discretisation 2.Time discretisation
System of ODEs for concentrationsat grid points
Finite differences:
When is large than homogenous modelling is sufficient!
Method of lines
)(RDi
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eModelling heterogeneity (PDE)
Sln1, Sln1AP, Sln1HP are fixed on the membraneYpd1, Ypd1P, Ssk1, Ssk1P diffuse freely in the cytoplasm
minor influence of heterogeneity due to fast diffusion
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eComparison of results
det
erm
inis
tic O
DE
mo
del
det
erm
inis
tic P
DE
mo
del
Mat
h. M
odel
lieru
ng in
der
Zel
lbio
logi
eConclusion
What are the benefits of computational biology?
What are the conclusions to draw?
What are the problems encountered?