Sven Bergmann Department of Medical Genetics – UNIL & Swiss Institute of Bioinformatics
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MSc GBE Course: Genes: from sequence to function
Brief Introduction to Systems Biology
Sven BergmannDepartment of Medical Genetics
University of LausanneRue de Bugnon 27 - DGM 328
CH-1005 Lausanne Switzerland
work: ++41-21-692-5452cell: ++41-78-663-4980
http://serverdgm.unil.ch/bergmann
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Pre-Steady-State Decoding of the Bicoid Morphogen Gradient
Sven BergmannDepartment of Medical Genetics – UNIL
&Swiss Institute of Bioinformatics
Modeling Crash course
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PLoS Biology 5(2) e46, 2007
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Drosophila as model for Development
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Development is a precise process
Normal Conditions
Environmental Changes
(Some )Genetic Changes
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How to ensure buffering when patterning proceeds rapidly?
Genetic buffering mechanisms are hard to establish in fast development!
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The Life Cycle of Drosophila
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Drosophila development
• Maternal bicoid mRNA is localized at anterior pole • Diffusion of the bicoid protein establishes gradient
(defining anterior-posterior axis)• Cascade of gene regulation refines segments of
bodyplan (that will determine shape of adult fly)
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Syncytial Blastoderm Stage
Nuclei divide, but no intercellular membranes yet
Free diffusion of developmentally important factors between the nuclei of the syncytium!
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Morphogen Gradients are used for translating cellular position into cell-
fate
Cell fates are determined according to the concentration of the morphogen
C1
C2
C3
fate 1 fate 2 fate 3
Morphogen gradient
fate 4
source diffusion
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The maternal and zygotic segmentation genes form a
hierarchical network of sequential transcriptional regulation
Maternal genes:Bicoid (bcd)Caudal )cad(
Zygotic genes:Hunchback (hb)Giant (gt)Kruppel (Kr)Knirps )kni(…
hbgt
Kr
bcd
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What happens when perturbing the system?
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Changes in bicoid mRNA dosage lead to shifts in expression domain of
downstream genes:
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Quantitative Study using Automated Image
Processing
a: mark anterior and posterior pole, first and last eve-stripeb: extract region around dorsal midlinec: semi-automatic determination of stripes/boundaries
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Our Experimental Results:
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Shifts are small and position-dependent!
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A bit of Theory…
The morphogen density M)x,t( can be modeled by a differential equation )reaction diffusion equation(:
Change in concentration of the morphogenat position x, time t
SourceDegradationα: decay rate
DiffusionD: diffusion const.
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The Canonical Model
Steady state:
)no change in time(
0 1 2 3 4 50
0.2
0.4
0.6
0.8
1
x
exp
)-x(
Solution:
)/exp()( 0 xMxM
DD /
Length scale:
decay time x
M(x)
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In steady-state induced shifts are independent of
position:
Original gradient
Gradient for half production rate
EL%logx 122
)]x(M/)(Mlog[x 0
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What if the profile has not reached its steady state yet?
• Steady state assumption is ad-hoc
• Early patterning processes are very rapid
• Consistent with typical values for diffusion
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Modeling the morphogen (Bcd) by a time-dependent
PDE:
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Shifts induced by altered bcd
dosage:
steady-state vs transient profile
Decoding the transient profile :• Position-dependent shifts• Smaller shifts towards the posterior pole
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Model vs Data
Prediction: Bcd diffusion is relatively small!
sec/~D 2m1
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Pattern Fixation
hbgt
Kr
Can mutual suppression of gap genes fixate their
expression domains after initial pattern is established?
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Simulating the systemModel using partial differential equations:
Change in concentration of gene i=Bcd, Gt, Hb, … at position x, time t
DiffusionDi: diffusion const.
SourceDegradationαi: decay rate
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Source term encodes
gene-interactions
Hill-function:
y=
h)y( n>0
n<0
1
½
Start at time ti
Multiply suppressors: ANDSum over activators: OR
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Gradient evolution in time
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Simulations agreewith naïve model
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Buffering is lost when patterning occurs after Bcd
has reachedsteady state (tinit >> τ)!
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time
“Nail down” experiment
Bcd KniKr Gt
activatorrepressors
BcdKni
position
position
BcdKni
lacZ
time
Bcd Kni
activator
lacZKr Gt
repressors
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lacZ reporter indicates that Bcd has not reached steady state during
patterning
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Conclusion:
Systems approach to the gap-gene
network reveals that dynamic decoding
of pre-steady state morphogen gradient
is consistent with experimental data
from the anterior-posterior patterning in
early Drosophila embryos
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Acknowledgements
Collaboration with Profs. Naama Barkai & Benny Shilo, Weizmann Institute of Science
Sven Bergmann, Oded Sandler, Hila Sberro, Sara Shnider, Ben-Zion Shilo, Eyal Schejter and Naama Barkai
PLoS Biology 5)2(: e46
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Gregor et al., 2007