Transcript Document

Modeling the mammalian circadian clock –
intracellular feedback loops and
synchronization of neurons
Hanspeter Herzel
Institute for Theoretical Biology
Humboldt University Berlin
together with
Sabine Becker-Weimann, Samuel Bernard, Pal Westermark (ITB),
Florian Geier (Freiburg), Didier Gonze (Brussels), Achim Kramer
(Exp. Chronobiology, Charite), Hitoshi Okamura (Kobe)
Outlook of the talk
1. The system, experimental data
2. Modeling intracellular feedbacks, bifurcation diagram and
double mutant
3. Entrainment by light for varying photoperiod
4. Synchronization of 10000 cells in silico – an ensemble of
driven damped oscillators
5. Single cell data – periods, phases, gradients, noise
Light synchronizes
the clock
SCN-neuron
nucleus
Positive
elements
The system
activation
Clock genes
(e.g. Period2)
inhibition
Regulation of
physiology and behavior
Negative
elements
Synchronization of
peripheral clocks
The circadian oscillator
Circadian rhythm
Oscillations
Oster et al., 2002
Reppert and Weaver, 2001
Feedback loops
experiments
Fibroblasts as experimental model
of the circadianen oscillator
genetic perturbations:
RNA interference
pharmakological perturbations:
Inhibitores
solvent
CKIe inhibitor
control
anti-Cry1
2000
Relative Amplitude
Luminescence [units]
2500
1500
1000
500
0
24
48
time [hrs]
72
96
time [hrs]
Simplified model of the
circadian core oscillator
S. Becker-Weimann, J. Wolf, H. Herzel,
A. Kramer: Biophys. J. 87, 3023-34 (2004)
Comparison with experimental observations
Wildtype: simulations reproduce period, amplitudes, phase
relations
Per2 mutant (less positive feedback): arythmic
Per2/Cry2 double knock-out: rescue of oscillations
Synchronization of circadian clocks to light input
Entrainment zone for different
periods and coupling
Phase-locking of internal variables
(mRNA peak) to sunset for
night-active animals
Problem: How can the internal clock follow changes of the photoperiod?
Simulation & PRC: Small free running period & gating allows to track light offset
F. Geier, S. Becker-Weimann, A. Kramer, H.Herzel: J. Biol. Rhythms, 20, 83-93 (2005)
the system
SCN-Neuron
nucleus
3.ventricle
Positive
Elements
Activation
clock-genes
(e.g.. Period2)
Inhibition
Hypothalamus
Suprachiasmatischer
Nukleus
3. Ventrikel
Negative
Elements
Oscillation
Optisches Chiasma
optical chiasm
Synchronisation
The real challenge: How to synchronize a network of
20000 heterogeneous limit cycle oscillators within a few
cycles?
Suprachiasmatic nucleus
 Located in the hypothalamus
 Contains about 10000 neurons
 Circadian pacemaker
 Two regions:
- Ventro-lateral (VL): VIP, light-sensitive
- Dorso-medial (DM): AVP
Organotypic SCN slices: periods of
synchronized and desynchronized cells
unpublished data from Hitoshi Okamura (Kobe) analyzed by Pal Westermark
mPer1-luc bioluminescence in single
SCN cells
Experimental findings:
- Synchronization is achieved within a few cycles
- Phase relations are re-established after transient desynchronization
- Driven DM region is phase leading
Model for the coupling in the SCN
Ventro-lateral part
(core)
Light
entrains
Self-sustained
oscillations
(synchronized
oscillations)
Dorso-medial part
(shell)
VL
drives
Damped oscillations
(unsynchronized
oscillations)
No/weak coupling
Coupling conveyed
by VIP, GABA
Phase leading (4h)
Receives light input
from the retina
Receives signal
from the VL part
Single cell model
Coupling through the mean field
Neurotransmitter
Mean field
Coupling through the mean field
Light
+ L(t)
L=0 in dark phase; L>0 in light phase
Order parameter
Coupling two cells through the mean field
Coupling two cells through the mean field
Coupling two cells through the mean field
Synchronization requires delicate balance of coupling and period ratio
Coupling through the mean field
D. Gonze, S. Bernard, C. Waltermann, A. Kramer, H. Herzel: Biophys. J., 89, 120-129 (2005)
Transient
uncoupling
Note:
Neurotransmitter level F has
positive mean & oscillatory
component
single cell + constant mean field
Coupling through the mean field
fast oscillators
are advanced
slow oscillators
are delayed
The phases of the oscillators in the coupled state are
uniquely determined by their autonomous periods
How circadian oscillators can be
synchronized quickly:
●
●
●
The average value of the coupling agent
dampens the individual oscillators
The oscillating part of the mean field drives
the „damped oscillators“
Predictions: Internal periods determine the
phase relations and damping ratio is related
to fast synchronizability
Interaction
between two
populations
VL region
DM region
Prediction from our model:
DM region can be phase leading
if its period is shorter
Experimental single cell data from Hitoshi Okamura (Kobe)
Gradients of phases and periods within the SCN
data from Hitoshi Okamura, analyses by Pal Westermark
Comparison of synchronized and desynchronized cells
Desynchronized cells exhibit:
synchr.
-variable amplitudes and phases
-higher noise level
-ultradian periodicities
desynchr.
red: desynchronized cells
Summary and discussion
●
mathematical models can describe intracellular clock
based on transcriptional/translational feedback loops
open problems: parameter estimations, origin of 6 h
delay, which nonlinearities essential?
●
possible synchronization mechanism: dampening of selfsustained single cell oscillations & forcing by periodic
mean field
open problems: alternative scenarios (specific PRCs
allowing quick and robust synchronization), coupling
mechanisms (neurotransmitters versus synapses versus
gap junctions)
●
single cell data provide informations about gradients of
phases and periods, noise, and ultradian rhythms
Modeling Signaling Cascades
and Gene Regulation
Nils Blüthgen, Szymon Kielbasa, Branka Cajavec, Maciej
Swat, Sabine Becker-Weimann, Christian Waltermann,
Didier Gonze, Samuel Bernard, Hanspeter Herzel
Institute for Theoretical Biology, Humboldt-Universität Berlin
Major collaborators:
Christine Sers, Reinhold Schäfer, Achim Kramer,
Erich Wanker Charite Berlin, MDC
Support:
BMBF Networks: Proteomics & Systems Biology, SFB Theoretical Biology
(A3, A4, A5), Stifterverband, GK Dynamics and Evolution, EU Biosimulation
Data
generation
Circadian oscillation of fibroblasts
can be monitored in living cells
3000
Per1 E-box_luc
Bmal1_luc
Synchronize cells by inducing
growth arrest
Induce circadian oscillation by
serum shock or forskolin
Luminescence [units]
Transfect NIH3T3 fibroblasts
with reporter construct
n=1
2000
1000
Culture cells with luciferase substrate
Continuously measure luminescence
0
0
24
48
Time [hrs]
Experiments in Kramer Lab (Charite)
72
96
120
correlation coefficients: 0.95
significantly different periods
despite synchronization
advanced
delayed
slow and delayed cells
fast and
advanced cells