Simulating Gene Expression Patterns During Zebrafish Embryo...
Transcript of Simulating Gene Expression Patterns During Zebrafish Embryo...
Simulating Gene Expression Patterns During Zebrafish
Embryo DevelopmentEi-Ei Gaw
Ajay B. ChitnisNational Institute of Health (NIH)
National Institute of Child Health and Human Development (NICHD)Laboratory of Molecular Genetics
Unit on Vertebrate Neural Development
June 2003 - August 2003
Projects
• Simulations1. Neurogenesis2. Somitogenesis3. Morphogenesis during A/P Patterning
• Model organism: Zebrafish
• Program simulations in StarLogoT/NetLogo
Why Zebrafish (Danio rerio)?
• Zebrafish are vertebrates• Inexpensive and easy to maintain and breed• Experimentally accessible• Easy to manipulate the genetics and the
embryos• Transparent during early development• Large community of resources (Zfin)
StarLogo/NetLogo
• Based on LOGO programming enviornment– Daniel Bobrow and Wallace Feurzeig at Bolt, Beranek and Newman, Inc.,
and Seymour Papert, at the MIT in the 1960's.
• StarLogo: 1989 - 90 (MIT Media Lab)• MacStarLogo: 1994• StarLogoT: 1997 (Center for connected Learning
and Computer-Based Modeling, Uri Wilensky)• StarLogo in Java: 1999 • NetLogo (StarLogoT in Java): 2002
What is StarLogo/NetLogo?
• Programmable modeling environment for exploring emergent phenomena.
• Logo language support agents: turtles, patches, and the observer.
• Simulate Parallelism on a one-processor computer.
Neurogenesis
• In early development, the neural plate consists of domains which give rise to primary neurons.
• Cells’ fate is determined by the expression of neuralgenin1 (ngn1).
• ngn1 is modulated by lateral inhibition through Delta/Notch signaling cascade.
Proneuro Domains
motor neurons
sensory neurons
interneurons
Spinal cordhindbrain
Lateral InhibitionDelta/Notch Signaling
huC
Injected with DeltaA RNANormal
delta
ngn1
huC
delta
ngn1
huC
her4 her4
Delta MO injected
ngn1ngn1 her4
Notch
her4
Notch
Delta
Delta
ngn1
ngn1
Notch
Notch
her4
her4
delta
delta
Autocatalytic/Lateral Model
• Self-enhancement and long-range inhibition leads to spatially-patterned differentiation (Meinhardt and Gierer, 1974)
bbb bxb
Dbrsatb +
∂∂+−=
∂∂
2
22
( )( ) 2
2
2
2
11 xa
DaraSb
as
ta
aaaa ∂
∂+−���
����
�
++=
∂∂
Neurogenesis Model
( )( )
.
and , 1
, 11
_
2
2
herherdeltotnotchherher
deldeldeldel
ngndel
del
ngnngnngnngnher
ngnngn
ngn
ARACPt
A
ARAS
AP
tA
ARASA
AP
t
A
−=∂
∂
−���
����
�
+=
∂∂
−��
�
�
��
�
�
++=
∂∂
ngn – neurogenin del – delta her – hairytot_del – total delta in neighboring cells
NetLogo Model
• Setup proneuro domains.
• Set Angn[0] and calculate Adel[0] and Aher[0]. Add Type 1 noise.
• Update Angn[t], Adel[t], and Aher[t] using Euler’s method with step size of 1. Add Type 2 noise.
• If Angn > threshold, the patch is fated to become neuron.
Neurogenesis Model Parameters
4Threshold
None0.300.06Rate of Saturation or Self-Inhibition (S)
0.900.910.20Rate of Degradation (R)
0.259.20.5Rate of synthesis (P)
herdeltangn
GeneParameter
Importance of Notch Signaling
Cnotch
0.025 0.05 0.075 0.3
1171(100%)
2(< 1%)
785(67%)
568(49%)
Number of Neurons
Initial Condition
0.52 0.53 0.63
Pngn[0]
Number of Neurons
208 430 685
Noise
No Noise Type 1 Noisevar = 0.04
Type 2 Noisevar = 0.04
Number of Neurons
536 532 539
Somitogenesis
• Somites are formed from the presomiticmesoderm (PSM)
• Segments are formed head to tail in periodic succession
• her1/her7 oscillate and regulated by Notch pathway
Zebrafishher1/7
Translation delay
Translation delay
delta
Transcription delay
Transcription delay
her1/7
Translation delay
Translation delay
Transcription delay
delta
Transcription delay
Lewis Model Two-cell her1/her7 Oscillator
[ ] [ ]
[ ] [ ]
[ ] [ ]
77777
11111
7
1
tdeldelTtdeldeldel
therherTtherherher
therherTtherherher
pbmadt
dp
pbmadt
dp
pbmadt
dp
pdel
pher
pher
−=
−=
−=
−
−
−
Lewis Model Two-cell her1/her7 Oscillator
( )[ ] [ ]
( )[ ] [ ]
( )[ ] [ ] ,,
,,
,,
_71
77_7177
11_7111
7
1
tdeldelTtdelnherherdeldel
therherTtdelnherherherher
therherTtdelnherherherher
mcpppfdt
dm
mcpppfdt
dm
mcpppfdt
dm
mdel
mher
mher
−=
−=
−=
−
−
−
Lewis Model Two-cell her1/her7 Oscillator
( ) ( )
( ) ( )
( ) ( ) 1
111
11
1
111
11
1
111
11
71_
_
71_
_0
71_
_
71_
_077
71_
_
71_
_011
��
�
�
��
�
�
+++
++
++=
��
�
�
��
�
�
+++
++
++=
��
�
�
��
�
�
+++
++
++=
herherdeln
delnhd
herherh
deln
delnddeldel
herherdeln
delnhd
herherh
deln
delndherher
herherdeln
delnhd
herherh
deln
delndherher
sssskf
rrrrkf
rrrrkf
φφφφ
φφφφ
φφφφ
φφφφ
φφφφ
φφφφ
Somitogenisis Simulation• Initial setup
1. mRNA gradients for her1 and her7 (noise can be added)2. Fgf gradient
• Update p and m for her1, her7, and delta using Euler’s method with step size of 1.
• Fgf gradient moves and the domain is extended w/ time.
• Oscillation ceases when Fgf is below critical point
Somitogenisis Simulation
her1/7 mRNA (Initial gradient)
Fgf Gradientmoving
Domain extended
Somitogenesis Simulation Parameters
200Threshold
1000405Critical protein level (Pcrit)
623Translation delay (Tp)
0.230.230.23Rate of mRNA gradation (c)
33333Rate of mRNA synthesis (k)
26610Transcription delay (Tm)
0.230.230.23Rate of protein degradation (b)
4.554.5Rate of protein synthesis (a)
deltaher7her1
GeneParameter
Synchronization & Oscillating Pattern
0.99
0.97
0.70
rhd =
Zebrafish A/P Patterning
• Rostral-caudal axis of the developing vertebrate nervous system differentially express genes.
• Morphogen, such as Wnt plays a critical role.
Anterior Posterior Patterningwt
hindbrainmidbrain
forebrain
MHB
gbx1
pax2.1
pax6
Headless Mutants
wthindbrain
midbrain
forebrain
MHBhdl
Repressor tcf3
Fz
(off)
GSKAxin
APC
dsh
(on)
β-catenin
Wnt target genestcf3
groucho
P P
proteosome
Wnt Target Genes Activated
Wnt
P
Fz
(on)
GSKAxin
APC
dsh
(off)
β-catenin
Wnt target genesTCF
groucho
Fz
(on)
GSKAxin
APC
dsh
(off)
β-catenin
Wnt target genestcf3
groucho
Neural Patterning and Morphogen Gradient
0 30position
1.5
0
morphogen
0 30position
1.5
0
morphogen
0 30position
1.5
0
morphogen
Meinhardt Model:Spatial Sequences/Morphogen Gradient
morphogen
Gene A Gene B Gene C Gene D
1
)(
1)(
1)(
1)(
2222
2
2222
2
2222
2
2222
2
dddcba
cdtddd
ccdcba
bctccc
bbdcba
abtbbb
aadcba
ataaa
GRGGGGGMMGS
dtdG
GRGGGGGMMGS
dtdG
GRGGGGGMMGS
dtdG
GRGGGG
MMGSdt
dG
−++++
+=
−++++
+=
−++++
+=
−++++
+=
Morphogensis Simulation
• Two regions:– Morphogen gradient– Time exposure to morphogen.
• Numerical method: Euler’s method with step size of 1.
Morphogenesis Simulation Parameters
0.40-C2
0.95-Decay Rate (D)
0.010.01C1
1.001.00Max Morphgen (Mmax)
Region 2Region 1Morphogen
4.53.251.750.50Importance of morphogen (M)
0.100.100.100.10Rate gradation (R)
1.71.81.92.0Rate synthesis (S)
DCBA
Sa > Sb > Sc > Sd and Ma < Mb < Mc < MdParameter
1.00-
0.30-
0.010.01
1.001.00
Region 2Region 1
1.401.301.201.10
0.100.100.100.10
6.74.42.81.8
DCBA
Sa < Sb < Sc < Sd and
Ma > Mb > Mc > Md
Morphogenesis Simulation
• Spatial differential expression1. Sa > Sb > Sc > Sd and Ma < Mb < Mc < Md
2. Sa < Sb < Sc < Sd and Ma > Mb > Mc > Md
• Similar patterns can be obtained from gradient and time-exposure.
Expression of Different Region
Spatial vs Time
Stable-Morphogen Conc Morphogen Time-Exposure
Spatial vs Time
Stable-Morphogen Conc Morphogen Time-Exposure
Future Work
• Study to see how much of the patterning is due to bias in the numerical approach.
– Runge-Kutta method
• Add more aspects to the model– Morphogensis: add antogonist, tcf3
Many Thanks!
Ajay ChitnisMoloy GoswamiMotoyuki ItohMichael KellerGregory PalardySang Yeob YeoDarcy Hampton