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)

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Neurogenesis Model

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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

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therherTtherherher

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Lewis Model Two-cell her1/her7 Oscillator

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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

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2

2222

2

2222

2

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dddcba

cdtddd

ccdcba

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ataaa

GRGGGGGMMGS

dtdG

GRGGGGGMMGS

dtdG

GRGGGGGMMGS

dtdG

GRGGGG

MMGSdt

dG

−++++

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−++++

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−++++

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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