Modeling neural patterning and exploring the gene networks in developing zebrafish embryos

Presented byCharu GaurCBS program, Dec 2004Arizona State University

Intern Advisor

Dr. Ajay ChitnisVertebrate Neural Development UnitLaboratory of Molecular Genetics, NICHDNational Institute of HealthBethesda, MD

Internship Details

Skills Acquired

• Understanding of mathematical models for modeling biological processes

• Learning about genetic networks and biochemical process in neurogenesis

• Applications programming for simulating and visualizing models

An interdisciplinary exposure involving mathematics, molecular biology and computational disciplines

Purpose of the Study

• formulate mathematical models that describe essential steps in neural development

•Use computer simulations to see if the models describe phenomena as observed experimentally

Model organism for study - Zebrafish: transparent embryos, easy to breed , short development time, genome sequenced

Methodology – understanding neurogenesis in embryos; integrated interdisciplinary approach : Genetics, Molecular Biology, Cell Biology and Computational disciplines

Focus of study - understand how neurons are made in the correct number and location in the developing nervous system.

Chitnis Lab, NICHD

Background Study

• Learning Analysis Methods

• Learning Analysis tools

• Learning Terminologies

Learning Terminologies

Neurogenesis

process of formation of neurons and nervous system

starts at early gastrulation involves dynamic process of neural induction and nerulation ( neural patterning and cell differentiation)

Morphogen

substances that are capable of organizing distinct territories into different tissue types

Gene Activity under morphogen gradient

Gene Activity under zero morphogen level

morphogen

removed

Learning Terminologies (ii)

Isthmic Organizer (IsO)

midbrain hindbrain boundary

controls growth and patterning across entire MH domain

Xiro1 gene important for IsO formation [Galvic et al (2002) ]

We model the Xiro1 gene network A model for the induction and positioning of the isthmus organizer

Source: Glavic et al. (2002)

Organizer 1: Dorso Ventral patterning

Organizer 2: Anterior Posterior patterning

Organizing centers

Involved in orientation and differentiation

ring-like organizer for AP patterning

spot like organizer for dorso-ventral patterning

Background Study

• Learning Terminologies

• Learning Analysis Methods

• Learning Analysis tools

Learning Analysis Methods

• Local Self enhancement and long range inhibition

• Autocatalysis and lateral inhibition

Mathematical modeling of genetic of processes in neural development

Ideas from Meinhardt models

Learning Analysis Methods (ii)

Local self enhancement and long range inhibition

aDarbash

aS

t

aaaa

a

2

2

2

)())1(

( ∇+×−×+

=∂∂

hDhrbSat

hhhh

22 )( ∇+×−+=∂∂

Equation describing model:

a-activator ; h- inhibitoraDa

2∇ Represents the diffusion term

– Basic mechanism in biological patterning

– Generation of pattern in homogeneous system

– Modeling organizer region, regeneration

S- source density,

r- removal rate

b- basic production rate

D- Diffusion rate

A-activator: autocatalytic effect, positive effect on inhibitor production & slow diffusion rate

I- inhibitor: negative effect on activator & fast diffusion

Learning Analysis Methods (iii)

– Gene expression in discreet domains under influence of morphogen gradient

– Positive auto regulatory feedback of gene on its activation

– Modeling somatogenesis, neural patterning

Source: Chitnis AB, Itoh M. (2004).

Gene activation of alternative genesActivation of 4 genes in a mutually exclusives manner : effect of morphogen gradient

Autocatalysis and lateral inhibition

Background Study

• Learning Terminologies

• Learning Analysis Methods

• Learning Analysis tools

Learning Analysis Tools

– NetLogo

– CompuCell

– NetBuilder

Modeling tools

– simulate and visualize the models

– helps in understand the dynamics and behavior of the system

Modeling Applications

NetLogo

• Multi-agent modeling environment

• Developed by a team led by Uri Wilensky[2002]

• Cross-platform • Easy to use, logic baed

programming• Well documented- tutorials

and examples

uses a set of agents to visualize complex systems, their interactions and emergent properties as a result of these interactions

A general setup in NetLogo environment

CompuCell

Multi-model software framework for modeling and simulation of the morphogenesis process

Developed by Izaguirre et.al (2004

Modeling environment based on theory of:

a) cellular automaton with stochastic local rules

    b) system of differential equations, that includes reaction-diffusion equations, describing the diffusible morphogen

Theory fits in our schema of modeling

NetBuilder

Tool to model gene regulatory network (GRN) ; a signaling network of on/off switches operating at genetic level controlling activity of gene

Developed by the bioinformatics group at University of Hertfordshire, Hatfield, UK

Model’s GRN as a system consisting of components that send, receive and respond to signals.

Signals are transformed at network nodes and transferred between nodes through links.

General' gene represented in NetBuilder

The green and the red rounds present input and output ports respectively

Internship project tasks

Experiment Procedures and Flow

Data Collection

Experimental Hypotheses

Analysis Methods Employed

Initial Data Visualization and Analysis

Project Implementation

Phase I : Modifying Existing models

Phase II: Creating New Models

Phase III: Showcasing the models – website development

Phase I: Modifying existing models

Converting old models in StarLogoT to NetLogo

- used NetLogo version 1.3

Simulating the models with new set of parameters

Updating the models with new functions if needed

Modifying existing model

Four Gene Model

Based on theory of self-activation and lateral inhibition Provides a basic understanding of the concepts of morphogen gradient

differential spatial expression of gene under Morphogen modeling process as a system of differential equations

Studying effect of Morphogen of the gene expression domains

baselinexedgescreenxcorpxedgescreen

baselinesourcemorphogen ++×−= )___()

__(

set up morphogen gradient as linear graded, non-moving gradient

Equation set up in NetLogo environment

source:maximum morphogen level ; baseline : lowest morphogen level

shallow gradient normal morphogen gradient

increase morphogen level after pattern stabilization

Results of simulation with NetLogo

source=4.6

baseline =0source=4.6

baseline =1.5

source= 8.0

baseline =0

Four Gene Model – Studying effect of morphogen gradient

Phase II: Creating New models

Task 1: Modeling formation of Isthmic Organizer - Xiro1_model

Xenopous Iro gene, Xiro1 plays an important role [ Galvic et al(2002)]

Model gene network involved in the nerula stage : simplified model

Gene network at nerula stage

Task 2: Modeling formation of organizer in morphogenesis

The Xiro1 system is represented by the following equations:

 

AfdecayAgeneAgeneDsDgeneCsCgeneBsBgeneAsA

morphogenmAgeneAsA

t

geneA =×−×+×+×+×

×+×=2222

2

δδ

BfdecayBgeneBgeneDsDgeneCsCgeneBsBgeneAsA

geneXmorphogenmBgeneBsB

t

geneB =×−×+×+×+×

××+×=2222

2

δδ

CfdecayCgeneCgeneDsDgeneCsCgeneBsBgeneAsA

geneBmorphogenmCgeneCsC

t

geneC =×−×+×+×+×

××+×=

2222

2

δδ

DfdecayDgeneDgeneDsDgeneCsCgeneBsBgeneAsA

geneBgeneAgeneDsD

t

geneD =×−×+×+×+×

×+×=

2222

2

δδ

XfdecayXgeneXgeneXsXgeneCsCgeneBsBgeneAsA

geneAmorphogenmXgeneXsX

t

geneX =×−×+×+×+×

××+×=

2222

2

δδ

Otx2 (geneA)

Caudal (geneC)

fgf8 (geneD)

Xiro1 (geneX)

Gbx2 (geneB)

The variables geneA, geneB, geneC, geneD and geneX represent the concentration (or the expression levels) sA, sB, sC, sD, sX the production rates, mA, mB, mC, mD and mX the responsiveness to the morphogen constants, and decayA, decayB, decayC, decayD and decayX the decay rates for the 5 genes involved.

Morphogen gradient is modeled as shown earlier for four gene model

Xiro1_model

Xiro1 Model – Studying effect of morphogen gradient

Parameter

Gene

A Otx2

BGbx2

Ccaudal

Dfgf 8

XXiro1

Production Rate (s) 1.1 2.1 2.7 1.7 2

Decay Rate (decay) 0.1 0.1 0.1 0.1 0.1

Importance of Morphogen (m)

2.6 1.95 1.25 1.55 2

Max. Morphogen (source)

7

Morphogen baseline 0

result of the NetLogo mathematical model is in sync with the experimental based model

Values used for simulation

Xiro1 Model – Simulating the model

Case 1: Xiro1 is switched off

Case 2:Over expression of Xiro1

over expression of Xiro1 at later stage displace the midbrain-hindbrain (MHB) boundary anteriorly

Experimental observationModeling Result

no expression of fgf8 (geneD) and very low expression of Gbx8 (geneB).

Xiro1 acts as an on/off switch for stimulating fgf8 production

Modeling Result Experimental observation

Phase II: Creating New Model (Task 2) – studying the formation of Organizing centers in zebrafish embryos

No success achieved in modeling or simulating a complete model for organizer formation in the above selected tools

Modeling of the development of organizer centers was done using :

NetBuilder

Compucell

NetLogo

Modeling Organizer formation (ii)

NetBuilder a failure

• can only models gene regulation at genetic level

• not user friendly, not well documented with examples

• tedious to set up a genetic network

CompuCell a failure

• Complicated installation procedure coupled with bugs in the Windows version

• No proper manuals, documentation for making new models

Limitations in NetLogo

• Defining the boundary condition

• Formulating Diffusion in a limited boundary condition

boundary and diffusion limitation in NetLogo

Phase III: Presenting the learning

Conceptualizing Web development

Website : an effective and efficient platform to get interaction of researchers worldwide and information sharing with a wide range of audiences

Content pages:General pages- Home page, What we do , Project List, Publications, Contact us

Showcasing the models on web as applet : built-in NetLogo feature to convert models to applets

Website Development

Computer programming - HTML, DHTML, JavaScript, style sheets

Software used-

Microsoft FrontPage, Dreamweaver, Photoshop,NetLogo 2.0.2

Conclusions

• Biological process modeling is useful– models can help in unveiling of some emergent

properties that may not be observed on experimental desk

• NetLogo an effective modeling environment– The models developed where found, by computer

simulation, to be able to account in a quantitative way for some initially chosen basic experimental observations

Future work

Modifying Xiro 1 modelModel from gastrula to neural stage

Remodeling Organizer formation modelReworking model in NetLogo

Modeling with new version of CompuCell

• Making fully functional website– Completing the content pages, uploading the site, adding

interactive feedback forms and database support if possible

References

1. Glavic A, Gomez-Skarmeta JL, Mayor R. (2002). The homeoprotein Xiro1 is required for midbrain-hindbrain boundary formation. Development. 2002 Apr; 129(7): 1609-21

2. Meinhardt H. Organizer and axes formation as a self-organizing process. Int J Dev Biol. 2001; 45(1): 177-88

3. Meinhardt, Hans. Models of Biological Pattern formation. (1982) Academic Press, london

4. Chitnis AB, Itoh M. (2004). Exploring alternative models of rostral–caudal patterning in the zebrafish neurectoderm with computer simulations. Curr Opin Genet Dev.2004 Aug; 14 (4): 415-21.

5. Izaguirre JA, Chaturvedi R, Huang C, Cickovski T, Coffland J, Thomas G, Forgacs G, Alber M, Hentschel G, Newman SA, Glazier JA. CompuCell, a multi-model framework for simulation of morphogenesis. Bioinformatics. 2004 May 1; 20(7): 1129-37. Epub 2004 Feb 05.

6. Wilensky, U. Modeling Nature' s Emergent Patterns with Multi-agent Languages. Proceedings of EuroLogo 2002. Linz, Austria.

Any Questions?

Thank you