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
Top Related