Segmenting the fly embryo: by means of non-linear dynamics or Boolean logic?

Joseph X. Zhou

Konrad Loetzsch

Presentations on lecture "Introduction to Mathematical Biology II", Jan. 29, 2008

Group advisor:

Group member:

Lutz Brusch

Pattern formation during embryonic development

• Central problem: 1D genetic information 3D complex structure

• Gradients pattern formation

• Intracellular signaling

Genetic network controlling segmentation in fly Drosophila

• Drosophila - easily cultured in mass in lab

- short generation time (7 – 60 days)

- easily genetically manipulated

• The genetic hierarchy controls segmentation in the fly Drosophila

Conventional physics Law

A B

Akdt

dBAB

It is to easy to guess the law in a simple system, such as:

Newton’s Gravity Law,

Coulomb's Law,

Schrodinger equation, etc.

When network plays a role

B

- “Bringing cartoons to life”, John J. Tyson, Nature, 445, 823

A

DC• It is harder to guess the law from a complex system.

• To bridge molecular biology to cell physiology, we need to build a network of interacting genes and proteins as a dynamic system .

A dynamical model of the segment polarity gene network

• The segment polarity gene network is modeled by kinetic equations

• It needs 50 free parameters, mRNA, proteins, rates & coop coef.

• Ask two questions:- How to build the network more systematically and quickly?- How to share these models more efficiently?

Pathways Database Network models

World-wide Pathways Database 1

Extract a sub-model

World-wide Pathways Database n

… … Integrate them to Network model

Coupled ODEs

Stochastic Model

Boolean Dynamics

SBML CellML

• Identify the nodes of the network

- ask experts, or go to websites: GO, KEGG, GenMAPP, PID

• Start qualitative network, identify sub-circle that

involve the process

• Build a network model involving markers and

interactions

• Build a kinetic model with parameters available

Build a Gene network modelfor early wing development of Drosophila

Build a Gene network modelfor early wing development of Drosophila

Build a Gene network modelfor early wing development of Drosophila

• By fixing the values of the nodes in the

network, simulate mutations

• Verified by phenotype observed in Exp.

• Study the robustness of gene network

Conclusion

• Network model is a powerful mathematical tool

to model interacting genes and proteins as a

dynamic complex system

• A network model can be built from WWW

pathways databases quickly

• SBML, CellML etc. make it more efficient to build

and share network models