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3D Substitution Model for Limb Growth and Pattern
Formation
Ying Zhang1, Stuart A. Newman2, James A. Glazier1
1.Biocomplexity Institute, Department of Physics, Indiana University
2.New York Medical College
:Substitution model
Tetsuya Tabata, et al. Nature, 2001
Patterning a Developmental Field by Long-range Signalling
Mechanisms of pattern formation in development and evolution
Salazar-Ciudad I et al. Development 2003 I
Relation: Embryonic Development & Substitution Model
• Cellular autonomy Neighbor independent substitution system Example: cell growth, cell differentiation
• Cell signaling relay, cell-cell interaction model neighbor-dependent substitution model Example: cell-cell adhesion, cell sorting, cell migration, cell growth and death
• Positional information/Morphogenesis field theory Probability substitution model Example: FGF
Development of Limb Bud
Newman SA. et al. Science 1979 Gilbert et al 2003
FGFs & FGFRs
Xu X. et al. Cell Tissue Res. 1999
Hox Gene ExpressionNelson et al. Development 1996
Expansion of Cell Populations
Vargesson N. et al. Development, 1997
Niswander, L. et al. Nature Reviews 2003
FGF ---outgrowth of the limb bud
BMP--- Cartilage formation & Cell Death
SHH<->Gli3—Patterning
SHH->HOX—Patterning
Gene Regulatory Network
Gene & Function
51015
20
5 10 15 200
0.25
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51015
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5 10 15 200
0.25
0.5
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51015
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5 10 15 200
0.25
0.5
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0.75
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Growth Rule && Growth Probability Field
Division
Differentiation
Condensation
Growth Probability Field
2D Subsitution Model
Shubin et al. 1986
3D Substitution Simulation
With Physical Branching and Differentiation rule
Fate Mapping
Vargesson N. et al. Development, 1997
Multilevel Modeling
Tissue LevelTissue Geometry Tissue Pattern Formation
Cellular Level--MitosisCell Division with DifferentiationCell Division without DifferentiationCell DeathCell CondensationRest
C e l l M o tio nB ia s e d R a n d o m W a lkD i ffu s io n B ia s e d R a n d o m W a lkC e l l C e l l In te ra c tio n
E ffe c ts fro m th e M o le c u la r L e ve lC e l l G ro w th Pro b a b i l i tyC e l l D e a th Pro b a b i l i tyD i ffe re n tia t io n Pro b a b i l i ty (G e o m e tr ic a l Pa ra m e te r )B ra n c h in g
Morphogen Gradient Field
• Example:SHH-Gli3
0 5 10 15 20
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Reaction Diffusion
0 5 10 15 20
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Oscillation or no Oscillation
0 5 10 15 20
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Activator Inhibitor
0 5 10 15 20
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With Different Activator strength, form different Pattern Initial
AS=2.9
AS=2.0
Fate Map Methods
Limb Bud Outgrowth
Limb Bud Outgrowth
Summary
• 1. The substitution system is a suitable tool to enumerate growth process in embryonic development.
• 2.The substitution system as applied here can simulate real biological process, like cell division and differentiation.
• 3. Global behavior can be described by probability fields, which can link the molecular-signaling level to the cellular level.
• 4. Under certain growth probabilities to, the cell motion is still random according to fate map test.
Future Work
• Find out the suitable growth probability function.• Implement the molecular information into the
model.• Application in other developmental system.• Explore random/robustness effects in embryonic
development.• Explore surface tension constraints using the
Cellular Potts model.
Acknowledgement
Reference• Wolfram S., A new kind of science (2003).• Wolfram S., Theory and Application of cellular automata (1986)• Newman, S. A., and Frisch H. L., Dynamics of skeletal pattern formation in developin
g chick limb. Science 205, 662-668 (1979)• Newman M. E. J., Barkema G.T., Monte Carlo Methods (1999).• Salazar-Ciudad I., Jernvall J. and Newman S.A., Mechanisms of pattern formation in
development and evolution, Development 130, 2027-2037 (2003). • Adrian C., Life's Patterns: no need to spell it out? Science 303, 782-783 (2004)• Chaplain M.A.J., On growth and form: Spatio-temporal pattern formation in Biology, (1
999).• Deneen M., Hox10 and Hox11 genes are required to globally pattern the mammalian
skeleton. Science 301, 363-368 (2003).• Murray J. D., Mathematical biology I: An introduction (2001).• Murray J. D., Mathematical biology II: Spatial models and biomedical applications (20
01).• Vargesson N., Cell fate in the chick limb bud and relationship to gene expression. De
velopment 124, 1909-18 1997.• Glazier J. A., Simulation of differential adhesion driven rearrangement of biological ce
lls, Phy. Rev. E, 47,2128-2155 (1993).
What matters most is how you do your modeling