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

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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

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Reaction Diffusion

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Oscillation or no Oscillation

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Activator Inhibitor

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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).

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