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3D Substitution Model for Limb Growth and Pattern Formation Ying Zhang 1, Stuart A. Newman 2, James A. Glazier 1 1.Biocomplexity Institute, Department of Physics, Indiana University 2.New York Medical College

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: Substitution model

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Tetsuya Tabata, et al. Nature, 2001 Patterning a Developmental Field by Long-range Signalling

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Mechanisms of pattern formation in development and evolution Salazar-Ciudad I et al. Development 2003 I

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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

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Development of Limb Bud Newman SA. et al. Science 1979Gilbert et al 2003

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FGFs & FGFRs Xu X. et al. Cell Tissue Res. 1999

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Hox Gene Expression Nelson et al. Development 1996

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Expansion of Cell Populations Vargesson N. et al. Development, 1997

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Niswander, L. et al. Nature Reviews 2003 FGF ---outgrowth of the limb bud BMP--- Cartilage formation & Cell Death SHH Gli3Patterning SHH->HOXPatterning Gene Regulatory Network Gene & Function

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Growth Rule && Growth Probability Field Division Differentiation Condensation Growth Probability Field

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2D Subsitution Model Shubin et al. 1986

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3D Substitution Simulation With Physical Branching and Differentiation rule

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Fate Mapping Vargesson N. et al. Development, 1997

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Multilevel Modeling

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Morphogen Gradient Field Example:SHH-Gli3 Reaction Diffusion Oscillation or no Oscillation

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Activator Inhibitor With Different Activator strength, form different Pattern Initial AS=2.9 AS=2.0

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Fate Map Methods

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Limb Bud Outgrowth

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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.

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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.

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Acknowledgement

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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 developing chick limb. Science 205, (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, (2003). Adrian C., Life's Patterns: no need to spell it out? Science 303, (2004) Chaplain M.A.J., On growth and form: Spatio-temporal pattern formation in Biology, (1999). Deneen M., Hox10 and Hox11 genes are required to globally pattern the mammalian skeleton. Science 301, (2003). Murray J. D., Mathematical biology I: An introduction (2001). Murray J. D., Mathematical biology II: Spatial models and biomedical applications (2001). Vargesson N., Cell fate in the chick limb bud and relationship to gene expression. Development 124, Glazier J. A., Simulation of differential adhesion driven rearrangement of biological cells, Phy. Rev. E, 47, (1993).

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What matters most is how you do your modeling

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