3D Substitution Model for Limb Growth and Pattern Formation
-
Upload
acton-gates -
Category
Documents
-
view
17 -
download
0
description
Transcript of 3D Substitution Model for Limb Growth and Pattern Formation
![Page 1: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/1.jpg)
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
![Page 2: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/2.jpg)
:Substitution model
![Page 3: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/3.jpg)
Tetsuya Tabata, et al. Nature, 2001
Patterning a Developmental Field by Long-range Signalling
![Page 4: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/4.jpg)
Mechanisms of pattern formation in development and evolution
Salazar-Ciudad I et al. Development 2003 I
![Page 5: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/5.jpg)
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
![Page 6: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/6.jpg)
Development of Limb Bud
Newman SA. et al. Science 1979 Gilbert et al 2003
![Page 7: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/7.jpg)
FGFs & FGFRs
Xu X. et al. Cell Tissue Res. 1999
![Page 8: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/8.jpg)
Hox Gene ExpressionNelson et al. Development 1996
![Page 9: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/9.jpg)
Expansion of Cell Populations
Vargesson N. et al. Development, 1997
![Page 10: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/10.jpg)
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
![Page 11: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/11.jpg)
51015
20
5 10 15 200
0.25
0.5
0.75
1
0
0.25
0.5
0.75
1
51015
20
5 10 15 200
0.25
0.5
0.75
1
0
0.25
0.5
0.75
1
51015
20
5 10 15 200
0.25
0.5
0.75
1
0
0.25
0.5
0.75
1
Growth Rule && Growth Probability Field
Division
Differentiation
Condensation
Growth Probability Field
![Page 12: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/12.jpg)
2D Subsitution Model
Shubin et al. 1986
![Page 13: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/13.jpg)
3D Substitution Simulation
With Physical Branching and Differentiation rule
![Page 14: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/14.jpg)
Fate Mapping
Vargesson N. et al. Development, 1997
![Page 15: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/15.jpg)
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
![Page 16: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/16.jpg)
Morphogen Gradient Field
• Example:SHH-Gli3
0 5 10 15 20
0
5
10
15
20
Reaction Diffusion
0 5 10 15 20
0
5
10
15
20
0 5 10 15 20
0
5
10
15
20
Oscillation or no Oscillation
0 5 10 15 20
0
5
10
15
20
![Page 17: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/17.jpg)
Activator Inhibitor
0 5 10 15 20
0
5
10
15
20
0 5 10 15 20
0
5
10
15
20
0 5 10 15 20
0
5
10
15
20
With Different Activator strength, form different Pattern Initial
AS=2.9
AS=2.0
![Page 18: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/18.jpg)
Fate Map Methods
![Page 19: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/19.jpg)
Limb Bud Outgrowth
![Page 20: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/20.jpg)
Limb Bud Outgrowth
![Page 21: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/21.jpg)
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.
![Page 22: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/22.jpg)
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.
![Page 23: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/23.jpg)
Acknowledgement
![Page 24: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/24.jpg)
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).
![Page 25: 3D Substitution Model for Limb Growth and Pattern Formation](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813624550346895d9d9aaa/html5/thumbnails/25.jpg)
What matters most is how you do your modeling