Modeling Morphogenesis in Multi-Cellular Systems (Complex Systems Project)

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Modeling Morphogenesis in Multi-Cellular Systems
(Complex Systems Project)

• Heather Koyuk
• Spring 2005
• Other Team Members
• CS Student Nick Armstrong
• Chemistry Student Heidi Geri
• Chemistry Advisor Dr. Jerzy Maselko
• Biology Advisor Dr. Garry Davies
• C.S. Advisor Dr. Kenrick Mock

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The Project

• Dr. Maselko
• Pattern formation in multi-cellular chemical
  systems has been the subject of intensive inquiry
  from the beginning of the study of oscillatory
  chemical reactions.  Most simulations of
  multi-cellular chemical systems have been done
  using the cellular automata grid that is
  unrealistic.  The number of cells is increasing
  in the order 1,5,9..  not like in biological
  system 1,2,4,8... In addition, the CA models have
  a four fold symmetry. Therefore, to simulate the
  morphogenesis of complex multi-cellular
  structures, a computer graphic program is
  necessary that will produce more realistic
  models. This model should be able to reproduce
  different morphogenesis seen in different
  biological and chemical cellular systems. 

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The Project

• Three subteams
• Computer Science Dr. Mock, Nick Armstrong, and
  Heather Koyuk (me)
• Biology Dr. Gerry Davis
• Chemistry Dr. Jerzy Maselko, Heidi Geri

• Three subprojects
• Implement a 3-D simulation and theoretical model
• Relate the chemical system to biological systems
• Implement the chemical system in the laboratory

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The Project

• Create a computer simulation capable of modeling
  multi-cellular chemical and biological growth
• Should model biological and chemical systems as
  accurately as possible
• Cells as spherical objects
• Cells bud or grow in spherical (non-discrete)
  directions
• Use both context-free and context-sensitive
  growth
• Easy to write a program that simulates growth
• Harder to use grammars to create a specific
  unique pattern

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Other Requirements, Progress

• Theoretical model for growth
• Both Context-Free and Context-Sensitive
• Include a variety of growth patterns
• Use concepts from a variety of theories as needed
• Ideally, should result in a semi-self replicating
  system

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Other Requirements, Progress

• Dynamic rules creation would be nice
• Hardcoded into Java code
• Code, compile, then run each time you want to
  change the rules
• Data Capture
• Rules captured by default (see above)
• Dynamic rules creation would save rule parameters
  in a separate file, capabilities to load previous
  rules, etc.

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The Environment

• Modified version of Collaborative Visualization
  Environment (Armstrong, et. al)
• Java and VTK (Kitwares Visualization Toolkit)
• 3-D animation, panning, zooming, pausing, data
  capture

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The Code

• CVE/VTK classes
• Cell class
• Rules class
• 3-dimensional binary tree stores cell locations
• Helper classes Direction, State, Point,
  GrowthVector, Neighbors
• RulesWindow class

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The Agents

• 3D spheres, uniform radii
• Magnitude (state)
• Spherical growth vectors
• Current model
• Sessile, rigid
• Die/become dormant after budding
• Not limited to the above!

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The Rules and Actions

• Rules comprise a grammar
• Context-free
• Unaware of neighbors behavior based on state
• Context-sensitive
• Behavior based on state state of neighbors
• Actions
• Implemented Budding
• Working on Cell Division
• Others Motility, growth, non-uniform shapes,
  etc.
• Working on dynamic rule creation (via user
  interface)

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Dynamic Rules Creation

• Working on the grammar/parsing
• Mockup is minimally functional

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Research Overview

• Morphogenesis
• Lots of plant morphogenesis research
  L-systems, etc.
• Chemical morphogenesis Mostly chemical
  reaction/diffusion

Image source Fowler, D., and Prusinkiewicz, P.
Maltese Cross. 1993. Visual Models of
Morphogenesis/ Algorithmic Botany at the
University of Calgary. 4/14/05.
lthttp//algorithmicbotany.org/vmm-deluxe/Section-0
7.htmlgt.
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Research Overview

• Cellular Automata
• Begin with grid of cells
• Usually 1-D, some 2-D
• Binary/discreet state variables (on or off)
• Cells change state based on their current state
  and state of immediate neighbors
• Our cells
• Do not fill grid
• 3-Dimensional and can grow in any direction
• Continuous state variables (not discreet)

Image source Fowler, D., and Prusinkiewicz, P.
Maltese Cross. 1993. Visual Models of
Morphogenesis/ Algorithmic Botany at the
University of Calgary. 4/14/05.
lthttp//algorithmicbotany.org/vmm-deluxe/Section-0
7.htmlgt.
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Cellular Automata

• Our cells are capable of everything a cellular
  automaton is, and more!

Wolframs Rule 110
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Context-Free
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Context-Sensitive
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Problems/Questions

• Infinite search space for possible rules
• How to narrow down and find interesting ones?
• Dynamic rule specification
• Entails specifying, executing a grammar during
  run-time
• Backward problem
• For a given macrostructure, how to define a rule
  set to produce that structure?
• Expand code functionality
• Budding/Cell Division, Cell Growth/L-Systems,
  Motility, Pliability

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Future Directions/Answers

• Create a language for specifying rules
• Use genetic algorithms to find interesting rules,
  and to solve backward problem
• Examine division/budding, motility, cell growth,
  L-Systems, and pliability separately and in great
  depth
• Keep trying to reproduce basic biological
  structures (e.g. developing embryo) in model and
  in lab

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Conclusion

• This project has widespread implications
• Biology
• Chemistry
• Computer science
• Complexity
• Weve laid the groundwork
• But weve only scratched the surface!

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Questions?