1. 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

2. 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. ”

3. 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

4. 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

5. 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

6. 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.

7. The Environment Modified version of Collaborative Visualization Environment (Armstrong, et. al) – Java and VTK (Kitware’s Visualization Toolkit) – 3-D animation, panning, zooming, pausing, data capture

8. 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

9. 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!

10. 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)

11. Dynamic Rules Creation Working on the grammar/parsing Mockup is minimally functional

12. 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..

13. 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..

14. Cellular Automata Our cells are capable of everything a cellular automaton is, and more! Wolfram’s Rule 110

15. Context-Free

16. Context-Sensitive

17. 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

18. 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

19. Conclusion This project has widespread implications – Biology – Chemistry – Computer science – Complexity We’ve laid the groundwork But we’ve only scratched the surface!

20. Questions?