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

Heather Koyuk

Spring 2005

Other Team MembersCS Student: Nick Armstrong

Chemistry Student: Heidi Geri

Chemistry Advisor: Dr. Jerzy Maselko

Biology Advisor: Dr. Garry Davies

C.S. Advisor: Dr. Kenrick Mock

The ProjectThe 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. ”

The ProjectThe 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

The ProjectThe 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

Other Requirements, ProgressOther 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

Other Requirements, ProgressOther Requirements, Progress

Dynamic rules creation would be nice– Hardcoded into Java code– Code, compile, then run each time you want to

change the rulesData Capture

– Rules captured by default (see above)– Dynamic rules creation would save rule

parameters in a separate file, capabilities to load previous rules, etc.

The EnvironmentThe 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

The CodeThe Code

CVE/VTK classesCell classRules class3-dimensional binary tree stores cell

locationsHelper classes: Direction, State, Point,

GrowthVector, NeighborsRulesWindow class

The AgentsThe Agents

3D spheres, uniform radii Magnitude (state) Spherical growth vectors Current model:

– Sessile, rigid– Die/become dormant after

budding

Not limited to the above!

The Rules and ActionsThe 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)

Dynamic Rules CreationDynamic Rules Creation

Working on the grammar/parsingMockup is minimally functional

Research OverviewResearch 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. <http://algorithmicbotany.org/vmm-deluxe/Section-07.html>.

Research OverviewResearch 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. <http://algorithmicbotany.org/vmm-deluxe/Section-07.html>.

Cellular AutomataCellular Automata Our cells are capable of everything a cellular

automaton is, and more!

Wolfram’s Rule 110

Context-FreeContext-Free

Context-SensitiveContext-Sensitive

Problems/QuestionsProblems/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

Future Directions/AnswersFuture 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

ConclusionConclusion

This project has widespread implications– Biology– Chemistry– Computer science– Complexity

We’ve laid the groundworkBut we’ve only scratched the surface!

Questions?Questions?