Discrete Event Models in Biology: Problems, Solutions, and Food for Thought

1. Discrete Event Models in Biology: Problems, Solutions, and Food for Thought Jim Nutaro, Ph.D. Oak Ridge National Laboratory nutarojj@ornl.gov

2. Outline • Food for thought: migration described by a computational procedure • What is a discrete event system? • Simultaneous events and their implications • From where might a solution come?

3. A computational procedures that models cell migration A chemo-attractant diffusion is simulated numerically with a step size Δtconc Cell positions are re-evaluated every Δtconc At this time, the cell moves a distance normally distributed with mean X with a probability Δtconc/Δtcell Jabbarzadeh, E. and C. F. Abrams (2005, July). Chemotaxis and Random Motility in Unsteady Chemoattractant Fields: A Computational Study. Journal of Theoretical Biology 235(2), 221–232.

4. A computational procedures that models cell migration, cont. How far does a cell move on average in an interval of length T? The average speed depends on the method of solution, not on the model: what is the model? Must correct X to avoid super cells on average. What, if anything, can be said for small T?

5. What is a discrete event system? • An event changes the state of a model at a particular time • A list of events, executed in time stamp order, is a discrete event simulation • This is a computational procedure! • What is a discrete event system?

6. Problem #1: Simultaneous events Shoot(Sheriff) at time t1 Shoot(Outlaw) at time t2

7. Simultaneous events, cont. If t1 > t2 Shoot(Outlaw) at time t2

8. Simultaneous events? • The outcome depends on your simulator • Will not necessarily be consistent from • simulator to simulator • simulation to simulation If t1 = t2? ? ?

9. Artificial life: self-clocked CA P1 = P2 P1 < P2 ? ? ? ? When duration Pk expires, adopt the color of the neighboring cell

10. What is a discrete event system? • Is it an algorithm? • Can a discrete event model be understood without access to its simulator: are these things distinct? • “Comparing simulation results between simulators will ultimately demonstrate differences in the interpretation of the SBML between the simulators. “ – Quote from http://www.sys-bio.org/sbwWiki/compare/themysterysolved in regards to comparing SBML simulators

11. Differences between SBML simulators Some differences are due to errors, others to incomplete implementations, but some due to fundamental differences in the (implicit) definition of a hybrid dynamic system http://www.sys-bio.org/sbwWiki/_detail/compare/2007-12-04_percentagreement.jpg?id=compare&cache=cache

12. Who is correct? How does the system behave? “The answer is C” “The answer is A” “The answer is B”

13. Simulation for the sciences? • Simulation experiments often can not be reproduced because the hypothesis (model) is encoded in software • Change the software, change the theory? • Standard model formats (e.g., SBML) do not solve this problem – the answer depends on how the specification is interpreted • The event list appeals to intuition in defining a discrete event system – this is not enough • Naïve set theory did not work for Cantor • Naïve systems theory can not solve the simulation problem

14. Abstract systems: an axiomatic theory of simulation Agree on axioms • Also see • The theory of abstract (or general) systems (Wymore, Klir, Mesarovic, Takahara, Zeigler, Ashby, etc) • Derive simulation procedures from basic axioms about structure and dynamics • Procedures dictate what a correct algorithm must do, not how it must be done • Effective simulation algorithms carry out these procedures efficiently Derive procedures Design and implement algorithms

15. modeling relation simulation relation Implications for current practice: A framework for M&S Experimental Frame Device for executing model Real World Simulator Data: Input/output relation pairs Experimental frame specifies conditions under which the system is experimented with and observed Model Each entity is formalized as a Mathematical Dynamic System Each relation is represented by a homomorphism or other equivalence Structure for generating behavior claimed to represent real world Thank you to B.P. Zeigler for the slide

16. Separate Models From Simulators • Models are goal oriented abstractions of reality. • Simulators are the computational engines that drive the models to obtain results. Currently… Simulation software tends to encapsulate models and simulators in tightly coupled packages. In the M&S-Framework-based approach.. • Models and Simulators are treated as distinct entities with their own software representations. • There are simulators for different kinds of models that can be selected according to the needs of the simulation, • For example, a simulator might be chosen for its efficiency on a single host, or for its ability to execute the model on multiple hosts (distributed simulation)

17. Putting this into practice: modeling cell migration with the Discrete Event System Specification

18. Comparison of cell densities produced by continuum and discrete models Continuum Discrete * * *

19. Further reading • Theory of Modeling and Simulation, 2nd edition. Bernard Zeigler, Herbert Praehofer, Tag Gon Kim. Academic Press, 2000. • An Introduction to Cybernetics. W. Ross Ashby. Chapman & Hall, London, 1956). Now available electronically. • Abstract Systems Theory. Mihajlo Mesarovic and Y. Takahara. Springer Verlag, 1990.