BioSysBio:abstracts/2007/Naoki Matsumaru

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Designing a Chemical Program using Chemical Organization Theory

Author(s): Naoki Matsumaru, Thorsten Lenser, Thomas Hinze, Peter Dittrich
Affiliations: Bio Systems Analysis Group, Institute of Computer Science, Friedrich-Schiller-University Jena
Contact:email: naoki@minet.uni-jena.de
Keywords: 'add-keyword_1' 'add_keyword_2' 'add_keyword_3' 'add_keyword_4'

Background/Introduction

Behaviors of biological organisms are results from the complex but orchestrated biochemical reactions. The complexity of the reaction network is the source of robustness and adaptability of the biological systems. When exploiting biochemical reaction systems for computation, however, that complexity hinders users to control and program the systems as desired. A small modification on the reaction may cause the system to enter unknown behavioral regions. A major modification may exhibit little change in the global level. In order to harness the complexity, the gap between micro level (e.g., reaction rules) and macro level (e.g., chemotaxis behavior) has to be bridged. As a method to link these two levels, we would like to introduce chemical organization theory. The utility of the theory is exemplified with a chemical program to solve maximal independent set problem on an undirected graph.

Maximal independent set problem is ...

Results

Given an undirected graph with [math]\displaystyle{ N }[/math], chemical reaction network is designed according to a recipe described in appendix. By analyzing the reaction network with chemical organization theory, we can prove that the reaction system can be utilized to solve the maximal independent set problem.

Chemical organization theory [1] has been developed to understand dynamical complex biochemical processes from only stoichiometry of the reaction network. The network is decomposed into overlapping sub-networks called organizations, and each organization represents a combination of molecular species (potentially) existing in a steady state.

Conclusion

Chemical organization theory as a tool to help programming chemical computing.

Appendix

Chemical organization theory

An organization is a set of molecular species that is closed and self-maintaining. A set of molecular species is closed, if they cannot produce any molecular species outside that set. A set of molecular species is self-maintaining, if all molecular species that are consumed by reactions within the set can be regenerated by reactions within the set. A set of molecules constituting a stable state must be an organization (Theorem 1)

Recipe

Chemical Reaction network is constructed as follows:

Proof

Here is the proof

References

[1] P. Dittrich, P. Speroni di Fenizio: Chemical Organization Theory. Bull. Math. Biol., 2006, (accepted)

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