An investigation of the brusselator on the mesoscopic scale

Abstract

In the unconventional model of computation with biochemical media, such as DNA computing, membrane computing, etc. most of the system is on a mesoscopic scale and its kinetics may vary compared to on a macroscopic scale. In order to consider the reason for the difference between macroscopic and mesoscopic, we introduce a novel model of computation: Abstract Rewriting System on Multisets (ARMS), which is inspired by chemical reactions. By using this model, we investigate the behavior of the brusselator model and confirm that the system on a mesoscopic scale is more likely to be destabilized than on a macroscopic scale. Furthermore, we consider an application of this destabilization in order to compose a novel computational framework.

Keywords:

• Computation
• DNA
• Macroscopic
• Mesoscopic

Acknowledgements

The authors are grateful to Ryosuke Ishiwata. This research was supported by Grants-in-Aid for Scientific Research No. 14085205.