Self-correcting self-assembly: growth models and the hammersley process

  • Authors:

  • Yuliy Baryshnikov;Ed Coffman;Nadrian Seeman;Teddy Yimwadsana

  • Affiliations:

  • Bell Labs, Lucent Technologies, Murray Hill, NJ;Department of Electrical Engineering, Columbia University, NY;Chemistry Dept., New York University, New York;Department of Electrical Engineering, Columbia University, NY

  • Venue:
  • DNA'05 Proceedings of the 11th international conference on DNA Computing
  • Year:
  • 2005

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Abstract

This paper extends the stochastic analysis of self assembly in DNA-based computation. The new analysis models an error-correcting technique called pulsing which is analogous to checkpointing in computer operation. The model is couched in terms of the well-known tiling models of DNA-based computation and focuses on the calculation of computation times, in particular the times to self assemble rectangular structures. Explicit asymptotic results are found for small error rates q, and exploit the connection between these times and the classical Hammersley process. Specifically, it is found that the expected number of pulsing stages needed to complete the self assembly of an N ×N square lattice is asymptotically $2N\sqrt{q}$ as N →∞ within a suitable scaling. Simulation studies are presented which yield performance under more general assumptions.