Optimizing Tile Concentrations to Minimize Errors and Time for DNA Tile Self-assembly Systems
نویسندگان
چکیده
DNA tile self-assembly has emerged as a rich and promising primitive for nano-technology. This paper studies the problems of minimizing assembly time and error rate by changing the tile concentrations because changing the tile concentrations is easy to implement in actual lab experiments. We prove that setting the concentration of tile Ti proportional to the square root of Ni where Ni is the number of times Ti appears outside the seed structure in the final assembled shape minimizes the rate of growth errors for rectilinear tile systems. We also show that the same concentrations minimize the expected assembly time for a feasible class of tile systems. Moreover, for general tile systems, given tile concentrations, we can approximate the expected assembly time with high accuracy and probability by running only a polynomial number of simulations in the size of the target shape. ∗Center for Mathematics of Information, California Institute of Technology, Pasadena, CA 91101, USA. Email: [email protected]. †Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, USA. Email: [email protected]. This author’s work was supported in part by NSF Grant CCF-1049899. ar X iv :1 21 0. 57 86 v1 [ cs .D S] 2 2 O ct 2 01 2
منابع مشابه
One-Time, Directed and Catalytic Activation of 1-D DNA Tiles
Experimental demonstration of the Turing universal tile based algorithmic DNA self-assembly has been limited by significant assembly errors. An important class of errors, called co-ordinated growth errors, occur when an incorrect tile binds to a growing assembly even when some of its pads are mismatched with its neighbors. Activatable DNA tiles, introduced originally by [12], employ a protectio...
متن کاملDNA Sticky End Design and Assignment for Robust Algorithmic Self-assembly
A major challenge in practical DNA tile self-assembly is the minimization of errors. Using the kinetic Tile Assembly Model, a theoretical model of self-assembly, it has been shown that errors can be reduced through abstract tile set design. In this paper, we instead investigate the effects of “sticky end” sequence choices in systems using the kinetic model along with the nearest-neighbor model ...
متن کاملReliable Self-assembly by Self-triggered Activation of Enveloped DNA Tiles
Although the design of DNA tiles has been optimised for efficient and specific self-assembly, assembly errors occur so often that applications for molecular computation remain limited. We propose the use of an enveloped tile consisting of a DXbase tile that carries a protector tile to suppress erroneous tile assembly. The design of the enveloped tile promotes the dissociation of the protector t...
متن کاملProofreading Tile Sets: Error Correction for Algorithmic Self-Assembly
For robust molecular implementation of tile-based algorithmic self-assembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low rate – but at the cost of reduced speed (r) for the self-assembly process. For tile sets directly implemen...
متن کاملImproving Efficiency of 3-SAT-Solving Tile Systems
The tile assembly model has allowed the study of the nature’s process of self-assembly and the development of self-assembling systems for solving complex computational problems. Research into this model has led to progress in two distinct classes of computational systems: Internet-sized distributed computation, such as software architectures for computational grids, and molecular computation, s...
متن کامل