Probabilistic models for damage and self-repair in DNA self-assembly

Abstract

To date, research on DNA self-assembly-based nanostructures has mostly been on one-time assembly. However, DNA nanostructures are very fragile and prone to damage. Knowing the extent of damage that can occur under various physical conditions can be useful in designing robust self-assembled nanostructures. This paper presents simple models for estimating the extent of damage in DNA nanostructures due to various external forces, with emphasis on mechanical and thermal forces. We note that these models have not been validated against experimental data. As such, they are only meant to serve as a basis for designing DNA nanostructures that are robust to external damage. We conclude with a discussion on computing the probability of repair of a damaged nanostructure assuming no change in the design of the self-assembling components.

Keywords:

• DNA
• self-assembly
• damage
• self-repair
• probability

Notes

^1. In our laboratory, we typically use a Mg²⁺ concentration of 12.5 mM in our TAE buffers.

^2. This is the tile we frequently use in our own laboratory.

^3. We assume in this equation that none of the boundary tiles receive the initial impact.

^4. In the computer simulation of the rigid lattice model, we allow both tiles on the boundary to be hit as well as cyclic shock wave propagation paths.

^5. The method of Lagrange multipliers provides a strategy for finding the maximum/minimum of a function subject to constraints.

^6. We assume no net force from the electron beam.