Geometric Constraint Optimization for Localized Strand Displacement Reactions

Abstract

Localized molecular circuits offer practical advantages over those implemented using components freely diffusing in bulk solution, such as computation speed and component reuse. A common framework for implementing such circuits uses DNA strand displacement reactions with components localized via tethering to a DNA origami tile. While a number of papers have demonstrated the capability of such circuits, design tools for enumerating localized reactions and analyzing their behavior are relatively scarce. The key difficulty in modeling such circuits is that the geometric constraints imposed by the tethering of specific components at specific points on the tile surface are critical in determining whether or not a particular reaction may occur. In previous work, we deployed simple techniques based on random sampling of the structure space in an attempt to find geometric structures for candidate reaction products that satisfy all of the geometric constraints. In this paper, we show that this approach can be enhanced by using an optimization algorithm that takes initial guessed structures that fail to satisfy certain constraints and attempts to refine them into structures that do satisfy all of the constraints. We illustrate this approach on simple example reactions as well as a strand displacement-based signal transmission example from the literature. This work thus advances the state of the art in modeling tools for localized molecular circuits.