Design of Geometric Molecular Bonds

TL;DR

This paper introduces geometric orthogonal codes to model DNA macrobonds, enabling the design of sets with low unintended binding through 2D geometric arrangements, inspired by optical orthogonal codes.

Contribution

It proposes a novel 2D geometric code framework for DNA nanotechnology, bridging concepts from optical orthogonal codes to improve macrobond orthogonality.

Findings

Developed a mathematical model for DNA macrobonds as 2D binary codewords.

Established conditions for orthogonality based on geometric arrangements.

Provided theoretical bounds and constructions for these codes.

Abstract

An example of a nonspecific molecular bond is the affinity of any positive charge for any negative charge (like-unlike), or of nonpolar material for itself when in aqueous solution (like-like). This contrasts specific bonds such as the affinity of the DNA base A for T, but not for C, G, or another A. Recent experimental breakthroughs in DNA nanotechnology demonstrate that a particular nonspecific like-like bond ("blunt-end DNA stacking" that occurs between the ends of any pair of DNA double-helices) can be used to create specific "macrobonds" by careful geometric arrangement of many nonspecific blunt ends, motivating the need for sets of macrobonds that are orthogonal: two macrobonds not intended to bind should have relatively low binding strength, even when misaligned. To address this need, we introduce geometric orthogonal codes that abstractly model the engineered DNA macrobonds as two-dimensional binary codewords. While motivated by completely different applications, geometric orthogonal codes share similar features to the optical orthogonal codes studied by Chung, Salehi, and Wei. The main technical difference is the importance of 2D geometry in defining codeword orthogonality.