Design of Geometric Molecular Bonds

An example of a specific molecular bond is the affinity of the DNA base A for T, but not for C, G, or another A. This contrasts nonspecific bonds, such as the affinity of any positive charge for any negative charge (like-unlike), or of nonpolar material for itself when in aqueous solution (like-like). 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 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 2-D binary codewords. While motivated by completely different applications, geometric orthogonal codes share similar features to the optical orthogonal codes studied by Chung et al. The main technical difference is the importance of 2-D geometry in defining codeword orthogonality.