Paranemic crossover (PX) DNA motifs were designed and used for self-assembly of two dimensional lattices. The PX motifs tested include overwound and underwound ones, and different forms of self-assembled two-dimensional (2D) lattices were generated, demonstrating the correlation between the helical torsional strain within the system and the quality of the lattice formed. Relief of the torsional strain by adjusting the number of base pairs in the JX region adjacent to the PX motifs, facilitates and optimizes DNA self-assembly, which leads to 2D lattices of greater uniformity and higher yield. This study demonstrated that the helical relationship among DNA building blocks is a critical factor for the tile-based self-assembly of large nanostructures.