A computational framework for DNA sequencing microscopy.

We describe a method whereby microscale spatial information such as the relative positions of biomolecules on a surface can be transferred to a sequence-based format and reconstructed into images without conventional optics. Barcoded DNA "polymerase colony" (polony) amplification techniques enable one to distinguish specific locations of a surface by their sequence. Image formation is based on pairwise fusion of uniquely tagged and spatially adjacent polonies. The network of polonies connected by shared borders forms a graph whose topology can be reconstructed from pairs of barcodes fused during a polony cross-linking phase, the sequences of which are determined by recovery from the surface and next-generation (next-gen) sequencing. We developed a mathematical and computational framework for this principle called polony adjacency reconstruction for spatial inference and topology and show that Euclidean spatial data may be stored and transmitted in the form of graph topology. Images are formed by transferring molecular information from a surface of interest, which we demonstrated in silico by reconstructing images formed from stochastic transfer of hypothetical molecular markers. The theory developed here could serve as a basis for an automated, multiplexable, and potentially superresolution imaging method based purely on molecular information.