Boosting multiplexing capabilities for error-robust spatial transcriptomic methods using a set exchange approach

In the last decades, image-based transcriptomic and proteomic experiments have moved from single-target probes to multiplexed experiments, allowing researchers to study hundreds or even thousands of mRNA and protein targets simultaneously. This large increase in scope necessitates methods in either increased specificity or in error correction, such as the Hamming codes used in the imaging-based spatial transcriptomic method MERFISH. For some experimental conditions, Hamming codes are efficient in encoding the highest possible number of genes for spatial analysis. However, for most experimental parameters, the optimal generation of error-robust codebooks is an unsolved mathematical problem. Here, we present a method to generate highly optimized extended Hamming codebooks compatible with established error-correctable methodologies such as MERFISH. Our method uses an iterative set-exchange approach and generally reaches over 90% of the theoretical maximum limit of gene set complexity. We also provide ready-to-use codebooks and discuss the advantages and disadvantages of changing probe density.