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 utilized 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.