Designing optimally multiplexed SNP genotyping assays

We consider the task of SNP (Single Nucleotide Polymorphism) genotyping. In many studies, genotyping of a large number of SNP must be performed. Multiple SNPs can be genotyped together in the same assay (a process called multiplexed genotyping), provided they adhere to some constraints. We address the optimization problem of designing assays that maximize the number of SNPs genotyped, subject to the multiplexing constraints. We focus on the SNP genotyping method based on primer extension and mass-spectrometry (PEA/MS). We translate the optimization problem to a graph coloring problem, and provide an essentially optimal heuristics for solving the corresponding coloring problem. In addition, we present a method that enables a dramatic increase in the multiplexing rate by modifying primer masses. In this case, the multiplexing design problem can be modelled as a matching problem in hypergraphs. We analyze the problem from both theoretical and practical aspects, providing theoretical hardness results and practical heuristics. The heuristics are tested using simulation methods, and prove to be close to optimal in practice.