Competitive hybridization models

Microarray technology, in its simplest form, allows one to gather abundance data for target DNA molecules, associated with genomes or gene-expressions, and relies on hybridizing the target to many short probe oligonucleotides arrayed on a surface. While for such multiplexed reactions conditions are optimized to make the most of each individual probe-target interaction, subsequent analysis of these experiments is based on the implicit assumption that a given experiment yields the same result regardless of whether it was conducted in isolation or in parallel with many others. It has been discussed in the literature that this assumption is frequently false, and its validity depends on the types of probes and their interactions with each other. We present a detailed physical model of hybridization as a means of understanding probe interactions in a multiplexed reaction. Ultimately, the model can be derived from a system of ordinary differential equations (ODE’s) describing kinetic mass action with conservation-of-mass equations completing the system. We examine pairwise probe interactions in detail and present a model of “competition” between the probes for the target—especially, when the target is effectively in short supply. These effects are shown to be predictable from the affinity constants for each of the four probe sequences involved, namely, the match and mismatch sequences for both probes. These affinity constants are calculated from the thermodynamic parameters such as the free energy of hybridization, which are in turn computed according to the nearest neighbor (NN) model for each probe and target sequence. Simulations based on the competitive hybridization model explain the observed variability in the signal of a given probe when measured in parallel with different groupings of other probes or individually. The results of the simulations can be used for experiment design and pooling strategies, based on which probes have been shown to have a strong effect on each other’s signal in the in silico experiment. These results are aimed at better design of multiplexed reactions on arrays used in genotyping (e.g., HLA typing, SNP, or CNV detection, etc.) and mutation analysis (e.g., cystic fibrosis, cancer, autism, etc.).