Discovering genetic networks using compressive sensing
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A first analysis applying compressive sensing to a quantitative biological trait and its compressible "frequency domain" is presented. Consider an n-bit genetic sequence and suppose we want to discover a function that maps participating alleles (or even environmental influences) to a particular trait. Under plausible assumptions of how they evolved, certain traits can be viewed as "smooth" functions on the n-dimensional Boolean lattice of possible genomes. This allows approximation of their Fourier transforms, i.e., their gene networks, as sparse, dominated by "low-frequency" components. In turn, we can apply compressive sensing methods to collect relatively few samples, yet achieve accurate recovery. For an arbitrary quantitative trait affected by n=26 genes and with 812 meaningful gene interactions, our simulations show noisy trait measurements (SNR=20 dB) from just M=44,336 genomes in a population of size N = 2^26 (undersample ratio M/N≈0.00066) permit discovering its gene network and predicting trait values, both with about 97.6% accuracy. More dramatic undersample ratios are possible for traits affected by more genes. Work is currently underway to see if empirical data fit the proposed model. If so, it could offer a radical reduction in the number of measurements – from exponential to polynomial in some cases – necessary to quantify the relationship between genomes and certain traits.
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