Compressed Genotyping

Abstract

Over the past three decades we have steadily increased our knowledge on the genetic basis of many severe disorders. Nevertheless, there are still great challenges in applying this knowledge routinely in the clinic, mainly due to the relatively tedious and expensive process of genotyping. Since the genetic variations that underlie the disorders are relatively rare in the population, they can be thought of as a sparse signal. Using methods and ideas from compressed sensing and group testing, we have developed a cost-effective genotyping protocol to detect carriers for severe genetic disorders. In particular, we have adapted our scheme to a recently developed class of high throughput DNA sequencing technologies. The mathematical framework presented here has some important distinctions from the ’traditional’ compressed sensing and group testing frameworks in order to address biological and technical constraints of our setting.

Semiquantitative Group Testing

“…At the core of every genotyping method is DNA sequencing -determining the genetic blueprint of an individual -and a comparative analysis of the sequences obtained from different individuals. Comparative studies of the DNA makeup play an indispensable role in medical genetics, the goals of which are to efficiently determine "outliers" in genetic codes that may lead to devastating disorders or illnesses [26].…”

“…As a result, group testing presents itself as a natural paradigm to address these challenges, and the first steps in this direction were taken in [31], [32], [26], [27]. Despite the promising results of applying the existing group testing models to genotyping, many practical problems still stand in the way of the wide-scale use of this method.…”

“…where C(j + (i − 1)m d , l) = 1 follows from (26), and (28) is a consequence of the following argument. First, note that using (20) and (25), one has ∑ k∈N C(j…”

“…Two notable exceptions were the early use of group testing for DNA sequence analysis [23] and the very recent work on group testing for genotyping and biosensing [26]- [28]. The reason behind this practical failure of group testing in life sciences is that most analytical models do not capture the full complexity of bioengineering systems.…”

Compressed sensing-based pooling experiments using next generation sequencing

“…These designs offer a significant saving in resources, as they enable genotype reconstruction for N individuals, by using only O(log N ) or O( √ N ) pools, respectively. We present a different approach to recovering the identity of individuals carrying rare variants, based on Compressed Sensing (CS) (a somewhat similar approach has independently been developed by Erlich et al [4].) We extend the scope of [2], enabling the recovery of multiple carriers, and dealing with heterozygous or homozygous rare alleles, testing larger cohorts of individuals, incorporating experimental barcoding techniques, as well as dealing with unknown sequencing read errors.…”