Abstract
In this paper, we consider the problem of learning the genetic interaction map, i.e., the topology of a directed acyclic graph (DAG) of genetic interactions from noisy double-knockout (DK) data. Based on a set of well-established biological interaction models, we detect and classify the interactions between genes. We propose a novel linear integer optimization program called the Genetic-Interactions-Detector (GENIE) to identify the complex biological dependencies among genes and to compute the DAG topology that matches the DK measurements best. Furthermore, we extend the GENIE program by incorporating genetic interaction profile (GI-profile) data to further enhance the detection performance. In addition, we propose a sequential scalability technique for large sets of genes under study, in order to provide statistically significant results for real measurement data. Finally, we show via numeric simulations that the GENIE program and the GI-profile data extended GENIE (GI-GENIE) program clearly outperform the conventional techniques and present real data results for our proposed sequential scalability technique.
Highlights
Genetic interaction analysis aims at uncovering the interactions among a set of genes with respect to a specified cell function of a biological system, e.g., the fitness of a specific bacteria colony
3.1 Hierarchical relationship class detection In order to quantify the mismatch between the measured DK phenotypes R(i, j) and the phenotype model μk(i, j) of class k ∈ K according to Fig. 2, under the hypothesis that the gene pairs i, j belong to class k given their respective SK values, we propose a simple quadratic score [2, 21], as given in Eq (2)
Since α4Da (1, 2) = α4Da (1, 3) = α4Da (1, 4) = 1 do not contain information on the number of paths from gene g1 to R that are independent of g2, g3 and g4, edges e1 and e2 do not affect the pattern of hierarchical relationship classes representing directed acyclic graph (DAG) Da, i.e., ADa, and this yields ambiguities in computing the topology of DAG Da based on its corresponding set of selection variables ADa. Since it is a common assumption in genomics research that genetic interaction (GI) maps, i.e., DAGs, are not overly dense but rather sparse, we propose a policy which computes the sparsest DAG topology based on the detected pattern of hierarchical relationship classes
Summary
Genetic interaction analysis aims at uncovering the interactions among a set of genes with respect to a specified cell function of a biological system, e.g., the fitness of a specific bacteria colony. 3.2 Edge computation Based on the detected set of selection variables AOGENIE which corresponds to the most consistent pattern of hierarchical relationship classes given the observed SK and DK phenotypes, an estimate EGENIE of the true set of edges ED of DAG D can be computed. Assume that we are given the pattern of hierarchical relationship classes that corresponds to DAG DR, i.e., ADR , and we want to compute all reporter node edges based on ADR , i.e., all edges that directly connect a gene in DAG DR with the reporter node R.
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