RESUMEN
Gene knockout studies suggest that ~300 genes in a bacterial genome and ~1,100 genes in a yeast genome cannot be deleted without loss of viability. These single-gene knockout experiments do not account for negative genetic interactions, when two or more genes can each be deleted without effect, but their joint deletion is lethal. Thus, large-scale single-gene deletion studies underestimate the size of a minimal gene set compatible with cell survival. In yeast Saccharomyces cerevisiae, the viability of all possible deletions of gene pairs (2-tuples), and of some deletions of gene triplets (3-tuples), has been experimentally tested. To estimate the size of a yeast minimal genome from that data, we first established that finding the size of a minimal gene set is equivalent to finding the minimum vertex cover in the lethality (hyper)graph, where the vertices are genes and (hyper)edges connect k-tuples of genes whose joint deletion is lethal. Using the Lovász-Johnson-Chvatal greedy approximation algorithm, we computed the minimum vertex cover of the synthetic-lethal 2-tuples graph to be 1,723 genes. We next simulated the genetic interactions in 3-tuples, extrapolating from the existing triplet sample, and again estimated minimum vertex covers. The size of a minimal gene set in yeast rapidly approaches the size of the entire genome even when considering only synthetic lethalities in k-tuples with small k. In contrast, several studies reported successful experimental reductions of yeast and bacterial genomes by simultaneous deletions of hundreds of genes, without eliciting synthetic lethality. We discuss possible reasons for this apparent contradiction.IMPORTANCEHow can we estimate the smallest number of genes sufficient for a unicellular organism to survive on a rich medium? One approach is to remove genes one at a time and count how many of such deletion strains are unable to grow. However, the single-gene knockout data are insufficient, because joint gene deletions may result in negative genetic interactions, also known as synthetic lethality. We used a technique from graph theory to estimate the size of minimal yeast genome from partial data on synthetic lethality. The number of potential synthetic lethal interactions grows very fast when multiple genes are deleted, revealing a paradoxical contrast with the experimental reductions of yeast genome by ~100 genes, and of bacterial genomes by several hundreds of genes.