Organisms face a constantly shifting landscape of environmental conditions and internal physiological states. How gene regulation and cellular functions are maintained across genetic and environmental variation is therefore a fundamental question in biology. Here, we analyze the Saccharomyces cerevisiae genetic interaction network to understand how the yeast cell maintains regulatory capacity across genetic backgrounds and environmental conditions. We used the recently characterized synthetic sick/lethal network in yeast, which measures the fitness effects of knocking out pairs of genes, to analyze interactions among 4,364 genes. Genes with large variance in epistatic effects on fitness are highly and ubiquitously expressed (with open chromatin conformations in their promoter regions) and evolve more slowly than genes with weak effects on fitness. Thus, rather than being the elements responsible for the regulation and responsiveness of the genetic network, genes with large epistatic effects tend to be more mundane "housekeeping" genes whose consistent expression is critical to fitness under all environments and that are thereby deeply embedded within the regulatory structure of the network. Our analysis shows that the yeast cell has evolved a system whereby a physical mechanism of regulation (nucleosome occupancy) buffers key genes from the variability experienced by the cell as a whole.