In recent years there has been considerable and growing interest in the 3-dimensional organization of genomes. In this manuscript we present an integrated computational-molecular study that produces an ensemble of high-resolution 3-dimensional conformations of the budding yeast genome. The compaction, folding and spatial organization of the chromosomes was based on empirical data determined using proximity-based ligation. Our models incorporate external constraints that allow the separation of gross organizational effects from those due to local interactions. Our models show that yeast chromosomes have preferred yet non-exclusive positions. They also identify interaction dependent clustering of tRNAs, early firing origins of replication, and Gal4 protein binding sites, yet the cluster composition is dynamic. Our results support a link between structure and transcription that occurs within the context of a flexible genome organization.