Ways to identify that proteins are regulating different genes experimentally
Chromatin immunoprecipitation (ChIP) or ChIP-Seq are the first methods that pop into my mind. Essentially, DNA is cross-linked to bound proteins (transcription factors, histones, etc.) by various methods, then broken into pieces by either sonication or digestion with micrococcal nuclease. An immunoprecipitation is then performed by adding antibodies targeting your protein of interest (HIF-1&alpha; and HIF-2&alpha; in this case), allowing them to bind to their targets, enriching them using bead-conjugated Protein G (or Protein A), then reversing the cross-linking. The enriched DNA can then either be subjected to PCR for known genes (ChIP), or it can be sequenced and aligned with a reference genome to determine all bound sequences (ChIP-Seq).