Cells adapt to changes in ambient oxygen by changing their gene expression patterns. In fission yeast, the sterol regulatory element-binding protein Sre1 is proteolytically cleaved under low oxygen, and its N-terminal segment (Sre1N) serves as a hypoxic transcription factor. When oxygen is present, the prolyl hydroxylase Ofd1 down-regulates Sre1N activity in two ways: first, by inhibiting its binding to DNA, and second, by accelerating its degradation. Here we use a mathematical model to assess what each of these two regulatory functions contributes to the hypoxic response of the cell. By disabling individual regulatory functions in the model, which would be difficult in vivo, we found that the Ofd1 function of inhibiting Sre1N binding to DNA is essential for oxygen-dependent Sre1N regulation. The other Ofd1 function of accelerating Sre1N degradation is necessary for the yeast to quickly turn off its hypoxic response when oxygen is restored. In addition, the model predicts that increased Ofd1 production at low oxygen plays an important role in the hypoxic response, and the model indicates that the Ofd1 binding partner Nro1 tunes the response to oxygen. This model quantifies our understanding of a novel oxygen-sensing mechanism that is widely conserved.